%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG142+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:37:14 EDT 2023 % Result : Unsatisfiable 11.00s 2.25s % Output : Proof 43.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG142+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n008.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Aug 28 03:55:32 EDT 2023 % 0.16/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.07/1.33 Prover 4: Preprocessing ... % 4.07/1.33 Prover 1: Preprocessing ... % 4.52/1.36 Prover 6: Preprocessing ... % 4.52/1.36 Prover 3: Preprocessing ... % 4.52/1.36 Prover 0: Preprocessing ... % 4.52/1.37 Prover 2: Preprocessing ... % 4.52/1.37 Prover 5: Preprocessing ... % 7.30/1.74 Prover 3: Constructing countermodel ... % 7.30/1.74 Prover 2: Constructing countermodel ... % 7.30/1.77 Prover 6: Constructing countermodel ... % 7.57/1.79 Prover 0: Constructing countermodel ... % 7.57/1.83 Prover 1: Constructing countermodel ... % 7.57/1.83 Prover 4: Constructing countermodel ... % 9.53/2.07 Prover 5: Constructing countermodel ... % 11.00/2.25 Prover 3: proved (1614ms) % 11.00/2.25 % 11.00/2.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.00/2.25 % 11.00/2.25 Prover 6: stopped % 11.00/2.25 Prover 2: stopped % 11.00/2.25 Prover 5: stopped % 11.00/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.00/2.25 Prover 0: stopped % 11.22/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.22/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.22/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.22/2.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.25/2.44 Prover 8: Preprocessing ... % 12.55/2.49 Prover 7: Preprocessing ... % 12.55/2.49 Prover 10: Preprocessing ... % 12.55/2.50 Prover 11: Preprocessing ... % 12.55/2.53 Prover 13: Preprocessing ... % 13.94/2.63 Prover 8: Constructing countermodel ... % 14.63/2.77 Prover 11: Constructing countermodel ... % 14.63/2.82 Prover 7: Constructing countermodel ... % 14.63/2.85 Prover 10: Constructing countermodel ... % 14.63/2.87 Prover 13: Constructing countermodel ... % 37.64/6.02 Prover 13: Found proof (size 23399) % 37.64/6.02 Prover 13: proved (3727ms) % 37.64/6.02 Prover 10: stopped % 37.64/6.02 Prover 11: stopped % 37.64/6.02 Prover 7: stopped % 37.64/6.02 Prover 8: stopped % 37.64/6.02 Prover 1: stopped % 37.64/6.02 Prover 4: stopped % 37.64/6.02 % 37.64/6.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 37.64/6.02 % 40.63/6.44 % SZS output start Proof for theBenchmark % 40.79/6.46 Assumptions after simplification: % 40.79/6.46 --------------------------------- % 40.79/6.46 % 40.79/6.46 (ax1) % 40.79/6.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.50 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 40.79/6.50 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 40.79/6.50 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 & % 40.79/6.50 op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 & % 40.79/6.50 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 & % 40.79/6.50 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 & % 40.79/6.50 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 40.79/6.50 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 40.79/6.50 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 40.79/6.50 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 40.79/6.50 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 40.79/6.50 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 40.79/6.50 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 40.79/6.50 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 40.79/6.50 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 40.79/6.50 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 40.79/6.50 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 40.79/6.50 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 40.79/6.50 % 40.79/6.50 (ax10) % 40.79/6.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.50 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.50 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 40.79/6.50 % 40.79/6.50 (ax11) % 40.79/6.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.51 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.51 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 40.79/6.51 % 40.79/6.51 (ax12) % 40.79/6.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.51 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.51 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 40.79/6.51 % 40.79/6.51 (ax13) % 40.79/6.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.51 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.51 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 40.79/6.51 % 40.79/6.51 (ax14) % 40.79/6.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.51 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.51 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 40.79/6.51 % 40.79/6.51 (ax15) % 40.79/6.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.51 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.51 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 40.79/6.51 % 40.79/6.51 (ax16) % 40.79/6.52 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.52 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.52 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 40.79/6.52 % 40.79/6.52 (ax17) % 40.79/6.52 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.52 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.52 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 40.79/6.52 % 40.79/6.52 (ax18) % 40.79/6.52 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.52 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.52 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 40.79/6.52 % 40.79/6.52 (ax19) % 40.79/6.52 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.52 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.52 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 40.79/6.52 % 40.79/6.52 (ax2) % 40.79/6.53 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.53 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 40.79/6.53 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 40.79/6.53 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v3 & op(e3, e2) = v6 & % 40.79/6.53 op(e3, e1) = v5 & op(e3, e0) = v4 & op(e2, e3) = v2 & op(e2, e2) = v9 & % 40.79/6.53 op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, e3) = v1 & op(e1, e2) = v8 & % 40.79/6.53 op(e1, e1) = v13 & op(e1, e0) = v14 & op(e0, e3) = v0 & op(e0, e2) = v7 & % 40.79/6.53 op(e0, e1) = v12 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 40.79/6.53 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 40.79/6.53 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v10 = e3 | v4 = % 40.79/6.53 e3) & (v15 = e3 | v12 = e3 | v7 = e3 | v0 = e3) & (v15 = e2 | v14 = e2 | % 40.79/6.54 v10 = e2 | v4 = e2) & (v15 = e2 | v12 = e2 | v7 = e2 | v0 = e2) & (v15 = % 40.79/6.54 e1 | v14 = e1 | v10 = e1 | v4 = e1) & (v15 = e1 | v12 = e1 | v7 = e1 | v0 % 40.79/6.54 = e1) & (v15 = e0 | v14 = e0 | v10 = e0 | v4 = e0) & (v15 = e0 | v12 = e0 % 40.79/6.54 | v7 = e0 | v0 = e0) & (v14 = e3 | v13 = e3 | v8 = e3 | v1 = e3) & (v14 = % 40.79/6.54 e2 | v13 = e2 | v8 = e2 | v1 = e2) & (v14 = e1 | v13 = e1 | v8 = e1 | v1 = % 40.79/6.54 e1) & (v14 = e0 | v13 = e0 | v8 = e0 | v1 = e0) & (v13 = e3 | v12 = e3 | % 40.79/6.54 v11 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v11 = e2 | v5 = e2) & (v13 = % 40.79/6.54 e1 | v12 = e1 | v11 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v11 = e0 | v5 % 40.79/6.54 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v2 = e3) & (v11 = e2 | v10 = e2 | % 40.79/6.54 v9 = e2 | v2 = e2) & (v11 = e1 | v10 = e1 | v9 = e1 | v2 = e1) & (v11 = e0 % 40.79/6.54 | v10 = e0 | v9 = e0 | v2 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v6 = e3) % 40.79/6.54 & (v9 = e2 | v8 = e2 | v7 = e2 | v6 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | % 40.79/6.54 v6 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v6 = e0) & (v6 = e3 | v5 = e3 | % 40.79/6.54 v4 = e3 | v3 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v3 = e2) & (v6 = e1 | % 40.79/6.54 v5 = e1 | v4 = e1 | v3 = e1) & (v6 = e0 | v5 = e0 | v4 = e0 | v3 = e0) & % 40.79/6.54 (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0 % 40.79/6.54 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = e0 | v1 % 40.79/6.54 = e0 | v0 = e0)) % 40.79/6.54 % 40.79/6.54 (ax20) % 40.79/6.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.54 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.54 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 40.79/6.54 % 40.79/6.54 (ax21) % 40.79/6.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.54 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.54 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 40.79/6.54 % 40.79/6.54 (ax22) % 40.79/6.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.54 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.54 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 40.79/6.54 % 40.79/6.54 (ax23) % 40.79/6.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.54 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.54 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 40.79/6.54 % 40.79/6.54 (ax24) % 40.79/6.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.54 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.54 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 40.79/6.54 % 40.79/6.54 (ax25) % 40.79/6.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.55 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.55 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 40.79/6.55 % 40.79/6.55 (ax26) % 40.79/6.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.55 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.55 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 40.79/6.55 % 40.79/6.55 (ax27) % 40.79/6.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.55 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.55 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 40.79/6.55 % 40.79/6.55 (ax28) % 40.79/6.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.55 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.55 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 40.79/6.55 % 40.79/6.55 (ax29) % 40.79/6.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.55 (op(v0, e0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 40.79/6.55 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 40.79/6.55 % 40.79/6.55 (ax3) % 40.79/6.56 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.56 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 40.79/6.56 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 40.79/6.56 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 40.79/6.56 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 40.79/6.56 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 40.79/6.56 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 40.79/6.56 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 40.79/6.56 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 40.79/6.56 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 40.79/6.56 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 40.79/6.56 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 40.79/6.56 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 40.79/6.56 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0 % 40.79/6.56 & op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 & % 40.79/6.56 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 & % 40.79/6.56 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) = v12 & % 40.79/6.56 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12) % 40.79/6.56 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 40.79/6.56 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 40.79/6.56 % 40.79/6.56 (ax4) % 40.79/6.56 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 40.79/6.56 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 40.79/6.56 % 40.79/6.56 (ax5) % 40.79/6.57 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.57 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 40.79/6.57 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 40.79/6.57 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v6 & op(e3, e2) = v9 & % 40.79/6.57 op(e3, e1) = v12 & op(e3, e0) = v15 & op(e2, e3) = v5 & op(e2, e2) = v4 & % 40.79/6.57 op(e2, e1) = v11 & op(e2, e0) = v14 & op(e1, e3) = v3 & op(e1, e2) = v8 & % 40.79/6.57 op(e1, e1) = v2 & op(e1, e0) = v13 & op(e0, e3) = v1 & op(e0, e2) = v7 & % 40.79/6.57 op(e0, e1) = v10 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 40.79/6.57 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 40.79/6.57 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = e2 & ~ (v9 = e3)) | (v2 = e2 & % 40.79/6.57 ~ (v8 = e1)) | (v0 = e2 & ~ (v7 = e0))) & ((v6 = e1 & ~ (v12 = e3)) | % 40.79/6.57 (v4 = e1 & ~ (v11 = e2)) | (v0 = e1 & ~ (v10 = e0))) & ((v6 = e0 & ~ % 40.79/6.57 (v15 = e3)) | (v4 = e0 & ~ (v14 = e2)) | (v2 = e0 & ~ (v13 = e1))) & % 40.79/6.57 ((v4 = e3 & ~ (v5 = e2)) | (v2 = e3 & ~ (v3 = e1)) | (v0 = e3 & ~ (v1 = % 40.79/6.57 e0)))) % 40.79/6.57 % 40.79/6.57 (ax6) % 40.79/6.57 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.57 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.57 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 40.79/6.57 % 40.79/6.57 (ax7) % 40.79/6.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.58 (op(v0, e2) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 40.79/6.58 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 40.79/6.58 % 40.79/6.58 (ax8) % 40.79/6.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.58 (op(v0, e3) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 40.79/6.58 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 40.79/6.58 % 40.79/6.58 (ax9) % 40.79/6.58 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 40.79/6.58 (op(v0, e1) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 40.79/6.58 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 40.79/6.58 % 40.79/6.58 (function-axioms) % 40.79/6.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 40.79/6.58 v2) = v1) | ~ (op(v3, v2) = v0)) % 40.79/6.58 % 40.79/6.58 Those formulas are unsatisfiable: % 40.79/6.58 --------------------------------- % 40.79/6.58 % 40.79/6.58 Begin of proof % 40.79/6.58 | % 40.79/6.58 | ALPHA: (ax1) implies: % 40.79/6.59 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 40.79/6.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 40.79/6.59 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 40.79/6.59 | ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 & op(e3, e1) = v2 & % 40.79/6.59 | op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 & op(e2, e1) = v6 % 40.79/6.59 | & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 & op(e1, e1) = % 40.79/6.59 | v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 & op(e0, % 40.79/6.59 | e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & % 40.79/6.59 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 40.79/6.59 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 40.79/6.59 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 40.79/6.59 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 40.79/6.59 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 40.79/6.59 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 40.79/6.59 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 40.79/6.59 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 40.79/6.59 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 40.79/6.59 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 40.79/6.59 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 40.79/6.59 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 40.79/6.59 | = e0)) % 40.79/6.59 | % 40.79/6.59 | ALPHA: (ax2) implies: % 40.79/6.60 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 40.79/6.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 40.79/6.60 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 40.79/6.60 | ? [v15: $i] : (op(e3, e3) = v3 & op(e3, e2) = v6 & op(e3, e1) = v5 & % 40.79/6.60 | op(e3, e0) = v4 & op(e2, e3) = v2 & op(e2, e2) = v9 & op(e2, e1) = % 40.79/6.60 | v11 & op(e2, e0) = v10 & op(e1, e3) = v1 & op(e1, e2) = v8 & op(e1, % 40.79/6.60 | e1) = v13 & op(e1, e0) = v14 & op(e0, e3) = v0 & op(e0, e2) = v7 & % 40.79/6.60 | op(e0, e1) = v12 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & % 40.79/6.60 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 40.79/6.60 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 % 40.79/6.60 | = e3 | v10 = e3 | v4 = e3) & (v15 = e3 | v12 = e3 | v7 = e3 | v0 = % 40.79/6.60 | e3) & (v15 = e2 | v14 = e2 | v10 = e2 | v4 = e2) & (v15 = e2 | v12 % 40.79/6.60 | = e2 | v7 = e2 | v0 = e2) & (v15 = e1 | v14 = e1 | v10 = e1 | v4 = % 40.79/6.60 | e1) & (v15 = e1 | v12 = e1 | v7 = e1 | v0 = e1) & (v15 = e0 | v14 = % 40.79/6.60 | e0 | v10 = e0 | v4 = e0) & (v15 = e0 | v12 = e0 | v7 = e0 | v0 = % 40.79/6.60 | e0) & (v14 = e3 | v13 = e3 | v8 = e3 | v1 = e3) & (v14 = e2 | v13 = % 40.79/6.60 | e2 | v8 = e2 | v1 = e2) & (v14 = e1 | v13 = e1 | v8 = e1 | v1 = e1) % 40.79/6.60 | & (v14 = e0 | v13 = e0 | v8 = e0 | v1 = e0) & (v13 = e3 | v12 = e3 | % 40.79/6.60 | v11 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v11 = e2 | v5 = e2) & % 40.79/6.60 | (v13 = e1 | v12 = e1 | v11 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | % 40.79/6.60 | v11 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v2 = e3) & % 40.79/6.60 | (v11 = e2 | v10 = e2 | v9 = e2 | v2 = e2) & (v11 = e1 | v10 = e1 | v9 % 40.79/6.60 | = e1 | v2 = e1) & (v11 = e0 | v10 = e0 | v9 = e0 | v2 = e0) & (v9 = % 40.79/6.60 | e3 | v8 = e3 | v7 = e3 | v6 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 | % 40.79/6.60 | v6 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v6 = e1) & (v9 = e0 | v8 % 40.79/6.60 | = e0 | v7 = e0 | v6 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v3 = e3) % 40.79/6.60 | & (v6 = e2 | v5 = e2 | v4 = e2 | v3 = e2) & (v6 = e1 | v5 = e1 | v4 = % 40.79/6.60 | e1 | v3 = e1) & (v6 = e0 | v5 = e0 | v4 = e0 | v3 = e0) & (v3 = e3 % 40.79/6.61 | | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0 % 40.79/6.61 | = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = % 40.79/6.61 | e0 | v1 = e0 | v0 = e0)) % 40.79/6.61 | % 40.79/6.61 | ALPHA: (ax3) implies: % 40.79/6.61 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 40.79/6.61 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 40.79/6.61 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 40.79/6.61 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 40.79/6.61 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 40.79/6.61 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 40.79/6.61 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 40.79/6.61 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 40.79/6.61 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 40.79/6.61 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 40.79/6.61 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 40.79/6.61 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 40.79/6.61 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 40.79/6.61 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 40.79/6.61 | v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0 & op(e3, e1) % 40.79/6.61 | = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 & op(e2, % 40.79/6.61 | e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 & % 40.79/6.61 | op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) = % 40.79/6.61 | v12 & op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & % 40.79/6.61 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 40.79/6.61 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 40.79/6.61 | % 40.79/6.61 | ALPHA: (ax4) implies: % 40.79/6.61 | (4) ~ (e1 = e0) % 40.79/6.61 | (5) ~ (e2 = e0) % 40.79/6.61 | (6) ~ (e2 = e1) % 40.79/6.61 | (7) ~ (e3 = e0) % 40.79/6.61 | (8) ~ (e3 = e1) % 40.79/6.61 | (9) ~ (e3 = e2) % 40.79/6.61 | % 40.79/6.61 | ALPHA: (ax5) implies: % 40.79/6.62 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 40.79/6.62 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 40.79/6.62 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 40.79/6.62 | $i] : ? [v15: $i] : (op(e3, e3) = v6 & op(e3, e2) = v9 & op(e3, e1) % 40.79/6.62 | = v12 & op(e3, e0) = v15 & op(e2, e3) = v5 & op(e2, e2) = v4 & % 40.79/6.62 | op(e2, e1) = v11 & op(e2, e0) = v14 & op(e1, e3) = v3 & op(e1, e2) = % 40.79/6.62 | v8 & op(e1, e1) = v2 & op(e1, e0) = v13 & op(e0, e3) = v1 & op(e0, % 40.79/6.62 | e2) = v7 & op(e0, e1) = v10 & op(e0, e0) = v0 & $i(v15) & $i(v14) % 40.79/6.62 | & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 40.79/6.62 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 % 40.79/6.62 | = e2 & ~ (v9 = e3)) | (v2 = e2 & ~ (v8 = e1)) | (v0 = e2 & ~ % 40.79/6.62 | (v7 = e0))) & ((v6 = e1 & ~ (v12 = e3)) | (v4 = e1 & ~ (v11 = % 40.79/6.62 | e2)) | (v0 = e1 & ~ (v10 = e0))) & ((v6 = e0 & ~ (v15 = e3)) % 40.79/6.62 | | (v4 = e0 & ~ (v14 = e2)) | (v2 = e0 & ~ (v13 = e1))) & ((v4 = % 40.79/6.62 | e3 & ~ (v5 = e2)) | (v2 = e3 & ~ (v3 = e1)) | (v0 = e3 & ~ % 40.79/6.62 | (v1 = e0)))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax6) implies: % 40.79/6.62 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.62 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax7) implies: % 40.79/6.62 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.62 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax8) implies: % 40.79/6.62 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.62 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax9) implies: % 40.79/6.62 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.62 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax10) implies: % 40.79/6.62 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.62 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax11) implies: % 40.79/6.62 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.62 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.62 | e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 40.79/6.62 | % 40.79/6.62 | ALPHA: (ax12) implies: % 40.79/6.63 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.63 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax13) implies: % 40.79/6.63 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.63 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax14) implies: % 40.79/6.63 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.63 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax15) implies: % 40.79/6.63 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.63 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax16) implies: % 40.79/6.63 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.63 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax17) implies: % 40.79/6.63 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.63 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax18) implies: % 40.79/6.63 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.63 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax19) implies: % 40.79/6.63 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.63 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax20) implies: % 40.79/6.63 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e3) = v2 & op(e3, % 40.79/6.63 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.63 | e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 40.79/6.63 | % 40.79/6.63 | ALPHA: (ax21) implies: % 40.79/6.64 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.64 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax22) implies: % 40.79/6.64 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.64 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax23) implies: % 40.79/6.64 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.64 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax24) implies: % 40.79/6.64 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.64 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax25) implies: % 40.79/6.64 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.64 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax26) implies: % 40.79/6.64 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e2) = v2 & op(e2, % 40.79/6.64 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax27) implies: % 40.79/6.64 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.64 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax28) implies: % 40.79/6.64 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e1) = v2 & op(e1, % 40.79/6.64 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 40.79/6.64 | % 40.79/6.64 | ALPHA: (ax29) implies: % 40.79/6.64 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, e0) = v2 & op(e0, % 40.79/6.64 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 40.79/6.64 | e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 40.79/6.64 | % 40.79/6.65 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 40.79/6.65 | (35) op(all_4_2, e0) = all_4_0 & op(e0, all_4_2) = all_4_1 & op(e0, e0) = % 40.79/6.65 | all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~ (all_4_0 = e2) % 40.79/6.65 | | ~ (all_4_1 = e1) | ~ (all_4_2 = e3)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (35) implies: % 40.79/6.65 | (36) op(e0, e0) = all_4_2 % 40.79/6.65 | (37) op(e0, all_4_2) = all_4_1 % 40.79/6.65 | (38) op(all_4_2, e0) = all_4_0 % 40.79/6.65 | (39) ~ (all_4_0 = e2) | ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 40.79/6.65 | % 40.79/6.65 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 40.79/6.65 | (40) op(all_6_2, e1) = all_6_0 & op(e1, all_6_2) = all_6_1 & op(e1, e1) = % 40.79/6.65 | all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~ (all_6_0 = e3) % 40.79/6.65 | | ~ (all_6_1 = e2) | ~ (all_6_2 = e0)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (40) implies: % 40.79/6.65 | (41) op(e1, e1) = all_6_2 % 40.79/6.65 | (42) op(e1, all_6_2) = all_6_1 % 40.79/6.65 | (43) op(all_6_2, e1) = all_6_0 % 40.79/6.65 | (44) ~ (all_6_0 = e3) | ~ (all_6_1 = e2) | ~ (all_6_2 = e0) % 40.79/6.65 | % 40.79/6.65 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 40.79/6.65 | (45) op(all_8_2, e2) = all_8_0 & op(e2, all_8_2) = all_8_1 & op(e2, e2) = % 40.79/6.65 | all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~ (all_8_0 = e3) % 40.79/6.65 | | ~ (all_8_1 = e1) | ~ (all_8_2 = e0)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (45) implies: % 40.79/6.65 | (46) op(e2, e2) = all_8_2 % 40.79/6.65 | (47) op(e2, all_8_2) = all_8_1 % 40.79/6.65 | (48) op(all_8_2, e2) = all_8_0 % 40.79/6.65 | (49) ~ (all_8_0 = e3) | ~ (all_8_1 = e1) | ~ (all_8_2 = e0) % 40.79/6.65 | % 40.79/6.65 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2 % 40.79/6.65 | gives: % 40.79/6.65 | (50) op(all_10_2, e3) = all_10_0 & op(e3, all_10_2) = all_10_1 & op(e3, e3) % 40.79/6.65 | = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & ( ~ % 40.79/6.65 | (all_10_0 = e1) | ~ (all_10_1 = e0) | ~ (all_10_2 = e2)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (50) implies: % 40.79/6.65 | (51) op(e3, e3) = all_10_2 % 40.79/6.65 | % 40.79/6.65 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2 % 40.79/6.65 | gives: % 40.79/6.65 | (52) op(all_12_2, e0) = all_12_0 & op(e0, all_12_2) = all_12_1 & op(e0, e0) % 40.79/6.65 | = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & ( ~ % 40.79/6.65 | (all_12_0 = e3) | ~ (all_12_1 = e1) | ~ (all_12_2 = e2)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (52) implies: % 40.79/6.65 | (53) op(e0, e0) = all_12_2 % 40.79/6.65 | (54) op(e0, all_12_2) = all_12_1 % 40.79/6.65 | (55) op(all_12_2, e0) = all_12_0 % 40.79/6.65 | (56) ~ (all_12_0 = e3) | ~ (all_12_1 = e1) | ~ (all_12_2 = e2) % 40.79/6.65 | % 40.79/6.65 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2 % 40.79/6.65 | gives: % 40.79/6.65 | (57) op(all_14_2, e2) = all_14_0 & op(e2, all_14_2) = all_14_1 & op(e2, e2) % 40.79/6.65 | = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & ( ~ % 40.79/6.65 | (all_14_0 = e0) | ~ (all_14_1 = e3) | ~ (all_14_2 = e1)) % 40.79/6.65 | % 40.79/6.65 | ALPHA: (57) implies: % 40.79/6.65 | (58) op(e2, e2) = all_14_2 % 40.79/6.66 | (59) op(e2, all_14_2) = all_14_1 % 40.79/6.66 | (60) op(all_14_2, e2) = all_14_0 % 40.79/6.66 | (61) ~ (all_14_0 = e0) | ~ (all_14_1 = e3) | ~ (all_14_2 = e1) % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1, all_16_2 % 40.79/6.66 | gives: % 40.79/6.66 | (62) op(all_16_2, e2) = all_16_0 & op(e2, all_16_2) = all_16_1 & op(e2, e2) % 40.79/6.66 | = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & ( ~ % 40.79/6.66 | (all_16_0 = e1) | ~ (all_16_1 = e3) | ~ (all_16_2 = e0)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (62) implies: % 40.79/6.66 | (63) op(e2, e2) = all_16_2 % 40.79/6.66 | (64) op(e2, all_16_2) = all_16_1 % 40.79/6.66 | (65) op(all_16_2, e2) = all_16_0 % 40.79/6.66 | (66) ~ (all_16_0 = e1) | ~ (all_16_1 = e3) | ~ (all_16_2 = e0) % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1, all_18_2 % 40.79/6.66 | gives: % 40.79/6.66 | (67) op(all_18_2, e3) = all_18_0 & op(e3, all_18_2) = all_18_1 & op(e3, e3) % 40.79/6.66 | = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & ( ~ % 40.79/6.66 | (all_18_0 = e0) | ~ (all_18_1 = e2) | ~ (all_18_2 = e1)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (67) implies: % 40.79/6.66 | (68) op(e3, e3) = all_18_2 % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2 % 40.79/6.66 | gives: % 40.79/6.66 | (69) op(all_20_2, e3) = all_20_0 & op(e3, all_20_2) = all_20_1 & op(e3, e3) % 40.79/6.66 | = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & ( ~ % 40.79/6.66 | (all_20_0 = e2) | ~ (all_20_1 = e0) | ~ (all_20_2 = e1)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (69) implies: % 40.79/6.66 | (70) op(e3, e3) = all_20_2 % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2 % 40.79/6.66 | gives: % 40.79/6.66 | (71) op(all_22_2, e0) = all_22_0 & op(e0, all_22_2) = all_22_1 & op(e0, e0) % 40.79/6.66 | = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & ( ~ % 40.79/6.66 | (all_22_0 = e3) | ~ (all_22_1 = e2) | ~ (all_22_2 = e1)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (71) implies: % 40.79/6.66 | (72) op(e0, e0) = all_22_2 % 40.79/6.66 | (73) op(e0, all_22_2) = all_22_1 % 40.79/6.66 | (74) op(all_22_2, e0) = all_22_0 % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2 % 40.79/6.66 | gives: % 40.79/6.66 | (75) op(all_24_2, e1) = all_24_0 & op(e1, all_24_2) = all_24_1 & op(e1, e1) % 40.79/6.66 | = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & ( ~ % 40.79/6.66 | (all_24_0 = e0) | ~ (all_24_1 = e3) | ~ (all_24_2 = e2)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (75) implies: % 40.79/6.66 | (76) op(e1, e1) = all_24_2 % 40.79/6.66 | (77) op(e1, all_24_2) = all_24_1 % 40.79/6.66 | (78) op(all_24_2, e1) = all_24_0 % 40.79/6.66 | (79) ~ (all_24_0 = e0) | ~ (all_24_1 = e3) | ~ (all_24_2 = e2) % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2 % 40.79/6.66 | gives: % 40.79/6.66 | (80) op(all_26_2, e2) = all_26_0 & op(e2, all_26_2) = all_26_1 & op(e2, e2) % 40.79/6.66 | = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & ( ~ % 40.79/6.66 | (all_26_0 = e1) | ~ (all_26_1 = e0) | ~ (all_26_2 = e3)) % 40.79/6.66 | % 40.79/6.66 | ALPHA: (80) implies: % 40.79/6.66 | (81) op(e2, e2) = all_26_2 % 40.79/6.66 | (82) op(e2, all_26_2) = all_26_1 % 40.79/6.66 | (83) op(all_26_2, e2) = all_26_0 % 40.79/6.66 | (84) ~ (all_26_0 = e1) | ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 40.79/6.66 | % 40.79/6.66 | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2 % 40.79/6.66 | gives: % 40.79/6.67 | (85) op(all_28_2, e3) = all_28_0 & op(e3, all_28_2) = all_28_1 & op(e3, e3) % 40.79/6.67 | = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & ( ~ % 40.79/6.67 | (all_28_0 = e2) | ~ (all_28_1 = e1) | ~ (all_28_2 = e0)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (85) implies: % 40.79/6.67 | (86) op(e3, e3) = all_28_2 % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2 % 40.79/6.67 | gives: % 40.79/6.67 | (87) op(all_30_2, e0) = all_30_0 & op(e0, all_30_2) = all_30_1 & op(e0, e0) % 40.79/6.67 | = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & ( ~ % 40.79/6.67 | (all_30_0 = e1) | ~ (all_30_1 = e3) | ~ (all_30_2 = e2)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (87) implies: % 40.79/6.67 | (88) op(e0, e0) = all_30_2 % 40.79/6.67 | (89) op(e0, all_30_2) = all_30_1 % 40.79/6.67 | (90) op(all_30_2, e0) = all_30_0 % 40.79/6.67 | (91) ~ (all_30_0 = e1) | ~ (all_30_1 = e3) | ~ (all_30_2 = e2) % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1, all_32_2 % 40.79/6.67 | gives: % 40.79/6.67 | (92) op(all_32_2, e0) = all_32_0 & op(e0, all_32_2) = all_32_1 & op(e0, e0) % 40.79/6.67 | = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & ( ~ % 40.79/6.67 | (all_32_0 = e2) | ~ (all_32_1 = e3) | ~ (all_32_2 = e1)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (92) implies: % 40.79/6.67 | (93) op(e0, e0) = all_32_2 % 40.79/6.67 | (94) op(e0, all_32_2) = all_32_1 % 40.79/6.67 | (95) op(all_32_2, e0) = all_32_0 % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1, all_34_2 % 40.79/6.67 | gives: % 40.79/6.67 | (96) op(all_34_2, e1) = all_34_0 & op(e1, all_34_2) = all_34_1 & op(e1, e1) % 40.79/6.67 | = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & ( ~ % 40.79/6.67 | (all_34_0 = e0) | ~ (all_34_1 = e2) | ~ (all_34_2 = e3)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (96) implies: % 40.79/6.67 | (97) op(e1, e1) = all_34_2 % 40.79/6.67 | (98) op(e1, all_34_2) = all_34_1 % 40.79/6.67 | (99) op(all_34_2, e1) = all_34_0 % 40.79/6.67 | (100) ~ (all_34_0 = e0) | ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2 % 40.79/6.67 | gives: % 40.79/6.67 | (101) op(all_36_2, e3) = all_36_0 & op(e3, all_36_2) = all_36_1 & op(e3, % 40.79/6.67 | e3) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) & ( ~ % 40.79/6.67 | (all_36_0 = e1) | ~ (all_36_1 = e2) | ~ (all_36_2 = e0)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (101) implies: % 40.79/6.67 | (102) op(e3, e3) = all_36_2 % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2 % 40.79/6.67 | gives: % 40.79/6.67 | (103) op(all_38_2, e1) = all_38_0 & op(e1, all_38_2) = all_38_1 & op(e1, % 40.79/6.67 | e1) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & ( ~ % 40.79/6.67 | (all_38_0 = e2) | ~ (all_38_1 = e3) | ~ (all_38_2 = e0)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (103) implies: % 40.79/6.67 | (104) op(e1, e1) = all_38_2 % 40.79/6.67 | (105) op(e1, all_38_2) = all_38_1 % 40.79/6.67 | (106) op(all_38_2, e1) = all_38_0 % 40.79/6.67 | (107) ~ (all_38_0 = e2) | ~ (all_38_1 = e3) | ~ (all_38_2 = e0) % 40.79/6.67 | % 40.79/6.67 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2 % 40.79/6.67 | gives: % 40.79/6.67 | (108) op(all_40_2, e0) = all_40_0 & op(e0, all_40_2) = all_40_1 & op(e0, % 40.79/6.67 | e0) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & ( ~ % 40.79/6.67 | (all_40_0 = e1) | ~ (all_40_1 = e2) | ~ (all_40_2 = e3)) % 40.79/6.67 | % 40.79/6.67 | ALPHA: (108) implies: % 40.79/6.67 | (109) op(e0, e0) = all_40_2 % 40.79/6.67 | (110) op(e0, all_40_2) = all_40_1 % 40.79/6.67 | (111) op(all_40_2, e0) = all_40_0 % 40.79/6.68 | (112) ~ (all_40_0 = e1) | ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2 % 40.79/6.68 | gives: % 40.79/6.68 | (113) op(all_42_2, e1) = all_42_0 & op(e1, all_42_2) = all_42_1 & op(e1, % 40.79/6.68 | e1) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & ( ~ % 40.79/6.68 | (all_42_0 = e2) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3)) % 40.79/6.68 | % 40.79/6.68 | ALPHA: (113) implies: % 40.79/6.68 | (114) op(e1, e1) = all_42_2 % 40.79/6.68 | (115) op(e1, all_42_2) = all_42_1 % 40.79/6.68 | (116) op(all_42_2, e1) = all_42_0 % 40.79/6.68 | (117) ~ (all_42_0 = e2) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1, all_44_2 % 40.79/6.68 | gives: % 40.79/6.68 | (118) op(all_44_2, e2) = all_44_0 & op(e2, all_44_2) = all_44_1 & op(e2, % 40.79/6.68 | e2) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & ( ~ % 40.79/6.68 | (all_44_0 = e3) | ~ (all_44_1 = e0) | ~ (all_44_2 = e1)) % 40.79/6.68 | % 40.79/6.68 | ALPHA: (118) implies: % 40.79/6.68 | (119) op(e2, e2) = all_44_2 % 40.79/6.68 | (120) op(e2, all_44_2) = all_44_1 % 40.79/6.68 | (121) op(all_44_2, e2) = all_44_0 % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2 % 40.79/6.68 | gives: % 40.79/6.68 | (122) op(all_46_2, e1) = all_46_0 & op(e1, all_46_2) = all_46_1 & op(e1, % 40.79/6.68 | e1) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) & ( ~ % 40.79/6.68 | (all_46_0 = e3) | ~ (all_46_1 = e0) | ~ (all_46_2 = e2)) % 40.79/6.68 | % 40.79/6.68 | ALPHA: (122) implies: % 40.79/6.68 | (123) op(e1, e1) = all_46_2 % 40.79/6.68 | (124) op(e1, all_46_2) = all_46_1 % 40.79/6.68 | (125) op(all_46_2, e1) = all_46_0 % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1, all_48_2 % 40.79/6.68 | gives: % 40.79/6.68 | (126) op(all_48_2, e3) = all_48_0 & op(e3, all_48_2) = all_48_1 & op(e3, % 40.79/6.68 | e3) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & ( ~ % 40.79/6.68 | (all_48_0 = e0) | ~ (all_48_1 = e1) | ~ (all_48_2 = e2)) % 40.79/6.68 | % 40.79/6.68 | ALPHA: (126) implies: % 40.79/6.68 | (127) op(e3, e3) = all_48_2 % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2 % 40.79/6.68 | gives: % 40.79/6.68 | (128) op(all_50_2, e2) = all_50_0 & op(e2, all_50_2) = all_50_1 & op(e2, % 40.79/6.68 | e2) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & ( ~ % 40.79/6.68 | (all_50_0 = e0) | ~ (all_50_1 = e1) | ~ (all_50_2 = e3)) % 40.79/6.68 | % 40.79/6.68 | ALPHA: (128) implies: % 40.79/6.68 | (129) op(e2, e2) = all_50_2 % 40.79/6.68 | (130) op(e2, all_50_2) = all_50_1 % 40.79/6.68 | (131) op(all_50_2, e2) = all_50_0 % 40.79/6.68 | (132) ~ (all_50_0 = e0) | ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 40.79/6.68 | % 40.79/6.68 | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2, % 40.79/6.68 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9, % 40.79/6.68 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives: % 41.91/6.69 | (133) op(e3, e3) = all_52_9 & op(e3, e2) = all_52_6 & op(e3, e1) = all_52_3 % 41.91/6.69 | & op(e3, e0) = all_52_0 & op(e2, e3) = all_52_10 & op(e2, e2) = % 41.91/6.69 | all_52_11 & op(e2, e1) = all_52_4 & op(e2, e0) = all_52_1 & op(e1, % 41.91/6.69 | e3) = all_52_12 & op(e1, e2) = all_52_7 & op(e1, e1) = all_52_13 & % 41.91/6.69 | op(e1, e0) = all_52_2 & op(e0, e3) = all_52_14 & op(e0, e2) = % 41.91/6.69 | all_52_8 & op(e0, e1) = all_52_5 & op(e0, e0) = all_52_15 & % 41.91/6.69 | $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & % 41.91/6.69 | $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) & % 41.91/6.69 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) & % 41.91/6.69 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15) & % 41.91/6.69 | ((all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ % 41.91/6.69 | (all_52_7 = e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0))) & % 41.91/6.69 | ((all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ % 41.91/6.69 | (all_52_4 = e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0))) & % 41.91/6.69 | ((all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ % 41.91/6.69 | (all_52_1 = e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1))) & % 41.91/6.69 | ((all_52_11 = e3 & ~ (all_52_10 = e2)) | (all_52_13 = e3 & ~ % 41.91/6.69 | (all_52_12 = e1)) | (all_52_15 = e3 & ~ (all_52_14 = e0))) % 41.91/6.69 | % 41.91/6.69 | ALPHA: (133) implies: % 41.91/6.69 | (134) op(e0, e0) = all_52_15 % 41.91/6.69 | (135) op(e0, e1) = all_52_5 % 41.91/6.69 | (136) op(e0, e2) = all_52_8 % 41.91/6.69 | (137) op(e0, e3) = all_52_14 % 41.91/6.69 | (138) op(e1, e0) = all_52_2 % 41.91/6.69 | (139) op(e1, e1) = all_52_13 % 41.91/6.69 | (140) op(e1, e2) = all_52_7 % 41.91/6.69 | (141) op(e1, e3) = all_52_12 % 41.91/6.69 | (142) op(e2, e0) = all_52_1 % 41.91/6.69 | (143) op(e2, e1) = all_52_4 % 41.91/6.69 | (144) op(e2, e2) = all_52_11 % 41.91/6.69 | (145) op(e2, e3) = all_52_10 % 41.91/6.69 | (146) op(e3, e0) = all_52_0 % 41.91/6.69 | (147) op(e3, e1) = all_52_3 % 41.91/6.69 | (148) op(e3, e2) = all_52_6 % 41.91/6.69 | (149) op(e3, e3) = all_52_9 % 41.91/6.69 | (150) (all_52_11 = e3 & ~ (all_52_10 = e2)) | (all_52_13 = e3 & ~ % 41.91/6.69 | (all_52_12 = e1)) | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 41.91/6.69 | (151) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 % 41.91/6.69 | = e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 41.91/6.69 | (152) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 % 41.91/6.69 | = e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 41.91/6.69 | (153) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 % 41.91/6.69 | = e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 41.91/6.69 | % 41.91/6.69 | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2, % 41.91/6.69 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9, % 41.91/6.69 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives: % 41.91/6.69 | (154) ~ (all_54_0 = all_54_1) & ~ (all_54_0 = all_54_2) & ~ (all_54_0 = % 41.91/6.69 | all_54_3) & ~ (all_54_0 = all_54_4) & ~ (all_54_0 = all_54_8) & % 41.91/6.69 | ~ (all_54_0 = all_54_12) & ~ (all_54_1 = all_54_2) & ~ (all_54_1 = % 41.91/6.69 | all_54_3) & ~ (all_54_1 = all_54_5) & ~ (all_54_1 = all_54_9) & % 41.91/6.69 | ~ (all_54_1 = all_54_13) & ~ (all_54_2 = all_54_3) & ~ (all_54_2 = % 41.91/6.69 | all_54_6) & ~ (all_54_2 = all_54_10) & ~ (all_54_2 = all_54_14) & % 41.91/6.69 | ~ (all_54_3 = all_54_7) & ~ (all_54_3 = all_54_11) & ~ (all_54_3 = % 41.91/6.69 | all_54_15) & ~ (all_54_4 = all_54_5) & ~ (all_54_4 = all_54_6) & % 41.91/6.69 | ~ (all_54_4 = all_54_7) & ~ (all_54_4 = all_54_8) & ~ (all_54_4 = % 41.91/6.69 | all_54_12) & ~ (all_54_5 = all_54_6) & ~ (all_54_5 = all_54_7) & % 41.91/6.70 | ~ (all_54_5 = all_54_9) & ~ (all_54_5 = all_54_13) & ~ (all_54_6 = % 41.91/6.70 | all_54_7) & ~ (all_54_6 = all_54_10) & ~ (all_54_6 = all_54_14) & % 41.91/6.70 | ~ (all_54_7 = all_54_11) & ~ (all_54_7 = all_54_15) & ~ (all_54_8 % 41.91/6.70 | = all_54_9) & ~ (all_54_8 = all_54_10) & ~ (all_54_8 = all_54_11) % 41.91/6.70 | & ~ (all_54_8 = all_54_12) & ~ (all_54_9 = all_54_10) & ~ % 41.91/6.70 | (all_54_9 = all_54_11) & ~ (all_54_9 = all_54_13) & ~ (all_54_10 = % 41.91/6.70 | all_54_11) & ~ (all_54_10 = all_54_14) & ~ (all_54_11 = % 41.91/6.70 | all_54_15) & ~ (all_54_12 = all_54_13) & ~ (all_54_12 = % 41.91/6.70 | all_54_14) & ~ (all_54_12 = all_54_15) & ~ (all_54_13 = % 41.91/6.70 | all_54_14) & ~ (all_54_13 = all_54_15) & ~ (all_54_14 = % 41.91/6.70 | all_54_15) & op(e3, e3) = all_54_14 & op(e3, e2) = all_54_15 & % 41.91/6.70 | op(e3, e1) = all_54_13 & op(e3, e0) = all_54_12 & op(e2, e3) = % 41.91/6.70 | all_54_10 & op(e2, e2) = all_54_11 & op(e2, e1) = all_54_9 & op(e2, % 41.91/6.70 | e0) = all_54_8 & op(e1, e3) = all_54_6 & op(e1, e2) = all_54_7 & % 41.91/6.70 | op(e1, e1) = all_54_5 & op(e1, e0) = all_54_4 & op(e0, e3) = all_54_2 % 41.91/6.70 | & op(e0, e2) = all_54_3 & op(e0, e1) = all_54_1 & op(e0, e0) = % 41.91/6.70 | all_54_0 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3) % 41.91/6.70 | & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & % 41.91/6.70 | $i(all_54_8) & $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & % 41.91/6.70 | $i(all_54_12) & $i(all_54_13) & $i(all_54_14) & $i(all_54_15) % 41.91/6.70 | % 41.91/6.70 | ALPHA: (154) implies: % 41.91/6.70 | (155) ~ (all_54_14 = all_54_15) % 41.91/6.70 | (156) ~ (all_54_13 = all_54_15) % 41.91/6.70 | (157) ~ (all_54_13 = all_54_14) % 41.91/6.70 | (158) ~ (all_54_12 = all_54_15) % 41.91/6.70 | (159) ~ (all_54_12 = all_54_14) % 41.91/6.70 | (160) ~ (all_54_12 = all_54_13) % 41.91/6.70 | (161) ~ (all_54_11 = all_54_15) % 41.91/6.70 | (162) ~ (all_54_10 = all_54_14) % 41.91/6.70 | (163) ~ (all_54_10 = all_54_11) % 41.91/6.70 | (164) ~ (all_54_9 = all_54_13) % 41.91/6.70 | (165) ~ (all_54_9 = all_54_11) % 41.91/6.70 | (166) ~ (all_54_8 = all_54_11) % 41.91/6.70 | (167) ~ (all_54_8 = all_54_10) % 41.91/6.70 | (168) ~ (all_54_7 = all_54_15) % 41.91/6.70 | (169) ~ (all_54_7 = all_54_11) % 41.91/6.70 | (170) ~ (all_54_6 = all_54_14) % 41.91/6.70 | (171) ~ (all_54_6 = all_54_10) % 41.91/6.70 | (172) ~ (all_54_6 = all_54_7) % 41.91/6.70 | (173) ~ (all_54_5 = all_54_13) % 41.91/6.70 | (174) ~ (all_54_5 = all_54_9) % 41.91/6.70 | (175) ~ (all_54_5 = all_54_7) % 41.91/6.70 | (176) ~ (all_54_5 = all_54_6) % 41.91/6.70 | (177) ~ (all_54_4 = all_54_12) % 41.91/6.70 | (178) ~ (all_54_4 = all_54_6) % 41.91/6.70 | (179) ~ (all_54_4 = all_54_5) % 41.91/6.70 | (180) ~ (all_54_2 = all_54_14) % 41.91/6.70 | (181) ~ (all_54_2 = all_54_6) % 41.91/6.70 | (182) ~ (all_54_2 = all_54_3) % 41.91/6.70 | (183) ~ (all_54_1 = all_54_9) % 41.91/6.70 | (184) ~ (all_54_1 = all_54_5) % 41.91/6.70 | (185) ~ (all_54_0 = all_54_12) % 41.91/6.70 | (186) ~ (all_54_0 = all_54_8) % 41.91/6.70 | (187) ~ (all_54_0 = all_54_4) % 41.91/6.70 | (188) ~ (all_54_0 = all_54_3) % 41.91/6.70 | (189) ~ (all_54_0 = all_54_2) % 41.91/6.70 | (190) ~ (all_54_0 = all_54_1) % 41.91/6.70 | (191) op(e0, e0) = all_54_0 % 41.91/6.70 | (192) op(e0, e1) = all_54_1 % 41.91/6.70 | (193) op(e0, e2) = all_54_3 % 41.91/6.70 | (194) op(e0, e3) = all_54_2 % 41.91/6.70 | (195) op(e1, e0) = all_54_4 % 41.91/6.70 | (196) op(e1, e1) = all_54_5 % 41.91/6.70 | (197) op(e1, e2) = all_54_7 % 41.91/6.70 | (198) op(e1, e3) = all_54_6 % 41.91/6.70 | (199) op(e2, e0) = all_54_8 % 41.91/6.70 | (200) op(e2, e1) = all_54_9 % 41.91/6.70 | (201) op(e2, e2) = all_54_11 % 41.91/6.70 | (202) op(e2, e3) = all_54_10 % 41.91/6.70 | (203) op(e3, e0) = all_54_12 % 41.91/6.70 | (204) op(e3, e1) = all_54_13 % 41.91/6.70 | (205) op(e3, e2) = all_54_15 % 41.91/6.70 | (206) op(e3, e3) = all_54_14 % 41.91/6.70 | % 41.91/6.70 | DELTA: instantiating (1) with fresh symbols all_56_0, all_56_1, all_56_2, % 41.91/6.70 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9, % 41.91/6.70 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives: % 41.91/6.70 | (207) op(e3, e3) = all_56_15 & op(e3, e2) = all_56_14 & op(e3, e1) = % 41.91/6.70 | all_56_13 & op(e3, e0) = all_56_12 & op(e2, e3) = all_56_11 & op(e2, % 41.91/6.70 | e2) = all_56_10 & op(e2, e1) = all_56_9 & op(e2, e0) = all_56_8 & % 41.91/6.70 | op(e1, e3) = all_56_7 & op(e1, e2) = all_56_6 & op(e1, e1) = all_56_5 % 41.91/6.70 | & op(e1, e0) = all_56_4 & op(e0, e3) = all_56_3 & op(e0, e2) = % 41.91/6.70 | all_56_2 & op(e0, e1) = all_56_1 & op(e0, e0) = all_56_0 & % 41.91/6.70 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & % 41.91/6.70 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & % 41.91/6.70 | $i(all_56_8) & $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & % 41.91/6.71 | $i(all_56_12) & $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & % 41.91/6.71 | (all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0) & % 41.91/6.71 | (all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0) & % 41.91/6.71 | (all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0) & % 41.91/6.71 | (all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0) & % 41.91/6.71 | (all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0) & % 41.91/6.71 | (all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0) & % 41.91/6.71 | (all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0) & % 41.91/6.71 | (all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0) & % 41.91/6.71 | (all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0) & % 41.91/6.71 | (all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0) & % 41.91/6.71 | (all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0) & % 41.91/6.71 | (all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0) & % 41.91/6.71 | (all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0) & % 41.91/6.71 | (all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0) & % 41.91/6.71 | (all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0) & % 41.91/6.71 | (all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0) % 41.91/6.71 | % 41.91/6.71 | ALPHA: (207) implies: % 41.91/6.71 | (208) op(e0, e0) = all_56_0 % 41.91/6.71 | (209) op(e0, e1) = all_56_1 % 41.91/6.71 | (210) op(e0, e2) = all_56_2 % 41.91/6.71 | (211) op(e0, e3) = all_56_3 % 41.91/6.71 | (212) op(e1, e0) = all_56_4 % 41.91/6.71 | (213) op(e1, e1) = all_56_5 % 41.91/6.71 | (214) op(e1, e2) = all_56_6 % 41.91/6.71 | (215) op(e1, e3) = all_56_7 % 41.91/6.71 | (216) op(e2, e0) = all_56_8 % 41.91/6.71 | (217) op(e2, e1) = all_56_9 % 41.91/6.71 | (218) op(e2, e2) = all_56_10 % 41.91/6.71 | (219) op(e2, e3) = all_56_11 % 41.91/6.71 | (220) op(e3, e0) = all_56_12 % 41.91/6.71 | (221) op(e3, e1) = all_56_13 % 41.91/6.71 | (222) op(e3, e2) = all_56_14 % 41.91/6.71 | (223) op(e3, e3) = all_56_15 % 41.91/6.71 | (224) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 41.91/6.71 | (225) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 41.91/6.71 | (226) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 41.91/6.71 | (227) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 41.91/6.71 | (228) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 41.91/6.71 | (229) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 41.91/6.71 | (230) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 41.91/6.71 | (231) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 41.91/6.71 | % 41.91/6.71 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2, % 41.91/6.71 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9, % 41.91/6.71 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives: % 41.91/6.71 | (232) op(e3, e3) = all_58_12 & op(e3, e2) = all_58_9 & op(e3, e1) = % 41.91/6.71 | all_58_10 & op(e3, e0) = all_58_11 & op(e2, e3) = all_58_13 & op(e2, % 41.91/6.71 | e2) = all_58_6 & op(e2, e1) = all_58_4 & op(e2, e0) = all_58_5 & % 41.91/6.71 | op(e1, e3) = all_58_14 & op(e1, e2) = all_58_7 & op(e1, e1) = % 41.91/6.71 | all_58_2 & op(e1, e0) = all_58_1 & op(e0, e3) = all_58_15 & op(e0, % 41.91/6.71 | e2) = all_58_8 & op(e0, e1) = all_58_3 & op(e0, e0) = all_58_0 & % 41.91/6.71 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & % 41.91/6.71 | $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) & % 41.91/6.71 | $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) & % 41.91/6.71 | $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) & % 41.91/6.71 | (all_58_0 = e3 | all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3) & % 41.91/6.71 | (all_58_0 = e3 | all_58_3 = e3 | all_58_8 = e3 | all_58_15 = e3) & % 41.91/6.71 | (all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2) & % 41.91/6.71 | (all_58_0 = e2 | all_58_3 = e2 | all_58_8 = e2 | all_58_15 = e2) & % 41.91/6.71 | (all_58_0 = e1 | all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1) & % 41.91/6.71 | (all_58_0 = e1 | all_58_3 = e1 | all_58_8 = e1 | all_58_15 = e1) & % 41.91/6.71 | (all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0) & % 41.91/6.71 | (all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0) & % 41.91/6.71 | (all_58_1 = e3 | all_58_2 = e3 | all_58_7 = e3 | all_58_14 = e3) & % 41.91/6.71 | (all_58_1 = e2 | all_58_2 = e2 | all_58_7 = e2 | all_58_14 = e2) & % 41.91/6.71 | (all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1) & % 41.91/6.71 | (all_58_1 = e0 | all_58_2 = e0 | all_58_7 = e0 | all_58_14 = e0) & % 41.91/6.71 | (all_58_2 = e3 | all_58_3 = e3 | all_58_4 = e3 | all_58_10 = e3) & % 41.91/6.71 | (all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2) & % 41.91/6.71 | (all_58_2 = e1 | all_58_3 = e1 | all_58_4 = e1 | all_58_10 = e1) & % 41.91/6.71 | (all_58_2 = e0 | all_58_3 = e0 | all_58_4 = e0 | all_58_10 = e0) & % 41.91/6.71 | (all_58_4 = e3 | all_58_5 = e3 | all_58_6 = e3 | all_58_13 = e3) & % 41.91/6.71 | (all_58_4 = e2 | all_58_5 = e2 | all_58_6 = e2 | all_58_13 = e2) & % 41.91/6.71 | (all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1) & % 41.91/6.71 | (all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0) & % 41.91/6.71 | (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3) & % 41.91/6.71 | (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2) & % 41.91/6.71 | (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_9 = e1) & % 41.91/6.71 | (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0) & % 41.91/6.71 | (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_12 = e3) & % 41.91/6.71 | (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_12 = e2) & % 41.91/6.71 | (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_12 = e1) & % 41.91/6.71 | (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0) & % 41.91/6.71 | (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) & % 41.91/6.71 | (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) & % 41.91/6.71 | (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) & % 41.91/6.71 | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0 | all_58_15 = e0) % 41.91/6.71 | % 41.91/6.71 | ALPHA: (232) implies: % 41.91/6.71 | (233) op(e0, e0) = all_58_0 % 41.91/6.71 | (234) op(e0, e1) = all_58_3 % 41.91/6.71 | (235) op(e0, e2) = all_58_8 % 41.91/6.72 | (236) op(e0, e3) = all_58_15 % 41.91/6.72 | (237) op(e1, e0) = all_58_1 % 41.91/6.72 | (238) op(e1, e1) = all_58_2 % 41.91/6.72 | (239) op(e1, e2) = all_58_7 % 41.91/6.72 | (240) op(e1, e3) = all_58_14 % 41.91/6.72 | (241) op(e2, e0) = all_58_5 % 41.91/6.72 | (242) op(e2, e1) = all_58_4 % 41.91/6.72 | (243) op(e2, e2) = all_58_6 % 41.91/6.72 | (244) op(e2, e3) = all_58_13 % 41.91/6.72 | (245) op(e3, e0) = all_58_11 % 41.91/6.72 | (246) op(e3, e1) = all_58_10 % 41.91/6.72 | (247) op(e3, e2) = all_58_9 % 41.91/6.72 | (248) op(e3, e3) = all_58_12 % 41.91/6.72 | (249) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 41.91/6.72 | (250) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 41.91/6.72 | (251) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0 % 41.91/6.72 | (252) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 41.91/6.72 | (253) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e0, e0, % 41.91/6.72 | simplifying with (72), (88) gives: % 41.91/6.72 | (254) all_30_2 = all_22_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_32_2, e0, e0, % 41.91/6.72 | simplifying with (88), (93) gives: % 41.91/6.72 | (255) all_32_2 = all_30_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_15, e0, e0, % 41.91/6.72 | simplifying with (109), (134) gives: % 41.91/6.72 | (256) all_52_15 = all_40_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_52_15, e0, e0, % 41.91/6.72 | simplifying with (93), (134) gives: % 41.91/6.72 | (257) all_52_15 = all_32_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_0, e0, e0, % 41.91/6.72 | simplifying with (134), (191) gives: % 41.91/6.72 | (258) all_54_0 = all_52_15 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_54_0, e0, e0, % 41.91/6.72 | simplifying with (36), (191) gives: % 41.91/6.72 | (259) all_54_0 = all_4_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_56_0, e0, e0, % 41.91/6.72 | simplifying with (72), (208) gives: % 41.91/6.72 | (260) all_56_0 = all_22_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_56_0, all_58_0, e0, e0, % 41.91/6.72 | simplifying with (208), (233) gives: % 41.91/6.72 | (261) all_58_0 = all_56_0 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_58_0, e0, e0, % 41.91/6.72 | simplifying with (53), (233) gives: % 41.91/6.72 | (262) all_58_0 = all_12_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_1, e1, e0, % 41.91/6.72 | simplifying with (192), (209) gives: % 41.91/6.72 | (263) all_56_1 = all_54_1 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_3, e1, e0, % 41.91/6.72 | simplifying with (209), (234) gives: % 41.91/6.72 | (264) all_58_3 = all_56_1 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_58_3, e1, e0, % 41.91/6.72 | simplifying with (135), (234) gives: % 41.91/6.72 | (265) all_58_3 = all_52_5 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_8, e2, e0, % 41.91/6.72 | simplifying with (210), (235) gives: % 41.91/6.72 | (266) all_58_8 = all_56_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_58_8, e2, e0, % 41.91/6.72 | simplifying with (193), (235) gives: % 41.91/6.72 | (267) all_58_8 = all_54_3 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_58_8, e2, e0, % 41.91/6.72 | simplifying with (136), (235) gives: % 41.91/6.72 | (268) all_58_8 = all_52_8 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_3, e3, e0, % 41.91/6.72 | simplifying with (194), (211) gives: % 41.91/6.72 | (269) all_56_3 = all_54_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_15, e3, e0, % 41.91/6.72 | simplifying with (211), (236) gives: % 41.91/6.72 | (270) all_58_15 = all_56_3 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_58_15, e3, % 41.91/6.72 | e0, simplifying with (137), (236) gives: % 41.91/6.72 | (271) all_58_15 = all_52_14 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_56_4, e0, e1, % 41.91/6.72 | simplifying with (138), (212) gives: % 41.91/6.72 | (272) all_56_4 = all_52_2 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_1, e0, e1, % 41.91/6.72 | simplifying with (212), (237) gives: % 41.91/6.72 | (273) all_58_1 = all_56_4 % 41.91/6.72 | % 41.91/6.72 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_58_1, e0, e1, % 41.91/6.72 | simplifying with (195), (237) gives: % 41.91/6.72 | (274) all_58_1 = all_54_4 % 41.91/6.72 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_46_2, e1, e1, % 41.91/6.73 | simplifying with (97), (123) gives: % 41.91/6.73 | (275) all_46_2 = all_34_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_13, e1, e1, % 41.91/6.73 | simplifying with (114), (139) gives: % 41.91/6.73 | (276) all_52_13 = all_42_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_13, e1, e1, % 41.91/6.73 | simplifying with (97), (139) gives: % 41.91/6.73 | (277) all_52_13 = all_34_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_5, e1, e1, % 41.91/6.73 | simplifying with (123), (196) gives: % 41.91/6.73 | (278) all_54_5 = all_46_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_5, e1, e1, % 41.91/6.73 | simplifying with (76), (196) gives: % 41.91/6.73 | (279) all_54_5 = all_24_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_5, e1, e1, % 41.91/6.73 | simplifying with (114), (213) gives: % 41.91/6.73 | (280) all_56_5 = all_42_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_56_5, e1, e1, % 41.91/6.73 | simplifying with (41), (213) gives: % 41.91/6.73 | (281) all_56_5 = all_6_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_2, e1, e1, % 41.91/6.73 | simplifying with (139), (238) gives: % 41.91/6.73 | (282) all_58_2 = all_52_13 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_58_2, e1, e1, % 41.91/6.73 | simplifying with (104), (238) gives: % 41.91/6.73 | (283) all_58_2 = all_38_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_7, all_56_6, e2, e1, % 41.91/6.73 | simplifying with (197), (214) gives: % 41.91/6.73 | (284) all_56_6 = all_54_7 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_7, e2, e1, % 41.91/6.73 | simplifying with (214), (239) gives: % 41.91/6.73 | (285) all_58_7 = all_56_6 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_58_7, e2, e1, % 41.91/6.73 | simplifying with (140), (239) gives: % 41.91/6.73 | (286) all_58_7 = all_52_7 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_56_7, e3, e1, % 41.91/6.73 | simplifying with (141), (215) gives: % 41.91/6.73 | (287) all_56_7 = all_52_12 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_14, e3, e1, % 41.91/6.73 | simplifying with (215), (240) gives: % 41.91/6.73 | (288) all_58_14 = all_56_7 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_58_14, e3, e1, % 41.91/6.73 | simplifying with (198), (240) gives: % 41.91/6.73 | (289) all_58_14 = all_54_6 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_56_8, e0, e2, % 41.91/6.73 | simplifying with (199), (216) gives: % 41.91/6.73 | (290) all_56_8 = all_54_8 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_5, e0, e2, % 41.91/6.73 | simplifying with (216), (241) gives: % 41.91/6.73 | (291) all_58_5 = all_56_8 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_5, e0, e2, % 41.91/6.73 | simplifying with (142), (241) gives: % 41.91/6.73 | (292) all_58_5 = all_52_1 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_9, e1, e2, % 41.91/6.73 | simplifying with (200), (217) gives: % 41.91/6.73 | (293) all_56_9 = all_54_9 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_4, e1, e2, % 41.91/6.73 | simplifying with (217), (242) gives: % 41.91/6.73 | (294) all_58_4 = all_56_9 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_58_4, e1, e2, % 41.91/6.73 | simplifying with (143), (242) gives: % 41.91/6.73 | (295) all_58_4 = all_52_4 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_16_2, e2, e2, % 41.91/6.73 | simplifying with (46), (63) gives: % 41.91/6.73 | (296) all_16_2 = all_8_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_11, e2, e2, % 41.91/6.73 | simplifying with (129), (201) gives: % 41.91/6.73 | (297) all_54_11 = all_50_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_11, e2, e2, % 41.91/6.73 | simplifying with (58), (201) gives: % 41.91/6.73 | (298) all_54_11 = all_14_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_56_10, e2, e2, % 41.91/6.73 | simplifying with (119), (218) gives: % 41.91/6.73 | (299) all_56_10 = all_44_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_10, all_58_6, e2, e2, % 41.91/6.73 | simplifying with (218), (243) gives: % 41.91/6.73 | (300) all_58_6 = all_56_10 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_58_6, e2, e2, % 41.91/6.73 | simplifying with (144), (243) gives: % 41.91/6.73 | (301) all_58_6 = all_52_11 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_58_6, e2, e2, % 41.91/6.73 | simplifying with (129), (243) gives: % 41.91/6.73 | (302) all_58_6 = all_50_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_58_6, e2, e2, % 41.91/6.73 | simplifying with (81), (243) gives: % 41.91/6.73 | (303) all_58_6 = all_26_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_58_6, e2, e2, % 41.91/6.73 | simplifying with (63), (243) gives: % 41.91/6.73 | (304) all_58_6 = all_16_2 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_11, e3, % 41.91/6.73 | e2, simplifying with (202), (219) gives: % 41.91/6.73 | (305) all_56_11 = all_54_10 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_13, e3, % 41.91/6.73 | e2, simplifying with (219), (244) gives: % 41.91/6.73 | (306) all_58_13 = all_56_11 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_58_13, e3, % 41.91/6.73 | e2, simplifying with (145), (244) gives: % 41.91/6.73 | (307) all_58_13 = all_52_10 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_56_12, e0, e3, % 41.91/6.73 | simplifying with (146), (220) gives: % 41.91/6.73 | (308) all_56_12 = all_52_0 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_11, e0, % 41.91/6.73 | e3, simplifying with (220), (245) gives: % 41.91/6.73 | (309) all_58_11 = all_56_12 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_58_11, e0, % 41.91/6.73 | e3, simplifying with (203), (245) gives: % 41.91/6.73 | (310) all_58_11 = all_54_12 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_56_13, e1, % 41.91/6.73 | e3, simplifying with (204), (221) gives: % 41.91/6.73 | (311) all_56_13 = all_54_13 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_10, e1, % 41.91/6.73 | e3, simplifying with (221), (246) gives: % 41.91/6.73 | (312) all_58_10 = all_56_13 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_58_10, e1, e3, % 41.91/6.73 | simplifying with (147), (246) gives: % 41.91/6.73 | (313) all_58_10 = all_52_3 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_56_14, e2, e3, % 41.91/6.73 | simplifying with (148), (222) gives: % 41.91/6.73 | (314) all_56_14 = all_52_6 % 41.91/6.73 | % 41.91/6.73 | GROUND_INST: instantiating (function-axioms) with all_56_14, all_58_9, e2, e3, % 41.91/6.73 | simplifying with (222), (247) gives: % 41.91/6.73 | (315) all_58_9 = all_56_14 % 41.91/6.73 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_58_9, e2, e3, % 41.91/6.74 | simplifying with (205), (247) gives: % 41.91/6.74 | (316) all_58_9 = all_54_15 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_48_2, e3, e3, % 41.91/6.74 | simplifying with (86), (127) gives: % 41.91/6.74 | (317) all_48_2 = all_28_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_48_2, e3, e3, % 41.91/6.74 | simplifying with (70), (127) gives: % 41.91/6.74 | (318) all_48_2 = all_20_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_52_9, e3, e3, % 41.91/6.74 | simplifying with (127), (149) gives: % 41.91/6.74 | (319) all_52_9 = all_48_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_52_9, e3, e3, % 41.91/6.74 | simplifying with (51), (149) gives: % 41.91/6.74 | (320) all_52_9 = all_10_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_54_14, e3, e3, % 41.91/6.74 | simplifying with (127), (206) gives: % 41.91/6.74 | (321) all_54_14 = all_48_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_56_15, e3, % 41.91/6.74 | e3, simplifying with (206), (223) gives: % 41.91/6.74 | (322) all_56_15 = all_54_14 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_56_15, e3, e3, % 41.91/6.74 | simplifying with (68), (223) gives: % 41.91/6.74 | (323) all_56_15 = all_18_2 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_58_12, e3, e3, % 41.91/6.74 | simplifying with (149), (248) gives: % 41.91/6.74 | (324) all_58_12 = all_52_9 % 41.91/6.74 | % 41.91/6.74 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_58_12, e3, e3, % 41.91/6.74 | simplifying with (102), (248) gives: % 41.91/6.74 | (325) all_58_12 = all_36_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (261), (262) imply: % 42.21/6.74 | (326) all_56_0 = all_12_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (326) implies: % 42.21/6.74 | (327) all_56_0 = all_12_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (273), (274) imply: % 42.21/6.74 | (328) all_56_4 = all_54_4 % 42.21/6.74 | % 42.21/6.74 | SIMP: (328) implies: % 42.21/6.74 | (329) all_56_4 = all_54_4 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (282), (283) imply: % 42.21/6.74 | (330) all_52_13 = all_38_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (330) implies: % 42.21/6.74 | (331) all_52_13 = all_38_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (264), (265) imply: % 42.21/6.74 | (332) all_56_1 = all_52_5 % 42.21/6.74 | % 42.21/6.74 | SIMP: (332) implies: % 42.21/6.74 | (333) all_56_1 = all_52_5 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (294), (295) imply: % 42.21/6.74 | (334) all_56_9 = all_52_4 % 42.21/6.74 | % 42.21/6.74 | SIMP: (334) implies: % 42.21/6.74 | (335) all_56_9 = all_52_4 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (291), (292) imply: % 42.21/6.74 | (336) all_56_8 = all_52_1 % 42.21/6.74 | % 42.21/6.74 | SIMP: (336) implies: % 42.21/6.74 | (337) all_56_8 = all_52_1 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (301), (302) imply: % 42.21/6.74 | (338) all_52_11 = all_50_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (301), (304) imply: % 42.21/6.74 | (339) all_52_11 = all_16_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (300), (301) imply: % 42.21/6.74 | (340) all_56_10 = all_52_11 % 42.21/6.74 | % 42.21/6.74 | SIMP: (340) implies: % 42.21/6.74 | (341) all_56_10 = all_52_11 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (301), (303) imply: % 42.21/6.74 | (342) all_52_11 = all_26_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (285), (286) imply: % 42.21/6.74 | (343) all_56_6 = all_52_7 % 42.21/6.74 | % 42.21/6.74 | SIMP: (343) implies: % 42.21/6.74 | (344) all_56_6 = all_52_7 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (266), (267) imply: % 42.21/6.74 | (345) all_56_2 = all_54_3 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (266), (268) imply: % 42.21/6.74 | (346) all_56_2 = all_52_8 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (315), (316) imply: % 42.21/6.74 | (347) all_56_14 = all_54_15 % 42.21/6.74 | % 42.21/6.74 | SIMP: (347) implies: % 42.21/6.74 | (348) all_56_14 = all_54_15 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (312), (313) imply: % 42.21/6.74 | (349) all_56_13 = all_52_3 % 42.21/6.74 | % 42.21/6.74 | SIMP: (349) implies: % 42.21/6.74 | (350) all_56_13 = all_52_3 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (309), (310) imply: % 42.21/6.74 | (351) all_56_12 = all_54_12 % 42.21/6.74 | % 42.21/6.74 | SIMP: (351) implies: % 42.21/6.74 | (352) all_56_12 = all_54_12 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (324), (325) imply: % 42.21/6.74 | (353) all_52_9 = all_36_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (353) implies: % 42.21/6.74 | (354) all_52_9 = all_36_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (306), (307) imply: % 42.21/6.74 | (355) all_56_11 = all_52_10 % 42.21/6.74 | % 42.21/6.74 | SIMP: (355) implies: % 42.21/6.74 | (356) all_56_11 = all_52_10 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (288), (289) imply: % 42.21/6.74 | (357) all_56_7 = all_54_6 % 42.21/6.74 | % 42.21/6.74 | SIMP: (357) implies: % 42.21/6.74 | (358) all_56_7 = all_54_6 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (270), (271) imply: % 42.21/6.74 | (359) all_56_3 = all_52_14 % 42.21/6.74 | % 42.21/6.74 | SIMP: (359) implies: % 42.21/6.74 | (360) all_56_3 = all_52_14 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (260), (327) imply: % 42.21/6.74 | (361) all_22_2 = all_12_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (361) implies: % 42.21/6.74 | (362) all_22_2 = all_12_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (263), (333) imply: % 42.21/6.74 | (363) all_54_1 = all_52_5 % 42.21/6.74 | % 42.21/6.74 | SIMP: (363) implies: % 42.21/6.74 | (364) all_54_1 = all_52_5 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (345), (346) imply: % 42.21/6.74 | (365) all_54_3 = all_52_8 % 42.21/6.74 | % 42.21/6.74 | SIMP: (365) implies: % 42.21/6.74 | (366) all_54_3 = all_52_8 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (269), (360) imply: % 42.21/6.74 | (367) all_54_2 = all_52_14 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (272), (329) imply: % 42.21/6.74 | (368) all_54_4 = all_52_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (280), (281) imply: % 42.21/6.74 | (369) all_42_2 = all_6_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (369) implies: % 42.21/6.74 | (370) all_42_2 = all_6_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (284), (344) imply: % 42.21/6.74 | (371) all_54_7 = all_52_7 % 42.21/6.74 | % 42.21/6.74 | SIMP: (371) implies: % 42.21/6.74 | (372) all_54_7 = all_52_7 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (287), (358) imply: % 42.21/6.74 | (373) all_54_6 = all_52_12 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (290), (337) imply: % 42.21/6.74 | (374) all_54_8 = all_52_1 % 42.21/6.74 | % 42.21/6.74 | SIMP: (374) implies: % 42.21/6.74 | (375) all_54_8 = all_52_1 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (293), (335) imply: % 42.21/6.74 | (376) all_54_9 = all_52_4 % 42.21/6.74 | % 42.21/6.74 | SIMP: (376) implies: % 42.21/6.74 | (377) all_54_9 = all_52_4 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (299), (341) imply: % 42.21/6.74 | (378) all_52_11 = all_44_2 % 42.21/6.74 | % 42.21/6.74 | SIMP: (378) implies: % 42.21/6.74 | (379) all_52_11 = all_44_2 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (305), (356) imply: % 42.21/6.74 | (380) all_54_10 = all_52_10 % 42.21/6.74 | % 42.21/6.74 | SIMP: (380) implies: % 42.21/6.74 | (381) all_54_10 = all_52_10 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (308), (352) imply: % 42.21/6.74 | (382) all_54_12 = all_52_0 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (311), (350) imply: % 42.21/6.74 | (383) all_54_13 = all_52_3 % 42.21/6.74 | % 42.21/6.74 | SIMP: (383) implies: % 42.21/6.74 | (384) all_54_13 = all_52_3 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (314), (348) imply: % 42.21/6.74 | (385) all_54_15 = all_52_6 % 42.21/6.74 | % 42.21/6.74 | SIMP: (385) implies: % 42.21/6.74 | (386) all_54_15 = all_52_6 % 42.21/6.74 | % 42.21/6.74 | COMBINE_EQS: (322), (323) imply: % 42.21/6.75 | (387) all_54_14 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (387) implies: % 42.21/6.75 | (388) all_54_14 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (258), (259) imply: % 42.21/6.75 | (389) all_52_15 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (389) implies: % 42.21/6.75 | (390) all_52_15 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (278), (279) imply: % 42.21/6.75 | (391) all_46_2 = all_24_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (391) implies: % 42.21/6.75 | (392) all_46_2 = all_24_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (297), (298) imply: % 42.21/6.75 | (393) all_50_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (393) implies: % 42.21/6.75 | (394) all_50_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (321), (388) imply: % 42.21/6.75 | (395) all_48_2 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (395) implies: % 42.21/6.75 | (396) all_48_2 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (320), (354) imply: % 42.21/6.75 | (397) all_36_2 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (319), (354) imply: % 42.21/6.75 | (398) all_48_2 = all_36_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (398) implies: % 42.21/6.75 | (399) all_48_2 = all_36_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (338), (379) imply: % 42.21/6.75 | (400) all_50_2 = all_44_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (400) implies: % 42.21/6.75 | (401) all_50_2 = all_44_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (339), (379) imply: % 42.21/6.75 | (402) all_44_2 = all_16_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (342), (379) imply: % 42.21/6.75 | (403) all_44_2 = all_26_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (277), (331) imply: % 42.21/6.75 | (404) all_38_2 = all_34_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (276), (331) imply: % 42.21/6.75 | (405) all_42_2 = all_38_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (405) implies: % 42.21/6.75 | (406) all_42_2 = all_38_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (256), (257) imply: % 42.21/6.75 | (407) all_40_2 = all_32_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (256), (390) imply: % 42.21/6.75 | (408) all_40_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (394), (401) imply: % 42.21/6.75 | (409) all_44_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (409) implies: % 42.21/6.75 | (410) all_44_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (317), (396) imply: % 42.21/6.75 | (411) all_28_2 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (317), (318) imply: % 42.21/6.75 | (412) all_28_2 = all_20_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (317), (399) imply: % 42.21/6.75 | (413) all_36_2 = all_28_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (413) implies: % 42.21/6.75 | (414) all_36_2 = all_28_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (275), (392) imply: % 42.21/6.75 | (415) all_34_2 = all_24_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (415) implies: % 42.21/6.75 | (416) all_34_2 = all_24_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (402), (403) imply: % 42.21/6.75 | (417) all_26_2 = all_16_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (403), (410) imply: % 42.21/6.75 | (418) all_26_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (370), (406) imply: % 42.21/6.75 | (419) all_38_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (419) implies: % 42.21/6.75 | (420) all_38_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (407), (408) imply: % 42.21/6.75 | (421) all_32_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (421) implies: % 42.21/6.75 | (422) all_32_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (404), (420) imply: % 42.21/6.75 | (423) all_34_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (423) implies: % 42.21/6.75 | (424) all_34_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (397), (414) imply: % 42.21/6.75 | (425) all_28_2 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (425) implies: % 42.21/6.75 | (426) all_28_2 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (416), (424) imply: % 42.21/6.75 | (427) all_24_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (427) implies: % 42.21/6.75 | (428) all_24_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (255), (422) imply: % 42.21/6.75 | (429) all_30_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (429) implies: % 42.21/6.75 | (430) all_30_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (254), (430) imply: % 42.21/6.75 | (431) all_22_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (431) implies: % 42.21/6.75 | (432) all_22_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (411), (412) imply: % 42.21/6.75 | (433) all_20_2 = all_18_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (412), (426) imply: % 42.21/6.75 | (434) all_20_2 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (417), (418) imply: % 42.21/6.75 | (435) all_16_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (435) implies: % 42.21/6.75 | (436) all_16_2 = all_14_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (362), (432) imply: % 42.21/6.75 | (437) all_12_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (437) implies: % 42.21/6.75 | (438) all_12_2 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (433), (434) imply: % 42.21/6.75 | (439) all_18_2 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (296), (436) imply: % 42.21/6.75 | (440) all_14_2 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | SIMP: (440) implies: % 42.21/6.75 | (441) all_14_2 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (418), (441) imply: % 42.21/6.75 | (442) all_26_2 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (403), (442) imply: % 42.21/6.75 | (443) all_44_2 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (392), (428) imply: % 42.21/6.75 | (444) all_46_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (394), (441) imply: % 42.21/6.75 | (445) all_50_2 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (331), (420) imply: % 42.21/6.75 | (446) all_52_13 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (379), (443) imply: % 42.21/6.75 | (447) all_52_11 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (388), (439) imply: % 42.21/6.75 | (448) all_54_14 = all_10_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (298), (441) imply: % 42.21/6.75 | (449) all_54_11 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (279), (428) imply: % 42.21/6.75 | (450) all_54_5 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (289), (373) imply: % 42.21/6.75 | (451) all_58_14 = all_52_12 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (310), (382) imply: % 42.21/6.75 | (452) all_58_11 = all_52_0 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (316), (386) imply: % 42.21/6.75 | (453) all_58_9 = all_52_6 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (301), (447) imply: % 42.21/6.75 | (454) all_58_6 = all_8_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (283), (420) imply: % 42.21/6.75 | (455) all_58_2 = all_6_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (274), (368) imply: % 42.21/6.75 | (456) all_58_1 = all_52_2 % 42.21/6.75 | % 42.21/6.75 | COMBINE_EQS: (262), (438) imply: % 42.21/6.75 | (457) all_58_0 = all_4_2 % 42.21/6.75 | % 42.21/6.75 | REDUCE: (190), (259), (364) imply: % 42.21/6.75 | (458) ~ (all_52_5 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | SIMP: (458) implies: % 42.21/6.75 | (459) ~ (all_52_5 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | REDUCE: (189), (259), (367) imply: % 42.21/6.75 | (460) ~ (all_52_14 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | SIMP: (460) implies: % 42.21/6.75 | (461) ~ (all_52_14 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | REDUCE: (188), (259), (366) imply: % 42.21/6.75 | (462) ~ (all_52_8 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | SIMP: (462) implies: % 42.21/6.75 | (463) ~ (all_52_8 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | REDUCE: (187), (259), (368) imply: % 42.21/6.75 | (464) ~ (all_52_2 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | SIMP: (464) implies: % 42.21/6.75 | (465) ~ (all_52_2 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | REDUCE: (186), (259), (375) imply: % 42.21/6.75 | (466) ~ (all_52_1 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | SIMP: (466) implies: % 42.21/6.75 | (467) ~ (all_52_1 = all_4_2) % 42.21/6.75 | % 42.21/6.75 | REDUCE: (185), (259), (382) imply: % 42.21/6.76 | (468) ~ (all_52_0 = all_4_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (468) implies: % 42.21/6.76 | (469) ~ (all_52_0 = all_4_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (184), (364), (450) imply: % 42.21/6.76 | (470) ~ (all_52_5 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (183), (364), (377) imply: % 42.21/6.76 | (471) ~ (all_52_4 = all_52_5) % 42.21/6.76 | % 42.21/6.76 | SIMP: (471) implies: % 42.21/6.76 | (472) ~ (all_52_4 = all_52_5) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (182), (366), (367) imply: % 42.21/6.76 | (473) ~ (all_52_8 = all_52_14) % 42.21/6.76 | % 42.21/6.76 | SIMP: (473) implies: % 42.21/6.76 | (474) ~ (all_52_8 = all_52_14) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (181), (367), (373) imply: % 42.21/6.76 | (475) ~ (all_52_12 = all_52_14) % 42.21/6.76 | % 42.21/6.76 | SIMP: (475) implies: % 42.21/6.76 | (476) ~ (all_52_12 = all_52_14) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (180), (367), (448) imply: % 42.21/6.76 | (477) ~ (all_52_14 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (179), (368), (450) imply: % 42.21/6.76 | (478) ~ (all_52_2 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (178), (368), (373) imply: % 42.21/6.76 | (479) ~ (all_52_2 = all_52_12) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (177), (368), (382) imply: % 42.21/6.76 | (480) ~ (all_52_0 = all_52_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (480) implies: % 42.21/6.76 | (481) ~ (all_52_0 = all_52_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (176), (373), (450) imply: % 42.21/6.76 | (482) ~ (all_52_12 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (482) implies: % 42.21/6.76 | (483) ~ (all_52_12 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (175), (372), (450) imply: % 42.21/6.76 | (484) ~ (all_52_7 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (484) implies: % 42.21/6.76 | (485) ~ (all_52_7 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (174), (377), (450) imply: % 42.21/6.76 | (486) ~ (all_52_4 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (486) implies: % 42.21/6.76 | (487) ~ (all_52_4 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (173), (384), (450) imply: % 42.21/6.76 | (488) ~ (all_52_3 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (488) implies: % 42.21/6.76 | (489) ~ (all_52_3 = all_6_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (172), (372), (373) imply: % 42.21/6.76 | (490) ~ (all_52_7 = all_52_12) % 42.21/6.76 | % 42.21/6.76 | SIMP: (490) implies: % 42.21/6.76 | (491) ~ (all_52_7 = all_52_12) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (171), (373), (381) imply: % 42.21/6.76 | (492) ~ (all_52_10 = all_52_12) % 42.21/6.76 | % 42.21/6.76 | SIMP: (492) implies: % 42.21/6.76 | (493) ~ (all_52_10 = all_52_12) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (170), (373), (448) imply: % 42.21/6.76 | (494) ~ (all_52_12 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (169), (372), (449) imply: % 42.21/6.76 | (495) ~ (all_52_7 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (168), (372), (386) imply: % 42.21/6.76 | (496) ~ (all_52_6 = all_52_7) % 42.21/6.76 | % 42.21/6.76 | SIMP: (496) implies: % 42.21/6.76 | (497) ~ (all_52_6 = all_52_7) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (167), (375), (381) imply: % 42.21/6.76 | (498) ~ (all_52_1 = all_52_10) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (166), (375), (449) imply: % 42.21/6.76 | (499) ~ (all_52_1 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (165), (377), (449) imply: % 42.21/6.76 | (500) ~ (all_52_4 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (164), (377), (384) imply: % 42.21/6.76 | (501) ~ (all_52_3 = all_52_4) % 42.21/6.76 | % 42.21/6.76 | SIMP: (501) implies: % 42.21/6.76 | (502) ~ (all_52_3 = all_52_4) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (163), (381), (449) imply: % 42.21/6.76 | (503) ~ (all_52_10 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (162), (381), (448) imply: % 42.21/6.76 | (504) ~ (all_52_10 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (161), (386), (449) imply: % 42.21/6.76 | (505) ~ (all_52_6 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (505) implies: % 42.21/6.76 | (506) ~ (all_52_6 = all_8_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (160), (382), (384) imply: % 42.21/6.76 | (507) ~ (all_52_0 = all_52_3) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (159), (382), (448) imply: % 42.21/6.76 | (508) ~ (all_52_0 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (158), (382), (386) imply: % 42.21/6.76 | (509) ~ (all_52_0 = all_52_6) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (157), (384), (448) imply: % 42.21/6.76 | (510) ~ (all_52_3 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (156), (384), (386) imply: % 42.21/6.76 | (511) ~ (all_52_3 = all_52_6) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (155), (386), (448) imply: % 42.21/6.76 | (512) ~ (all_52_6 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | SIMP: (512) implies: % 42.21/6.76 | (513) ~ (all_52_6 = all_10_2) % 42.21/6.76 | % 42.21/6.76 | REDUCE: (131), (445) imply: % 42.21/6.76 | (514) op(all_8_2, e2) = all_50_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (125), (444) imply: % 42.21/6.76 | (515) op(all_6_2, e1) = all_46_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (121), (443) imply: % 42.21/6.76 | (516) op(all_8_2, e2) = all_44_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (116), (370) imply: % 42.21/6.76 | (517) op(all_6_2, e1) = all_42_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (111), (408) imply: % 42.21/6.76 | (518) op(all_4_2, e0) = all_40_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (106), (420) imply: % 42.21/6.76 | (519) op(all_6_2, e1) = all_38_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (99), (424) imply: % 42.21/6.76 | (520) op(all_6_2, e1) = all_34_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (95), (422) imply: % 42.21/6.76 | (521) op(all_4_2, e0) = all_32_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (90), (430) imply: % 42.21/6.76 | (522) op(all_4_2, e0) = all_30_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (83), (442) imply: % 42.21/6.76 | (523) op(all_8_2, e2) = all_26_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (78), (428) imply: % 42.21/6.76 | (524) op(all_6_2, e1) = all_24_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (74), (432) imply: % 42.21/6.76 | (525) op(all_4_2, e0) = all_22_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (65), (296) imply: % 42.21/6.76 | (526) op(all_8_2, e2) = all_16_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (60), (441) imply: % 42.21/6.76 | (527) op(all_8_2, e2) = all_14_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (55), (438) imply: % 42.21/6.76 | (528) op(all_4_2, e0) = all_12_0 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (130), (445) imply: % 42.21/6.76 | (529) op(e2, all_8_2) = all_50_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (120), (443) imply: % 42.21/6.76 | (530) op(e2, all_8_2) = all_44_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (82), (442) imply: % 42.21/6.76 | (531) op(e2, all_8_2) = all_26_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (64), (296) imply: % 42.21/6.76 | (532) op(e2, all_8_2) = all_16_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (59), (441) imply: % 42.21/6.76 | (533) op(e2, all_8_2) = all_14_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (124), (444) imply: % 42.21/6.76 | (534) op(e1, all_6_2) = all_46_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (115), (370) imply: % 42.21/6.76 | (535) op(e1, all_6_2) = all_42_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (105), (420) imply: % 42.21/6.76 | (536) op(e1, all_6_2) = all_38_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (98), (424) imply: % 42.21/6.76 | (537) op(e1, all_6_2) = all_34_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (77), (428) imply: % 42.21/6.76 | (538) op(e1, all_6_2) = all_24_1 % 42.21/6.76 | % 42.21/6.76 | REDUCE: (110), (408) imply: % 42.21/6.77 | (539) op(e0, all_4_2) = all_40_1 % 42.21/6.77 | % 42.21/6.77 | REDUCE: (94), (422) imply: % 42.21/6.77 | (540) op(e0, all_4_2) = all_32_1 % 42.21/6.77 | % 42.21/6.77 | REDUCE: (89), (430) imply: % 42.21/6.77 | (541) op(e0, all_4_2) = all_30_1 % 42.21/6.77 | % 42.21/6.77 | REDUCE: (73), (432) imply: % 42.21/6.77 | (542) op(e0, all_4_2) = all_22_1 % 42.21/6.77 | % 42.21/6.77 | REDUCE: (54), (438) imply: % 42.21/6.77 | (543) op(e0, all_4_2) = all_12_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_22_1, all_4_2, % 42.21/6.77 | e0, simplifying with (542), (543) gives: % 42.21/6.77 | (544) all_22_1 = all_12_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_30_1, all_4_2, % 42.21/6.77 | e0, simplifying with (541), (542) gives: % 42.21/6.77 | (545) all_30_1 = all_22_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_32_1, all_4_2, % 42.21/6.77 | e0, simplifying with (540), (541) gives: % 42.21/6.77 | (546) all_32_1 = all_30_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_40_1, all_4_2, % 42.21/6.77 | e0, simplifying with (37), (539) gives: % 42.21/6.77 | (547) all_40_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_40_1, all_4_2, % 42.21/6.77 | e0, simplifying with (539), (540) gives: % 42.21/6.77 | (548) all_40_1 = all_32_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_34_1, all_6_2, % 42.21/6.77 | e1, simplifying with (537), (538) gives: % 42.21/6.77 | (549) all_34_1 = all_24_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_42_1, all_6_2, % 42.21/6.77 | e1, simplifying with (42), (535) gives: % 42.21/6.77 | (550) all_42_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_46_1, all_6_2, % 42.21/6.77 | e1, simplifying with (534), (535) gives: % 42.21/6.77 | (551) all_46_1 = all_42_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_46_1, all_6_2, % 42.21/6.77 | e1, simplifying with (534), (536) gives: % 42.21/6.77 | (552) all_46_1 = all_38_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_34_1, all_46_1, all_6_2, % 42.21/6.77 | e1, simplifying with (534), (537) gives: % 42.21/6.77 | (553) all_46_1 = all_34_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_44_1, all_8_2, % 42.21/6.77 | e2, simplifying with (47), (530) gives: % 42.21/6.77 | (554) all_44_1 = all_8_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_44_1, all_8_2, % 42.21/6.77 | e2, simplifying with (530), (532) gives: % 42.21/6.77 | (555) all_44_1 = all_16_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_44_1, all_8_2, % 42.21/6.77 | e2, simplifying with (530), (533) gives: % 42.21/6.77 | (556) all_44_1 = all_14_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_44_1, all_50_1, all_8_2, % 42.21/6.77 | e2, simplifying with (529), (530) gives: % 42.21/6.77 | (557) all_50_1 = all_44_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_50_1, all_8_2, % 42.21/6.77 | e2, simplifying with (529), (531) gives: % 42.21/6.77 | (558) all_50_1 = all_26_1 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_32_0, e0, % 42.21/6.77 | all_4_2, simplifying with (38), (521) gives: % 42.21/6.77 | (559) all_32_0 = all_4_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_32_0, e0, % 42.21/6.77 | all_4_2, simplifying with (521), (525) gives: % 42.21/6.77 | (560) all_32_0 = all_22_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_12_0, all_32_0, e0, % 42.21/6.77 | all_4_2, simplifying with (521), (528) gives: % 42.21/6.77 | (561) all_32_0 = all_12_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_40_0, e0, % 42.21/6.77 | all_4_2, simplifying with (518), (521) gives: % 42.21/6.77 | (562) all_40_0 = all_32_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_30_0, all_40_0, e0, % 42.21/6.77 | all_4_2, simplifying with (518), (522) gives: % 42.21/6.77 | (563) all_40_0 = all_30_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_34_0, all_42_0, e1, % 42.21/6.77 | all_6_2, simplifying with (517), (520) gives: % 42.21/6.77 | (564) all_42_0 = all_34_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_42_0, e1, % 42.21/6.77 | all_6_2, simplifying with (517), (524) gives: % 42.21/6.77 | (565) all_42_0 = all_24_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_46_0, e1, % 42.21/6.77 | all_6_2, simplifying with (43), (515) gives: % 42.21/6.77 | (566) all_46_0 = all_6_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_42_0, all_46_0, e1, % 42.21/6.77 | all_6_2, simplifying with (515), (517) gives: % 42.21/6.77 | (567) all_46_0 = all_42_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_38_0, all_46_0, e1, % 42.21/6.77 | all_6_2, simplifying with (515), (519) gives: % 42.21/6.77 | (568) all_46_0 = all_38_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_26_0, e2, % 42.21/6.77 | all_8_2, simplifying with (48), (523) gives: % 42.21/6.77 | (569) all_26_0 = all_8_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_26_0, all_44_0, e2, % 42.21/6.77 | all_8_2, simplifying with (516), (523) gives: % 42.21/6.77 | (570) all_44_0 = all_26_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_14_0, all_44_0, e2, % 42.21/6.77 | all_8_2, simplifying with (516), (527) gives: % 42.21/6.77 | (571) all_44_0 = all_14_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_44_0, all_50_0, e2, % 42.21/6.77 | all_8_2, simplifying with (514), (516) gives: % 42.21/6.77 | (572) all_50_0 = all_44_0 % 42.21/6.77 | % 42.21/6.77 | GROUND_INST: instantiating (function-axioms) with all_16_0, all_50_0, e2, % 42.21/6.77 | all_8_2, simplifying with (514), (526) gives: % 42.21/6.77 | (573) all_50_0 = all_16_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (572), (573) imply: % 42.21/6.77 | (574) all_44_0 = all_16_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (574) implies: % 42.21/6.77 | (575) all_44_0 = all_16_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (557), (558) imply: % 42.21/6.77 | (576) all_44_1 = all_26_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (576) implies: % 42.21/6.77 | (577) all_44_1 = all_26_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (567), (568) imply: % 42.21/6.77 | (578) all_42_0 = all_38_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (578) implies: % 42.21/6.77 | (579) all_42_0 = all_38_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (566), (568) imply: % 42.21/6.77 | (580) all_38_0 = all_6_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (551), (552) imply: % 42.21/6.77 | (581) all_42_1 = all_38_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (581) implies: % 42.21/6.77 | (582) all_42_1 = all_38_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (552), (553) imply: % 42.21/6.77 | (583) all_38_1 = all_34_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (571), (575) imply: % 42.21/6.77 | (584) all_16_0 = all_14_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (570), (575) imply: % 42.21/6.77 | (585) all_26_0 = all_16_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (585) implies: % 42.21/6.77 | (586) all_26_0 = all_16_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (556), (577) imply: % 42.21/6.77 | (587) all_26_1 = all_14_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (555), (577) imply: % 42.21/6.77 | (588) all_26_1 = all_16_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (554), (577) imply: % 42.21/6.77 | (589) all_26_1 = all_8_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (564), (565) imply: % 42.21/6.77 | (590) all_34_0 = all_24_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (564), (579) imply: % 42.21/6.77 | (591) all_38_0 = all_34_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (591) implies: % 42.21/6.77 | (592) all_38_0 = all_34_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (550), (582) imply: % 42.21/6.77 | (593) all_38_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (593) implies: % 42.21/6.77 | (594) all_38_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (562), (563) imply: % 42.21/6.77 | (595) all_32_0 = all_30_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (595) implies: % 42.21/6.77 | (596) all_32_0 = all_30_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (547), (548) imply: % 42.21/6.77 | (597) all_32_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (597) implies: % 42.21/6.77 | (598) all_32_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (580), (592) imply: % 42.21/6.77 | (599) all_34_0 = all_6_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (599) implies: % 42.21/6.77 | (600) all_34_0 = all_6_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (583), (594) imply: % 42.21/6.77 | (601) all_34_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (601) implies: % 42.21/6.77 | (602) all_34_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (590), (600) imply: % 42.21/6.77 | (603) all_24_0 = all_6_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (549), (602) imply: % 42.21/6.77 | (604) all_24_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (604) implies: % 42.21/6.77 | (605) all_24_1 = all_6_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (560), (596) imply: % 42.21/6.77 | (606) all_30_0 = all_22_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (559), (596) imply: % 42.21/6.77 | (607) all_30_0 = all_4_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (561), (596) imply: % 42.21/6.77 | (608) all_30_0 = all_12_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (546), (598) imply: % 42.21/6.77 | (609) all_30_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (609) implies: % 42.21/6.77 | (610) all_30_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (606), (607) imply: % 42.21/6.77 | (611) all_22_0 = all_4_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (606), (608) imply: % 42.21/6.77 | (612) all_22_0 = all_12_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (545), (610) imply: % 42.21/6.77 | (613) all_22_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | SIMP: (613) implies: % 42.21/6.77 | (614) all_22_1 = all_4_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (569), (586) imply: % 42.21/6.77 | (615) all_16_0 = all_8_0 % 42.21/6.77 | % 42.21/6.77 | SIMP: (615) implies: % 42.21/6.77 | (616) all_16_0 = all_8_0 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (587), (588) imply: % 42.21/6.77 | (617) all_16_1 = all_14_1 % 42.21/6.77 | % 42.21/6.77 | COMBINE_EQS: (588), (589) imply: % 42.21/6.78 | (618) all_16_1 = all_8_1 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (611), (612) imply: % 42.21/6.78 | (619) all_12_0 = all_4_0 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (544), (614) imply: % 42.21/6.78 | (620) all_12_1 = all_4_1 % 42.21/6.78 | % 42.21/6.78 | SIMP: (620) implies: % 42.21/6.78 | (621) all_12_1 = all_4_1 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (584), (616) imply: % 42.21/6.78 | (622) all_14_0 = all_8_0 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (617), (618) imply: % 42.21/6.78 | (623) all_14_1 = all_8_1 % 42.21/6.78 | % 42.21/6.78 | SIMP: (623) implies: % 42.21/6.78 | (624) all_14_1 = all_8_1 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (563), (607) imply: % 42.21/6.78 | (625) all_40_0 = all_4_0 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (564), (600) imply: % 42.21/6.78 | (626) all_42_0 = all_6_0 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (558), (589) imply: % 42.21/6.78 | (627) all_50_1 = all_8_1 % 42.21/6.78 | % 42.21/6.78 | COMBINE_EQS: (573), (616) imply: % 42.21/6.78 | (628) all_50_0 = all_8_0 % 42.21/6.78 | % 42.21/6.78 | BETA: splitting (39) gives: % 42.21/6.78 | % 42.21/6.78 | Case 1: % 42.21/6.78 | | % 42.21/6.78 | | (629) ~ (all_4_0 = e2) % 42.21/6.78 | | % 42.21/6.78 | | BETA: splitting (44) gives: % 42.21/6.78 | | % 42.21/6.78 | | Case 1: % 42.21/6.78 | | | % 42.21/6.78 | | | (630) ~ (all_6_0 = e3) % 42.21/6.78 | | | % 42.21/6.78 | | | BETA: splitting (49) gives: % 42.21/6.78 | | | % 42.21/6.78 | | | Case 1: % 42.21/6.78 | | | | % 42.21/6.78 | | | | (631) ~ (all_8_0 = e3) % 42.21/6.78 | | | | % 42.21/6.78 | | | | BETA: splitting (56) gives: % 42.21/6.78 | | | | % 42.21/6.78 | | | | Case 1: % 42.21/6.78 | | | | | % 42.21/6.78 | | | | | (632) ~ (all_12_0 = e3) % 42.21/6.78 | | | | | % 42.21/6.78 | | | | | REDUCE: (619), (632) imply: % 42.21/6.78 | | | | | (633) ~ (all_4_0 = e3) % 42.21/6.78 | | | | | % 42.21/6.78 | | | | | BETA: splitting (61) gives: % 42.21/6.78 | | | | | % 42.21/6.78 | | | | | Case 1: % 42.21/6.78 | | | | | | % 42.21/6.78 | | | | | | (634) ~ (all_14_0 = e0) % 42.21/6.78 | | | | | | % 42.21/6.78 | | | | | | REDUCE: (622), (634) imply: % 42.21/6.78 | | | | | | (635) ~ (all_8_0 = e0) % 42.21/6.78 | | | | | | % 42.21/6.78 | | | | | | BETA: splitting (66) gives: % 42.21/6.78 | | | | | | % 42.21/6.78 | | | | | | Case 1: % 42.21/6.78 | | | | | | | % 42.21/6.78 | | | | | | | (636) ~ (all_16_0 = e1) % 42.21/6.78 | | | | | | | % 42.21/6.78 | | | | | | | REDUCE: (616), (636) imply: % 42.21/6.78 | | | | | | | (637) ~ (all_8_0 = e1) % 42.21/6.78 | | | | | | | % 42.21/6.78 | | | | | | | BETA: splitting (79) gives: % 42.21/6.78 | | | | | | | % 42.21/6.78 | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | % 42.21/6.78 | | | | | | | | (638) ~ (all_24_0 = e0) % 42.21/6.78 | | | | | | | | % 42.21/6.78 | | | | | | | | REDUCE: (603), (638) imply: % 42.21/6.78 | | | | | | | | (639) ~ (all_6_0 = e0) % 42.21/6.78 | | | | | | | | % 42.21/6.78 | | | | | | | | BETA: splitting (91) gives: % 42.21/6.78 | | | | | | | | % 42.21/6.78 | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | % 42.21/6.78 | | | | | | | | | (640) ~ (all_30_0 = e1) % 42.21/6.78 | | | | | | | | | % 42.21/6.78 | | | | | | | | | REDUCE: (607), (640) imply: % 42.21/6.78 | | | | | | | | | (641) ~ (all_4_0 = e1) % 42.21/6.78 | | | | | | | | | % 42.21/6.78 | | | | | | | | | BETA: splitting (107) gives: % 42.21/6.78 | | | | | | | | | % 42.21/6.78 | | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | (642) ~ (all_38_0 = e2) % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | REDUCE: (580), (642) imply: % 42.21/6.78 | | | | | | | | | | (643) ~ (all_6_0 = e2) % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | BETA: splitting (150) gives: % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | (644) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.21/6.78 | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.21/6.78 | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.21/6.78 | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.21/6.78 | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (644), % 42.21/6.78 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.78 | | | | | | | | | | | #65. % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | Case 2: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | (645) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.21/6.78 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | BETA: splitting (645) gives: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | | (646) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.21/6.78 | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.21/6.78 | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.21/6.78 | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.21/6.78 | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.21/6.78 | | | | | | | | | | | | (508), (510), (639), (643), (646), % 42.21/6.78 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.78 | | | | | | | | | | | | #55. % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | Case 2: % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | | (647) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.21/6.78 | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.21/6.78 | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.21/6.78 | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.21/6.78 | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (641), % 42.21/6.78 | | | | | | | | | | | | (647), (function-axioms) are inconsistent by % 42.21/6.78 | | | | | | | | | | | | sub-proof #46. % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | End of split % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | End of split % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | Case 2: % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | (648) all_38_0 = e2 % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | COMBINE_EQS: (580), (648) imply: % 42.21/6.78 | | | | | | | | | | (649) all_6_0 = e2 % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | SIMP: (649) implies: % 42.21/6.78 | | | | | | | | | | (650) all_6_0 = e2 % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | COMBINE_EQS: (626), (650) imply: % 42.21/6.78 | | | | | | | | | | (651) all_42_0 = e2 % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | REDUCE: (630), (650) imply: % 42.21/6.78 | | | | | | | | | | (652) ~ (e3 = e2) % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | REDUCE: (43), (650) imply: % 42.21/6.78 | | | | | | | | | | (653) op(all_6_2, e1) = e2 % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | BETA: splitting (117) gives: % 42.21/6.78 | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | (654) ~ (all_42_0 = e2) % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | REDUCE: (651), (654) imply: % 42.21/6.78 | | | | | | | | | | | (655) $false % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | CLOSE: (655) is inconsistent. % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | Case 2: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | (656) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | BETA: splitting (150) gives: % 42.21/6.78 | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | Case 1: % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.78 | | | | | | | | | | | | (657) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.21/6.78 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.21/6.79 | | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.21/6.79 | | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.21/6.79 | | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.21/6.79 | | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (657), % 42.21/6.79 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.79 | | | | | | | | | | | | #45. % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | (658) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.21/6.79 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (37), (38), (42), (137), % 42.21/6.79 | | | | | | | | | | | | (141), (146), (147), (151), (152), (153), (225), % 42.21/6.79 | | | | | | | | | | | | (226), (229), (230), (249), (250), (253), (268), % 42.21/6.79 | | | | | | | | | | | | (286), (287), (292), (308), (320), (350), (360), % 42.21/6.79 | | | | | | | | | | | | (370), (390), (446), (447), (451), (452), (453), % 42.21/6.79 | | | | | | | | | | | | (454), (455), (456), (457), (461), (463), (469), % 42.21/6.79 | | | | | | | | | | | | (476), (477), (479), (483), (489), (491), (494), % 42.21/6.79 | | | | | | | | | | | | (495), (499), (507), (508), (510), (511), (550), % 42.21/6.79 | | | | | | | | | | | | (629), (641), (653), (656), (658), % 42.21/6.79 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.79 | | | | | | | | | | | | #36. % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | (659) all_30_0 = e1 % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | COMBINE_EQS: (607), (659) imply: % 42.21/6.79 | | | | | | | | | (660) all_4_0 = e1 % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | SIMP: (660) implies: % 42.21/6.79 | | | | | | | | | (661) all_4_0 = e1 % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | COMBINE_EQS: (625), (661) imply: % 42.21/6.79 | | | | | | | | | (662) all_40_0 = e1 % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | REDUCE: (633), (661) imply: % 42.21/6.79 | | | | | | | | | (663) ~ (e3 = e1) % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | REDUCE: (38), (661) imply: % 42.21/6.79 | | | | | | | | | (664) op(all_4_2, e0) = e1 % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | BETA: splitting (107) gives: % 42.21/6.79 | | | | | | | | | % 42.21/6.79 | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | (665) ~ (all_38_0 = e2) % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | REDUCE: (580), (665) imply: % 42.21/6.79 | | | | | | | | | | (666) ~ (all_6_0 = e2) % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | BETA: splitting (112) gives: % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | (667) ~ (all_40_0 = e1) % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | REDUCE: (662), (667) imply: % 42.21/6.79 | | | | | | | | | | | (668) $false % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | CLOSE: (668) is inconsistent. % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | (669) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | BETA: splitting (150) gives: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | (670) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.21/6.79 | | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.21/6.79 | | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.21/6.79 | | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.21/6.79 | | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (670), % 42.21/6.79 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.79 | | | | | | | | | | | | #45. % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | (671) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.21/6.79 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | BETA: splitting (671) gives: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | | (672) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.21/6.79 | | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.21/6.79 | | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.21/6.79 | | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.21/6.79 | | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.21/6.79 | | | | | | | | | | | | | (508), (510), (639), (666), (672), % 42.21/6.79 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.79 | | | | | | | | | | | | | #35. % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | | (673) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.21/6.79 | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.21/6.79 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.21/6.79 | | | | | | | | | | | | | (476), (481), (495), (508), (547), (664), (669), % 42.21/6.79 | | | | | | | | | | | | | (673), (function-axioms) are inconsistent by % 42.21/6.79 | | | | | | | | | | | | | sub-proof #32. % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | End of split % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | (674) all_38_0 = e2 % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | COMBINE_EQS: (580), (674) imply: % 42.21/6.79 | | | | | | | | | | (675) all_6_0 = e2 % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | SIMP: (675) implies: % 42.21/6.79 | | | | | | | | | | (676) all_6_0 = e2 % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | COMBINE_EQS: (626), (676) imply: % 42.21/6.79 | | | | | | | | | | (677) all_42_0 = e2 % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | REDUCE: (630), (676) imply: % 42.21/6.79 | | | | | | | | | | (678) ~ (e3 = e2) % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | REDUCE: (43), (676) imply: % 42.21/6.79 | | | | | | | | | | (679) op(all_6_2, e1) = e2 % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | BETA: splitting (112) gives: % 42.21/6.79 | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | (680) ~ (all_40_0 = e1) % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | REDUCE: (662), (680) imply: % 42.21/6.79 | | | | | | | | | | | (681) $false % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | CLOSE: (681) is inconsistent. % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | (682) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | BETA: splitting (117) gives: % 42.21/6.79 | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | (683) ~ (all_42_0 = e2) % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | REDUCE: (677), (683) imply: % 42.21/6.79 | | | | | | | | | | | | (684) $false % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | CLOSE: (684) is inconsistent. % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | Case 2: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | (685) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | BETA: splitting (150) gives: % 42.21/6.79 | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | Case 1: % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.79 | | | | | | | | | | | | | (686) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.21/6.79 | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.21/6.80 | | | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.21/6.80 | | | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.21/6.80 | | | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.21/6.80 | | | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (686), % 42.21/6.80 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.21/6.80 | | | | | | | | | | | | | #65. % 42.21/6.80 | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | Case 2: % 42.21/6.80 | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | | (687) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.21/6.80 | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.21/6.80 | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | | BETA: splitting (687) gives: % 42.21/6.80 | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | | Case 1: % 42.21/6.80 | | | | | | | | | | | | | | % 42.21/6.80 | | | | | | | | | | | | | | (688) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.21/6.80 | | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.49/6.80 | | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.49/6.80 | | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.49/6.80 | | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.49/6.80 | | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.49/6.80 | | | | | | | | | | | | | | (679), (685), (688), (function-axioms) are % 42.49/6.80 | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.49/6.80 | | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | | | (689) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.80 | | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.80 | | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.80 | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.80 | | | | | | | | | | | | | | (476), (481), (495), (508), (547), (664), (682), % 42.49/6.80 | | | | | | | | | | | | | | (689), (function-axioms) are inconsistent by % 42.49/6.80 | | | | | | | | | | | | | | sub-proof #30. % 42.49/6.80 | | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | End of split % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | (690) all_24_0 = e0 % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | COMBINE_EQS: (603), (690) imply: % 42.49/6.80 | | | | | | | | (691) all_6_0 = e0 % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | SIMP: (691) implies: % 42.49/6.80 | | | | | | | | (692) all_6_0 = e0 % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | COMBINE_EQS: (600), (692) imply: % 42.49/6.80 | | | | | | | | (693) all_34_0 = e0 % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | REDUCE: (630), (692) imply: % 42.49/6.80 | | | | | | | | (694) ~ (e3 = e0) % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | REDUCE: (43), (692) imply: % 42.49/6.80 | | | | | | | | (695) op(all_6_2, e1) = e0 % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | BETA: splitting (91) gives: % 42.49/6.80 | | | | | | | | % 42.49/6.80 | | | | | | | | Case 1: % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | (696) ~ (all_30_0 = e1) % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | REDUCE: (607), (696) imply: % 42.49/6.80 | | | | | | | | | (697) ~ (all_4_0 = e1) % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | BETA: splitting (100) gives: % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | Case 1: % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | (698) ~ (all_34_0 = e0) % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | REDUCE: (693), (698) imply: % 42.49/6.80 | | | | | | | | | | (699) $false % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | CLOSE: (699) is inconsistent. % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | (700) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | Case 1: % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | (701) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.49/6.80 | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.49/6.80 | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.49/6.80 | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.49/6.80 | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (701), % 42.49/6.80 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.80 | | | | | | | | | | | #45. % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | (702) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.80 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | BETA: splitting (702) gives: % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | Case 1: % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | (703) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | ALPHA: (703) implies: % 42.49/6.80 | | | | | | | | | | | | (704) all_52_13 = e3 % 42.49/6.80 | | | | | | | | | | | | (705) ~ (all_52_12 = e1) % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | COMBINE_EQS: (446), (704) imply: % 42.49/6.80 | | | | | | | | | | | | (706) all_6_2 = e3 % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | COMBINE_EQS: (424), (706) imply: % 42.49/6.80 | | | | | | | | | | | | (707) all_34_2 = e3 % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.80 | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.80 | | | | | | | | | | | | (447), (452), (456), (457), (479), (483), (489), % 42.49/6.80 | | | | | | | | | | | | (499), (507), (510), (602), (695), (700), (704), % 42.49/6.80 | | | | | | | | | | | | (705), (706), (707), (function-axioms) are % 42.49/6.80 | | | | | | | | | | | | inconsistent by sub-proof #26. % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | (708) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.80 | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.80 | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.80 | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.80 | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (697), % 42.49/6.80 | | | | | | | | | | | | (708), (function-axioms) are inconsistent by % 42.49/6.80 | | | | | | | | | | | | sub-proof #37. % 42.49/6.80 | | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | End of split % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | Case 2: % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | (709) all_30_0 = e1 % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | COMBINE_EQS: (607), (709) imply: % 42.49/6.80 | | | | | | | | | (710) all_4_0 = e1 % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | SIMP: (710) implies: % 42.49/6.80 | | | | | | | | | (711) all_4_0 = e1 % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | COMBINE_EQS: (625), (711) imply: % 42.49/6.80 | | | | | | | | | (712) all_40_0 = e1 % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | REDUCE: (633), (711) imply: % 42.49/6.80 | | | | | | | | | (713) ~ (e3 = e1) % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | REDUCE: (629), (711) imply: % 42.49/6.80 | | | | | | | | | (714) ~ (e2 = e1) % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | REDUCE: (38), (711) imply: % 42.49/6.80 | | | | | | | | | (715) op(all_4_2, e0) = e1 % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | BETA: splitting (100) gives: % 42.49/6.80 | | | | | | | | | % 42.49/6.80 | | | | | | | | | Case 1: % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | (716) ~ (all_34_0 = e0) % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | REDUCE: (693), (716) imply: % 42.49/6.80 | | | | | | | | | | (717) $false % 42.49/6.80 | | | | | | | | | | % 42.49/6.80 | | | | | | | | | | CLOSE: (717) is inconsistent. % 42.49/6.80 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | (718) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | (719) ~ (all_40_0 = e1) % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | REDUCE: (712), (719) imply: % 42.49/6.81 | | | | | | | | | | | (720) $false % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | CLOSE: (720) is inconsistent. % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | (721) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (722) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.49/6.81 | | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.49/6.81 | | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.49/6.81 | | | | | | | | | | | | (509), (510), (511), (513), (635), (637), (722), % 42.49/6.81 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.81 | | | | | | | | | | | | #65. % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (723) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.81 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | BETA: splitting (723) gives: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (724) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.81 | | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.49/6.81 | | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (695), % 42.49/6.81 | | | | | | | | | | | | | (718), (724), (function-axioms) are inconsistent % 42.49/6.81 | | | | | | | | | | | | | by sub-proof #25. % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (725) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.81 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.81 | | | | | | | | | | | | | (476), (481), (495), (508), (547), (715), (721), % 42.49/6.81 | | | | | | | | | | | | | (725), (function-axioms) are inconsistent by % 42.49/6.81 | | | | | | | | | | | | | sub-proof #30. % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | % 42.49/6.81 | | | | | | | | End of split % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | End of split % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | Case 2: % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | (726) all_16_0 = e1 % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | COMBINE_EQS: (616), (726) imply: % 42.49/6.81 | | | | | | | (727) all_8_0 = e1 % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | COMBINE_EQS: (569), (727) imply: % 42.49/6.81 | | | | | | | (728) all_26_0 = e1 % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | REDUCE: (631), (727) imply: % 42.49/6.81 | | | | | | | (729) ~ (e3 = e1) % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | REDUCE: (48), (727) imply: % 42.49/6.81 | | | | | | | (730) op(all_8_2, e2) = e1 % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | BETA: splitting (84) gives: % 42.49/6.81 | | | | | | | % 42.49/6.81 | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | (731) ~ (all_26_0 = e1) % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | REDUCE: (728), (731) imply: % 42.49/6.81 | | | | | | | | (732) $false % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | CLOSE: (732) is inconsistent. % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | (733) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | BETA: splitting (79) gives: % 42.49/6.81 | | | | | | | | % 42.49/6.81 | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | % 42.49/6.81 | | | | | | | | | (734) ~ (all_24_0 = e0) % 42.49/6.81 | | | | | | | | | % 42.49/6.81 | | | | | | | | | REDUCE: (603), (734) imply: % 42.49/6.81 | | | | | | | | | (735) ~ (all_6_0 = e0) % 42.49/6.81 | | | | | | | | | % 42.49/6.81 | | | | | | | | | BETA: splitting (91) gives: % 42.49/6.81 | | | | | | | | | % 42.49/6.81 | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | (736) ~ (all_30_0 = e1) % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | REDUCE: (607), (736) imply: % 42.49/6.81 | | | | | | | | | | (737) ~ (all_4_0 = e1) % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | BETA: splitting (107) gives: % 42.49/6.81 | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | (738) ~ (all_38_0 = e2) % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | REDUCE: (580), (738) imply: % 42.49/6.81 | | | | | | | | | | | (739) ~ (all_6_0 = e2) % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (740) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.81 | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.81 | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.81 | | | | | | | | | | | | (733), (740), (function-axioms) are inconsistent % 42.49/6.81 | | | | | | | | | | | | by sub-proof #18. % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (741) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.81 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | BETA: splitting (741) gives: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (742) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.49/6.81 | | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.49/6.81 | | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.49/6.81 | | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.49/6.81 | | | | | | | | | | | | | (508), (510), (735), (739), (742), % 42.49/6.81 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.81 | | | | | | | | | | | | | #35. % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (743) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.81 | | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.81 | | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.81 | | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.81 | | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (737), % 42.49/6.81 | | | | | | | | | | | | | (743), (function-axioms) are inconsistent by % 42.49/6.81 | | | | | | | | | | | | | sub-proof #37. % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | End of split % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | (744) all_38_0 = e2 % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | COMBINE_EQS: (580), (744) imply: % 42.49/6.81 | | | | | | | | | | | (745) all_6_0 = e2 % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | COMBINE_EQS: (626), (745) imply: % 42.49/6.81 | | | | | | | | | | | (746) all_42_0 = e2 % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | REDUCE: (630), (745) imply: % 42.49/6.81 | | | | | | | | | | | (747) ~ (e3 = e2) % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | REDUCE: (43), (745) imply: % 42.49/6.81 | | | | | | | | | | | (748) op(all_6_2, e1) = e2 % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | BETA: splitting (117) gives: % 42.49/6.81 | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (749) ~ (all_42_0 = e2) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | REDUCE: (746), (749) imply: % 42.49/6.81 | | | | | | | | | | | | (750) $false % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | CLOSE: (750) is inconsistent. % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | (751) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.81 | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (752) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.81 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.81 | | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.81 | | | | | | | | | | | | | (733), (752), (function-axioms) are inconsistent % 42.49/6.81 | | | | | | | | | | | | | by sub-proof #17. % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | (753) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.81 | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | BETA: splitting (753) gives: % 42.49/6.81 | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | Case 1: % 42.49/6.81 | | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | | (754) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.81 | | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.49/6.81 | | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.49/6.81 | | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.49/6.81 | | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.49/6.81 | | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.49/6.81 | | | | | | | | | | | | | | (748), (751), (754), (function-axioms) are % 42.49/6.81 | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.49/6.81 | | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | Case 2: % 42.49/6.81 | | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | | (755) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.81 | | | | | | | | | | | | | | % 42.49/6.81 | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.81 | | | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.82 | | | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.82 | | | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.82 | | | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (737), % 42.49/6.82 | | | | | | | | | | | | | | (755), (function-axioms) are inconsistent by % 42.49/6.82 | | | | | | | | | | | | | | sub-proof #46. % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | (756) all_30_0 = e1 % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | COMBINE_EQS: (607), (756) imply: % 42.49/6.82 | | | | | | | | | | (757) all_4_0 = e1 % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | COMBINE_EQS: (625), (757) imply: % 42.49/6.82 | | | | | | | | | | (758) all_40_0 = e1 % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | REDUCE: (38), (757) imply: % 42.49/6.82 | | | | | | | | | | (759) op(all_4_2, e0) = e1 % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | BETA: splitting (107) gives: % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | (760) ~ (all_38_0 = e2) % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | REDUCE: (580), (760) imply: % 42.49/6.82 | | | | | | | | | | | (761) ~ (all_6_0 = e2) % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (762) ~ (all_40_0 = e1) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | REDUCE: (758), (762) imply: % 42.49/6.82 | | | | | | | | | | | | (763) $false % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | CLOSE: (763) is inconsistent. % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (764) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (765) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.82 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.82 | | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.82 | | | | | | | | | | | | | (733), (765), (function-axioms) are inconsistent % 42.49/6.82 | | | | | | | | | | | | | by sub-proof #17. % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (766) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.82 | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | BETA: splitting (766) gives: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | (767) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.49/6.82 | | | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.49/6.82 | | | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.49/6.82 | | | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.49/6.82 | | | | | | | | | | | | | | (508), (510), (735), (761), (767), % 42.49/6.82 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.82 | | | | | | | | | | | | | | #55. % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | (768) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.82 | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.82 | | | | | | | | | | | | | | (476), (481), (495), (508), (547), (759), (764), % 42.49/6.82 | | | | | | | | | | | | | | (768), (function-axioms) are inconsistent by % 42.49/6.82 | | | | | | | | | | | | | | sub-proof #30. % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | (769) all_38_0 = e2 % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | COMBINE_EQS: (580), (769) imply: % 42.49/6.82 | | | | | | | | | | | (770) all_6_0 = e2 % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | SIMP: (770) implies: % 42.49/6.82 | | | | | | | | | | | (771) all_6_0 = e2 % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | COMBINE_EQS: (626), (771) imply: % 42.49/6.82 | | | | | | | | | | | (772) all_42_0 = e2 % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | REDUCE: (630), (771) imply: % 42.49/6.82 | | | | | | | | | | | (773) ~ (e3 = e2) % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | REDUCE: (43), (771) imply: % 42.49/6.82 | | | | | | | | | | | (774) op(all_6_2, e1) = e2 % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (775) ~ (all_40_0 = e1) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | REDUCE: (758), (775) imply: % 42.49/6.82 | | | | | | | | | | | | (776) $false % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | CLOSE: (776) is inconsistent. % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (777) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | BETA: splitting (117) gives: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (778) ~ (all_42_0 = e2) % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | REDUCE: (772), (778) imply: % 42.49/6.82 | | | | | | | | | | | | | (779) $false % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | CLOSE: (779) is inconsistent. % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (780) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | (781) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.82 | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.82 | | | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.82 | | | | | | | | | | | | | | (733), (781), (function-axioms) are inconsistent % 42.49/6.82 | | | | | | | | | | | | | | by sub-proof #17. % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | (782) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.82 | | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | BETA: splitting (782) gives: % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | | (783) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.49/6.82 | | | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.49/6.82 | | | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.49/6.82 | | | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.49/6.82 | | | | | | | | | | | | | | | (774), (780), (783), (function-axioms) are % 42.49/6.82 | | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | | (784) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.82 | | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.82 | | | | | | | | | | | | | | | (476), (481), (495), (508), (547), (759), (777), % 42.49/6.82 | | | | | | | | | | | | | | | (784), (function-axioms) are inconsistent by % 42.49/6.82 | | | | | | | | | | | | | | | sub-proof #30. % 42.49/6.82 | | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | End of split % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | (785) all_24_0 = e0 % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | COMBINE_EQS: (603), (785) imply: % 42.49/6.82 | | | | | | | | | (786) all_6_0 = e0 % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | SIMP: (786) implies: % 42.49/6.82 | | | | | | | | | (787) all_6_0 = e0 % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | COMBINE_EQS: (600), (787) imply: % 42.49/6.82 | | | | | | | | | (788) all_34_0 = e0 % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | REDUCE: (630), (787) imply: % 42.49/6.82 | | | | | | | | | (789) ~ (e3 = e0) % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | REDUCE: (43), (787) imply: % 42.49/6.82 | | | | | | | | | (790) op(all_6_2, e1) = e0 % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | BETA: splitting (91) gives: % 42.49/6.82 | | | | | | | | | % 42.49/6.82 | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | (791) ~ (all_30_0 = e1) % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | REDUCE: (607), (791) imply: % 42.49/6.82 | | | | | | | | | | (792) ~ (all_4_0 = e1) % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | BETA: splitting (100) gives: % 42.49/6.82 | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | (793) ~ (all_34_0 = e0) % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | REDUCE: (788), (793) imply: % 42.49/6.82 | | | | | | | | | | | (794) $false % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | CLOSE: (794) is inconsistent. % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | (795) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.82 | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (796) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.82 | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.82 | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.82 | | | | | | | | | | | | (733), (796), (function-axioms) are inconsistent % 42.49/6.82 | | | | | | | | | | | | by sub-proof #17. % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | (797) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.82 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | BETA: splitting (797) gives: % 42.49/6.82 | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 1: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (798) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.82 | | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.82 | | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.49/6.82 | | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (790), % 42.49/6.82 | | | | | | | | | | | | | (795), (798), (function-axioms) are inconsistent % 42.49/6.82 | | | | | | | | | | | | | by sub-proof #25. % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | Case 2: % 42.49/6.82 | | | | | | | | | | | | | % 42.49/6.82 | | | | | | | | | | | | | (799) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.83 | | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.83 | | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.83 | | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.83 | | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (792), % 42.49/6.83 | | | | | | | | | | | | | (799), (function-axioms) are inconsistent by % 42.49/6.83 | | | | | | | | | | | | | sub-proof #46. % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | (800) all_30_0 = e1 % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | COMBINE_EQS: (607), (800) imply: % 42.49/6.83 | | | | | | | | | | (801) all_4_0 = e1 % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | SIMP: (801) implies: % 42.49/6.83 | | | | | | | | | | (802) all_4_0 = e1 % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | COMBINE_EQS: (625), (802) imply: % 42.49/6.83 | | | | | | | | | | (803) all_40_0 = e1 % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | REDUCE: (629), (802) imply: % 42.49/6.83 | | | | | | | | | | (804) ~ (e2 = e1) % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | REDUCE: (38), (802) imply: % 42.49/6.83 | | | | | | | | | | (805) op(all_4_2, e0) = e1 % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | BETA: splitting (100) gives: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (806) ~ (all_34_0 = e0) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | REDUCE: (788), (806) imply: % 42.49/6.83 | | | | | | | | | | | (807) $false % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | CLOSE: (807) is inconsistent. % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (808) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | (809) ~ (all_40_0 = e1) % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | REDUCE: (803), (809) imply: % 42.49/6.83 | | | | | | | | | | | | (810) $false % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | CLOSE: (810) is inconsistent. % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | (811) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | (812) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.49/6.83 | | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.49/6.83 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.49/6.83 | | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (730), % 42.49/6.83 | | | | | | | | | | | | | (733), (812), (function-axioms) are inconsistent % 42.49/6.83 | | | | | | | | | | | | | by sub-proof #17. % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | (813) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.83 | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | BETA: splitting (813) gives: % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | | (814) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.83 | | | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.83 | | | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.49/6.83 | | | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (790), % 42.49/6.83 | | | | | | | | | | | | | | (808), (814), (function-axioms) are inconsistent % 42.49/6.83 | | | | | | | | | | | | | | by sub-proof #25. % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | | (815) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.83 | | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.83 | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.83 | | | | | | | | | | | | | | (476), (481), (495), (508), (547), (805), (811), % 42.49/6.83 | | | | | | | | | | | | | | (815), (function-axioms) are inconsistent by % 42.49/6.83 | | | | | | | | | | | | | | sub-proof #30. % 42.49/6.83 | | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | End of split % 42.49/6.83 | | | | | | | | % 42.49/6.83 | | | | | | | End of split % 42.49/6.83 | | | | | | | % 42.49/6.83 | | | | | | End of split % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | Case 2: % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | (816) all_14_0 = e0 % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | COMBINE_EQS: (622), (816) imply: % 42.49/6.83 | | | | | | (817) all_8_0 = e0 % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | SIMP: (817) implies: % 42.49/6.83 | | | | | | (818) all_8_0 = e0 % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | COMBINE_EQS: (628), (818) imply: % 42.49/6.83 | | | | | | (819) all_50_0 = e0 % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | REDUCE: (631), (818) imply: % 42.49/6.83 | | | | | | (820) ~ (e3 = e0) % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | REDUCE: (48), (818) imply: % 42.49/6.83 | | | | | | (821) op(all_8_2, e2) = e0 % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | BETA: splitting (79) gives: % 42.49/6.83 | | | | | | % 42.49/6.83 | | | | | | Case 1: % 42.49/6.83 | | | | | | | % 42.49/6.83 | | | | | | | (822) ~ (all_24_0 = e0) % 42.49/6.83 | | | | | | | % 42.49/6.83 | | | | | | | REDUCE: (603), (822) imply: % 42.49/6.83 | | | | | | | (823) ~ (all_6_0 = e0) % 42.49/6.83 | | | | | | | % 42.49/6.83 | | | | | | | BETA: splitting (91) gives: % 42.49/6.83 | | | | | | | % 42.49/6.83 | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | % 42.49/6.83 | | | | | | | | (824) ~ (all_30_0 = e1) % 42.49/6.83 | | | | | | | | % 42.49/6.83 | | | | | | | | REDUCE: (607), (824) imply: % 42.49/6.83 | | | | | | | | (825) ~ (all_4_0 = e1) % 42.49/6.83 | | | | | | | | % 42.49/6.83 | | | | | | | | BETA: splitting (107) gives: % 42.49/6.83 | | | | | | | | % 42.49/6.83 | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | (826) ~ (all_38_0 = e2) % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | REDUCE: (580), (826) imply: % 42.49/6.83 | | | | | | | | | (827) ~ (all_6_0 = e2) % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | (828) ~ (all_50_0 = e0) % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | REDUCE: (819), (828) imply: % 42.49/6.83 | | | | | | | | | | (829) $false % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | CLOSE: (829) is inconsistent. % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | (830) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (831) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.83 | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.83 | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.83 | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (830), % 42.49/6.83 | | | | | | | | | | | (831), (function-axioms) are inconsistent by % 42.49/6.83 | | | | | | | | | | | sub-proof #14. % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (832) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.83 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | BETA: splitting (832) gives: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | (833) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.49/6.83 | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.49/6.83 | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.49/6.83 | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.49/6.83 | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.49/6.83 | | | | | | | | | | | | (508), (510), (823), (827), (833), % 42.49/6.83 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.83 | | | | | | | | | | | | #35. % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | (834) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.83 | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.83 | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.83 | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.83 | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (825), % 42.49/6.83 | | | | | | | | | | | | (834), (function-axioms) are inconsistent by % 42.49/6.83 | | | | | | | | | | | | sub-proof #37. % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | End of split % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | (835) all_38_0 = e2 % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | COMBINE_EQS: (580), (835) imply: % 42.49/6.83 | | | | | | | | | (836) all_6_0 = e2 % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | SIMP: (836) implies: % 42.49/6.83 | | | | | | | | | (837) all_6_0 = e2 % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | COMBINE_EQS: (626), (837) imply: % 42.49/6.83 | | | | | | | | | (838) all_42_0 = e2 % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | REDUCE: (630), (837) imply: % 42.49/6.83 | | | | | | | | | (839) ~ (e3 = e2) % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | REDUCE: (43), (837) imply: % 42.49/6.83 | | | | | | | | | (840) op(all_6_2, e1) = e2 % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | BETA: splitting (117) gives: % 42.49/6.83 | | | | | | | | | % 42.49/6.83 | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | (841) ~ (all_42_0 = e2) % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | REDUCE: (838), (841) imply: % 42.49/6.83 | | | | | | | | | | (842) $false % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | CLOSE: (842) is inconsistent. % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | (843) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.83 | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (844) ~ (all_50_0 = e0) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | REDUCE: (819), (844) imply: % 42.49/6.83 | | | | | | | | | | | (845) $false % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | CLOSE: (845) is inconsistent. % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | Case 2: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | (846) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.83 | | | | | | | | | | | % 42.49/6.83 | | | | | | | | | | | Case 1: % 42.49/6.83 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (847) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.84 | | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.84 | | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (846), % 42.49/6.84 | | | | | | | | | | | | (847), (function-axioms) are inconsistent by % 42.49/6.84 | | | | | | | | | | | | sub-proof #13. % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (848) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.84 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | BETA: splitting (848) gives: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (849) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.49/6.84 | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.49/6.84 | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.49/6.84 | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.49/6.84 | | | | | | | | | | | | | (840), (843), (849), (function-axioms) are % 42.49/6.84 | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (850) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.84 | | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.84 | | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.84 | | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.84 | | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (825), % 42.49/6.84 | | | | | | | | | | | | | (850), (function-axioms) are inconsistent by % 42.49/6.84 | | | | | | | | | | | | | sub-proof #46. % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | End of split % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | (851) all_30_0 = e1 % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | COMBINE_EQS: (607), (851) imply: % 42.49/6.84 | | | | | | | | (852) all_4_0 = e1 % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | SIMP: (852) implies: % 42.49/6.84 | | | | | | | | (853) all_4_0 = e1 % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | COMBINE_EQS: (625), (853) imply: % 42.49/6.84 | | | | | | | | (854) all_40_0 = e1 % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | REDUCE: (633), (853) imply: % 42.49/6.84 | | | | | | | | (855) ~ (e3 = e1) % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | REDUCE: (629), (853) imply: % 42.49/6.84 | | | | | | | | (856) ~ (e2 = e1) % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | REDUCE: (38), (853) imply: % 42.49/6.84 | | | | | | | | (857) op(all_4_2, e0) = e1 % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | BETA: splitting (107) gives: % 42.49/6.84 | | | | | | | | % 42.49/6.84 | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | (858) ~ (all_38_0 = e2) % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | REDUCE: (580), (858) imply: % 42.49/6.84 | | | | | | | | | (859) ~ (all_6_0 = e2) % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | (860) ~ (all_40_0 = e1) % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | REDUCE: (854), (860) imply: % 42.49/6.84 | | | | | | | | | | (861) $false % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | CLOSE: (861) is inconsistent. % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | (862) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | (863) ~ (all_50_0 = e0) % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | REDUCE: (819), (863) imply: % 42.49/6.84 | | | | | | | | | | | (864) $false % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | CLOSE: (864) is inconsistent. % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | (865) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (866) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.84 | | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.84 | | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (865), % 42.49/6.84 | | | | | | | | | | | | (866), (function-axioms) are inconsistent by % 42.49/6.84 | | | | | | | | | | | | sub-proof #13. % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (867) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.84 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | BETA: splitting (867) gives: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (868) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.49/6.84 | | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.49/6.84 | | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.49/6.84 | | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.49/6.84 | | | | | | | | | | | | | (508), (510), (823), (859), (868), % 42.49/6.84 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.84 | | | | | | | | | | | | | #55. % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (869) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.84 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.84 | | | | | | | | | | | | | (476), (481), (495), (508), (547), (857), (862), % 42.49/6.84 | | | | | | | | | | | | | (869), (function-axioms) are inconsistent by % 42.49/6.84 | | | | | | | | | | | | | sub-proof #30. % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | End of split % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | (870) all_38_0 = e2 % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | COMBINE_EQS: (580), (870) imply: % 42.49/6.84 | | | | | | | | | (871) all_6_0 = e2 % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | SIMP: (871) implies: % 42.49/6.84 | | | | | | | | | (872) all_6_0 = e2 % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | COMBINE_EQS: (626), (872) imply: % 42.49/6.84 | | | | | | | | | (873) all_42_0 = e2 % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | REDUCE: (630), (872) imply: % 42.49/6.84 | | | | | | | | | (874) ~ (e3 = e2) % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | REDUCE: (43), (872) imply: % 42.49/6.84 | | | | | | | | | (875) op(all_6_2, e1) = e2 % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.84 | | | | | | | | | % 42.49/6.84 | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | (876) ~ (all_40_0 = e1) % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | REDUCE: (854), (876) imply: % 42.49/6.84 | | | | | | | | | | (877) $false % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | CLOSE: (877) is inconsistent. % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | (878) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | BETA: splitting (117) gives: % 42.49/6.84 | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | (879) ~ (all_42_0 = e2) % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | REDUCE: (873), (879) imply: % 42.49/6.84 | | | | | | | | | | | (880) $false % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | CLOSE: (880) is inconsistent. % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | (881) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.84 | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (882) ~ (all_50_0 = e0) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | REDUCE: (819), (882) imply: % 42.49/6.84 | | | | | | | | | | | | (883) $false % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | CLOSE: (883) is inconsistent. % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | (884) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.84 | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (885) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.84 | | | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.84 | | | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (884), % 42.49/6.84 | | | | | | | | | | | | | (885), (function-axioms) are inconsistent by % 42.49/6.84 | | | | | | | | | | | | | sub-proof #13. % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | (886) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.84 | | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | BETA: splitting (886) gives: % 42.49/6.84 | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | Case 1: % 42.49/6.84 | | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | | (887) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.84 | | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.49/6.84 | | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.49/6.84 | | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.49/6.84 | | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.49/6.84 | | | | | | | | | | | | | | (875), (881), (887), (function-axioms) are % 42.49/6.84 | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.49/6.84 | | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | Case 2: % 42.49/6.84 | | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | | (888) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.84 | | | | | | | | | | | | | | % 42.49/6.84 | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.84 | | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.84 | | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.84 | | | | | | | | | | | | | | (476), (481), (495), (508), (547), (857), (878), % 42.49/6.85 | | | | | | | | | | | | | | (888), (function-axioms) are inconsistent by % 42.49/6.85 | | | | | | | | | | | | | | sub-proof #30. % 42.49/6.85 | | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | End of split % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | End of split % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | Case 2: % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | (889) all_24_0 = e0 % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | COMBINE_EQS: (603), (889) imply: % 42.49/6.85 | | | | | | | (890) all_6_0 = e0 % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | COMBINE_EQS: (600), (890) imply: % 42.49/6.85 | | | | | | | (891) all_34_0 = e0 % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | REDUCE: (43), (890) imply: % 42.49/6.85 | | | | | | | (892) op(all_6_2, e1) = e0 % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | BETA: splitting (91) gives: % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | (893) ~ (all_30_0 = e1) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | REDUCE: (607), (893) imply: % 42.49/6.85 | | | | | | | | (894) ~ (all_4_0 = e1) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | BETA: splitting (100) gives: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | (895) ~ (all_34_0 = e0) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | REDUCE: (891), (895) imply: % 42.49/6.85 | | | | | | | | | (896) $false % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | CLOSE: (896) is inconsistent. % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | (897) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (898) ~ (all_50_0 = e0) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | REDUCE: (819), (898) imply: % 42.49/6.85 | | | | | | | | | | (899) $false % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | CLOSE: (899) is inconsistent. % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (900) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | (901) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.85 | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.85 | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (900), % 42.49/6.85 | | | | | | | | | | | (901), (function-axioms) are inconsistent by % 42.49/6.85 | | | | | | | | | | | sub-proof #13. % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | (902) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.85 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | BETA: splitting (902) gives: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | (903) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.85 | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.49/6.85 | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (892), % 42.49/6.85 | | | | | | | | | | | | (897), (903), (function-axioms) are inconsistent % 42.49/6.85 | | | | | | | | | | | | by sub-proof #25. % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | (904) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.49/6.85 | | | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.49/6.85 | | | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.49/6.85 | | | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.49/6.85 | | | | | | | | | | | | (489), (495), (507), (508), (510), (629), (894), % 42.49/6.85 | | | | | | | | | | | | (904), (function-axioms) are inconsistent by % 42.49/6.85 | | | | | | | | | | | | sub-proof #46. % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | End of split % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | (905) all_30_0 = e1 % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | COMBINE_EQS: (607), (905) imply: % 42.49/6.85 | | | | | | | | (906) all_4_0 = e1 % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | SIMP: (906) implies: % 42.49/6.85 | | | | | | | | (907) all_4_0 = e1 % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | COMBINE_EQS: (625), (907) imply: % 42.49/6.85 | | | | | | | | (908) all_40_0 = e1 % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | REDUCE: (633), (907) imply: % 42.49/6.85 | | | | | | | | (909) ~ (e3 = e1) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | REDUCE: (629), (907) imply: % 42.49/6.85 | | | | | | | | (910) ~ (e2 = e1) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | REDUCE: (38), (907) imply: % 42.49/6.85 | | | | | | | | (911) op(all_4_2, e0) = e1 % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | BETA: splitting (100) gives: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | (912) ~ (all_34_0 = e0) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | REDUCE: (891), (912) imply: % 42.49/6.85 | | | | | | | | | (913) $false % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | CLOSE: (913) is inconsistent. % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | (914) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | BETA: splitting (112) gives: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (915) ~ (all_40_0 = e1) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | REDUCE: (908), (915) imply: % 42.49/6.85 | | | | | | | | | | (916) $false % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | CLOSE: (916) is inconsistent. % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (917) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | BETA: splitting (132) gives: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | (918) ~ (all_50_0 = e0) % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | REDUCE: (819), (918) imply: % 42.49/6.85 | | | | | | | | | | | (919) $false % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | CLOSE: (919) is inconsistent. % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | (920) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | (921) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.49/6.85 | | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.49/6.85 | | | | | | | | | | | | (503), (506), (509), (513), (627), (821), (920), % 42.49/6.85 | | | | | | | | | | | | (921), (function-axioms) are inconsistent by % 42.49/6.85 | | | | | | | | | | | | sub-proof #13. % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | (922) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.49/6.85 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | BETA: splitting (922) gives: % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | | (923) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.49/6.85 | | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.49/6.85 | | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (892), % 42.49/6.85 | | | | | | | | | | | | | (914), (923), (function-axioms) are inconsistent % 42.49/6.85 | | | | | | | | | | | | | by sub-proof #25. % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | | (924) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.49/6.85 | | | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.49/6.85 | | | | | | | | | | | | | (476), (481), (495), (508), (547), (911), (917), % 42.49/6.85 | | | | | | | | | | | | | (924), (function-axioms) are inconsistent by % 42.49/6.85 | | | | | | | | | | | | | sub-proof #30. % 42.49/6.85 | | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | End of split % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | End of split % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | End of split % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | End of split % 42.49/6.85 | | | | | | % 42.49/6.85 | | | | | End of split % 42.49/6.85 | | | | | % 42.49/6.85 | | | | Case 2: % 42.49/6.85 | | | | | % 42.49/6.85 | | | | | (925) all_12_0 = e3 % 42.49/6.85 | | | | | % 42.49/6.85 | | | | | COMBINE_EQS: (619), (925) imply: % 42.49/6.85 | | | | | (926) all_4_0 = e3 % 42.49/6.85 | | | | | % 42.49/6.85 | | | | | REDUCE: (38), (926) imply: % 42.49/6.85 | | | | | (927) op(all_4_2, e0) = e3 % 42.49/6.85 | | | | | % 42.49/6.85 | | | | | BETA: splitting (61) gives: % 42.49/6.85 | | | | | % 42.49/6.85 | | | | | Case 1: % 42.49/6.85 | | | | | | % 42.49/6.85 | | | | | | (928) ~ (all_14_0 = e0) % 42.49/6.85 | | | | | | % 42.49/6.85 | | | | | | REDUCE: (622), (928) imply: % 42.49/6.85 | | | | | | (929) ~ (all_8_0 = e0) % 42.49/6.85 | | | | | | % 42.49/6.85 | | | | | | BETA: splitting (66) gives: % 42.49/6.85 | | | | | | % 42.49/6.85 | | | | | | Case 1: % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | (930) ~ (all_16_0 = e1) % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | REDUCE: (616), (930) imply: % 42.49/6.85 | | | | | | | (931) ~ (all_8_0 = e1) % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | BETA: splitting (79) gives: % 42.49/6.85 | | | | | | | % 42.49/6.85 | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | (932) ~ (all_24_0 = e0) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | REDUCE: (603), (932) imply: % 42.49/6.85 | | | | | | | | (933) ~ (all_6_0 = e0) % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | BETA: splitting (107) gives: % 42.49/6.85 | | | | | | | | % 42.49/6.85 | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | (934) ~ (all_38_0 = e2) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | REDUCE: (580), (934) imply: % 42.49/6.85 | | | | | | | | | (935) ~ (all_6_0 = e2) % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.85 | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (936) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.49/6.85 | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.49/6.85 | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.49/6.85 | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.49/6.85 | | | | | | | | | | (509), (510), (511), (513), (929), (931), (936), % 42.49/6.85 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.85 | | | | | | | | | | #45. % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | Case 2: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | (937) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.49/6.85 | | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | BETA: splitting (937) gives: % 42.49/6.85 | | | | | | | | | | % 42.49/6.85 | | | | | | | | | | Case 1: % 42.49/6.85 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | (938) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.49/6.86 | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.49/6.86 | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.49/6.86 | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.49/6.86 | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.49/6.86 | | | | | | | | | | | (508), (510), (933), (935), (938), % 42.49/6.86 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.49/6.86 | | | | | | | | | | | #35. % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | Case 2: % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | (939) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | ALPHA: (939) implies: % 42.49/6.86 | | | | | | | | | | | (940) all_52_15 = e3 % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | COMBINE_EQS: (390), (940) imply: % 42.49/6.86 | | | | | | | | | | | (941) all_4_2 = e3 % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | REF_CLOSE: (146), (469), (927), (941), (function-axioms) are % 42.49/6.86 | | | | | | | | | | | inconsistent by sub-proof #12. % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | End of split % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | End of split % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | Case 2: % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | (942) all_38_0 = e2 % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | COMBINE_EQS: (580), (942) imply: % 42.49/6.86 | | | | | | | | | (943) all_6_0 = e2 % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | COMBINE_EQS: (626), (943) imply: % 42.49/6.86 | | | | | | | | | (944) all_42_0 = e2 % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | REDUCE: (43), (943) imply: % 42.49/6.86 | | | | | | | | | (945) op(all_6_2, e1) = e2 % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | BETA: splitting (117) gives: % 42.49/6.86 | | | | | | | | | % 42.49/6.86 | | | | | | | | | Case 1: % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | (946) ~ (all_42_0 = e2) % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | REDUCE: (944), (946) imply: % 42.49/6.86 | | | | | | | | | | (947) $false % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | CLOSE: (947) is inconsistent. % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | Case 2: % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | (948) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | BETA: splitting (150) gives: % 42.49/6.86 | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | Case 1: % 42.49/6.86 | | | | | | | | | | | % 42.49/6.86 | | | | | | | | | | | (949) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.49/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.74/6.86 | | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.74/6.86 | | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.74/6.86 | | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.74/6.86 | | | | | | | | | | | (509), (510), (511), (513), (929), (931), (949), % 42.74/6.86 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.74/6.86 | | | | | | | | | | | #65. % 42.74/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | Case 2: % 42.74/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | (950) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.74/6.86 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.74/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | BETA: splitting (950) gives: % 42.74/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | Case 1: % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | | (951) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.74/6.86 | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.74/6.86 | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.74/6.86 | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.74/6.86 | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.74/6.86 | | | | | | | | | | | | (945), (948), (951), (function-axioms) are % 42.74/6.86 | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | Case 2: % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | | (952) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (952), % 42.74/6.86 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.74/6.86 | | | | | | | | | | | | #11. % 42.74/6.86 | | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | | End of split % 42.74/6.86 | | | | | | | | | | | % 42.74/6.86 | | | | | | | | | | End of split % 42.74/6.86 | | | | | | | | | | % 42.74/6.86 | | | | | | | | | End of split % 42.74/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | End of split % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | (953) all_24_0 = e0 % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | COMBINE_EQS: (603), (953) imply: % 42.75/6.86 | | | | | | | | (954) all_6_0 = e0 % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | SIMP: (954) implies: % 42.75/6.86 | | | | | | | | (955) all_6_0 = e0 % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | COMBINE_EQS: (600), (955) imply: % 42.75/6.86 | | | | | | | | (956) all_34_0 = e0 % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | REDUCE: (630), (955) imply: % 42.75/6.86 | | | | | | | | (957) ~ (e3 = e0) % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | REDUCE: (43), (955) imply: % 42.75/6.86 | | | | | | | | (958) op(all_6_2, e1) = e0 % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | BETA: splitting (100) gives: % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | (959) ~ (all_34_0 = e0) % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | REDUCE: (956), (959) imply: % 42.75/6.86 | | | | | | | | | (960) $false % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | CLOSE: (960) is inconsistent. % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | (961) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | (962) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.75/6.86 | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.75/6.86 | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.75/6.86 | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.75/6.86 | | | | | | | | | | (509), (510), (511), (513), (929), (931), (962), % 42.75/6.86 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.86 | | | | | | | | | | #65. % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | (963) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.75/6.86 | | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | BETA: splitting (963) gives: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | (964) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.75/6.86 | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.75/6.86 | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.75/6.86 | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (958), % 42.75/6.86 | | | | | | | | | | | (961), (964), (function-axioms) are inconsistent % 42.75/6.86 | | | | | | | | | | | by sub-proof #25. % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | (965) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (965), % 42.75/6.86 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.86 | | | | | | | | | | | #11. % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | End of split % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | End of split % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | End of split % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | End of split % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | Case 2: % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | (966) all_16_0 = e1 % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | COMBINE_EQS: (616), (966) imply: % 42.75/6.86 | | | | | | | (967) all_8_0 = e1 % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | COMBINE_EQS: (569), (967) imply: % 42.75/6.86 | | | | | | | (968) all_26_0 = e1 % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | REDUCE: (48), (967) imply: % 42.75/6.86 | | | | | | | (969) op(all_8_2, e2) = e1 % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | BETA: splitting (84) gives: % 42.75/6.86 | | | | | | | % 42.75/6.86 | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | (970) ~ (all_26_0 = e1) % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | REDUCE: (968), (970) imply: % 42.75/6.86 | | | | | | | | (971) $false % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | CLOSE: (971) is inconsistent. % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | (972) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | BETA: splitting (79) gives: % 42.75/6.86 | | | | | | | | % 42.75/6.86 | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | (973) ~ (all_24_0 = e0) % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | REDUCE: (603), (973) imply: % 42.75/6.86 | | | | | | | | | (974) ~ (all_6_0 = e0) % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | BETA: splitting (107) gives: % 42.75/6.86 | | | | | | | | | % 42.75/6.86 | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | (975) ~ (all_38_0 = e2) % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | REDUCE: (580), (975) imply: % 42.75/6.86 | | | | | | | | | | (976) ~ (all_6_0 = e2) % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | (977) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.75/6.86 | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.75/6.86 | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.75/6.86 | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (969), % 42.75/6.86 | | | | | | | | | | | (972), (977), (function-axioms) are inconsistent % 42.75/6.86 | | | | | | | | | | | by sub-proof #17. % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | (978) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.86 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | BETA: splitting (978) gives: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | | (979) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.75/6.86 | | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.75/6.86 | | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.75/6.86 | | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.75/6.86 | | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.75/6.86 | | | | | | | | | | | | (508), (510), (974), (976), (979), % 42.75/6.86 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.86 | | | | | | | | | | | | #55. % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | | (980) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (980), % 42.75/6.86 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.86 | | | | | | | | | | | | #11. % 42.75/6.86 | | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | End of split % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | End of split % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | Case 2: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | (981) all_38_0 = e2 % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | COMBINE_EQS: (580), (981) imply: % 42.75/6.86 | | | | | | | | | | (982) all_6_0 = e2 % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | COMBINE_EQS: (626), (982) imply: % 42.75/6.86 | | | | | | | | | | (983) all_42_0 = e2 % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | REDUCE: (43), (982) imply: % 42.75/6.86 | | | | | | | | | | (984) op(all_6_2, e1) = e2 % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | BETA: splitting (117) gives: % 42.75/6.86 | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | Case 1: % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | (985) ~ (all_42_0 = e2) % 42.75/6.86 | | | | | | | | | | | % 42.75/6.86 | | | | | | | | | | | REDUCE: (983), (985) imply: % 42.75/6.86 | | | | | | | | | | | (986) $false % 42.75/6.86 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | CLOSE: (986) is inconsistent. % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (987) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (988) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.75/6.87 | | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.75/6.87 | | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (969), % 42.75/6.87 | | | | | | | | | | | | (972), (988), (function-axioms) are inconsistent % 42.75/6.87 | | | | | | | | | | | | by sub-proof #17. % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (989) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.87 | | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | BETA: splitting (989) gives: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | | (990) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.75/6.87 | | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.75/6.87 | | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.75/6.87 | | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.75/6.87 | | | | | | | | | | | | | (984), (987), (990), (function-axioms) are % 42.75/6.87 | | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | | (991) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (991), % 42.75/6.87 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.87 | | | | | | | | | | | | | #11. % 42.75/6.87 | | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | (992) all_24_0 = e0 % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | COMBINE_EQS: (603), (992) imply: % 42.75/6.87 | | | | | | | | | (993) all_6_0 = e0 % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | SIMP: (993) implies: % 42.75/6.87 | | | | | | | | | (994) all_6_0 = e0 % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | COMBINE_EQS: (600), (994) imply: % 42.75/6.87 | | | | | | | | | (995) all_34_0 = e0 % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | REDUCE: (630), (994) imply: % 42.75/6.87 | | | | | | | | | (996) ~ (e3 = e0) % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | REDUCE: (43), (994) imply: % 42.75/6.87 | | | | | | | | | (997) op(all_6_2, e1) = e0 % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | BETA: splitting (100) gives: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (998) ~ (all_34_0 = e0) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | REDUCE: (995), (998) imply: % 42.75/6.87 | | | | | | | | | | (999) $false % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | CLOSE: (999) is inconsistent. % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (1000) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1001) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.75/6.87 | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.75/6.87 | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (969), % 42.75/6.87 | | | | | | | | | | | (972), (1001), (function-axioms) are inconsistent % 42.75/6.87 | | | | | | | | | | | by sub-proof #17. % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1002) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.87 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | BETA: splitting (1002) gives: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (1003) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.75/6.87 | | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.75/6.87 | | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (997), % 42.75/6.87 | | | | | | | | | | | | (1000), (1003), (function-axioms) are inconsistent % 42.75/6.87 | | | | | | | | | | | | by sub-proof #25. % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (1004) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (1004), % 42.75/6.87 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.87 | | | | | | | | | | | | #11. % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | End of split % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | End of split % 42.75/6.87 | | | | | | | % 42.75/6.87 | | | | | | End of split % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | Case 2: % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | (1005) all_14_0 = e0 % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | COMBINE_EQS: (622), (1005) imply: % 42.75/6.87 | | | | | | (1006) all_8_0 = e0 % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | COMBINE_EQS: (628), (1006) imply: % 42.75/6.87 | | | | | | (1007) all_50_0 = e0 % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | REDUCE: (631), (1006) imply: % 42.75/6.87 | | | | | | (1008) ~ (e3 = e0) % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | REDUCE: (48), (1006) imply: % 42.75/6.87 | | | | | | (1009) op(all_8_2, e2) = e0 % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | BETA: splitting (79) gives: % 42.75/6.87 | | | | | | % 42.75/6.87 | | | | | | Case 1: % 42.75/6.87 | | | | | | | % 42.75/6.87 | | | | | | | (1010) ~ (all_24_0 = e0) % 42.75/6.87 | | | | | | | % 42.75/6.87 | | | | | | | REDUCE: (603), (1010) imply: % 42.75/6.87 | | | | | | | (1011) ~ (all_6_0 = e0) % 42.75/6.87 | | | | | | | % 42.75/6.87 | | | | | | | BETA: splitting (107) gives: % 42.75/6.87 | | | | | | | % 42.75/6.87 | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | (1012) ~ (all_38_0 = e2) % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | REDUCE: (580), (1012) imply: % 42.75/6.87 | | | | | | | | (1013) ~ (all_6_0 = e2) % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | BETA: splitting (132) gives: % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | (1014) ~ (all_50_0 = e0) % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | REDUCE: (1007), (1014) imply: % 42.75/6.87 | | | | | | | | | (1015) $false % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | CLOSE: (1015) is inconsistent. % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | (1016) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (1017) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.75/6.87 | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.75/6.87 | | | | | | | | | | (503), (506), (509), (513), (627), (1009), (1016), % 42.75/6.87 | | | | | | | | | | (1017), (function-axioms) are inconsistent by % 42.75/6.87 | | | | | | | | | | sub-proof #13. % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (1018) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.87 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | BETA: splitting (1018) gives: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1019) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.75/6.87 | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.75/6.87 | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.75/6.87 | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.75/6.87 | | | | | | | | | | | (508), (510), (1011), (1013), (1019), % 42.75/6.87 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.87 | | | | | | | | | | | #55. % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1020) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (1020), % 42.75/6.87 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.87 | | | | | | | | | | | #11. % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | End of split % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | End of split % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | (1021) all_38_0 = e2 % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | COMBINE_EQS: (580), (1021) imply: % 42.75/6.87 | | | | | | | | (1022) all_6_0 = e2 % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | SIMP: (1022) implies: % 42.75/6.87 | | | | | | | | (1023) all_6_0 = e2 % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | COMBINE_EQS: (626), (1023) imply: % 42.75/6.87 | | | | | | | | (1024) all_42_0 = e2 % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | REDUCE: (43), (1023) imply: % 42.75/6.87 | | | | | | | | (1025) op(all_6_2, e1) = e2 % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | BETA: splitting (117) gives: % 42.75/6.87 | | | | | | | | % 42.75/6.87 | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | (1026) ~ (all_42_0 = e2) % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | REDUCE: (1024), (1026) imply: % 42.75/6.87 | | | | | | | | | (1027) $false % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | CLOSE: (1027) is inconsistent. % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | (1028) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | BETA: splitting (132) gives: % 42.75/6.87 | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (1029) ~ (all_50_0 = e0) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | REDUCE: (1007), (1029) imply: % 42.75/6.87 | | | | | | | | | | (1030) $false % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | CLOSE: (1030) is inconsistent. % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | (1031) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.87 | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1032) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.75/6.87 | | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.75/6.87 | | | | | | | | | | | (503), (506), (509), (513), (627), (1009), (1031), % 42.75/6.87 | | | | | | | | | | | (1032), (function-axioms) are inconsistent by % 42.75/6.87 | | | | | | | | | | | sub-proof #13. % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | (1033) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.87 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | BETA: splitting (1033) gives: % 42.75/6.87 | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 1: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (1034) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.75/6.87 | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.75/6.87 | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.75/6.87 | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.75/6.87 | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.75/6.87 | | | | | | | | | | | | (1025), (1028), (1034), (function-axioms) are % 42.75/6.87 | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | Case 2: % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.87 | | | | | | | | | | | | (1035) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.87 | | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (1035), % 42.75/6.88 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.88 | | | | | | | | | | | | #11. % 42.75/6.88 | | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | End of split % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | End of split % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | End of split % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | End of split % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | End of split % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | Case 2: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | (1036) all_24_0 = e0 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | COMBINE_EQS: (603), (1036) imply: % 42.75/6.88 | | | | | | | (1037) all_6_0 = e0 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | SIMP: (1037) implies: % 42.75/6.88 | | | | | | | (1038) all_6_0 = e0 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | COMBINE_EQS: (600), (1038) imply: % 42.75/6.88 | | | | | | | (1039) all_34_0 = e0 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | REDUCE: (43), (1038) imply: % 42.75/6.88 | | | | | | | (1040) op(all_6_2, e1) = e0 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | BETA: splitting (100) gives: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1041) ~ (all_34_0 = e0) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | REDUCE: (1039), (1041) imply: % 42.75/6.88 | | | | | | | | (1042) $false % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | CLOSE: (1042) is inconsistent. % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1043) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | BETA: splitting (132) gives: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1044) ~ (all_50_0 = e0) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REDUCE: (1007), (1044) imply: % 42.75/6.88 | | | | | | | | | (1045) $false % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | CLOSE: (1045) is inconsistent. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1046) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | (1047) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.75/6.88 | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.75/6.88 | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.75/6.88 | | | | | | | | | | (503), (506), (509), (513), (627), (1009), (1046), % 42.75/6.88 | | | | | | | | | | (1047), (function-axioms) are inconsistent by % 42.75/6.88 | | | | | | | | | | sub-proof #13. % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | (1048) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.88 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | BETA: splitting (1048) gives: % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | (1049) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.75/6.88 | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.75/6.88 | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.75/6.88 | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (1040), % 42.75/6.88 | | | | | | | | | | | (1043), (1049), (function-axioms) are inconsistent % 42.75/6.88 | | | | | | | | | | | by sub-proof #25. % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | (1050) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | | REF_CLOSE: (146), (390), (469), (927), (1050), % 42.75/6.88 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.88 | | | | | | | | | | | #11. % 42.75/6.88 | | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | End of split % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | End of split % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | End of split % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | End of split % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | End of split % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | End of split % 42.75/6.88 | | | | | % 42.75/6.88 | | | | End of split % 42.75/6.88 | | | | % 42.75/6.88 | | | Case 2: % 42.75/6.88 | | | | % 42.75/6.88 | | | | (1051) all_8_0 = e3 % 42.75/6.88 | | | | % 42.75/6.88 | | | | REDUCE: (48), (1051) imply: % 42.75/6.88 | | | | (1052) op(all_8_2, e2) = e3 % 42.75/6.88 | | | | % 42.75/6.88 | | | | BETA: splitting (79) gives: % 42.75/6.88 | | | | % 42.75/6.88 | | | | Case 1: % 42.75/6.88 | | | | | % 42.75/6.88 | | | | | (1053) ~ (all_24_0 = e0) % 42.75/6.88 | | | | | % 42.75/6.88 | | | | | REDUCE: (603), (1053) imply: % 42.75/6.88 | | | | | (1054) ~ (all_6_0 = e0) % 42.75/6.88 | | | | | % 42.75/6.88 | | | | | BETA: splitting (91) gives: % 42.75/6.88 | | | | | % 42.75/6.88 | | | | | Case 1: % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | (1055) ~ (all_30_0 = e1) % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | REDUCE: (607), (1055) imply: % 42.75/6.88 | | | | | | (1056) ~ (all_4_0 = e1) % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | BETA: splitting (107) gives: % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | Case 1: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | (1057) ~ (all_38_0 = e2) % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | REDUCE: (580), (1057) imply: % 42.75/6.88 | | | | | | | (1058) ~ (all_6_0 = e2) % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | BETA: splitting (150) gives: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1059) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | REF_CLOSE: (148), (447), (506), (1052), (1059), % 42.75/6.88 | | | | | | | | (function-axioms) are inconsistent by sub-proof #9. % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1060) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 42.75/6.88 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | BETA: splitting (1060) gives: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1061) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.75/6.88 | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.75/6.88 | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.75/6.88 | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.75/6.88 | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.75/6.88 | | | | | | | | | (508), (510), (1054), (1058), (1061), % 42.75/6.88 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.88 | | | | | | | | | #55. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1062) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.75/6.88 | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.75/6.88 | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.75/6.88 | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.75/6.88 | | | | | | | | | (489), (495), (507), (508), (510), (629), (1056), % 42.75/6.88 | | | | | | | | | (1062), (function-axioms) are inconsistent by % 42.75/6.88 | | | | | | | | | sub-proof #46. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | End of split % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | End of split % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | Case 2: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | (1063) all_38_0 = e2 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | COMBINE_EQS: (580), (1063) imply: % 42.75/6.88 | | | | | | | (1064) all_6_0 = e2 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | SIMP: (1064) implies: % 42.75/6.88 | | | | | | | (1065) all_6_0 = e2 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | COMBINE_EQS: (626), (1065) imply: % 42.75/6.88 | | | | | | | (1066) all_42_0 = e2 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | REDUCE: (630), (1065) imply: % 42.75/6.88 | | | | | | | (1067) ~ (e3 = e2) % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | REDUCE: (43), (1065) imply: % 42.75/6.88 | | | | | | | (1068) op(all_6_2, e1) = e2 % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | BETA: splitting (117) gives: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1069) ~ (all_42_0 = e2) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | REDUCE: (1066), (1069) imply: % 42.75/6.88 | | | | | | | | (1070) $false % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | CLOSE: (1070) is inconsistent. % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1071) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | BETA: splitting (150) gives: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1072) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | ALPHA: (1072) implies: % 42.75/6.88 | | | | | | | | | (1073) all_52_11 = e3 % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | COMBINE_EQS: (447), (1073) imply: % 42.75/6.88 | | | | | | | | | (1074) all_8_2 = e3 % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REF_CLOSE: (148), (506), (1052), (1074), (function-axioms) are % 42.75/6.88 | | | | | | | | | inconsistent by sub-proof #10. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1075) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.75/6.88 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (37), (38), (42), (137), % 42.75/6.88 | | | | | | | | | (141), (146), (147), (151), (152), (153), (225), % 42.75/6.88 | | | | | | | | | (226), (229), (230), (249), (250), (253), (268), % 42.75/6.88 | | | | | | | | | (286), (287), (292), (308), (320), (350), (360), % 42.75/6.88 | | | | | | | | | (370), (390), (446), (447), (451), (452), (453), % 42.75/6.88 | | | | | | | | | (454), (455), (456), (457), (461), (463), (469), % 42.75/6.88 | | | | | | | | | (476), (477), (479), (483), (489), (491), (494), % 42.75/6.88 | | | | | | | | | (495), (499), (507), (508), (510), (511), (550), % 42.75/6.88 | | | | | | | | | (629), (1056), (1068), (1071), (1075), % 42.75/6.88 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.88 | | | | | | | | | #36. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | End of split % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | End of split % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | End of split % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | Case 2: % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | (1076) all_30_0 = e1 % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | COMBINE_EQS: (607), (1076) imply: % 42.75/6.88 | | | | | | (1077) all_4_0 = e1 % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | COMBINE_EQS: (625), (1077) imply: % 42.75/6.88 | | | | | | (1078) all_40_0 = e1 % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | REDUCE: (38), (1077) imply: % 42.75/6.88 | | | | | | (1079) op(all_4_2, e0) = e1 % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | BETA: splitting (112) gives: % 42.75/6.88 | | | | | | % 42.75/6.88 | | | | | | Case 1: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | (1080) ~ (all_40_0 = e1) % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | REDUCE: (1078), (1080) imply: % 42.75/6.88 | | | | | | | (1081) $false % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | CLOSE: (1081) is inconsistent. % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | Case 2: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | (1082) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | BETA: splitting (107) gives: % 42.75/6.88 | | | | | | | % 42.75/6.88 | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | (1083) ~ (all_38_0 = e2) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | REDUCE: (580), (1083) imply: % 42.75/6.88 | | | | | | | | (1084) ~ (all_6_0 = e2) % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | BETA: splitting (150) gives: % 42.75/6.88 | | | | | | | | % 42.75/6.88 | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1085) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | ALPHA: (1085) implies: % 42.75/6.88 | | | | | | | | | (1086) all_52_11 = e3 % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | COMBINE_EQS: (447), (1086) imply: % 42.75/6.88 | | | | | | | | | (1087) all_8_2 = e3 % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | REF_CLOSE: (148), (506), (1052), (1087), (function-axioms) are % 42.75/6.88 | | | | | | | | | inconsistent by sub-proof #10. % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | Case 2: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | (1088) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.75/6.88 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | BETA: splitting (1088) gives: % 42.75/6.88 | | | | | | | | | % 42.75/6.88 | | | | | | | | | Case 1: % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | (1089) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | ALPHA: (1089) implies: % 42.75/6.88 | | | | | | | | | | (1090) all_52_13 = e3 % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | COMBINE_EQS: (446), (1090) imply: % 42.75/6.88 | | | | | | | | | | (1091) all_6_2 = e3 % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REDUCE: (489), (1091) imply: % 42.75/6.88 | | | | | | | | | | (1092) ~ (all_52_3 = e3) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REDUCE: (487), (1091) imply: % 42.75/6.88 | | | | | | | | | | (1093) ~ (all_52_4 = e3) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REDUCE: (470), (1091) imply: % 42.75/6.88 | | | | | | | | | | (1094) ~ (all_52_5 = e3) % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REDUCE: (43), (1091) imply: % 42.75/6.88 | | | | | | | | | | (1095) op(e3, e1) = all_6_0 % 42.75/6.88 | | | | | | | | | | % 42.75/6.88 | | | | | | | | | | REF_CLOSE: (5), (7), (9), (147), (151), (152), (153), (225), % 42.75/6.88 | | | | | | | | | | (226), (228), (231), (253), (292), (308), (320), % 42.75/6.88 | | | | | | | | | | (333), (335), (350), (390), (447), (452), (456), % 42.75/6.88 | | | | | | | | | | (457), (459), (465), (467), (469), (472), (500), % 42.75/6.88 | | | | | | | | | | (502), (507), (508), (510), (1054), (1084), % 42.75/6.88 | | | | | | | | | | (1090), (1092), (1093), (1094), (1095), % 42.75/6.88 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.88 | | | | | | | | | | #57. % 42.75/6.88 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | (1096) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.75/6.89 | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.75/6.89 | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.75/6.89 | | | | | | | | | | (476), (481), (495), (508), (547), (1079), (1082), % 42.75/6.89 | | | | | | | | | | (1096), (function-axioms) are inconsistent by % 42.75/6.89 | | | | | | | | | | sub-proof #32. % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | End of split % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | End of split % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | (1097) all_38_0 = e2 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | COMBINE_EQS: (580), (1097) imply: % 42.75/6.89 | | | | | | | | (1098) all_6_0 = e2 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | SIMP: (1098) implies: % 42.75/6.89 | | | | | | | | (1099) all_6_0 = e2 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | COMBINE_EQS: (626), (1099) imply: % 42.75/6.89 | | | | | | | | (1100) all_42_0 = e2 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | REDUCE: (630), (1099) imply: % 42.75/6.89 | | | | | | | | (1101) ~ (e3 = e2) % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | REDUCE: (43), (1099) imply: % 42.75/6.89 | | | | | | | | (1102) op(all_6_2, e1) = e2 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | BETA: splitting (117) gives: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1103) ~ (all_42_0 = e2) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REDUCE: (1100), (1103) imply: % 42.75/6.89 | | | | | | | | | (1104) $false % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | CLOSE: (1104) is inconsistent. % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1105) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | (1106) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | REF_CLOSE: (148), (447), (506), (1052), (1106), % 42.75/6.89 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.89 | | | | | | | | | | #9. % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | (1107) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.75/6.89 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | BETA: splitting (1107) gives: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | (1108) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | ALPHA: (1108) implies: % 42.75/6.89 | | | | | | | | | | | (1109) all_52_13 = e3 % 42.75/6.89 | | | | | | | | | | | (1110) ~ (all_52_12 = e1) % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | COMBINE_EQS: (446), (1109) imply: % 42.75/6.89 | | | | | | | | | | | (1111) all_6_2 = e3 % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | SIMP: (1111) implies: % 42.75/6.89 | | | | | | | | | | | (1112) all_6_2 = e3 % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | COMBINE_EQS: (370), (1112) imply: % 42.75/6.89 | | | | | | | | | | | (1113) all_42_2 = e3 % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REDUCE: (489), (1112) imply: % 42.75/6.89 | | | | | | | | | | | (1114) ~ (all_52_3 = e3) % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REDUCE: (483), (1112) imply: % 42.75/6.89 | | | | | | | | | | | (1115) ~ (all_52_12 = e3) % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REDUCE: (1102), (1112) imply: % 42.75/6.89 | | | | | | | | | | | (1116) op(e3, e1) = e2 % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REDUCE: (42), (1112) imply: % 42.75/6.89 | | | | | | | | | | | (1117) op(e1, e3) = all_6_1 % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REF_CLOSE: (4), (7), (141), (147), (151), (152), (153), % 42.75/6.89 | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.75/6.89 | | | | | | | | | | | (320), (390), (447), (452), (453), (454), (456), % 42.75/6.89 | | | | | | | | | | | (457), (463), (469), (479), (491), (494), (499), % 42.75/6.89 | | | | | | | | | | | (510), (511), (550), (1105), (1109), (1110), % 42.75/6.89 | | | | | | | | | | | (1113), (1114), (1115), (1116), (1117), % 42.75/6.89 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.89 | | | | | | | | | | | #39. % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | (1118) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.75/6.89 | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.75/6.89 | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.75/6.89 | | | | | | | | | | | (476), (481), (495), (508), (547), (1079), (1082), % 42.75/6.89 | | | | | | | | | | | (1118), (function-axioms) are inconsistent by % 42.75/6.89 | | | | | | | | | | | sub-proof #30. % 42.75/6.89 | | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | End of split % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | End of split % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | End of split % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | End of split % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | End of split % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | End of split % 42.75/6.89 | | | | | % 42.75/6.89 | | | | Case 2: % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | (1119) all_24_0 = e0 % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | COMBINE_EQS: (603), (1119) imply: % 42.75/6.89 | | | | | (1120) all_6_0 = e0 % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | COMBINE_EQS: (600), (1120) imply: % 42.75/6.89 | | | | | (1121) all_34_0 = e0 % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | REDUCE: (43), (1120) imply: % 42.75/6.89 | | | | | (1122) op(all_6_2, e1) = e0 % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | BETA: splitting (91) gives: % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | Case 1: % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | (1123) ~ (all_30_0 = e1) % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | REDUCE: (607), (1123) imply: % 42.75/6.89 | | | | | | (1124) ~ (all_4_0 = e1) % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | BETA: splitting (100) gives: % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | Case 1: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | (1125) ~ (all_34_0 = e0) % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | REDUCE: (1121), (1125) imply: % 42.75/6.89 | | | | | | | (1126) $false % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | CLOSE: (1126) is inconsistent. % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | Case 2: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | (1127) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | BETA: splitting (150) gives: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | (1128) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | ALPHA: (1128) implies: % 42.75/6.89 | | | | | | | | (1129) all_52_11 = e3 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | COMBINE_EQS: (447), (1129) imply: % 42.75/6.89 | | | | | | | | (1130) all_8_2 = e3 % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | REF_CLOSE: (148), (506), (1052), (1130), (function-axioms) are % 42.75/6.89 | | | | | | | | inconsistent by sub-proof #10. % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | (1131) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 42.75/6.89 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | BETA: splitting (1131) gives: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1132) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | ALPHA: (1132) implies: % 42.75/6.89 | | | | | | | | | (1133) all_52_13 = e3 % 42.75/6.89 | | | | | | | | | (1134) ~ (all_52_12 = e1) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | COMBINE_EQS: (446), (1133) imply: % 42.75/6.89 | | | | | | | | | (1135) all_6_2 = e3 % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | COMBINE_EQS: (424), (1135) imply: % 42.75/6.89 | | | | | | | | | (1136) all_34_2 = e3 % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REDUCE: (489), (1135) imply: % 42.75/6.89 | | | | | | | | | (1137) ~ (all_52_3 = e3) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REDUCE: (483), (1135) imply: % 42.75/6.89 | | | | | | | | | (1138) ~ (all_52_12 = e3) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REDUCE: (1122), (1135) imply: % 42.75/6.89 | | | | | | | | | (1139) op(e3, e1) = e0 % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REDUCE: (42), (1135) imply: % 42.75/6.89 | | | | | | | | | (1140) op(e1, e3) = all_6_1 % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REF_CLOSE: (6), (9), (141), (147), (151), (152), (153), (229), % 42.75/6.89 | | | | | | | | | (251), (252), (287), (292), (320), (390), (447), % 42.75/6.89 | | | | | | | | | (452), (456), (457), (479), (499), (507), (510), % 42.75/6.89 | | | | | | | | | (602), (1127), (1133), (1134), (1136), (1137), % 42.75/6.89 | | | | | | | | | (1138), (1139), (1140), (function-axioms) are % 42.75/6.89 | | | | | | | | | inconsistent by sub-proof #27. % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1141) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.75/6.89 | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.75/6.89 | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.75/6.89 | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.75/6.89 | | | | | | | | | (489), (495), (507), (508), (510), (629), (1124), % 42.75/6.89 | | | | | | | | | (1141), (function-axioms) are inconsistent by % 42.75/6.89 | | | | | | | | | sub-proof #37. % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | End of split % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | End of split % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | End of split % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | Case 2: % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | (1142) all_30_0 = e1 % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | COMBINE_EQS: (607), (1142) imply: % 42.75/6.89 | | | | | | (1143) all_4_0 = e1 % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | SIMP: (1143) implies: % 42.75/6.89 | | | | | | (1144) all_4_0 = e1 % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | COMBINE_EQS: (625), (1144) imply: % 42.75/6.89 | | | | | | (1145) all_40_0 = e1 % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | REDUCE: (629), (1144) imply: % 42.75/6.89 | | | | | | (1146) ~ (e2 = e1) % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | REDUCE: (38), (1144) imply: % 42.75/6.89 | | | | | | (1147) op(all_4_2, e0) = e1 % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | BETA: splitting (100) gives: % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | | Case 1: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | (1148) ~ (all_34_0 = e0) % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | REDUCE: (1121), (1148) imply: % 42.75/6.89 | | | | | | | (1149) $false % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | CLOSE: (1149) is inconsistent. % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | Case 2: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | (1150) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | BETA: splitting (112) gives: % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | (1151) ~ (all_40_0 = e1) % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | REDUCE: (1145), (1151) imply: % 42.75/6.89 | | | | | | | | (1152) $false % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | CLOSE: (1152) is inconsistent. % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | (1153) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | BETA: splitting (150) gives: % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1154) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | REF_CLOSE: (148), (447), (506), (1052), (1154), % 42.75/6.89 | | | | | | | | | (function-axioms) are inconsistent by sub-proof #9. % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | (1155) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.75/6.89 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | BETA: splitting (1155) gives: % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | | Case 1: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | (1156) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.75/6.89 | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.75/6.89 | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.75/6.89 | | | | | | | | | | (483), (489), (499), (507), (510), (602), (1122), % 42.75/6.89 | | | | | | | | | | (1150), (1156), (function-axioms) are inconsistent % 42.75/6.89 | | | | | | | | | | by sub-proof #25. % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | Case 2: % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | (1157) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.75/6.89 | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.75/6.89 | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.75/6.89 | | | | | | | | | | (476), (481), (495), (508), (547), (1147), (1153), % 42.75/6.89 | | | | | | | | | | (1157), (function-axioms) are inconsistent by % 42.75/6.89 | | | | | | | | | | sub-proof #30. % 42.75/6.89 | | | | | | | | | | % 42.75/6.89 | | | | | | | | | End of split % 42.75/6.89 | | | | | | | | | % 42.75/6.89 | | | | | | | | End of split % 42.75/6.89 | | | | | | | | % 42.75/6.89 | | | | | | | End of split % 42.75/6.89 | | | | | | | % 42.75/6.89 | | | | | | End of split % 42.75/6.89 | | | | | | % 42.75/6.89 | | | | | End of split % 42.75/6.89 | | | | | % 42.75/6.89 | | | | End of split % 42.75/6.89 | | | | % 42.75/6.89 | | | End of split % 42.75/6.89 | | | % 42.75/6.89 | | Case 2: % 42.75/6.89 | | | % 42.75/6.89 | | | (1158) all_6_0 = e3 % 42.75/6.89 | | | % 42.75/6.89 | | | REDUCE: (43), (1158) imply: % 42.75/6.89 | | | (1159) op(all_6_2, e1) = e3 % 42.75/6.89 | | | % 42.75/6.89 | | | BETA: splitting (49) gives: % 42.75/6.89 | | | % 42.75/6.89 | | | Case 1: % 42.75/6.89 | | | | % 42.75/6.89 | | | | (1160) ~ (all_8_0 = e3) % 42.75/6.89 | | | | % 42.75/6.89 | | | | BETA: splitting (56) gives: % 42.75/6.89 | | | | % 42.75/6.89 | | | | Case 1: % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | (1161) ~ (all_12_0 = e3) % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | REDUCE: (619), (1161) imply: % 42.75/6.89 | | | | | (1162) ~ (all_4_0 = e3) % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | BETA: splitting (61) gives: % 42.75/6.89 | | | | | % 42.75/6.89 | | | | | Case 1: % 42.75/6.89 | | | | | | % 42.75/6.90 | | | | | | (1163) ~ (all_14_0 = e0) % 42.75/6.90 | | | | | | % 42.75/6.90 | | | | | | REDUCE: (622), (1163) imply: % 42.75/6.90 | | | | | | (1164) ~ (all_8_0 = e0) % 42.75/6.90 | | | | | | % 42.75/6.90 | | | | | | BETA: splitting (66) gives: % 42.75/6.90 | | | | | | % 42.75/6.90 | | | | | | Case 1: % 42.75/6.90 | | | | | | | % 42.75/6.90 | | | | | | | (1165) ~ (all_16_0 = e1) % 42.75/6.90 | | | | | | | % 42.75/6.90 | | | | | | | REDUCE: (616), (1165) imply: % 42.75/6.90 | | | | | | | (1166) ~ (all_8_0 = e1) % 42.75/6.90 | | | | | | | % 42.75/6.90 | | | | | | | BETA: splitting (91) gives: % 42.75/6.90 | | | | | | | % 42.75/6.90 | | | | | | | Case 1: % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | (1167) ~ (all_30_0 = e1) % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | REDUCE: (607), (1167) imply: % 42.75/6.90 | | | | | | | | (1168) ~ (all_4_0 = e1) % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | BETA: splitting (150) gives: % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | Case 1: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | (1169) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | ALPHA: (1169) implies: % 42.75/6.90 | | | | | | | | | (1170) all_52_11 = e3 % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | COMBINE_EQS: (447), (1170) imply: % 42.75/6.90 | | | | | | | | | (1171) all_8_2 = e3 % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | SIMP: (1171) implies: % 42.75/6.90 | | | | | | | | | (1172) all_8_2 = e3 % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | REDUCE: (506), (1172) imply: % 42.75/6.90 | | | | | | | | | (1173) ~ (all_52_6 = e3) % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | REDUCE: (48), (1172) imply: % 42.75/6.90 | | | | | | | | | (1174) op(e3, e2) = all_8_0 % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | REF_CLOSE: (4), (7), (8), (148), (151), (152), (153), (224), % 42.75/6.90 | | | | | | | | | (225), (226), (253), (292), (308), (314), (320), % 42.75/6.90 | | | | | | | | | (350), (390), (446), (452), (456), (457), (465), % 42.75/6.90 | | | | | | | | | (467), (469), (489), (508), (509), (510), (511), % 42.75/6.90 | | | | | | | | | (513), (1164), (1166), (1170), (1173), (1174), % 42.75/6.90 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.90 | | | | | | | | | #67. % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | Case 2: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | (1175) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.75/6.90 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | BETA: splitting (1175) gives: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | Case 1: % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | | (1176) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | | REF_CLOSE: (147), (446), (489), (1159), (1176), % 42.75/6.90 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.75/6.90 | | | | | | | | | | #7. % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | Case 2: % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | | (1177) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (151), % 42.75/6.90 | | | | | | | | | | (152), (153), (225), (226), (230), (250), (286), % 42.75/6.90 | | | | | | | | | | (308), (320), (350), (360), (390), (446), (447), % 42.75/6.90 | | | | | | | | | | (451), (455), (456), (461), (469), (476), (477), % 42.75/6.90 | | | | | | | | | | (489), (495), (507), (508), (510), (629), (1168), % 42.75/6.90 | | | | | | | | | | (1177), (function-axioms) are inconsistent by % 42.75/6.90 | | | | | | | | | | sub-proof #46. % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | End of split % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | End of split % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | Case 2: % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | (1178) all_30_0 = e1 % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | COMBINE_EQS: (607), (1178) imply: % 42.75/6.90 | | | | | | | | (1179) all_4_0 = e1 % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | SIMP: (1179) implies: % 42.75/6.90 | | | | | | | | (1180) all_4_0 = e1 % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | COMBINE_EQS: (625), (1180) imply: % 42.75/6.90 | | | | | | | | (1181) all_40_0 = e1 % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | REDUCE: (1162), (1180) imply: % 42.75/6.90 | | | | | | | | (1182) ~ (e3 = e1) % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | REDUCE: (38), (1180) imply: % 42.75/6.90 | | | | | | | | (1183) op(all_4_2, e0) = e1 % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | BETA: splitting (112) gives: % 42.75/6.90 | | | | | | | | % 42.75/6.90 | | | | | | | | Case 1: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | (1184) ~ (all_40_0 = e1) % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | REDUCE: (1181), (1184) imply: % 42.75/6.90 | | | | | | | | | (1185) $false % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | CLOSE: (1185) is inconsistent. % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | Case 2: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | (1186) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | BETA: splitting (150) gives: % 42.75/6.90 | | | | | | | | | % 42.75/6.90 | | | | | | | | | Case 1: % 42.75/6.90 | | | | | | | | | | % 42.75/6.90 | | | | | | | | | | (1187) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.75/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.93/6.90 | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.93/6.90 | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.93/6.90 | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.93/6.90 | | | | | | | | | | (509), (510), (511), (513), (1164), (1166), % 42.93/6.90 | | | | | | | | | | (1187), (function-axioms) are inconsistent by % 42.93/6.90 | | | | | | | | | | sub-proof #45. % 42.93/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | Case 2: % 42.93/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | (1188) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.90 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | BETA: splitting (1188) gives: % 42.93/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | Case 1: % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | (1189) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | ALPHA: (1189) implies: % 42.93/6.90 | | | | | | | | | | | (1190) all_52_13 = e3 % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | COMBINE_EQS: (446), (1190) imply: % 42.93/6.90 | | | | | | | | | | | (1191) all_6_2 = e3 % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | REF_CLOSE: (147), (489), (1159), (1191), (function-axioms) % 42.93/6.90 | | | | | | | | | | | are inconsistent by sub-proof #8. % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | Case 2: % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | (1192) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.93/6.90 | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.93/6.90 | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.93/6.90 | | | | | | | | | | | (476), (481), (495), (508), (547), (1183), (1186), % 42.93/6.90 | | | | | | | | | | | (1192), (function-axioms) are inconsistent by % 42.93/6.90 | | | | | | | | | | | sub-proof #32. % 42.93/6.90 | | | | | | | | | | | % 42.93/6.90 | | | | | | | | | | End of split % 42.93/6.90 | | | | | | | | | | % 42.93/6.90 | | | | | | | | | End of split % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | End of split % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | End of split % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | Case 2: % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | (1193) all_16_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | COMBINE_EQS: (616), (1193) imply: % 42.93/6.90 | | | | | | | (1194) all_8_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | COMBINE_EQS: (569), (1194) imply: % 42.93/6.90 | | | | | | | (1195) all_26_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (1160), (1194) imply: % 42.93/6.90 | | | | | | | (1196) ~ (e3 = e1) % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (48), (1194) imply: % 42.93/6.90 | | | | | | | (1197) op(all_8_2, e2) = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (37), (38), (47), (84), (91), % 42.93/6.90 | | | | | | | (112), (137), (145), (146), (147), (148), (150), (151), % 42.93/6.90 | | | | | | | (152), (153), (225), (226), (227), (230), (250), (286), % 42.93/6.90 | | | | | | | (308), (320), (350), (356), (360), (390), (408), (442), % 42.93/6.90 | | | | | | | (446), (447), (451), (455), (456), (461), (465), (469), % 42.93/6.90 | | | | | | | (476), (477), (481), (489), (493), (495), (497), (503), % 42.93/6.90 | | | | | | | (504), (506), (507), (508), (510), (513), (547), (589), % 42.93/6.90 | | | | | | | (607), (625), (629), (1159), (1195), (1197), % 42.93/6.90 | | | | | | | (function-axioms) are inconsistent by sub-proof #5. % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | End of split % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | Case 2: % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | (1198) all_14_0 = e0 % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | COMBINE_EQS: (622), (1198) imply: % 42.93/6.90 | | | | | | (1199) all_8_0 = e0 % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | COMBINE_EQS: (628), (1199) imply: % 42.93/6.90 | | | | | | (1200) all_50_0 = e0 % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | REDUCE: (48), (1199) imply: % 42.93/6.90 | | | | | | (1201) op(all_8_2, e2) = e0 % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | BETA: splitting (91) gives: % 42.93/6.90 | | | | | | % 42.93/6.90 | | | | | | Case 1: % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | (1202) ~ (all_30_0 = e1) % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (607), (1202) imply: % 42.93/6.90 | | | | | | | (1203) ~ (all_4_0 = e1) % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | BETA: splitting (132) gives: % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | Case 1: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | (1204) ~ (all_50_0 = e0) % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | REDUCE: (1200), (1204) imply: % 42.93/6.90 | | | | | | | | (1205) $false % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | CLOSE: (1205) is inconsistent. % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | Case 2: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | (1206) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | BETA: splitting (150) gives: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | Case 1: % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | (1207) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | ALPHA: (1207) implies: % 42.93/6.90 | | | | | | | | | (1208) all_52_11 = e3 % 42.93/6.90 | | | | | | | | | (1209) ~ (all_52_10 = e2) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | COMBINE_EQS: (447), (1208) imply: % 42.93/6.90 | | | | | | | | | (1210) all_8_2 = e3 % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | COMBINE_EQS: (445), (1210) imply: % 42.93/6.90 | | | | | | | | | (1211) all_50_2 = e3 % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REDUCE: (506), (1210) imply: % 42.93/6.90 | | | | | | | | | (1212) ~ (all_52_6 = e3) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REDUCE: (503), (1210) imply: % 42.93/6.90 | | | | | | | | | (1213) ~ (all_52_10 = e3) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REDUCE: (1201), (1210) imply: % 42.93/6.90 | | | | | | | | | (1214) op(e3, e2) = e0 % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REDUCE: (47), (1210) imply: % 42.93/6.90 | | | | | | | | | (1215) op(e2, e3) = all_8_1 % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REF_CLOSE: (6), (8), (145), (148), (151), (152), (153), (227), % 42.93/6.90 | | | | | | | | | (252), (292), (320), (356), (390), (446), (452), % 42.93/6.90 | | | | | | | | | (456), (457), (478), (498), (509), (513), (627), % 42.93/6.90 | | | | | | | | | (1206), (1208), (1209), (1211), (1212), (1213), % 42.93/6.90 | | | | | | | | | (1214), (1215), (function-axioms) are inconsistent % 42.93/6.90 | | | | | | | | | by sub-proof #16. % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | Case 2: % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | (1216) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.93/6.90 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REF_CLOSE: (6), (8), (9), (37), (38), (137), (146), (147), % 42.93/6.90 | | | | | | | | | (151), (152), (153), (225), (226), (230), (250), % 42.93/6.90 | | | | | | | | | (286), (308), (320), (350), (360), (390), (446), % 42.93/6.90 | | | | | | | | | (447), (451), (455), (456), (461), (469), (476), % 42.93/6.90 | | | | | | | | | (477), (489), (495), (507), (508), (510), (629), % 42.93/6.90 | | | | | | | | | (1159), (1203), (1216), (function-axioms) are % 42.93/6.90 | | | | | | | | | inconsistent by sub-proof #6. % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | End of split % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | End of split % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | Case 2: % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | (1217) all_30_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | COMBINE_EQS: (607), (1217) imply: % 42.93/6.90 | | | | | | | (1218) all_4_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | SIMP: (1218) implies: % 42.93/6.90 | | | | | | | (1219) all_4_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | COMBINE_EQS: (625), (1219) imply: % 42.93/6.90 | | | | | | | (1220) all_40_0 = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (1162), (1219) imply: % 42.93/6.90 | | | | | | | (1221) ~ (e3 = e1) % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (629), (1219) imply: % 42.93/6.90 | | | | | | | (1222) ~ (e2 = e1) % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | REDUCE: (38), (1219) imply: % 42.93/6.90 | | | | | | | (1223) op(all_4_2, e0) = e1 % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | BETA: splitting (112) gives: % 42.93/6.90 | | | | | | | % 42.93/6.90 | | | | | | | Case 1: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | (1224) ~ (all_40_0 = e1) % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | REDUCE: (1220), (1224) imply: % 42.93/6.90 | | | | | | | | (1225) $false % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | CLOSE: (1225) is inconsistent. % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | Case 2: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | (1226) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | BETA: splitting (132) gives: % 42.93/6.90 | | | | | | | | % 42.93/6.90 | | | | | | | | Case 1: % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | (1227) ~ (all_50_0 = e0) % 42.93/6.90 | | | | | | | | | % 42.93/6.90 | | | | | | | | | REDUCE: (1200), (1227) imply: % 42.93/6.90 | | | | | | | | | (1228) $false % 42.93/6.90 | | | | | | | | | % 42.93/6.91 | | | | | | | | | CLOSE: (1228) is inconsistent. % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | (1229) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | (1230) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.93/6.91 | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.93/6.91 | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.93/6.91 | | | | | | | | | | (503), (506), (509), (513), (627), (1201), (1229), % 42.93/6.91 | | | | | | | | | | (1230), (function-axioms) are inconsistent by % 42.93/6.91 | | | | | | | | | | sub-proof #13. % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | (1231) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.91 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | BETA: splitting (1231) gives: % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | | (1232) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | | REF_CLOSE: (147), (446), (489), (1159), (1232), % 42.93/6.91 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.91 | | | | | | | | | | | #7. % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | | (1233) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | | REF_CLOSE: (5), (9), (37), (137), (146), (151), (152), (153), % 42.93/6.91 | | | | | | | | | | | (230), (250), (286), (320), (360), (390), (408), % 42.93/6.91 | | | | | | | | | | | (446), (447), (451), (455), (456), (461), (469), % 42.93/6.91 | | | | | | | | | | | (476), (481), (495), (508), (547), (1223), (1226), % 42.93/6.91 | | | | | | | | | | | (1233), (function-axioms) are inconsistent by % 42.93/6.91 | | | | | | | | | | | sub-proof #30. % 42.93/6.91 | | | | | | | | | | | % 42.93/6.91 | | | | | | | | | | End of split % 42.93/6.91 | | | | | | | | | | % 42.93/6.91 | | | | | | | | | End of split % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | End of split % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | End of split % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | End of split % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | End of split % 42.93/6.91 | | | | | % 42.93/6.91 | | | | Case 2: % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | (1234) all_12_0 = e3 % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | COMBINE_EQS: (619), (1234) imply: % 42.93/6.91 | | | | | (1235) all_4_0 = e3 % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | SIMP: (1235) implies: % 42.93/6.91 | | | | | (1236) all_4_0 = e3 % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | REDUCE: (38), (1236) imply: % 42.93/6.91 | | | | | (1237) op(all_4_2, e0) = e3 % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | BETA: splitting (61) gives: % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | Case 1: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | (1238) ~ (all_14_0 = e0) % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | REDUCE: (622), (1238) imply: % 42.93/6.91 | | | | | | (1239) ~ (all_8_0 = e0) % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | BETA: splitting (66) gives: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | Case 1: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1240) ~ (all_16_0 = e1) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (616), (1240) imply: % 42.93/6.91 | | | | | | | (1241) ~ (all_8_0 = e1) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | BETA: splitting (150) gives: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | (1242) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.93/6.91 | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.93/6.91 | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.93/6.91 | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.93/6.91 | | | | | | | | (509), (510), (511), (513), (1239), (1241), (1242), % 42.93/6.91 | | | | | | | | (function-axioms) are inconsistent by sub-proof #45. % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | (1243) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 42.93/6.91 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | BETA: splitting (1243) gives: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | (1244) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | ALPHA: (1244) implies: % 42.93/6.91 | | | | | | | | | (1245) all_52_13 = e3 % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | COMBINE_EQS: (446), (1245) imply: % 42.93/6.91 | | | | | | | | | (1246) all_6_2 = e3 % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | REF_CLOSE: (147), (489), (1159), (1246), (function-axioms) are % 42.93/6.91 | | | | | | | | | inconsistent by sub-proof #8. % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | (1247) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | ALPHA: (1247) implies: % 42.93/6.91 | | | | | | | | | (1248) all_52_15 = e3 % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | COMBINE_EQS: (390), (1248) imply: % 42.93/6.91 | | | | | | | | | (1249) all_4_2 = e3 % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | REF_CLOSE: (146), (469), (1237), (1249), (function-axioms) are % 42.93/6.91 | | | | | | | | | inconsistent by sub-proof #12. % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | End of split % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | End of split % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | Case 2: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1250) all_16_0 = e1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | COMBINE_EQS: (616), (1250) imply: % 42.93/6.91 | | | | | | | (1251) all_8_0 = e1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | SIMP: (1251) implies: % 42.93/6.91 | | | | | | | (1252) all_8_0 = e1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | COMBINE_EQS: (569), (1252) imply: % 42.93/6.91 | | | | | | | (1253) all_26_0 = e1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (1160), (1252) imply: % 42.93/6.91 | | | | | | | (1254) ~ (e3 = e1) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (48), (1252) imply: % 42.93/6.91 | | | | | | | (1255) op(all_8_2, e2) = e1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (37), (38), (47), (84), (91), % 42.93/6.91 | | | | | | | (112), (137), (145), (146), (147), (148), (150), (151), % 42.93/6.91 | | | | | | | (152), (153), (225), (226), (227), (230), (250), (286), % 42.93/6.91 | | | | | | | (308), (320), (350), (356), (360), (390), (408), (442), % 42.93/6.91 | | | | | | | (446), (447), (451), (455), (456), (461), (465), (469), % 42.93/6.91 | | | | | | | (476), (477), (481), (489), (493), (495), (497), (503), % 42.93/6.91 | | | | | | | (504), (506), (507), (508), (510), (513), (547), (589), % 42.93/6.91 | | | | | | | (607), (625), (629), (1159), (1253), (1255), % 42.93/6.91 | | | | | | | (function-axioms) are inconsistent by sub-proof #5. % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | End of split % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | Case 2: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | (1256) all_14_0 = e0 % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | COMBINE_EQS: (622), (1256) imply: % 42.93/6.91 | | | | | | (1257) all_8_0 = e0 % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | SIMP: (1257) implies: % 42.93/6.91 | | | | | | (1258) all_8_0 = e0 % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | COMBINE_EQS: (628), (1258) imply: % 42.93/6.91 | | | | | | (1259) all_50_0 = e0 % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | REDUCE: (48), (1258) imply: % 42.93/6.91 | | | | | | (1260) op(all_8_2, e2) = e0 % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | BETA: splitting (132) gives: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | Case 1: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1261) ~ (all_50_0 = e0) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (1259), (1261) imply: % 42.93/6.91 | | | | | | | (1262) $false % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | CLOSE: (1262) is inconsistent. % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | Case 2: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1263) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | BETA: splitting (150) gives: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | (1264) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.93/6.91 | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.93/6.91 | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.93/6.91 | | | | | | | | (503), (506), (509), (513), (627), (1260), (1263), % 42.93/6.91 | | | | | | | | (1264), (function-axioms) are inconsistent by % 42.93/6.91 | | | | | | | | sub-proof #13. % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | (1265) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 42.93/6.91 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | BETA: splitting (1265) gives: % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | | Case 1: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | (1266) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | REF_CLOSE: (147), (446), (489), (1159), (1266), % 42.93/6.91 | | | | | | | | | (function-axioms) are inconsistent by sub-proof #7. % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | Case 2: % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | (1267) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | | REF_CLOSE: (146), (390), (469), (1237), (1267), % 42.93/6.91 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.91 | | | | | | | | | #11. % 42.93/6.91 | | | | | | | | | % 42.93/6.91 | | | | | | | | End of split % 42.93/6.91 | | | | | | | | % 42.93/6.91 | | | | | | | End of split % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | End of split % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | End of split % 42.93/6.91 | | | | | % 42.93/6.91 | | | | End of split % 42.93/6.91 | | | | % 42.93/6.91 | | | Case 2: % 42.93/6.91 | | | | % 42.93/6.91 | | | | (1268) all_8_0 = e3 % 42.93/6.91 | | | | % 42.93/6.91 | | | | REDUCE: (48), (1268) imply: % 42.93/6.91 | | | | (1269) op(all_8_2, e2) = e3 % 42.93/6.91 | | | | % 42.93/6.91 | | | | BETA: splitting (91) gives: % 42.93/6.91 | | | | % 42.93/6.91 | | | | Case 1: % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | (1270) ~ (all_30_0 = e1) % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | REDUCE: (607), (1270) imply: % 42.93/6.91 | | | | | (1271) ~ (all_4_0 = e1) % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | BETA: splitting (150) gives: % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | Case 1: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | (1272) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | REF_CLOSE: (148), (447), (506), (1269), (1272), (function-axioms) % 42.93/6.91 | | | | | | are inconsistent by sub-proof #9. % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | Case 2: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | (1273) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & % 42.93/6.91 | | | | | | ~ (all_52_14 = e0)) % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | BETA: splitting (1273) gives: % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | | Case 1: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1274) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REF_CLOSE: (147), (446), (489), (1159), (1274), (function-axioms) % 42.93/6.91 | | | | | | | are inconsistent by sub-proof #7. % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | Case 2: % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | (1275) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | ALPHA: (1275) implies: % 42.93/6.91 | | | | | | | (1276) all_52_15 = e3 % 42.93/6.91 | | | | | | | (1277) ~ (all_52_14 = e0) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | COMBINE_EQS: (390), (1276) imply: % 42.93/6.91 | | | | | | | (1278) all_4_2 = e3 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | SIMP: (1278) implies: % 42.93/6.91 | | | | | | | (1279) all_4_2 = e3 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (469), (1279) imply: % 42.93/6.91 | | | | | | | (1280) ~ (all_52_0 = e3) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (461), (1279) imply: % 42.93/6.91 | | | | | | | (1281) ~ (all_52_14 = e3) % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (38), (1279) imply: % 42.93/6.91 | | | | | | | (1282) op(e3, e0) = all_4_0 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REDUCE: (37), (1279) imply: % 42.93/6.91 | | | | | | | (1283) op(e0, e3) = all_4_1 % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | | REF_CLOSE: (6), (8), (9), (137), (146), (151), (152), (153), % 42.93/6.91 | | | | | | | (225), (226), (230), (250), (286), (308), (320), (350), % 42.93/6.91 | | | | | | | (360), (446), (447), (451), (455), (456), (476), (477), % 42.93/6.91 | | | | | | | (489), (495), (507), (508), (510), (629), (1271), % 42.93/6.91 | | | | | | | (1276), (1277), (1280), (1281), (1282), (1283), % 42.93/6.91 | | | | | | | (function-axioms) are inconsistent by sub-proof #48. % 42.93/6.91 | | | | | | | % 42.93/6.91 | | | | | | End of split % 42.93/6.91 | | | | | | % 42.93/6.91 | | | | | End of split % 42.93/6.91 | | | | | % 42.93/6.91 | | | | Case 2: % 42.93/6.91 | | | | | % 42.93/6.91 | | | | | (1284) all_30_0 = e1 % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | COMBINE_EQS: (607), (1284) imply: % 42.93/6.92 | | | | | (1285) all_4_0 = e1 % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | SIMP: (1285) implies: % 42.93/6.92 | | | | | (1286) all_4_0 = e1 % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | COMBINE_EQS: (625), (1286) imply: % 42.93/6.92 | | | | | (1287) all_40_0 = e1 % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | REDUCE: (38), (1286) imply: % 42.93/6.92 | | | | | (1288) op(all_4_2, e0) = e1 % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | BETA: splitting (112) gives: % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | Case 1: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | (1289) ~ (all_40_0 = e1) % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | REDUCE: (1287), (1289) imply: % 42.93/6.92 | | | | | | (1290) $false % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | CLOSE: (1290) is inconsistent. % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | Case 2: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | (1291) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | BETA: splitting (150) gives: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | Case 1: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | (1292) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | ALPHA: (1292) implies: % 42.93/6.92 | | | | | | | (1293) all_52_11 = e3 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | COMBINE_EQS: (447), (1293) imply: % 42.93/6.92 | | | | | | | (1294) all_8_2 = e3 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | REF_CLOSE: (148), (506), (1269), (1294), (function-axioms) are % 42.93/6.92 | | | | | | | inconsistent by sub-proof #10. % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | Case 2: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | (1295) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 % 42.93/6.92 | | | | | | | & ~ (all_52_14 = e0)) % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | BETA: splitting (1295) gives: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1296) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | ALPHA: (1296) implies: % 42.93/6.92 | | | | | | | | (1297) all_52_13 = e3 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | COMBINE_EQS: (446), (1297) imply: % 42.93/6.92 | | | | | | | | (1298) all_6_2 = e3 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REF_CLOSE: (147), (489), (1159), (1298), (function-axioms) are % 42.93/6.92 | | | | | | | | inconsistent by sub-proof #8. % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1299) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | ALPHA: (1299) implies: % 42.93/6.92 | | | | | | | | (1300) all_52_15 = e3 % 42.93/6.92 | | | | | | | | (1301) ~ (all_52_14 = e0) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | COMBINE_EQS: (390), (1300) imply: % 42.93/6.92 | | | | | | | | (1302) all_4_2 = e3 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | COMBINE_EQS: (408), (1302) imply: % 42.93/6.92 | | | | | | | | (1303) all_40_2 = e3 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (469), (1302) imply: % 42.93/6.92 | | | | | | | | (1304) ~ (all_52_0 = e3) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (461), (1302) imply: % 42.93/6.92 | | | | | | | | (1305) ~ (all_52_14 = e3) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (1288), (1302) imply: % 42.93/6.92 | | | | | | | | (1306) op(e3, e0) = e1 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (37), (1302) imply: % 42.93/6.92 | | | | | | | | (1307) op(e0, e3) = all_4_1 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REF_CLOSE: (5), (9), (137), (146), (151), (152), (153), (230), % 42.93/6.92 | | | | | | | | (250), (286), (320), (360), (446), (447), (451), % 42.93/6.92 | | | | | | | | (455), (456), (476), (481), (495), (508), (547), % 42.93/6.92 | | | | | | | | (1291), (1300), (1301), (1303), (1304), (1305), % 42.93/6.92 | | | | | | | | (1306), (1307), (function-axioms) are inconsistent by % 42.93/6.92 | | | | | | | | sub-proof #34. % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | End of split % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | End of split % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | End of split % 42.93/6.92 | | | | | % 42.93/6.92 | | | | End of split % 42.93/6.92 | | | | % 42.93/6.92 | | | End of split % 42.93/6.92 | | | % 42.93/6.92 | | End of split % 42.93/6.92 | | % 42.93/6.92 | Case 2: % 42.93/6.92 | | % 42.93/6.92 | | (1308) all_4_0 = e2 % 42.93/6.92 | | (1309) ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 42.93/6.92 | | % 42.93/6.92 | | REDUCE: (38), (1308) imply: % 42.93/6.92 | | (1310) op(all_4_2, e0) = e2 % 42.93/6.92 | | % 42.93/6.92 | | BETA: splitting (44) gives: % 42.93/6.92 | | % 42.93/6.92 | | Case 1: % 42.93/6.92 | | | % 42.93/6.92 | | | (1311) ~ (all_6_0 = e3) % 42.93/6.92 | | | % 42.93/6.92 | | | BETA: splitting (49) gives: % 42.93/6.92 | | | % 42.93/6.92 | | | Case 1: % 42.93/6.92 | | | | % 42.93/6.92 | | | | (1312) ~ (all_8_0 = e3) % 42.93/6.92 | | | | % 42.93/6.92 | | | | BETA: splitting (61) gives: % 42.93/6.92 | | | | % 42.93/6.92 | | | | Case 1: % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | (1313) ~ (all_14_0 = e0) % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | REDUCE: (622), (1313) imply: % 42.93/6.92 | | | | | (1314) ~ (all_8_0 = e0) % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | BETA: splitting (66) gives: % 42.93/6.92 | | | | | % 42.93/6.92 | | | | | Case 1: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | (1315) ~ (all_16_0 = e1) % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | REDUCE: (616), (1315) imply: % 42.93/6.92 | | | | | | (1316) ~ (all_8_0 = e1) % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | BETA: splitting (79) gives: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | Case 1: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | (1317) ~ (all_24_0 = e0) % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | REDUCE: (603), (1317) imply: % 42.93/6.92 | | | | | | | (1318) ~ (all_6_0 = e0) % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | BETA: splitting (107) gives: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1319) ~ (all_38_0 = e2) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (580), (1319) imply: % 42.93/6.92 | | | | | | | | (1320) ~ (all_6_0 = e2) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | BETA: splitting (150) gives: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1321) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.93/6.92 | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.93/6.92 | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.93/6.92 | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.93/6.92 | | | | | | | | | (509), (510), (511), (513), (1314), (1316), (1321), % 42.93/6.92 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | #65. % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1322) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.93/6.92 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | BETA: splitting (1322) gives: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1323) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.93/6.92 | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.93/6.92 | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.93/6.92 | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.93/6.92 | | | | | | | | | | (508), (510), (1318), (1320), (1323), % 42.93/6.92 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | | #35. % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1324) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.92 | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.92 | | | | | | | | | | (485), (508), (509), (1309), (1310), (1324), % 42.93/6.92 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | | #2. % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | End of split % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | End of split % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1325) all_38_0 = e2 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | COMBINE_EQS: (580), (1325) imply: % 42.93/6.92 | | | | | | | | (1326) all_6_0 = e2 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | COMBINE_EQS: (626), (1326) imply: % 42.93/6.92 | | | | | | | | (1327) all_42_0 = e2 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (43), (1326) imply: % 42.93/6.92 | | | | | | | | (1328) op(all_6_2, e1) = e2 % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | BETA: splitting (117) gives: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1329) ~ (all_42_0 = e2) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | REDUCE: (1327), (1329) imply: % 42.93/6.92 | | | | | | | | | (1330) $false % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | CLOSE: (1330) is inconsistent. % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1331) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1332) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.93/6.92 | | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.93/6.92 | | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.93/6.92 | | | | | | | | | | (509), (510), (511), (513), (1314), (1316), % 42.93/6.92 | | | | | | | | | | (1332), (function-axioms) are inconsistent by % 42.93/6.92 | | | | | | | | | | sub-proof #45. % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1333) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.92 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | BETA: splitting (1333) gives: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | | (1334) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.93/6.92 | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.93/6.92 | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.93/6.92 | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.93/6.92 | | | | | | | | | | | (1328), (1331), (1334), (function-axioms) are % 42.93/6.92 | | | | | | | | | | | inconsistent by sub-proof #31. % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | | (1335) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.92 | | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.92 | | | | | | | | | | | (485), (508), (509), (1309), (1310), (1335), % 42.93/6.92 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | | | #2. % 42.93/6.92 | | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | End of split % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | End of split % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | End of split % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | End of split % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | Case 2: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | (1336) all_24_0 = e0 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | COMBINE_EQS: (603), (1336) imply: % 42.93/6.92 | | | | | | | (1337) all_6_0 = e0 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | COMBINE_EQS: (600), (1337) imply: % 42.93/6.92 | | | | | | | (1338) all_34_0 = e0 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | REDUCE: (1311), (1337) imply: % 42.93/6.92 | | | | | | | (1339) ~ (e3 = e0) % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | REDUCE: (43), (1337) imply: % 42.93/6.92 | | | | | | | (1340) op(all_6_2, e1) = e0 % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | BETA: splitting (100) gives: % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1341) ~ (all_34_0 = e0) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | REDUCE: (1338), (1341) imply: % 42.93/6.92 | | | | | | | | (1342) $false % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | CLOSE: (1342) is inconsistent. % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | (1343) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | BETA: splitting (150) gives: % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1344) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), % 42.93/6.92 | | | | | | | | | (224), (225), (226), (253), (292), (308), (314), % 42.93/6.92 | | | | | | | | | (320), (350), (390), (446), (447), (452), (456), % 42.93/6.92 | | | | | | | | | (457), (465), (467), (469), (489), (506), (508), % 42.93/6.92 | | | | | | | | | (509), (510), (511), (513), (1314), (1316), (1344), % 42.93/6.92 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | #45. % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | (1345) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.93/6.92 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | BETA: splitting (1345) gives: % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 1: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1346) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.93/6.92 | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.93/6.92 | | | | | | | | | | (483), (489), (499), (507), (510), (602), (1340), % 42.93/6.92 | | | | | | | | | | (1343), (1346), (function-axioms) are inconsistent % 42.93/6.92 | | | | | | | | | | by sub-proof #25. % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | Case 2: % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | (1347) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.92 | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.92 | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.92 | | | | | | | | | | (485), (508), (509), (1309), (1310), (1347), % 42.93/6.92 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.92 | | | | | | | | | | #2. % 42.93/6.92 | | | | | | | | | | % 42.93/6.92 | | | | | | | | | End of split % 42.93/6.92 | | | | | | | | | % 42.93/6.92 | | | | | | | | End of split % 42.93/6.92 | | | | | | | | % 42.93/6.92 | | | | | | | End of split % 42.93/6.92 | | | | | | | % 42.93/6.92 | | | | | | End of split % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | Case 2: % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | (1348) all_16_0 = e1 % 42.93/6.92 | | | | | | % 42.93/6.92 | | | | | | COMBINE_EQS: (616), (1348) imply: % 42.93/6.93 | | | | | | (1349) all_8_0 = e1 % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | SIMP: (1349) implies: % 42.93/6.93 | | | | | | (1350) all_8_0 = e1 % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | COMBINE_EQS: (569), (1350) imply: % 42.93/6.93 | | | | | | (1351) all_26_0 = e1 % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | REDUCE: (1312), (1350) imply: % 42.93/6.93 | | | | | | (1352) ~ (e3 = e1) % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | REDUCE: (48), (1350) imply: % 42.93/6.93 | | | | | | (1353) op(all_8_2, e2) = e1 % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | BETA: splitting (84) gives: % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | Case 1: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | (1354) ~ (all_26_0 = e1) % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | REDUCE: (1351), (1354) imply: % 42.93/6.93 | | | | | | | (1355) $false % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | CLOSE: (1355) is inconsistent. % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | Case 2: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | (1356) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | BETA: splitting (79) gives: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1357) ~ (all_24_0 = e0) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | REDUCE: (603), (1357) imply: % 42.93/6.93 | | | | | | | | (1358) ~ (all_6_0 = e0) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | BETA: splitting (107) gives: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1359) ~ (all_38_0 = e2) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | REDUCE: (580), (1359) imply: % 42.93/6.93 | | | | | | | | | (1360) ~ (all_6_0 = e2) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1361) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.93/6.93 | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.93/6.93 | | | | | | | | | | (497), (503), (504), (506), (513), (589), (1353), % 42.93/6.93 | | | | | | | | | | (1356), (1361), (function-axioms) are inconsistent % 42.93/6.93 | | | | | | | | | | by sub-proof #17. % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1362) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.93 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | BETA: splitting (1362) gives: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1363) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.93/6.93 | | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.93/6.93 | | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.93/6.93 | | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.93/6.93 | | | | | | | | | | | (508), (510), (1358), (1360), (1363), % 42.93/6.93 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | | #35. % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1364) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.93 | | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.93 | | | | | | | | | | | (485), (508), (509), (1309), (1310), (1364), % 42.93/6.93 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | | #2. % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1365) all_38_0 = e2 % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | COMBINE_EQS: (580), (1365) imply: % 42.93/6.93 | | | | | | | | | (1366) all_6_0 = e2 % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | SIMP: (1366) implies: % 42.93/6.93 | | | | | | | | | (1367) all_6_0 = e2 % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | COMBINE_EQS: (626), (1367) imply: % 42.93/6.93 | | | | | | | | | (1368) all_42_0 = e2 % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | REDUCE: (43), (1367) imply: % 42.93/6.93 | | | | | | | | | (1369) op(all_6_2, e1) = e2 % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | BETA: splitting (117) gives: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1370) ~ (all_42_0 = e2) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | REDUCE: (1368), (1370) imply: % 42.93/6.93 | | | | | | | | | | (1371) $false % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | CLOSE: (1371) is inconsistent. % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1372) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1373) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.93/6.93 | | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.93/6.93 | | | | | | | | | | | (497), (503), (504), (506), (513), (589), (1353), % 42.93/6.93 | | | | | | | | | | | (1356), (1373), (function-axioms) are inconsistent % 42.93/6.93 | | | | | | | | | | | by sub-proof #18. % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1374) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.93 | | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | BETA: splitting (1374) gives: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | | (1375) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.93/6.93 | | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.93/6.93 | | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.93/6.93 | | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.93/6.93 | | | | | | | | | | | | (1369), (1372), (1375), (function-axioms) are % 42.93/6.93 | | | | | | | | | | | | inconsistent by sub-proof #31. % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | | (1376) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.93 | | | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.93 | | | | | | | | | | | | (485), (508), (509), (1309), (1310), (1376), % 42.93/6.93 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | | | #2. % 42.93/6.93 | | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | End of split % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1377) all_24_0 = e0 % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | COMBINE_EQS: (603), (1377) imply: % 42.93/6.93 | | | | | | | | (1378) all_6_0 = e0 % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | SIMP: (1378) implies: % 42.93/6.93 | | | | | | | | (1379) all_6_0 = e0 % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | COMBINE_EQS: (600), (1379) imply: % 42.93/6.93 | | | | | | | | (1380) all_34_0 = e0 % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | REDUCE: (1311), (1379) imply: % 42.93/6.93 | | | | | | | | (1381) ~ (e3 = e0) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | REDUCE: (43), (1379) imply: % 42.93/6.93 | | | | | | | | (1382) op(all_6_2, e1) = e0 % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | BETA: splitting (100) gives: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1383) ~ (all_34_0 = e0) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | REDUCE: (1380), (1383) imply: % 42.93/6.93 | | | | | | | | | (1384) $false % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | CLOSE: (1384) is inconsistent. % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1385) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1386) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 42.93/6.93 | | | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 42.93/6.93 | | | | | | | | | | (497), (503), (504), (506), (513), (589), (1353), % 42.93/6.93 | | | | | | | | | | (1356), (1386), (function-axioms) are inconsistent % 42.93/6.93 | | | | | | | | | | by sub-proof #18. % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1387) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.93 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | BETA: splitting (1387) gives: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1388) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 42.93/6.93 | | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 42.93/6.93 | | | | | | | | | | | (483), (489), (499), (507), (510), (602), (1382), % 42.93/6.93 | | | | | | | | | | | (1385), (1388), (function-axioms) are inconsistent % 42.93/6.93 | | | | | | | | | | | by sub-proof #25. % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | (1389) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.93 | | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.93 | | | | | | | | | | | (485), (508), (509), (1309), (1310), (1389), % 42.93/6.93 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | | #2. % 42.93/6.93 | | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | End of split % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | End of split % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | End of split % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | End of split % 42.93/6.93 | | | | | % 42.93/6.93 | | | | Case 2: % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | (1390) all_14_0 = e0 % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | COMBINE_EQS: (622), (1390) imply: % 42.93/6.93 | | | | | (1391) all_8_0 = e0 % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | SIMP: (1391) implies: % 42.93/6.93 | | | | | (1392) all_8_0 = e0 % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | COMBINE_EQS: (628), (1392) imply: % 42.93/6.93 | | | | | (1393) all_50_0 = e0 % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | REDUCE: (1312), (1392) imply: % 42.93/6.93 | | | | | (1394) ~ (e3 = e0) % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | REDUCE: (48), (1392) imply: % 42.93/6.93 | | | | | (1395) op(all_8_2, e2) = e0 % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | BETA: splitting (79) gives: % 42.93/6.93 | | | | | % 42.93/6.93 | | | | | Case 1: % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | (1396) ~ (all_24_0 = e0) % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | REDUCE: (603), (1396) imply: % 42.93/6.93 | | | | | | (1397) ~ (all_6_0 = e0) % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | BETA: splitting (107) gives: % 42.93/6.93 | | | | | | % 42.93/6.93 | | | | | | Case 1: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | (1398) ~ (all_38_0 = e2) % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | REDUCE: (580), (1398) imply: % 42.93/6.93 | | | | | | | (1399) ~ (all_6_0 = e2) % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | BETA: splitting (132) gives: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1400) ~ (all_50_0 = e0) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | REDUCE: (1393), (1400) imply: % 42.93/6.93 | | | | | | | | (1401) $false % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | CLOSE: (1401) is inconsistent. % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1402) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | BETA: splitting (150) gives: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1403) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.93/6.93 | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.93/6.93 | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.93/6.93 | | | | | | | | | (503), (506), (509), (513), (627), (1395), (1402), % 42.93/6.93 | | | | | | | | | (1403), (function-axioms) are inconsistent by % 42.93/6.93 | | | | | | | | | sub-proof #13. % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | (1404) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 42.93/6.93 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | BETA: splitting (1404) gives: % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1405) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 42.93/6.93 | | | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 42.93/6.93 | | | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 42.93/6.93 | | | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 42.93/6.93 | | | | | | | | | | (508), (510), (1397), (1399), (1405), % 42.93/6.93 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | #35. % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | (1406) all_52_15 = e3 & ~ (all_52_14 = e0) % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 42.93/6.93 | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 42.93/6.93 | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 42.93/6.93 | | | | | | | | | | (485), (508), (509), (1309), (1310), (1406), % 42.93/6.93 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 42.93/6.93 | | | | | | | | | | #2. % 42.93/6.93 | | | | | | | | | | % 42.93/6.93 | | | | | | | | | End of split % 42.93/6.93 | | | | | | | | | % 42.93/6.93 | | | | | | | | End of split % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | End of split % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | Case 2: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | (1407) all_38_0 = e2 % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | COMBINE_EQS: (580), (1407) imply: % 42.93/6.93 | | | | | | | (1408) all_6_0 = e2 % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | COMBINE_EQS: (626), (1408) imply: % 42.93/6.93 | | | | | | | (1409) all_42_0 = e2 % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | REDUCE: (43), (1408) imply: % 42.93/6.93 | | | | | | | (1410) op(all_6_2, e1) = e2 % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | BETA: splitting (117) gives: % 42.93/6.93 | | | | | | | % 42.93/6.93 | | | | | | | Case 1: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1411) ~ (all_42_0 = e2) % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | REDUCE: (1409), (1411) imply: % 42.93/6.93 | | | | | | | | (1412) $false % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | CLOSE: (1412) is inconsistent. % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | Case 2: % 42.93/6.93 | | | | | | | | % 42.93/6.93 | | | | | | | | (1413) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 42.93/6.94 | | | | | | | | % 42.93/6.94 | | | | | | | | BETA: splitting (132) gives: % 42.93/6.94 | | | | | | | | % 42.93/6.94 | | | | | | | | Case 1: % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | (1414) ~ (all_50_0 = e0) % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | REDUCE: (1393), (1414) imply: % 42.93/6.94 | | | | | | | | | (1415) $false % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | CLOSE: (1415) is inconsistent. % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | Case 2: % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | (1416) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | BETA: splitting (150) gives: % 42.93/6.94 | | | | | | | | | % 42.93/6.94 | | | | | | | | | Case 1: % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | (1417) all_52_11 = e3 & ~ (all_52_10 = e2) % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 42.93/6.94 | | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 42.93/6.94 | | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 42.93/6.94 | | | | | | | | | | (503), (506), (509), (513), (627), (1395), (1416), % 42.93/6.94 | | | | | | | | | | (1417), (function-axioms) are inconsistent by % 42.93/6.94 | | | | | | | | | | sub-proof #14. % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | Case 2: % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | (1418) (all_52_13 = e3 & ~ (all_52_12 = e1)) | % 42.93/6.94 | | | | | | | | | | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | BETA: splitting (1418) gives: % 42.93/6.94 | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | Case 1: % 42.93/6.94 | | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | | (1419) all_52_13 = e3 & ~ (all_52_12 = e1) % 42.93/6.94 | | | | | | | | | | | % 42.93/6.94 | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 42.93/6.94 | | | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 42.93/6.94 | | | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 42.93/6.94 | | | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 42.93/6.94 | | | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 42.93/6.94 | | | | | | | | | | | (1410), (1413), (1419), (function-axioms) are % 42.93/6.94 | | | | | | | | | | | inconsistent by sub-proof #31. % 42.93/6.94 | | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | | (1420) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.94 | | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.94 | | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.94 | | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.94 | | | | | | | | | | | (485), (508), (509), (1309), (1310), (1420), % 43.11/6.94 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 43.11/6.94 | | | | | | | | | | | #2. % 43.11/6.94 | | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | End of split % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | End of split % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | End of split % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | End of split % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | End of split % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | Case 2: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | (1421) all_24_0 = e0 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | COMBINE_EQS: (603), (1421) imply: % 43.11/6.94 | | | | | | (1422) all_6_0 = e0 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | COMBINE_EQS: (600), (1422) imply: % 43.11/6.94 | | | | | | (1423) all_34_0 = e0 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | REDUCE: (43), (1422) imply: % 43.11/6.94 | | | | | | (1424) op(all_6_2, e1) = e0 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | BETA: splitting (100) gives: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | Case 1: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1425) ~ (all_34_0 = e0) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | REDUCE: (1423), (1425) imply: % 43.11/6.94 | | | | | | | (1426) $false % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | CLOSE: (1426) is inconsistent. % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | Case 2: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1427) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | BETA: splitting (132) gives: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1428) ~ (all_50_0 = e0) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | REDUCE: (1393), (1428) imply: % 43.11/6.94 | | | | | | | | (1429) $false % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | CLOSE: (1429) is inconsistent. % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1430) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | BETA: splitting (150) gives: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | (1431) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 43.11/6.94 | | | | | | | | | (227), (252), (292), (320), (356), (390), (445), % 43.11/6.94 | | | | | | | | | (446), (447), (452), (456), (457), (478), (498), % 43.11/6.94 | | | | | | | | | (503), (506), (509), (513), (627), (1395), (1430), % 43.11/6.94 | | | | | | | | | (1431), (function-axioms) are inconsistent by % 43.11/6.94 | | | | | | | | | sub-proof #14. % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | (1432) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 % 43.11/6.94 | | | | | | | | | = e3 & ~ (all_52_14 = e0)) % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | BETA: splitting (1432) gives: % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | (1433) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 43.11/6.94 | | | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 43.11/6.94 | | | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 43.11/6.94 | | | | | | | | | | (483), (489), (499), (507), (510), (602), (1424), % 43.11/6.94 | | | | | | | | | | (1427), (1433), (function-axioms) are inconsistent % 43.11/6.94 | | | | | | | | | | by sub-proof #25. % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | (1434) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.94 | | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.94 | | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.94 | | | | | | | | | | (485), (508), (509), (1309), (1310), (1434), % 43.11/6.94 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 43.11/6.94 | | | | | | | | | | #2. % 43.11/6.94 | | | | | | | | | | % 43.11/6.94 | | | | | | | | | End of split % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | End of split % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | End of split % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | End of split % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | End of split % 43.11/6.94 | | | | | % 43.11/6.94 | | | | End of split % 43.11/6.94 | | | | % 43.11/6.94 | | | Case 2: % 43.11/6.94 | | | | % 43.11/6.94 | | | | (1435) all_8_0 = e3 % 43.11/6.94 | | | | % 43.11/6.94 | | | | REDUCE: (48), (1435) imply: % 43.11/6.94 | | | | (1436) op(all_8_2, e2) = e3 % 43.11/6.94 | | | | % 43.11/6.94 | | | | BETA: splitting (79) gives: % 43.11/6.94 | | | | % 43.11/6.94 | | | | Case 1: % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | (1437) ~ (all_24_0 = e0) % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | REDUCE: (603), (1437) imply: % 43.11/6.94 | | | | | (1438) ~ (all_6_0 = e0) % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | BETA: splitting (107) gives: % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | Case 1: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | (1439) ~ (all_38_0 = e2) % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | REDUCE: (580), (1439) imply: % 43.11/6.94 | | | | | | (1440) ~ (all_6_0 = e2) % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | BETA: splitting (150) gives: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | Case 1: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1441) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | ALPHA: (1441) implies: % 43.11/6.94 | | | | | | | (1442) all_52_11 = e3 % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | COMBINE_EQS: (447), (1442) imply: % 43.11/6.94 | | | | | | | (1443) all_8_2 = e3 % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | REF_CLOSE: (148), (506), (1436), (1443), (function-axioms) are % 43.11/6.94 | | | | | | | inconsistent by sub-proof #10. % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | Case 2: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1444) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 % 43.11/6.94 | | | | | | | & ~ (all_52_14 = e0)) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | BETA: splitting (1444) gives: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1445) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | REF_CLOSE: (5), (7), (9), (43), (147), (151), (152), (153), % 43.11/6.94 | | | | | | | | (225), (226), (228), (231), (253), (292), (308), % 43.11/6.94 | | | | | | | | (320), (333), (335), (350), (390), (446), (447), % 43.11/6.94 | | | | | | | | (452), (456), (457), (459), (465), (467), (469), % 43.11/6.94 | | | | | | | | (470), (472), (487), (489), (500), (502), (507), % 43.11/6.94 | | | | | | | | (508), (510), (1438), (1440), (1445), % 43.11/6.94 | | | | | | | | (function-axioms) are inconsistent by sub-proof #35. % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1446) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.94 | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.94 | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.94 | | | | | | | | (485), (508), (509), (1309), (1310), (1446), % 43.11/6.94 | | | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | End of split % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | End of split % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | Case 2: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | (1447) all_38_0 = e2 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | COMBINE_EQS: (580), (1447) imply: % 43.11/6.94 | | | | | | (1448) all_6_0 = e2 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | SIMP: (1448) implies: % 43.11/6.94 | | | | | | (1449) all_6_0 = e2 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | COMBINE_EQS: (626), (1449) imply: % 43.11/6.94 | | | | | | (1450) all_42_0 = e2 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | REDUCE: (43), (1449) imply: % 43.11/6.94 | | | | | | (1451) op(all_6_2, e1) = e2 % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | BETA: splitting (117) gives: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | Case 1: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1452) ~ (all_42_0 = e2) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | REDUCE: (1450), (1452) imply: % 43.11/6.94 | | | | | | | (1453) $false % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | CLOSE: (1453) is inconsistent. % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | Case 2: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1454) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | BETA: splitting (150) gives: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1455) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | REF_CLOSE: (148), (447), (506), (1436), (1455), % 43.11/6.94 | | | | | | | | (function-axioms) are inconsistent by sub-proof #9. % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1456) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 43.11/6.94 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | BETA: splitting (1456) gives: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | (1457) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | REF_CLOSE: (4), (7), (42), (141), (147), (151), (152), (153), % 43.11/6.94 | | | | | | | | | (229), (249), (253), (268), (286), (287), (292), % 43.11/6.94 | | | | | | | | | (320), (370), (390), (446), (447), (452), (453), % 43.11/6.94 | | | | | | | | | (454), (456), (457), (463), (469), (479), (483), % 43.11/6.94 | | | | | | | | | (489), (491), (494), (499), (510), (511), (550), % 43.11/6.94 | | | | | | | | | (1451), (1454), (1457), (function-axioms) are % 43.11/6.94 | | | | | | | | | inconsistent by sub-proof #31. % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | Case 2: % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | (1458) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.94 | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.94 | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.94 | | | | | | | | | (485), (508), (509), (1309), (1310), (1458), % 43.11/6.94 | | | | | | | | | (function-axioms) are inconsistent by sub-proof #1. % 43.11/6.94 | | | | | | | | | % 43.11/6.94 | | | | | | | | End of split % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | End of split % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | End of split % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | End of split % 43.11/6.94 | | | | | % 43.11/6.94 | | | | Case 2: % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | (1459) all_24_0 = e0 % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | COMBINE_EQS: (603), (1459) imply: % 43.11/6.94 | | | | | (1460) all_6_0 = e0 % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | SIMP: (1460) implies: % 43.11/6.94 | | | | | (1461) all_6_0 = e0 % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | COMBINE_EQS: (600), (1461) imply: % 43.11/6.94 | | | | | (1462) all_34_0 = e0 % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | REDUCE: (43), (1461) imply: % 43.11/6.94 | | | | | (1463) op(all_6_2, e1) = e0 % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | BETA: splitting (100) gives: % 43.11/6.94 | | | | | % 43.11/6.94 | | | | | Case 1: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | (1464) ~ (all_34_0 = e0) % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | REDUCE: (1462), (1464) imply: % 43.11/6.94 | | | | | | (1465) $false % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | CLOSE: (1465) is inconsistent. % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | Case 2: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | (1466) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | BETA: splitting (150) gives: % 43.11/6.94 | | | | | | % 43.11/6.94 | | | | | | Case 1: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1467) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | REF_CLOSE: (148), (447), (506), (1436), (1467), (function-axioms) % 43.11/6.94 | | | | | | | are inconsistent by sub-proof #9. % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | Case 2: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | (1468) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 % 43.11/6.94 | | | | | | | & ~ (all_52_14 = e0)) % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | BETA: splitting (1468) gives: % 43.11/6.94 | | | | | | | % 43.11/6.94 | | | | | | | Case 1: % 43.11/6.94 | | | | | | | | % 43.11/6.94 | | | | | | | | (1469) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.94 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (6), (9), (42), (141), (147), (151), (152), (153), % 43.11/6.95 | | | | | | | | (229), (251), (252), (287), (292), (320), (390), % 43.11/6.95 | | | | | | | | (424), (446), (447), (452), (456), (457), (479), % 43.11/6.95 | | | | | | | | (483), (489), (499), (507), (510), (602), (1463), % 43.11/6.95 | | | | | | | | (1466), (1469), (function-axioms) are inconsistent by % 43.11/6.95 | | | | | | | | sub-proof #25. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | Case 2: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1470) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.95 | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.95 | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.95 | | | | | | | | (485), (508), (509), (1309), (1310), (1470), % 43.11/6.95 | | | | | | | | (function-axioms) are inconsistent by sub-proof #1. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | End of split % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | End of split % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | End of split % 43.11/6.95 | | | | | % 43.11/6.95 | | | | End of split % 43.11/6.95 | | | | % 43.11/6.95 | | | End of split % 43.11/6.95 | | | % 43.11/6.95 | | Case 2: % 43.11/6.95 | | | % 43.11/6.95 | | | (1471) all_6_0 = e3 % 43.11/6.95 | | | % 43.11/6.95 | | | REDUCE: (43), (1471) imply: % 43.11/6.95 | | | (1472) op(all_6_2, e1) = e3 % 43.11/6.95 | | | % 43.11/6.95 | | | BETA: splitting (49) gives: % 43.11/6.95 | | | % 43.11/6.95 | | | Case 1: % 43.11/6.95 | | | | % 43.11/6.95 | | | | (1473) ~ (all_8_0 = e3) % 43.11/6.95 | | | | % 43.11/6.95 | | | | BETA: splitting (61) gives: % 43.11/6.95 | | | | % 43.11/6.95 | | | | Case 1: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | (1474) ~ (all_14_0 = e0) % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | REDUCE: (622), (1474) imply: % 43.11/6.95 | | | | | (1475) ~ (all_8_0 = e0) % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | BETA: splitting (66) gives: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | Case 1: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1476) ~ (all_16_0 = e1) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (616), (1476) imply: % 43.11/6.95 | | | | | | (1477) ~ (all_8_0 = e1) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | BETA: splitting (150) gives: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | Case 1: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1478) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | REF_CLOSE: (4), (7), (8), (48), (148), (151), (152), (153), (224), % 43.11/6.95 | | | | | | | (225), (226), (253), (292), (308), (314), (320), (350), % 43.11/6.95 | | | | | | | (390), (446), (447), (452), (456), (457), (465), (467), % 43.11/6.95 | | | | | | | (469), (489), (506), (508), (509), (510), (511), (513), % 43.11/6.95 | | | | | | | (1475), (1477), (1478), (function-axioms) are % 43.11/6.95 | | | | | | | inconsistent by sub-proof #65. % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | Case 2: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1479) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 % 43.11/6.95 | | | | | | | & ~ (all_52_14 = e0)) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | BETA: splitting (1479) gives: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | Case 1: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1480) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | ALPHA: (1480) implies: % 43.11/6.95 | | | | | | | | (1481) all_52_13 = e3 % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | COMBINE_EQS: (446), (1481) imply: % 43.11/6.95 | | | | | | | | (1482) all_6_2 = e3 % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (147), (489), (1472), (1482), (function-axioms) are % 43.11/6.95 | | | | | | | | inconsistent by sub-proof #8. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | Case 2: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1483) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.95 | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.95 | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.95 | | | | | | | | (485), (508), (509), (1309), (1310), (1483), % 43.11/6.95 | | | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | End of split % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | End of split % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | Case 2: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1484) all_16_0 = e1 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | COMBINE_EQS: (616), (1484) imply: % 43.11/6.95 | | | | | | (1485) all_8_0 = e1 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | COMBINE_EQS: (569), (1485) imply: % 43.11/6.95 | | | | | | (1486) all_26_0 = e1 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (1473), (1485) imply: % 43.11/6.95 | | | | | | (1487) ~ (e3 = e1) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (48), (1485) imply: % 43.11/6.95 | | | | | | (1488) op(all_8_2, e2) = e1 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | BETA: splitting (84) gives: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | Case 1: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1489) ~ (all_26_0 = e1) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | REDUCE: (1486), (1489) imply: % 43.11/6.95 | | | | | | | (1490) $false % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | CLOSE: (1490) is inconsistent. % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | Case 2: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1491) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | BETA: splitting (150) gives: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | Case 1: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1492) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (5), (7), (47), (145), (148), (151), (152), (153), % 43.11/6.95 | | | | | | | | (227), (250), (286), (320), (356), (390), (442), % 43.11/6.95 | | | | | | | | (446), (447), (451), (455), (456), (465), (493), % 43.11/6.95 | | | | | | | | (497), (503), (504), (506), (513), (589), (1488), % 43.11/6.95 | | | | | | | | (1491), (1492), (function-axioms) are inconsistent by % 43.11/6.95 | | | | | | | | sub-proof #18. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | Case 2: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1493) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = % 43.11/6.95 | | | | | | | | e3 & ~ (all_52_14 = e0)) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | BETA: splitting (1493) gives: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | Case 1: % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | | (1494) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | | REF_CLOSE: (147), (446), (489), (1472), (1494), % 43.11/6.95 | | | | | | | | | (function-axioms) are inconsistent by sub-proof #7. % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | Case 2: % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | | (1495) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.95 | | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.95 | | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.95 | | | | | | | | | (485), (508), (509), (1309), (1310), (1495), % 43.11/6.95 | | | | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 43.11/6.95 | | | | | | | | | % 43.11/6.95 | | | | | | | | End of split % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | End of split % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | End of split % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | End of split % 43.11/6.95 | | | | | % 43.11/6.95 | | | | Case 2: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | (1496) all_14_0 = e0 % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | COMBINE_EQS: (622), (1496) imply: % 43.11/6.95 | | | | | (1497) all_8_0 = e0 % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | SIMP: (1497) implies: % 43.11/6.95 | | | | | (1498) all_8_0 = e0 % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | COMBINE_EQS: (628), (1498) imply: % 43.11/6.95 | | | | | (1499) all_50_0 = e0 % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | REDUCE: (48), (1498) imply: % 43.11/6.95 | | | | | (1500) op(all_8_2, e2) = e0 % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | BETA: splitting (132) gives: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | Case 1: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1501) ~ (all_50_0 = e0) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (1499), (1501) imply: % 43.11/6.95 | | | | | | (1502) $false % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | CLOSE: (1502) is inconsistent. % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | Case 2: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1503) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | BETA: splitting (150) gives: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | Case 1: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1504) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | REF_CLOSE: (6), (8), (47), (145), (148), (151), (152), (153), % 43.11/6.95 | | | | | | | (227), (252), (292), (320), (356), (390), (445), (446), % 43.11/6.95 | | | | | | | (447), (452), (456), (457), (478), (498), (503), (506), % 43.11/6.95 | | | | | | | (509), (513), (627), (1500), (1503), (1504), % 43.11/6.95 | | | | | | | (function-axioms) are inconsistent by sub-proof #14. % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | Case 2: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | (1505) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 % 43.11/6.95 | | | | | | | & ~ (all_52_14 = e0)) % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | BETA: splitting (1505) gives: % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | | Case 1: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1506) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (147), (446), (489), (1472), (1506), % 43.11/6.95 | | | | | | | | (function-axioms) are inconsistent by sub-proof #7. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | Case 2: % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | (1507) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | | REF_CLOSE: (4), (8), (37), (137), (146), (151), (152), (153), % 43.11/6.95 | | | | | | | | (230), (249), (268), (286), (320), (360), (390), % 43.11/6.95 | | | | | | | | (446), (447), (453), (454), (461), (469), (474), % 43.11/6.95 | | | | | | | | (485), (508), (509), (1309), (1310), (1507), % 43.11/6.95 | | | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 43.11/6.95 | | | | | | | | % 43.11/6.95 | | | | | | | End of split % 43.11/6.95 | | | | | | | % 43.11/6.95 | | | | | | End of split % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | End of split % 43.11/6.95 | | | | | % 43.11/6.95 | | | | End of split % 43.11/6.95 | | | | % 43.11/6.95 | | | Case 2: % 43.11/6.95 | | | | % 43.11/6.95 | | | | (1508) all_8_0 = e3 % 43.11/6.95 | | | | % 43.11/6.95 | | | | REDUCE: (48), (1508) imply: % 43.11/6.95 | | | | (1509) op(all_8_2, e2) = e3 % 43.11/6.95 | | | | % 43.11/6.95 | | | | BETA: splitting (150) gives: % 43.11/6.95 | | | | % 43.11/6.95 | | | | Case 1: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | (1510) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | REF_CLOSE: (148), (447), (506), (1509), (1510), (function-axioms) are % 43.11/6.95 | | | | | inconsistent by sub-proof #9. % 43.11/6.95 | | | | | % 43.11/6.95 | | | | Case 2: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | (1511) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & % 43.11/6.95 | | | | | ~ (all_52_14 = e0)) % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | BETA: splitting (1511) gives: % 43.11/6.95 | | | | | % 43.11/6.95 | | | | | Case 1: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1512) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | ALPHA: (1512) implies: % 43.11/6.95 | | | | | | (1513) all_52_13 = e3 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | COMBINE_EQS: (446), (1513) imply: % 43.11/6.95 | | | | | | (1514) all_6_2 = e3 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REF_CLOSE: (147), (489), (1472), (1514), (function-axioms) are % 43.11/6.95 | | | | | | inconsistent by sub-proof #8. % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | Case 2: % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | (1515) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | ALPHA: (1515) implies: % 43.11/6.95 | | | | | | (1516) all_52_15 = e3 % 43.11/6.95 | | | | | | (1517) ~ (all_52_14 = e0) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | COMBINE_EQS: (390), (1516) imply: % 43.11/6.95 | | | | | | (1518) all_4_2 = e3 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (469), (1518) imply: % 43.11/6.95 | | | | | | (1519) ~ (all_52_0 = e3) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (461), (1518) imply: % 43.11/6.95 | | | | | | (1520) ~ (all_52_14 = e3) % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (1310), (1518) imply: % 43.11/6.95 | | | | | | (1521) op(e3, e0) = e2 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REDUCE: (37), (1518) imply: % 43.11/6.95 | | | | | | (1522) op(e0, e3) = all_4_1 % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | | REF_CLOSE: (4), (8), (137), (146), (151), (152), (153), (230), % 43.11/6.95 | | | | | | (249), (268), (286), (320), (360), (446), (447), (453), % 43.11/6.95 | | | | | | (454), (474), (485), (508), (509), (1309), (1516), % 43.11/6.95 | | | | | | (1517), (1518), (1519), (1520), (1521), (1522), % 43.11/6.95 | | | | | | (function-axioms) are inconsistent by sub-proof #4. % 43.11/6.95 | | | | | | % 43.11/6.95 | | | | | End of split % 43.11/6.95 | | | | | % 43.11/6.95 | | | | End of split % 43.11/6.95 | | | | % 43.11/6.95 | | | End of split % 43.11/6.95 | | | % 43.11/6.95 | | End of split % 43.11/6.95 | | % 43.11/6.95 | End of split % 43.11/6.95 | % 43.11/6.95 End of proof % 43.11/6.95 % 43.11/6.95 Sub-proof #1 shows that the following formulas are inconsistent: % 43.11/6.95 ---------------------------------------------------------------- % 43.11/6.95 (1) ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 43.11/6.95 (2) all_58_9 = all_52_6 % 43.11/6.95 (3) op(e0, all_4_2) = all_4_1 % 43.11/6.95 (4) ~ (all_52_8 = all_52_14) % 43.11/6.95 (5) ~ (all_52_0 = all_52_6) % 43.11/6.95 (6) ~ (all_52_14 = all_4_2) % 43.11/6.95 (7) all_58_7 = all_52_7 % 43.11/6.95 (8) op(all_4_2, e0) = e2 % 43.11/6.95 (9) ~ (e3 = e1) % 43.11/6.95 (10) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.95 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.95 (11) op(e3, e0) = all_52_0 % 43.11/6.95 (12) all_52_11 = all_8_2 % 43.11/6.95 (13) op(e0, e3) = all_52_14 % 43.11/6.95 (14) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.95 (15) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.95 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.95 (16) all_56_3 = all_52_14 % 43.11/6.95 (17) all_52_9 = all_10_2 % 43.11/6.95 (18) all_52_13 = all_6_2 % 43.11/6.95 (19) ~ (all_52_0 = all_4_2) % 43.11/6.95 (20) all_58_6 = all_8_2 % 43.11/6.95 (21) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/6.95 (22) ~ (e1 = e0) % 43.11/6.95 (23) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.95 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.95 (24) ~ (all_52_0 = all_10_2) % 43.11/6.95 (25) ~ (all_52_7 = all_6_2) % 43.11/6.95 (26) all_58_8 = all_52_8 % 43.11/6.95 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.96 (28) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.96 (29) all_52_15 = all_4_2 % 43.11/6.96 % 43.11/6.96 Begin of proof % 43.11/6.96 | % 43.11/6.96 | ALPHA: (14) implies: % 43.11/6.96 | (30) all_52_15 = e3 % 43.11/6.96 | (31) ~ (all_52_14 = e0) % 43.11/6.96 | % 43.11/6.96 | COMBINE_EQS: (29), (30) imply: % 43.11/6.96 | (32) all_4_2 = e3 % 43.11/6.96 | % 43.11/6.96 | SIMP: (32) implies: % 43.11/6.96 | (33) all_4_2 = e3 % 43.11/6.96 | % 43.11/6.96 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.11/6.96 | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.11/6.96 | (25), (26), (27), (28), (30), (31), (33) are inconsistent by % 43.11/6.96 | sub-proof #3. % 43.11/6.96 | % 43.11/6.96 End of proof % 43.11/6.96 % 43.11/6.96 Sub-proof #2 shows that the following formulas are inconsistent: % 43.11/6.96 ---------------------------------------------------------------- % 43.11/6.96 (1) ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 43.11/6.96 (2) all_58_9 = all_52_6 % 43.11/6.96 (3) op(e0, all_4_2) = all_4_1 % 43.11/6.96 (4) ~ (all_52_8 = all_52_14) % 43.11/6.96 (5) ~ (all_52_0 = all_52_6) % 43.11/6.96 (6) ~ (all_52_14 = all_4_2) % 43.11/6.96 (7) all_58_7 = all_52_7 % 43.11/6.96 (8) op(all_4_2, e0) = e2 % 43.11/6.96 (9) ~ (e3 = e1) % 43.11/6.96 (10) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.96 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.96 (11) op(e3, e0) = all_52_0 % 43.11/6.96 (12) all_52_11 = all_8_2 % 43.11/6.96 (13) op(e0, e3) = all_52_14 % 43.11/6.96 (14) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.96 (15) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.96 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.96 (16) all_56_3 = all_52_14 % 43.11/6.96 (17) all_52_9 = all_10_2 % 43.11/6.96 (18) all_52_13 = all_6_2 % 43.11/6.96 (19) ~ (all_52_0 = all_4_2) % 43.11/6.96 (20) all_58_6 = all_8_2 % 43.11/6.96 (21) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/6.96 (22) ~ (e1 = e0) % 43.11/6.96 (23) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.96 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.96 (24) ~ (all_52_0 = all_10_2) % 43.11/6.96 (25) ~ (all_52_7 = all_6_2) % 43.11/6.96 (26) all_58_8 = all_52_8 % 43.11/6.96 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.96 (28) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.96 (29) all_52_15 = all_4_2 % 43.11/6.96 % 43.11/6.96 Begin of proof % 43.11/6.96 | % 43.11/6.96 | ALPHA: (14) implies: % 43.11/6.96 | (30) all_52_15 = e3 % 43.11/6.96 | (31) ~ (all_52_14 = e0) % 43.11/6.96 | % 43.11/6.96 | COMBINE_EQS: (29), (30) imply: % 43.11/6.96 | (32) all_4_2 = e3 % 43.11/6.96 | % 43.11/6.96 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.11/6.96 | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.11/6.96 | (25), (26), (27), (28), (30), (31), (32) are inconsistent by % 43.11/6.96 | sub-proof #3. % 43.11/6.96 | % 43.11/6.96 End of proof % 43.11/6.96 % 43.11/6.96 Sub-proof #3 shows that the following formulas are inconsistent: % 43.11/6.96 ---------------------------------------------------------------- % 43.11/6.96 (1) ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 43.11/6.96 (2) all_58_9 = all_52_6 % 43.11/6.96 (3) op(e0, all_4_2) = all_4_1 % 43.11/6.96 (4) ~ (all_52_8 = all_52_14) % 43.11/6.96 (5) ~ (all_52_0 = all_52_6) % 43.11/6.96 (6) ~ (all_52_14 = all_4_2) % 43.11/6.96 (7) all_58_7 = all_52_7 % 43.11/6.96 (8) op(all_4_2, e0) = e2 % 43.11/6.96 (9) ~ (e3 = e1) % 43.11/6.96 (10) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.96 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.96 (11) op(e3, e0) = all_52_0 % 43.11/6.96 (12) all_52_11 = all_8_2 % 43.11/6.96 (13) op(e0, e3) = all_52_14 % 43.11/6.96 (14) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.96 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.96 (15) all_56_3 = all_52_14 % 43.11/6.96 (16) all_52_9 = all_10_2 % 43.11/6.96 (17) all_52_13 = all_6_2 % 43.11/6.96 (18) ~ (all_52_0 = all_4_2) % 43.11/6.96 (19) all_4_2 = e3 % 43.11/6.96 (20) all_58_6 = all_8_2 % 43.11/6.96 (21) ~ (all_52_14 = e0) % 43.11/6.96 (22) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/6.96 (23) ~ (e1 = e0) % 43.11/6.96 (24) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.96 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.96 (25) ~ (all_52_0 = all_10_2) % 43.11/6.96 (26) ~ (all_52_7 = all_6_2) % 43.11/6.96 (27) all_58_8 = all_52_8 % 43.11/6.96 (28) all_52_15 = e3 % 43.11/6.96 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.96 (30) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.96 % 43.11/6.96 Begin of proof % 43.11/6.96 | % 43.11/6.96 | REDUCE: (18), (19) imply: % 43.11/6.96 | (31) ~ (all_52_0 = e3) % 43.11/6.96 | % 43.11/6.96 | REDUCE: (6), (19) imply: % 43.11/6.96 | (32) ~ (all_52_14 = e3) % 43.11/6.96 | % 43.11/6.96 | REDUCE: (8), (19) imply: % 43.11/6.96 | (33) op(e3, e0) = e2 % 43.11/6.96 | % 43.11/6.96 | REDUCE: (3), (19) imply: % 43.11/6.96 | (34) op(e0, e3) = all_4_1 % 43.11/6.96 | % 43.11/6.96 | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12), (13), (14), (15), % 43.11/6.96 | (16), (17), (19), (20), (21), (22), (23), (24), (25), (26), (27), % 43.11/6.96 | (28), (29), (30), (31), (32), (33), (34) are inconsistent by % 43.11/6.96 | sub-proof #4. % 43.11/6.96 | % 43.11/6.96 End of proof % 43.11/6.96 % 43.11/6.96 Sub-proof #4 shows that the following formulas are inconsistent: % 43.11/6.96 ---------------------------------------------------------------- % 43.11/6.96 (1) ~ (all_4_1 = e1) | ~ (all_4_2 = e3) % 43.11/6.96 (2) all_58_9 = all_52_6 % 43.11/6.96 (3) ~ (all_52_8 = all_52_14) % 43.11/6.96 (4) ~ (all_52_0 = all_52_6) % 43.11/6.96 (5) all_58_7 = all_52_7 % 43.11/6.96 (6) ~ (e3 = e1) % 43.11/6.96 (7) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.96 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.96 (8) op(e3, e0) = all_52_0 % 43.11/6.96 (9) all_52_11 = all_8_2 % 43.11/6.96 (10) op(e0, e3) = all_52_14 % 43.11/6.96 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.96 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.96 (12) all_56_3 = all_52_14 % 43.11/6.96 (13) op(e3, e0) = e2 % 43.11/6.96 (14) all_52_9 = all_10_2 % 43.11/6.96 (15) all_52_13 = all_6_2 % 43.11/6.96 (16) ~ (all_52_0 = e3) % 43.11/6.96 (17) all_4_2 = e3 % 43.11/6.96 (18) all_58_6 = all_8_2 % 43.11/6.96 (19) op(e0, e3) = all_4_1 % 43.11/6.96 (20) ~ (all_52_14 = e0) % 43.11/6.96 (21) ~ (all_52_14 = e3) % 43.11/6.96 (22) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/6.96 (23) ~ (e1 = e0) % 43.11/6.96 (24) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.96 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.96 (25) ~ (all_52_0 = all_10_2) % 43.11/6.96 (26) ~ (all_52_7 = all_6_2) % 43.11/6.96 (27) all_58_8 = all_52_8 % 43.11/6.96 (28) all_52_15 = e3 % 43.11/6.96 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.96 (30) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.96 % 43.11/6.96 Begin of proof % 43.11/6.96 | % 43.11/6.96 | BETA: splitting (1) gives: % 43.11/6.96 | % 43.11/6.96 | Case 1: % 43.11/6.96 | | % 43.11/6.96 | | (31) ~ (all_4_1 = e1) % 43.11/6.96 | | % 43.11/6.96 | | GROUND_INST: instantiating (29) with all_52_14, all_4_1, e3, e0, simplifying % 43.11/6.96 | | with (10), (19) gives: % 43.11/6.96 | | (32) all_52_14 = all_4_1 % 43.11/6.96 | | % 43.11/6.96 | | GROUND_INST: instantiating (29) with all_52_0, e2, e0, e3, simplifying with % 43.11/6.96 | | (8), (13) gives: % 43.11/6.96 | | (33) all_52_0 = e2 % 43.11/6.96 | | % 43.11/6.96 | | COMBINE_EQS: (12), (32) imply: % 43.11/6.96 | | (34) all_56_3 = all_4_1 % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (4), (33) imply: % 43.11/6.96 | | (35) ~ (all_52_6 = e2) % 43.11/6.96 | | % 43.11/6.96 | | SIMP: (35) implies: % 43.11/6.96 | | (36) ~ (all_52_6 = e2) % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (25), (33) imply: % 43.11/6.96 | | (37) ~ (all_10_2 = e2) % 43.11/6.96 | | % 43.11/6.96 | | SIMP: (37) implies: % 43.11/6.96 | | (38) ~ (all_10_2 = e2) % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (16), (33) imply: % 43.11/6.96 | | (39) ~ (e3 = e2) % 43.11/6.96 | | % 43.11/6.96 | | SIMP: (39) implies: % 43.11/6.96 | | (40) ~ (e3 = e2) % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (3), (32) imply: % 43.11/6.96 | | (41) ~ (all_52_8 = all_4_1) % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (21), (32) imply: % 43.11/6.96 | | (42) ~ (all_4_1 = e3) % 43.11/6.96 | | % 43.11/6.96 | | REDUCE: (20), (32) imply: % 43.11/6.96 | | (43) ~ (all_4_1 = e0) % 43.11/6.96 | | % 43.11/6.96 | | BETA: splitting (30) gives: % 43.11/6.96 | | % 43.11/6.96 | | Case 1: % 43.11/6.96 | | | % 43.11/6.96 | | | (44) all_56_3 = e3 % 43.11/6.96 | | | % 43.11/6.96 | | | COMBINE_EQS: (34), (44) imply: % 43.11/6.96 | | | (45) all_4_1 = e3 % 43.11/6.96 | | | % 43.11/6.96 | | | REDUCE: (42), (45) imply: % 43.11/6.96 | | | (46) $false % 43.11/6.96 | | | % 43.11/6.96 | | | CLOSE: (46) is inconsistent. % 43.11/6.96 | | | % 43.11/6.96 | | Case 2: % 43.11/6.96 | | | % 43.11/6.96 | | | (47) ~ (all_56_3 = e3) % 43.11/6.96 | | | (48) all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.96 | | | % 43.11/6.96 | | | BETA: splitting (7) gives: % 43.11/6.96 | | | % 43.11/6.96 | | | Case 1: % 43.11/6.96 | | | | % 43.11/6.96 | | | | (49) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.11/6.96 | | | | % 43.11/6.96 | | | | REF_CLOSE: (14), (38), (49) are inconsistent by sub-proof #72. % 43.11/6.96 | | | | % 43.11/6.96 | | | Case 2: % 43.11/6.96 | | | | % 43.11/6.96 | | | | (50) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.11/6.96 | | | | (all_52_8 = e0)) % 43.11/6.96 | | | | % 43.11/6.96 | | | | BETA: splitting (50) gives: % 43.11/6.96 | | | | % 43.11/6.96 | | | | Case 1: % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | (51) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | ALPHA: (51) implies: % 43.11/6.96 | | | | | (52) all_52_13 = e2 % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | COMBINE_EQS: (15), (52) imply: % 43.11/6.96 | | | | | (53) all_6_2 = e2 % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | REDUCE: (26), (53) imply: % 43.11/6.96 | | | | | (54) ~ (all_52_7 = e2) % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | BETA: splitting (48) gives: % 43.11/6.96 | | | | | % 43.11/6.96 | | | | | Case 1: % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | (55) all_56_3 = e2 % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | COMBINE_EQS: (34), (55) imply: % 43.11/6.96 | | | | | | (56) all_4_1 = e2 % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | REDUCE: (41), (56) imply: % 43.11/6.96 | | | | | | (57) ~ (all_52_8 = e2) % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | REDUCE: (31), (56) imply: % 43.11/6.96 | | | | | | (58) ~ (e2 = e1) % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | REDUCE: (43), (56) imply: % 43.11/6.96 | | | | | | (59) ~ (e2 = e0) % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | BETA: splitting (22) gives: % 43.11/6.96 | | | | | | % 43.11/6.96 | | | | | | Case 1: % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | (60) all_58_6 = e2 % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | COMBINE_EQS: (18), (60) imply: % 43.11/6.96 | | | | | | | (61) all_8_2 = e2 % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | SIMP: (61) implies: % 43.11/6.96 | | | | | | | (62) all_8_2 = e2 % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | COMBINE_EQS: (9), (62) imply: % 43.11/6.96 | | | | | | | (63) all_52_11 = e2 % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | BETA: splitting (24) gives: % 43.11/6.96 | | | | | | | % 43.11/6.96 | | | | | | | Case 1: % 43.11/6.96 | | | | | | | | % 43.11/6.96 | | | | | | | | (64) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.11/6.96 | | | | | | | | % 43.11/6.96 | | | | | | | | ALPHA: (64) implies: % 43.11/6.96 | | | | | | | | (65) all_52_9 = e1 % 43.11/6.96 | | | | | | | | % 43.11/6.96 | | | | | | | | BETA: splitting (11) gives: % 43.11/6.96 | | | | | | | | % 43.11/6.96 | | | | | | | | Case 1: % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | (66) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | ALPHA: (66) implies: % 43.11/6.96 | | | | | | | | | (67) all_52_9 = e0 % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | REF_CLOSE: (23), (65), (67) are inconsistent by sub-proof #75. % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | Case 2: % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | (68) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = % 43.11/6.96 | | | | | | | | | e0 & ~ (all_52_2 = e1)) % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | BETA: splitting (68) gives: % 43.11/6.96 | | | | | | | | | % 43.11/6.96 | | | | | | | | | Case 1: % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | (69) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | ALPHA: (69) implies: % 43.11/6.96 | | | | | | | | | | (70) all_52_11 = e0 % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | COMBINE_EQS: (63), (70) imply: % 43.11/6.96 | | | | | | | | | | (71) e2 = e0 % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | SIMP: (71) implies: % 43.11/6.96 | | | | | | | | | | (72) e2 = e0 % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | REDUCE: (59), (72) imply: % 43.11/6.96 | | | | | | | | | | (73) $false % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | CLOSE: (73) is inconsistent. % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | Case 2: % 43.11/6.96 | | | | | | | | | | % 43.11/6.96 | | | | | | | | | | (74) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.11/6.96 | | | | | | | | | | % 43.11/6.97 | | | | | | | | | | REF_CLOSE: (52), (59), (74) are inconsistent by sub-proof % 43.11/6.97 | | | | | | | | | | #50. % 43.11/6.97 | | | | | | | | | | % 43.11/6.97 | | | | | | | | | End of split % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | End of split % 43.11/6.97 | | | | | | | | % 43.11/6.97 | | | | | | | Case 2: % 43.11/6.97 | | | | | | | | % 43.11/6.97 | | | | | | | | (75) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 % 43.11/6.97 | | | | | | | | & ~ (all_52_5 = e0)) % 43.11/6.97 | | | | | | | | % 43.11/6.97 | | | | | | | | BETA: splitting (75) gives: % 43.11/6.97 | | | | | | | | % 43.11/6.97 | | | | | | | | Case 1: % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | (76) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | ALPHA: (76) implies: % 43.11/6.97 | | | | | | | | | (77) all_52_11 = e1 % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | COMBINE_EQS: (63), (77) imply: % 43.11/6.97 | | | | | | | | | (78) e2 = e1 % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | SIMP: (78) implies: % 43.11/6.97 | | | | | | | | | (79) e2 = e1 % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | COMBINE_EQS: (52), (79) imply: % 43.11/6.97 | | | | | | | | | (80) all_52_13 = e1 % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | REF_CLOSE: (7), (11), (23), (28), (40), (58), (59), (77), (80) % 43.11/6.97 | | | | | | | | | are inconsistent by sub-proof #54. % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | Case 2: % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | (81) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | | REF_CLOSE: (6), (28), (81) are inconsistent by sub-proof #51. % 43.11/6.97 | | | | | | | | | % 43.11/6.97 | | | | | | | | End of split % 43.11/6.97 | | | | | | | | % 43.11/6.97 | | | | | | | End of split % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | Case 2: % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | (82) all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | REF_CLOSE: (2), (5), (27), (36), (54), (57), (82) are inconsistent % 43.11/6.97 | | | | | | | by sub-proof #40. % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | End of split % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | Case 2: % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | (83) all_56_3 = e1 | all_56_3 = e0 % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | BETA: splitting (83) gives: % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | Case 1: % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | (84) all_56_3 = e1 % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | COMBINE_EQS: (34), (84) imply: % 43.11/6.97 | | | | | | | (85) all_4_1 = e1 % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | REDUCE: (31), (85) imply: % 43.11/6.97 | | | | | | | (86) $false % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | CLOSE: (86) is inconsistent. % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | Case 2: % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | (87) all_56_3 = e0 % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | COMBINE_EQS: (34), (87) imply: % 43.11/6.97 | | | | | | | (88) all_4_1 = e0 % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | REDUCE: (43), (88) imply: % 43.11/6.97 | | | | | | | (89) $false % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | | CLOSE: (89) is inconsistent. % 43.11/6.97 | | | | | | | % 43.11/6.97 | | | | | | End of split % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | End of split % 43.11/6.97 | | | | | % 43.11/6.97 | | | | Case 2: % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | (90) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REF_CLOSE: (28), (40), (90) are inconsistent by sub-proof #49. % 43.11/6.97 | | | | | % 43.11/6.97 | | | | End of split % 43.11/6.97 | | | | % 43.11/6.97 | | | End of split % 43.11/6.97 | | | % 43.11/6.97 | | End of split % 43.11/6.97 | | % 43.11/6.97 | Case 2: % 43.11/6.97 | | % 43.11/6.97 | | (91) ~ (all_4_2 = e3) % 43.11/6.97 | | % 43.11/6.97 | | REDUCE: (17), (91) imply: % 43.11/6.97 | | (92) $false % 43.11/6.97 | | % 43.11/6.97 | | CLOSE: (92) is inconsistent. % 43.11/6.97 | | % 43.11/6.97 | End of split % 43.11/6.97 | % 43.11/6.97 End of proof % 43.11/6.97 % 43.11/6.97 Sub-proof #5 shows that the following formulas are inconsistent: % 43.11/6.97 ---------------------------------------------------------------- % 43.11/6.97 (1) ~ (all_52_0 = all_52_3) % 43.11/6.97 (2) op(all_8_2, e2) = e1 % 43.11/6.97 (3) ~ (all_52_10 = all_10_2) % 43.11/6.97 (4) op(e3, e2) = all_52_6 % 43.11/6.97 (5) ~ (all_4_0 = e2) % 43.11/6.97 (6) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/6.97 (7) ~ (all_30_0 = e1) | ~ (all_30_1 = e3) | ~ (all_30_2 = e2) % 43.11/6.97 (8) ~ (e2 = e0) % 43.11/6.97 (9) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.11/6.97 (10) op(e0, all_4_2) = all_4_1 % 43.11/6.97 (11) ~ (all_52_0 = all_52_2) % 43.11/6.97 (12) ~ (all_52_14 = all_4_2) % 43.11/6.97 (13) all_58_7 = all_52_7 % 43.11/6.97 (14) ~ (all_52_3 = all_6_2) % 43.11/6.97 (15) all_26_0 = e1 % 43.11/6.97 (16) all_40_2 = all_4_2 % 43.11/6.97 (17) ~ (all_52_14 = all_10_2) % 43.11/6.97 (18) all_26_1 = all_8_1 % 43.11/6.97 (19) ~ (e3 = e1) % 43.11/6.97 (20) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.97 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.97 (21) op(e3, e0) = all_52_0 % 43.11/6.97 (22) all_52_11 = all_8_2 % 43.11/6.97 (23) op(e0, e3) = all_52_14 % 43.11/6.97 (24) op(e2, all_8_2) = all_8_1 % 43.11/6.97 (25) op(all_4_2, e0) = all_4_0 % 43.11/6.97 (26) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.97 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.97 (27) ~ (all_26_0 = e1) | ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/6.97 (28) all_56_3 = all_52_14 % 43.11/6.97 (29) ~ (all_52_10 = all_52_12) % 43.11/6.97 (30) all_56_12 = all_52_0 % 43.11/6.97 (31) all_30_0 = all_4_0 % 43.11/6.97 (32) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.11/6.97 (33) all_56_13 = all_52_3 % 43.11/6.97 (34) ~ (all_52_7 = all_8_2) % 43.11/6.97 (35) ~ (all_52_6 = all_10_2) % 43.11/6.97 (36) op(all_6_2, e1) = e3 % 43.11/6.97 (37) all_40_1 = all_4_1 % 43.11/6.97 (38) ~ (all_52_12 = all_52_14) % 43.11/6.97 (39) ~ (all_52_3 = all_10_2) % 43.11/6.97 (40) all_52_9 = all_10_2 % 43.11/6.97 (41) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.97 (42) all_52_13 = all_6_2 % 43.11/6.97 (43) ~ (all_52_0 = all_4_2) % 43.11/6.97 (44) all_58_2 = all_6_2 % 43.11/6.97 (45) all_58_14 = all_52_12 % 43.11/6.97 (46) ~ (e3 = e0) % 43.11/6.97 (47) all_58_1 = all_52_2 % 43.11/6.97 (48) op(e3, e1) = all_52_3 % 43.11/6.97 (49) ~ (e2 = e1) % 43.11/6.97 (50) all_26_2 = all_8_2 % 43.11/6.97 (51) ~ (all_52_6 = all_52_7) % 43.11/6.97 (52) ~ (all_52_10 = all_8_2) % 43.11/6.97 (53) ~ (all_40_0 = e1) | ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/6.97 (54) all_40_0 = all_4_0 % 43.11/6.97 (55) ~ (all_52_6 = all_8_2) % 43.11/6.97 (56) op(e2, e3) = all_52_10 % 43.11/6.97 (57) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.97 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.97 (58) all_56_11 = all_52_10 % 43.11/6.97 (59) ~ (all_52_0 = all_10_2) % 43.11/6.97 (60) ~ (all_52_2 = all_4_2) % 43.11/6.97 (61) (all_52_11 = e3 & ~ (all_52_10 = e2)) | (all_52_13 = e3 & ~ (all_52_12 % 43.11/6.97 = e1)) | (all_52_15 = e3 & ~ (all_52_14 = e0)) % 43.11/6.97 (62) ~ (e3 = e2) % 43.11/6.97 (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.97 (64) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.97 (65) all_52_15 = all_4_2 % 43.11/6.97 % 43.11/6.97 Begin of proof % 43.11/6.97 | % 43.11/6.97 | BETA: splitting (27) gives: % 43.11/6.97 | % 43.11/6.97 | Case 1: % 43.11/6.97 | | % 43.11/6.97 | | (66) ~ (all_26_0 = e1) % 43.11/6.97 | | % 43.11/6.97 | | REDUCE: (15), (66) imply: % 43.11/6.97 | | (67) $false % 43.11/6.97 | | % 43.11/6.97 | | CLOSE: (67) is inconsistent. % 43.11/6.97 | | % 43.11/6.97 | Case 2: % 43.11/6.97 | | % 43.11/6.97 | | (68) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/6.97 | | % 43.11/6.97 | | BETA: splitting (7) gives: % 43.11/6.97 | | % 43.11/6.97 | | Case 1: % 43.11/6.97 | | | % 43.11/6.97 | | | (69) ~ (all_30_0 = e1) % 43.11/6.97 | | | % 43.11/6.97 | | | REDUCE: (31), (69) imply: % 43.11/6.97 | | | (70) ~ (all_4_0 = e1) % 43.11/6.97 | | | % 43.11/6.97 | | | BETA: splitting (61) gives: % 43.11/6.97 | | | % 43.11/6.97 | | | Case 1: % 43.11/6.97 | | | | % 43.11/6.97 | | | | (71) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.97 | | | | % 43.11/6.97 | | | | REF_CLOSE: (2), (3), (4), (6), (8), (13), (18), (20), (22), (24), (26), % 43.11/6.97 | | | | (29), (35), (40), (41), (42), (44), (45), (46), (47), (50), % 43.11/6.97 | | | | (51), (52), (55), (56), (57), (58), (60), (63), (65), (68), % 43.11/6.97 | | | | (71) are inconsistent by sub-proof #18. % 43.11/6.97 | | | | % 43.11/6.97 | | | Case 2: % 43.11/6.97 | | | | % 43.11/6.97 | | | | (72) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & ~ % 43.11/6.97 | | | | (all_52_14 = e0)) % 43.11/6.97 | | | | % 43.11/6.97 | | | | REF_CLOSE: (1), (5), (6), (9), (10), (12), (13), (14), (17), (19), (20), % 43.11/6.97 | | | | (21), (22), (23), (25), (26), (28), (30), (32), (33), (34), % 43.11/6.97 | | | | (36), (38), (39), (40), (42), (43), (44), (45), (47), (48), % 43.11/6.97 | | | | (49), (57), (59), (62), (63), (64), (65), (70), (72) are % 43.11/6.97 | | | | inconsistent by sub-proof #6. % 43.11/6.97 | | | | % 43.11/6.97 | | | End of split % 43.11/6.97 | | | % 43.11/6.97 | | Case 2: % 43.11/6.97 | | | % 43.11/6.97 | | | (73) all_30_0 = e1 % 43.11/6.97 | | | % 43.11/6.97 | | | COMBINE_EQS: (31), (73) imply: % 43.11/6.97 | | | (74) all_4_0 = e1 % 43.11/6.97 | | | % 43.11/6.97 | | | SIMP: (74) implies: % 43.11/6.97 | | | (75) all_4_0 = e1 % 43.11/6.97 | | | % 43.11/6.97 | | | COMBINE_EQS: (54), (75) imply: % 43.11/6.97 | | | (76) all_40_0 = e1 % 43.11/6.97 | | | % 43.11/6.97 | | | REDUCE: (25), (75) imply: % 43.11/6.97 | | | (77) op(all_4_2, e0) = e1 % 43.11/6.97 | | | % 43.11/6.97 | | | BETA: splitting (53) gives: % 43.11/6.97 | | | % 43.11/6.97 | | | Case 1: % 43.11/6.97 | | | | % 43.11/6.97 | | | | (78) ~ (all_40_0 = e1) % 43.11/6.97 | | | | % 43.11/6.97 | | | | REDUCE: (76), (78) imply: % 43.11/6.97 | | | | (79) $false % 43.11/6.97 | | | | % 43.11/6.97 | | | | CLOSE: (79) is inconsistent. % 43.11/6.97 | | | | % 43.11/6.97 | | | Case 2: % 43.11/6.97 | | | | % 43.11/6.97 | | | | (80) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/6.97 | | | | % 43.11/6.97 | | | | BETA: splitting (61) gives: % 43.11/6.97 | | | | % 43.11/6.97 | | | | Case 1: % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | (81) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | ALPHA: (81) implies: % 43.11/6.97 | | | | | (82) all_52_11 = e3 % 43.11/6.97 | | | | | (83) ~ (all_52_10 = e2) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | COMBINE_EQS: (22), (82) imply: % 43.11/6.97 | | | | | (84) all_8_2 = e3 % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | SIMP: (84) implies: % 43.11/6.97 | | | | | (85) all_8_2 = e3 % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | COMBINE_EQS: (50), (85) imply: % 43.11/6.97 | | | | | (86) all_26_2 = e3 % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REDUCE: (55), (85) imply: % 43.11/6.97 | | | | | (87) ~ (all_52_6 = e3) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REDUCE: (52), (85) imply: % 43.11/6.97 | | | | | (88) ~ (all_52_10 = e3) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REDUCE: (2), (85) imply: % 43.11/6.97 | | | | | (89) op(e3, e2) = e1 % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REDUCE: (24), (85) imply: % 43.11/6.97 | | | | | (90) op(e2, e3) = all_8_1 % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | REF_CLOSE: (3), (4), (6), (8), (13), (18), (20), (26), (29), (35), % 43.11/6.97 | | | | | (40), (41), (42), (44), (45), (46), (47), (51), (56), (57), % 43.11/6.97 | | | | | (58), (60), (63), (65), (68), (82), (83), (86), (87), (88), % 43.11/6.97 | | | | | (89), (90) are inconsistent by sub-proof #20. % 43.11/6.97 | | | | | % 43.11/6.97 | | | | Case 2: % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | (91) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & ~ % 43.11/6.97 | | | | | (all_52_14 = e0)) % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | BETA: splitting (91) gives: % 43.11/6.97 | | | | | % 43.11/6.97 | | | | | Case 1: % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | (92) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | REF_CLOSE: (14), (36), (42), (48), (63), (92) are inconsistent by % 43.11/6.97 | | | | | | sub-proof #7. % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | Case 2: % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | (93) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | | REF_CLOSE: (6), (8), (10), (11), (12), (13), (16), (20), (21), (22), % 43.11/6.97 | | | | | | (23), (26), (28), (34), (37), (38), (40), (42), (43), % 43.11/6.97 | | | | | | (44), (45), (47), (57), (59), (62), (63), (64), (65), % 43.11/6.97 | | | | | | (77), (80), (93) are inconsistent by sub-proof #30. % 43.11/6.97 | | | | | | % 43.11/6.97 | | | | | End of split % 43.11/6.97 | | | | | % 43.11/6.97 | | | | End of split % 43.11/6.97 | | | | % 43.11/6.97 | | | End of split % 43.11/6.97 | | | % 43.11/6.97 | | End of split % 43.11/6.97 | | % 43.11/6.97 | End of split % 43.11/6.97 | % 43.11/6.97 End of proof % 43.11/6.97 % 43.11/6.97 Sub-proof #6 shows that the following formulas are inconsistent: % 43.11/6.97 ---------------------------------------------------------------- % 43.11/6.97 (1) ~ (all_52_0 = all_52_3) % 43.11/6.97 (2) ~ (all_4_0 = e2) % 43.11/6.97 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/6.97 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.11/6.97 (5) op(e0, all_4_2) = all_4_1 % 43.11/6.97 (6) ~ (all_52_14 = all_4_2) % 43.11/6.97 (7) all_58_7 = all_52_7 % 43.11/6.97 (8) ~ (all_52_3 = all_6_2) % 43.11/6.97 (9) ~ (all_52_14 = all_10_2) % 43.11/6.97 (10) ~ (e3 = e1) % 43.11/6.97 (11) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.97 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.97 (12) op(e3, e0) = all_52_0 % 43.11/6.97 (13) all_52_11 = all_8_2 % 43.11/6.97 (14) op(e0, e3) = all_52_14 % 43.11/6.97 (15) op(all_4_2, e0) = all_4_0 % 43.11/6.97 (16) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.97 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.97 (17) all_56_3 = all_52_14 % 43.11/6.97 (18) ~ (all_4_0 = e1) % 43.11/6.97 (19) all_56_12 = all_52_0 % 43.11/6.97 (20) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.11/6.97 (21) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & ~ (all_52_14 % 43.11/6.97 = e0)) % 43.11/6.97 (22) all_56_13 = all_52_3 % 43.11/6.97 (23) ~ (all_52_7 = all_8_2) % 43.11/6.97 (24) op(all_6_2, e1) = e3 % 43.11/6.97 (25) ~ (all_52_12 = all_52_14) % 43.11/6.97 (26) ~ (all_52_3 = all_10_2) % 43.11/6.97 (27) all_52_9 = all_10_2 % 43.11/6.97 (28) all_52_13 = all_6_2 % 43.11/6.97 (29) ~ (all_52_0 = all_4_2) % 43.11/6.97 (30) all_58_2 = all_6_2 % 43.11/6.97 (31) all_58_14 = all_52_12 % 43.11/6.97 (32) all_58_1 = all_52_2 % 43.11/6.97 (33) op(e3, e1) = all_52_3 % 43.11/6.97 (34) ~ (e2 = e1) % 43.11/6.97 (35) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.97 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.97 (36) ~ (all_52_0 = all_10_2) % 43.11/6.97 (37) ~ (e3 = e2) % 43.11/6.97 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.97 (39) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/6.97 (40) all_52_15 = all_4_2 % 43.11/6.97 % 43.11/6.97 Begin of proof % 43.11/6.97 | % 43.11/6.97 | BETA: splitting (21) gives: % 43.11/6.97 | % 43.11/6.97 | Case 1: % 43.11/6.97 | | % 43.11/6.98 | | (41) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.98 | | % 43.11/6.98 | | ALPHA: (41) implies: % 43.11/6.98 | | (42) all_52_13 = e3 % 43.11/6.98 | | % 43.11/6.98 | | COMBINE_EQS: (28), (42) imply: % 43.11/6.98 | | (43) all_6_2 = e3 % 43.11/6.98 | | % 43.11/6.98 | | REF_CLOSE: (8), (24), (33), (38), (43) are inconsistent by sub-proof #8. % 43.11/6.98 | | % 43.11/6.98 | Case 2: % 43.11/6.98 | | % 43.11/6.98 | | (44) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.98 | | % 43.11/6.98 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.11/6.98 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (25), % 43.11/6.98 | | (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37), % 43.11/6.98 | | (38), (39), (40), (44) are inconsistent by sub-proof #37. % 43.11/6.98 | | % 43.11/6.98 | End of split % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #7 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) ~ (all_52_3 = all_6_2) % 43.11/6.98 (2) op(all_6_2, e1) = e3 % 43.11/6.98 (3) all_52_13 = all_6_2 % 43.11/6.98 (4) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/6.98 (5) op(e3, e1) = all_52_3 % 43.11/6.98 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | ALPHA: (4) implies: % 43.11/6.98 | (7) all_52_13 = e3 % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (3), (7) imply: % 43.11/6.98 | (8) all_6_2 = e3 % 43.11/6.98 | % 43.11/6.98 | SIMP: (8) implies: % 43.11/6.98 | (9) all_6_2 = e3 % 43.11/6.98 | % 43.11/6.98 | REF_CLOSE: (1), (2), (5), (6), (9) are inconsistent by sub-proof #8. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #8 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) ~ (all_52_3 = all_6_2) % 43.11/6.98 (2) op(all_6_2, e1) = e3 % 43.11/6.98 (3) all_6_2 = e3 % 43.11/6.98 (4) op(e3, e1) = all_52_3 % 43.11/6.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | REDUCE: (1), (3) imply: % 43.11/6.98 | (6) ~ (all_52_3 = e3) % 43.11/6.98 | % 43.11/6.98 | REDUCE: (2), (3) imply: % 43.11/6.98 | (7) op(e3, e1) = e3 % 43.11/6.98 | % 43.11/6.98 | GROUND_INST: instantiating (5) with all_52_3, e3, e1, e3, simplifying with % 43.11/6.98 | (4), (7) gives: % 43.11/6.98 | (8) all_52_3 = e3 % 43.11/6.98 | % 43.11/6.98 | REDUCE: (6), (8) imply: % 43.11/6.98 | (9) $false % 43.11/6.98 | % 43.11/6.98 | CLOSE: (9) is inconsistent. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #9 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) op(e3, e2) = all_52_6 % 43.11/6.98 (2) all_52_11 = all_8_2 % 43.11/6.98 (3) ~ (all_52_6 = all_8_2) % 43.11/6.98 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 (5) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.98 (6) op(all_8_2, e2) = e3 % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | ALPHA: (5) implies: % 43.11/6.98 | (7) all_52_11 = e3 % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (2), (7) imply: % 43.11/6.98 | (8) all_8_2 = e3 % 43.11/6.98 | % 43.11/6.98 | SIMP: (8) implies: % 43.11/6.98 | (9) all_8_2 = e3 % 43.11/6.98 | % 43.11/6.98 | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #10. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #10 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) op(e3, e2) = all_52_6 % 43.11/6.98 (2) all_8_2 = e3 % 43.11/6.98 (3) ~ (all_52_6 = all_8_2) % 43.11/6.98 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 (5) op(all_8_2, e2) = e3 % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | REDUCE: (2), (3) imply: % 43.11/6.98 | (6) ~ (all_52_6 = e3) % 43.11/6.98 | % 43.11/6.98 | REDUCE: (2), (5) imply: % 43.11/6.98 | (7) op(e3, e2) = e3 % 43.11/6.98 | % 43.11/6.98 | GROUND_INST: instantiating (4) with all_52_6, e3, e2, e3, simplifying with % 43.11/6.98 | (1), (7) gives: % 43.11/6.98 | (8) all_52_6 = e3 % 43.11/6.98 | % 43.11/6.98 | REDUCE: (6), (8) imply: % 43.11/6.98 | (9) $false % 43.11/6.98 | % 43.11/6.98 | CLOSE: (9) is inconsistent. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #11 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) op(all_4_2, e0) = e3 % 43.11/6.98 (2) op(e3, e0) = all_52_0 % 43.11/6.98 (3) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/6.98 (4) ~ (all_52_0 = all_4_2) % 43.11/6.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 (6) all_52_15 = all_4_2 % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | ALPHA: (3) implies: % 43.11/6.98 | (7) all_52_15 = e3 % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (6), (7) imply: % 43.11/6.98 | (8) all_4_2 = e3 % 43.11/6.98 | % 43.11/6.98 | SIMP: (8) implies: % 43.11/6.98 | (9) all_4_2 = e3 % 43.11/6.98 | % 43.11/6.98 | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #12. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #12 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) op(all_4_2, e0) = e3 % 43.11/6.98 (2) op(e3, e0) = all_52_0 % 43.11/6.98 (3) ~ (all_52_0 = all_4_2) % 43.11/6.98 (4) all_4_2 = e3 % 43.11/6.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | REDUCE: (3), (4) imply: % 43.11/6.98 | (6) ~ (all_52_0 = e3) % 43.11/6.98 | % 43.11/6.98 | REDUCE: (1), (4) imply: % 43.11/6.98 | (7) op(e3, e0) = e3 % 43.11/6.98 | % 43.11/6.98 | GROUND_INST: instantiating (5) with all_52_0, e3, e0, e3, simplifying with % 43.11/6.98 | (2), (7) gives: % 43.11/6.98 | (8) all_52_0 = e3 % 43.11/6.98 | % 43.11/6.98 | REDUCE: (6), (8) imply: % 43.11/6.98 | (9) $false % 43.11/6.98 | % 43.11/6.98 | CLOSE: (9) is inconsistent. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #13 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) all_50_1 = all_8_1 % 43.11/6.98 (2) op(e3, e2) = all_52_6 % 43.11/6.98 (3) all_58_0 = all_4_2 % 43.11/6.98 (4) ~ (all_52_0 = all_52_6) % 43.11/6.98 (5) ~ (e3 = e1) % 43.11/6.98 (6) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.98 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.98 (7) all_52_11 = all_8_2 % 43.11/6.98 (8) op(e2, all_8_2) = all_8_1 % 43.11/6.98 (9) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.98 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.98 (10) ~ (all_52_1 = all_52_10) % 43.11/6.98 (11) ~ (all_52_6 = all_10_2) % 43.11/6.98 (12) all_58_5 = all_52_1 % 43.11/6.98 (13) all_58_11 = all_52_0 % 43.11/6.98 (14) op(all_8_2, e2) = e0 % 43.11/6.98 (15) all_52_9 = all_10_2 % 43.11/6.98 (16) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.98 (17) all_52_13 = all_6_2 % 43.11/6.98 (18) all_58_1 = all_52_2 % 43.11/6.98 (19) ~ (e2 = e1) % 43.11/6.98 (20) all_50_2 = all_8_2 % 43.11/6.98 (21) ~ (all_52_10 = all_8_2) % 43.11/6.98 (22) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.98 (23) ~ (all_52_6 = all_8_2) % 43.11/6.98 (24) op(e2, e3) = all_52_10 % 43.11/6.98 (25) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.98 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.98 (26) all_56_11 = all_52_10 % 43.11/6.98 (27) ~ (all_52_2 = all_6_2) % 43.11/6.98 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 (29) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.98 (30) all_52_15 = all_4_2 % 43.11/6.98 (31) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | ALPHA: (29) implies: % 43.11/6.98 | (32) all_52_11 = e3 % 43.11/6.98 | (33) ~ (all_52_10 = e2) % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (7), (32) imply: % 43.11/6.98 | (34) all_8_2 = e3 % 43.11/6.98 | % 43.11/6.98 | SIMP: (34) implies: % 43.11/6.98 | (35) all_8_2 = e3 % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (20), (35) imply: % 43.11/6.98 | (36) all_50_2 = e3 % 43.11/6.98 | % 43.11/6.98 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 43.11/6.98 | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), % 43.11/6.98 | (26), (27), (28), (30), (31), (32), (33), (35), (36) are % 43.11/6.98 | inconsistent by sub-proof #15. % 43.11/6.98 | % 43.11/6.98 End of proof % 43.11/6.98 % 43.11/6.98 Sub-proof #14 shows that the following formulas are inconsistent: % 43.11/6.98 ---------------------------------------------------------------- % 43.11/6.98 (1) all_50_1 = all_8_1 % 43.11/6.98 (2) op(e3, e2) = all_52_6 % 43.11/6.98 (3) all_58_0 = all_4_2 % 43.11/6.98 (4) ~ (all_52_0 = all_52_6) % 43.11/6.98 (5) ~ (e3 = e1) % 43.11/6.98 (6) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.98 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.98 (7) all_52_11 = all_8_2 % 43.11/6.98 (8) op(e2, all_8_2) = all_8_1 % 43.11/6.98 (9) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.98 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.98 (10) ~ (all_52_1 = all_52_10) % 43.11/6.98 (11) ~ (all_52_6 = all_10_2) % 43.11/6.98 (12) all_58_5 = all_52_1 % 43.11/6.98 (13) all_58_11 = all_52_0 % 43.11/6.98 (14) op(all_8_2, e2) = e0 % 43.11/6.98 (15) all_52_9 = all_10_2 % 43.11/6.98 (16) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.98 (17) all_52_13 = all_6_2 % 43.11/6.98 (18) all_58_1 = all_52_2 % 43.11/6.98 (19) ~ (e2 = e1) % 43.11/6.98 (20) all_50_2 = all_8_2 % 43.11/6.98 (21) ~ (all_52_10 = all_8_2) % 43.11/6.98 (22) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.98 (23) ~ (all_52_6 = all_8_2) % 43.11/6.98 (24) op(e2, e3) = all_52_10 % 43.11/6.98 (25) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.98 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.98 (26) all_56_11 = all_52_10 % 43.11/6.98 (27) ~ (all_52_2 = all_6_2) % 43.11/6.98 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.98 (29) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.98 (30) all_52_15 = all_4_2 % 43.11/6.98 (31) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/6.98 % 43.11/6.98 Begin of proof % 43.11/6.98 | % 43.11/6.98 | ALPHA: (29) implies: % 43.11/6.98 | (32) all_52_11 = e3 % 43.11/6.98 | (33) ~ (all_52_10 = e2) % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (7), (32) imply: % 43.11/6.98 | (34) all_8_2 = e3 % 43.11/6.98 | % 43.11/6.98 | COMBINE_EQS: (20), (34) imply: % 43.11/6.98 | (35) all_50_2 = e3 % 43.11/6.98 | % 43.11/6.99 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 43.11/6.99 | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), % 43.11/6.99 | (26), (27), (28), (30), (31), (32), (33), (34), (35) are % 43.11/6.99 | inconsistent by sub-proof #15. % 43.11/6.99 | % 43.11/6.99 End of proof % 43.11/6.99 % 43.11/6.99 Sub-proof #15 shows that the following formulas are inconsistent: % 43.11/6.99 ---------------------------------------------------------------- % 43.11/6.99 (1) all_50_1 = all_8_1 % 43.11/6.99 (2) op(e3, e2) = all_52_6 % 43.11/6.99 (3) all_58_0 = all_4_2 % 43.11/6.99 (4) all_8_2 = e3 % 43.11/6.99 (5) ~ (all_52_0 = all_52_6) % 43.11/6.99 (6) ~ (e3 = e1) % 43.11/6.99 (7) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.99 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.99 (8) op(e2, all_8_2) = all_8_1 % 43.11/6.99 (9) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.99 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.99 (10) ~ (all_52_10 = e2) % 43.11/6.99 (11) ~ (all_52_1 = all_52_10) % 43.11/6.99 (12) ~ (all_52_6 = all_10_2) % 43.11/6.99 (13) all_58_5 = all_52_1 % 43.11/6.99 (14) all_58_11 = all_52_0 % 43.11/6.99 (15) op(all_8_2, e2) = e0 % 43.11/6.99 (16) all_52_9 = all_10_2 % 43.11/6.99 (17) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.99 (18) all_52_13 = all_6_2 % 43.11/6.99 (19) all_52_11 = e3 % 43.11/6.99 (20) all_58_1 = all_52_2 % 43.11/6.99 (21) ~ (e2 = e1) % 43.11/6.99 (22) ~ (all_52_10 = all_8_2) % 43.11/6.99 (23) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.99 (24) ~ (all_52_6 = all_8_2) % 43.11/6.99 (25) op(e2, e3) = all_52_10 % 43.11/6.99 (26) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.99 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.99 (27) all_56_11 = all_52_10 % 43.11/6.99 (28) ~ (all_52_2 = all_6_2) % 43.11/6.99 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.99 (30) all_50_2 = e3 % 43.11/6.99 (31) all_52_15 = all_4_2 % 43.11/6.99 (32) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/6.99 % 43.11/6.99 Begin of proof % 43.11/6.99 | % 43.11/6.99 | REDUCE: (4), (24) imply: % 43.11/6.99 | (33) ~ (all_52_6 = e3) % 43.11/6.99 | % 43.11/6.99 | REDUCE: (4), (22) imply: % 43.11/6.99 | (34) ~ (all_52_10 = e3) % 43.11/6.99 | % 43.11/6.99 | REDUCE: (4), (15) imply: % 43.11/6.99 | (35) op(e3, e2) = e0 % 43.11/6.99 | % 43.11/6.99 | REDUCE: (4), (8) imply: % 43.11/6.99 | (36) op(e2, e3) = all_8_1 % 43.11/6.99 | % 43.11/6.99 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), % 43.11/6.99 | (16), (17), (18), (19), (20), (21), (23), (25), (26), (27), (28), % 43.11/6.99 | (29), (30), (31), (32), (33), (34), (35), (36) are inconsistent by % 43.11/6.99 | sub-proof #16. % 43.11/6.99 | % 43.11/6.99 End of proof % 43.11/6.99 % 43.11/6.99 Sub-proof #16 shows that the following formulas are inconsistent: % 43.11/6.99 ---------------------------------------------------------------- % 43.11/6.99 (1) all_50_1 = all_8_1 % 43.11/6.99 (2) op(e3, e2) = all_52_6 % 43.11/6.99 (3) all_58_0 = all_4_2 % 43.11/6.99 (4) ~ (all_52_0 = all_52_6) % 43.11/6.99 (5) ~ (e3 = e1) % 43.11/6.99 (6) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.99 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.99 (7) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.99 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.99 (8) op(e2, e3) = all_8_1 % 43.11/6.99 (9) ~ (all_52_10 = e2) % 43.11/6.99 (10) ~ (all_52_1 = all_52_10) % 43.11/6.99 (11) ~ (all_52_6 = all_10_2) % 43.11/6.99 (12) all_58_5 = all_52_1 % 43.11/6.99 (13) all_58_11 = all_52_0 % 43.11/6.99 (14) all_52_9 = all_10_2 % 43.11/6.99 (15) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.99 (16) all_52_13 = all_6_2 % 43.11/6.99 (17) ~ (all_52_6 = e3) % 43.11/6.99 (18) all_52_11 = e3 % 43.11/6.99 (19) all_58_1 = all_52_2 % 43.11/6.99 (20) ~ (e2 = e1) % 43.11/6.99 (21) ~ (all_50_1 = e1) | ~ (all_50_2 = e3) % 43.11/6.99 (22) op(e2, e3) = all_52_10 % 43.11/6.99 (23) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.99 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.99 (24) all_56_11 = all_52_10 % 43.11/6.99 (25) ~ (all_52_2 = all_6_2) % 43.11/6.99 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.99 (27) op(e3, e2) = e0 % 43.11/6.99 (28) all_50_2 = e3 % 43.11/6.99 (29) all_52_15 = all_4_2 % 43.11/6.99 (30) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/6.99 (31) ~ (all_52_10 = e3) % 43.11/6.99 % 43.11/6.99 Begin of proof % 43.11/6.99 | % 43.11/6.99 | BETA: splitting (21) gives: % 43.11/6.99 | % 43.11/6.99 | Case 1: % 43.11/6.99 | | % 43.11/6.99 | | (32) ~ (all_50_1 = e1) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (1), (32) imply: % 43.11/6.99 | | (33) ~ (all_8_1 = e1) % 43.11/6.99 | | % 43.11/6.99 | | GROUND_INST: instantiating (26) with all_52_10, all_8_1, e3, e2, simplifying % 43.11/6.99 | | with (8), (22) gives: % 43.11/6.99 | | (34) all_52_10 = all_8_1 % 43.11/6.99 | | % 43.11/6.99 | | GROUND_INST: instantiating (26) with all_52_6, e0, e2, e3, simplifying with % 43.11/6.99 | | (2), (27) gives: % 43.11/6.99 | | (35) all_52_6 = e0 % 43.11/6.99 | | % 43.11/6.99 | | COMBINE_EQS: (24), (34) imply: % 43.11/6.99 | | (36) all_56_11 = all_8_1 % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (4), (35) imply: % 43.11/6.99 | | (37) ~ (all_52_0 = e0) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (10), (34) imply: % 43.11/6.99 | | (38) ~ (all_52_1 = all_8_1) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (11), (35) imply: % 43.11/6.99 | | (39) ~ (all_10_2 = e0) % 43.11/6.99 | | % 43.11/6.99 | | SIMP: (39) implies: % 43.11/6.99 | | (40) ~ (all_10_2 = e0) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (17), (35) imply: % 43.11/6.99 | | (41) ~ (e3 = e0) % 43.11/6.99 | | % 43.11/6.99 | | SIMP: (41) implies: % 43.11/6.99 | | (42) ~ (e3 = e0) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (31), (34) imply: % 43.11/6.99 | | (43) ~ (all_8_1 = e3) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (9), (34) imply: % 43.11/6.99 | | (44) ~ (all_8_1 = e2) % 43.11/6.99 | | % 43.11/6.99 | | BETA: splitting (7) gives: % 43.11/6.99 | | % 43.11/6.99 | | Case 1: % 43.11/6.99 | | | % 43.11/6.99 | | | (45) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.11/6.99 | | | % 43.11/6.99 | | | REF_CLOSE: (14), (40), (45) are inconsistent by sub-proof #29. % 43.11/6.99 | | | % 43.11/6.99 | | Case 2: % 43.11/6.99 | | | % 43.11/6.99 | | | (46) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.11/6.99 | | | (all_52_2 = e1)) % 43.11/6.99 | | | % 43.11/6.99 | | | BETA: splitting (46) gives: % 43.11/6.99 | | | % 43.11/6.99 | | | Case 1: % 43.11/6.99 | | | | % 43.11/6.99 | | | | (47) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.11/6.99 | | | | % 43.11/6.99 | | | | REF_CLOSE: (18), (42), (47) are inconsistent by sub-proof #22. % 43.11/6.99 | | | | % 43.11/6.99 | | | Case 2: % 43.11/6.99 | | | | % 43.11/6.99 | | | | (48) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.11/6.99 | | | | % 43.11/6.99 | | | | ALPHA: (48) implies: % 43.11/6.99 | | | | (49) all_52_13 = e0 % 43.11/6.99 | | | | % 43.11/6.99 | | | | COMBINE_EQS: (16), (49) imply: % 43.11/6.99 | | | | (50) all_6_2 = e0 % 43.11/6.99 | | | | % 43.11/6.99 | | | | SIMP: (50) implies: % 43.11/6.99 | | | | (51) all_6_2 = e0 % 43.11/6.99 | | | | % 43.11/6.99 | | | | REDUCE: (25), (51) imply: % 43.11/6.99 | | | | (52) ~ (all_52_2 = e0) % 43.11/6.99 | | | | % 43.11/6.99 | | | | BETA: splitting (15) gives: % 43.11/6.99 | | | | % 43.11/6.99 | | | | Case 1: % 43.11/6.99 | | | | | % 43.11/6.99 | | | | | (53) all_56_11 = e3 % 43.11/6.99 | | | | | % 43.11/6.99 | | | | | REF_CLOSE: (36), (43), (53) are inconsistent by sub-proof #24. % 43.11/6.99 | | | | | % 43.11/6.99 | | | | Case 2: % 43.11/6.99 | | | | | % 43.11/6.99 | | | | | (54) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.99 | | | | | % 43.11/6.99 | | | | | BETA: splitting (54) gives: % 43.11/6.99 | | | | | % 43.11/6.99 | | | | | Case 1: % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | | (55) all_56_11 = e2 % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | | REF_CLOSE: (36), (44), (55) are inconsistent by sub-proof #23. % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | Case 2: % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | | (56) ~ (all_56_11 = e2) % 43.11/6.99 | | | | | | (57) all_56_11 = e1 | all_56_11 = e0 % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | | BETA: splitting (57) gives: % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | | Case 1: % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | (58) all_56_11 = e1 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | COMBINE_EQS: (36), (58) imply: % 43.11/6.99 | | | | | | | (59) all_8_1 = e1 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | SIMP: (59) implies: % 43.11/6.99 | | | | | | | (60) all_8_1 = e1 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | REDUCE: (33), (60) imply: % 43.11/6.99 | | | | | | | (61) $false % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | CLOSE: (61) is inconsistent. % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | Case 2: % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | (62) all_56_11 = e0 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | COMBINE_EQS: (36), (62) imply: % 43.11/6.99 | | | | | | | (63) all_8_1 = e0 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | SIMP: (63) implies: % 43.11/6.99 | | | | | | | (64) all_8_1 = e0 % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | REDUCE: (38), (64) imply: % 43.11/6.99 | | | | | | | (65) ~ (all_52_1 = e0) % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | REDUCE: (44), (64) imply: % 43.11/6.99 | | | | | | | (66) ~ (e2 = e0) % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | SIMP: (66) implies: % 43.11/6.99 | | | | | | | (67) ~ (e2 = e0) % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | REDUCE: (33), (64) imply: % 43.11/6.99 | | | | | | | (68) ~ (e1 = e0) % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | SIMP: (68) implies: % 43.11/6.99 | | | | | | | (69) ~ (e1 = e0) % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | BETA: splitting (30) gives: % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | | Case 1: % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | (70) all_58_0 = e0 % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | COMBINE_EQS: (3), (70) imply: % 43.11/6.99 | | | | | | | | (71) all_4_2 = e0 % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | COMBINE_EQS: (29), (71) imply: % 43.11/6.99 | | | | | | | | (72) all_52_15 = e0 % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | REF_CLOSE: (5), (6), (18), (20), (23), (49), (67), (69), (72) % 43.11/6.99 | | | | | | | | are inconsistent by sub-proof #21. % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | Case 2: % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | (73) all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | | REF_CLOSE: (12), (13), (19), (37), (52), (65), (73) are % 43.11/6.99 | | | | | | | | inconsistent by sub-proof #28. % 43.11/6.99 | | | | | | | | % 43.11/6.99 | | | | | | | End of split % 43.11/6.99 | | | | | | | % 43.11/6.99 | | | | | | End of split % 43.11/6.99 | | | | | | % 43.11/6.99 | | | | | End of split % 43.11/6.99 | | | | | % 43.11/6.99 | | | | End of split % 43.11/6.99 | | | | % 43.11/6.99 | | | End of split % 43.11/6.99 | | | % 43.11/6.99 | | End of split % 43.11/6.99 | | % 43.11/6.99 | Case 2: % 43.11/6.99 | | % 43.11/6.99 | | (74) ~ (all_50_2 = e3) % 43.11/6.99 | | % 43.11/6.99 | | REDUCE: (28), (74) imply: % 43.11/6.99 | | (75) $false % 43.11/6.99 | | % 43.11/6.99 | | CLOSE: (75) is inconsistent. % 43.11/6.99 | | % 43.11/6.99 | End of split % 43.11/6.99 | % 43.11/6.99 End of proof % 43.11/6.99 % 43.11/6.99 Sub-proof #17 shows that the following formulas are inconsistent: % 43.11/6.99 ---------------------------------------------------------------- % 43.11/6.99 (1) op(all_8_2, e2) = e1 % 43.11/6.99 (2) ~ (all_52_10 = all_10_2) % 43.11/6.99 (3) op(e3, e2) = all_52_6 % 43.11/6.99 (4) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/6.99 (5) ~ (e2 = e0) % 43.11/6.99 (6) all_58_7 = all_52_7 % 43.11/6.99 (7) all_26_1 = all_8_1 % 43.11/6.99 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.99 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.99 (9) all_52_11 = all_8_2 % 43.11/6.99 (10) op(e2, all_8_2) = all_8_1 % 43.11/6.99 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/6.99 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/6.99 (12) ~ (all_52_10 = all_52_12) % 43.11/6.99 (13) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/6.99 (14) ~ (all_52_6 = all_10_2) % 43.11/6.99 (15) all_52_9 = all_10_2 % 43.11/6.99 (16) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/6.99 (17) all_52_13 = all_6_2 % 43.11/6.99 (18) all_58_2 = all_6_2 % 43.11/6.99 (19) all_58_14 = all_52_12 % 43.11/6.99 (20) ~ (e3 = e0) % 43.11/6.99 (21) all_58_1 = all_52_2 % 43.11/6.99 (22) all_26_2 = all_8_2 % 43.11/6.99 (23) ~ (all_52_6 = all_52_7) % 43.11/6.99 (24) ~ (all_52_10 = all_8_2) % 43.11/6.99 (25) ~ (all_52_6 = all_8_2) % 43.11/6.99 (26) op(e2, e3) = all_52_10 % 43.11/6.99 (27) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/6.99 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/6.99 (28) all_56_11 = all_52_10 % 43.11/6.99 (29) ~ (all_52_2 = all_4_2) % 43.11/6.99 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/6.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/6.99 (31) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/6.99 (32) all_52_15 = all_4_2 % 43.11/6.99 % 43.11/6.99 Begin of proof % 43.11/6.99 | % 43.11/6.99 | ALPHA: (31) implies: % 43.11/6.99 | (33) all_52_11 = e3 % 43.11/6.99 | (34) ~ (all_52_10 = e2) % 43.11/6.99 | % 43.11/6.99 | COMBINE_EQS: (9), (33) imply: % 43.11/6.99 | (35) all_8_2 = e3 % 43.11/6.99 | % 43.11/6.99 | SIMP: (35) implies: % 43.11/6.99 | (36) all_8_2 = e3 % 43.11/6.99 | % 43.11/6.99 | COMBINE_EQS: (22), (36) imply: % 43.11/6.99 | (37) all_26_2 = e3 % 43.11/6.99 | % 43.11/6.99 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 43.11/6.99 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 43.11/6.99 | (26), (27), (28), (29), (30), (32), (33), (34), (36), (37) are % 43.11/6.99 | inconsistent by sub-proof #19. % 43.11/6.99 | % 43.11/6.99 End of proof % 43.11/6.99 % 43.11/6.99 Sub-proof #18 shows that the following formulas are inconsistent: % 43.11/6.99 ---------------------------------------------------------------- % 43.11/6.99 (1) op(all_8_2, e2) = e1 % 43.11/6.99 (2) ~ (all_52_10 = all_10_2) % 43.11/6.99 (3) op(e3, e2) = all_52_6 % 43.11/6.99 (4) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/6.99 (5) ~ (e2 = e0) % 43.11/6.99 (6) all_58_7 = all_52_7 % 43.11/6.99 (7) all_26_1 = all_8_1 % 43.11/6.99 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/6.99 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/6.99 (9) all_52_11 = all_8_2 % 43.11/6.99 (10) op(e2, all_8_2) = all_8_1 % 43.11/7.00 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.00 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.00 (12) ~ (all_52_10 = all_52_12) % 43.11/7.00 (13) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/7.00 (14) ~ (all_52_6 = all_10_2) % 43.11/7.00 (15) all_52_9 = all_10_2 % 43.11/7.00 (16) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/7.00 (17) all_52_13 = all_6_2 % 43.11/7.00 (18) all_58_2 = all_6_2 % 43.11/7.00 (19) all_58_14 = all_52_12 % 43.11/7.00 (20) ~ (e3 = e0) % 43.11/7.00 (21) all_58_1 = all_52_2 % 43.11/7.00 (22) all_26_2 = all_8_2 % 43.11/7.00 (23) ~ (all_52_6 = all_52_7) % 43.11/7.00 (24) ~ (all_52_10 = all_8_2) % 43.11/7.00 (25) ~ (all_52_6 = all_8_2) % 43.11/7.00 (26) op(e2, e3) = all_52_10 % 43.11/7.00 (27) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.00 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.00 (28) all_56_11 = all_52_10 % 43.11/7.00 (29) ~ (all_52_2 = all_4_2) % 43.11/7.00 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.00 (31) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.11/7.00 (32) all_52_15 = all_4_2 % 43.11/7.00 % 43.11/7.00 Begin of proof % 43.11/7.00 | % 43.11/7.00 | ALPHA: (31) implies: % 43.11/7.00 | (33) all_52_11 = e3 % 43.11/7.00 | (34) ~ (all_52_10 = e2) % 43.11/7.00 | % 43.11/7.00 | COMBINE_EQS: (9), (33) imply: % 43.11/7.00 | (35) all_8_2 = e3 % 43.11/7.00 | % 43.11/7.00 | COMBINE_EQS: (22), (35) imply: % 43.11/7.00 | (36) all_26_2 = e3 % 43.11/7.00 | % 43.11/7.00 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 43.11/7.00 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 43.11/7.00 | (26), (27), (28), (29), (30), (32), (33), (34), (35), (36) are % 43.11/7.00 | inconsistent by sub-proof #19. % 43.11/7.00 | % 43.11/7.00 End of proof % 43.11/7.00 % 43.11/7.00 Sub-proof #19 shows that the following formulas are inconsistent: % 43.11/7.00 ---------------------------------------------------------------- % 43.11/7.00 (1) op(all_8_2, e2) = e1 % 43.11/7.00 (2) ~ (all_52_10 = all_10_2) % 43.11/7.00 (3) op(e3, e2) = all_52_6 % 43.11/7.00 (4) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.00 (5) all_8_2 = e3 % 43.11/7.00 (6) ~ (e2 = e0) % 43.11/7.00 (7) all_58_7 = all_52_7 % 43.11/7.00 (8) all_26_1 = all_8_1 % 43.11/7.00 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.00 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.00 (10) op(e2, all_8_2) = all_8_1 % 43.11/7.00 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.00 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.00 (12) ~ (all_52_10 = all_52_12) % 43.11/7.00 (13) ~ (all_52_10 = e2) % 43.11/7.00 (14) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/7.00 (15) ~ (all_52_6 = all_10_2) % 43.11/7.00 (16) all_52_9 = all_10_2 % 43.11/7.00 (17) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/7.00 (18) all_52_13 = all_6_2 % 43.11/7.00 (19) all_58_2 = all_6_2 % 43.11/7.00 (20) all_58_14 = all_52_12 % 43.11/7.00 (21) all_26_2 = e3 % 43.11/7.00 (22) ~ (e3 = e0) % 43.11/7.00 (23) all_52_11 = e3 % 43.11/7.00 (24) all_58_1 = all_52_2 % 43.11/7.00 (25) ~ (all_52_6 = all_52_7) % 43.11/7.00 (26) ~ (all_52_10 = all_8_2) % 43.11/7.00 (27) ~ (all_52_6 = all_8_2) % 43.11/7.00 (28) op(e2, e3) = all_52_10 % 43.11/7.00 (29) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.00 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.00 (30) all_56_11 = all_52_10 % 43.11/7.00 (31) ~ (all_52_2 = all_4_2) % 43.11/7.00 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.00 (33) all_52_15 = all_4_2 % 43.11/7.00 % 43.11/7.00 Begin of proof % 43.11/7.00 | % 43.11/7.00 | REDUCE: (5), (27) imply: % 43.11/7.00 | (34) ~ (all_52_6 = e3) % 43.11/7.00 | % 43.11/7.00 | REDUCE: (5), (26) imply: % 43.11/7.00 | (35) ~ (all_52_10 = e3) % 43.11/7.00 | % 43.11/7.00 | REDUCE: (1), (5) imply: % 43.11/7.00 | (36) op(e3, e2) = e1 % 43.11/7.00 | % 43.11/7.00 | REDUCE: (5), (10) imply: % 43.11/7.00 | (37) op(e2, e3) = all_8_1 % 43.11/7.00 | % 43.11/7.00 | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), % 43.11/7.00 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (28), % 43.11/7.00 | (29), (30), (31), (32), (33), (34), (35), (36), (37) are % 43.11/7.00 | inconsistent by sub-proof #20. % 43.11/7.00 | % 43.11/7.00 End of proof % 43.11/7.00 % 43.11/7.00 Sub-proof #20 shows that the following formulas are inconsistent: % 43.11/7.00 ---------------------------------------------------------------- % 43.11/7.00 (1) ~ (all_52_10 = all_10_2) % 43.11/7.00 (2) op(e3, e2) = all_52_6 % 43.11/7.00 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.00 (4) ~ (e2 = e0) % 43.11/7.00 (5) all_58_7 = all_52_7 % 43.11/7.00 (6) all_26_1 = all_8_1 % 43.11/7.00 (7) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.00 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.00 (8) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.00 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.00 (9) ~ (all_52_10 = all_52_12) % 43.11/7.00 (10) op(e2, e3) = all_8_1 % 43.11/7.00 (11) ~ (all_52_10 = e2) % 43.11/7.00 (12) ~ (all_26_1 = e0) | ~ (all_26_2 = e3) % 43.11/7.00 (13) ~ (all_52_6 = all_10_2) % 43.11/7.00 (14) all_52_9 = all_10_2 % 43.11/7.00 (15) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/7.00 (16) all_52_13 = all_6_2 % 43.11/7.00 (17) all_58_2 = all_6_2 % 43.11/7.00 (18) all_58_14 = all_52_12 % 43.11/7.00 (19) all_26_2 = e3 % 43.11/7.00 (20) ~ (all_52_6 = e3) % 43.11/7.00 (21) ~ (e3 = e0) % 43.11/7.00 (22) all_52_11 = e3 % 43.11/7.00 (23) op(e3, e2) = e1 % 43.11/7.00 (24) all_58_1 = all_52_2 % 43.11/7.00 (25) ~ (all_52_6 = all_52_7) % 43.11/7.00 (26) op(e2, e3) = all_52_10 % 43.11/7.00 (27) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.00 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.00 (28) all_56_11 = all_52_10 % 43.11/7.00 (29) ~ (all_52_2 = all_4_2) % 43.11/7.00 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.00 (31) all_52_15 = all_4_2 % 43.11/7.00 (32) ~ (all_52_10 = e3) % 43.11/7.00 % 43.11/7.00 Begin of proof % 43.11/7.00 | % 43.11/7.00 | BETA: splitting (12) gives: % 43.11/7.00 | % 43.11/7.00 | Case 1: % 43.11/7.00 | | % 43.11/7.00 | | (33) ~ (all_26_1 = e0) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (6), (33) imply: % 43.11/7.00 | | (34) ~ (all_8_1 = e0) % 43.11/7.00 | | % 43.11/7.00 | | GROUND_INST: instantiating (30) with all_52_10, all_8_1, e3, e2, simplifying % 43.11/7.00 | | with (10), (26) gives: % 43.11/7.00 | | (35) all_52_10 = all_8_1 % 43.11/7.00 | | % 43.11/7.00 | | GROUND_INST: instantiating (30) with all_52_6, e1, e2, e3, simplifying with % 43.11/7.00 | | (2), (23) gives: % 43.11/7.00 | | (36) all_52_6 = e1 % 43.11/7.00 | | % 43.11/7.00 | | COMBINE_EQS: (28), (35) imply: % 43.11/7.00 | | (37) all_56_11 = all_8_1 % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (25), (36) imply: % 43.11/7.00 | | (38) ~ (all_52_7 = e1) % 43.11/7.00 | | % 43.11/7.00 | | SIMP: (38) implies: % 43.11/7.00 | | (39) ~ (all_52_7 = e1) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (13), (36) imply: % 43.11/7.00 | | (40) ~ (all_10_2 = e1) % 43.11/7.00 | | % 43.11/7.00 | | SIMP: (40) implies: % 43.11/7.00 | | (41) ~ (all_10_2 = e1) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (20), (36) imply: % 43.11/7.00 | | (42) ~ (e3 = e1) % 43.11/7.00 | | % 43.11/7.00 | | SIMP: (42) implies: % 43.11/7.00 | | (43) ~ (e3 = e1) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (9), (35) imply: % 43.11/7.00 | | (44) ~ (all_52_12 = all_8_1) % 43.11/7.00 | | % 43.11/7.00 | | SIMP: (44) implies: % 43.11/7.00 | | (45) ~ (all_52_12 = all_8_1) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (1), (35) imply: % 43.11/7.00 | | (46) ~ (all_10_2 = all_8_1) % 43.11/7.00 | | % 43.11/7.00 | | SIMP: (46) implies: % 43.11/7.00 | | (47) ~ (all_10_2 = all_8_1) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (32), (35) imply: % 43.11/7.00 | | (48) ~ (all_8_1 = e3) % 43.11/7.00 | | % 43.11/7.00 | | REDUCE: (11), (35) imply: % 43.11/7.00 | | (49) ~ (all_8_1 = e2) % 43.11/7.00 | | % 43.11/7.00 | | BETA: splitting (27) gives: % 43.11/7.00 | | % 43.11/7.00 | | Case 1: % 43.11/7.00 | | | % 43.11/7.00 | | | (50) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.11/7.00 | | | % 43.11/7.00 | | | REF_CLOSE: (14), (41), (50) are inconsistent by sub-proof #58. % 43.11/7.00 | | | % 43.11/7.00 | | Case 2: % 43.11/7.00 | | | % 43.11/7.00 | | | (51) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.11/7.00 | | | (all_52_5 = e0)) % 43.11/7.00 | | | % 43.11/7.00 | | | BETA: splitting (51) gives: % 43.11/7.00 | | | % 43.11/7.00 | | | Case 1: % 43.11/7.00 | | | | % 43.11/7.00 | | | | (52) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.11/7.00 | | | | % 43.11/7.00 | | | | REF_CLOSE: (22), (43), (52) are inconsistent by sub-proof #74. % 43.11/7.00 | | | | % 43.11/7.00 | | | Case 2: % 43.11/7.00 | | | | % 43.11/7.00 | | | | (53) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.11/7.00 | | | | % 43.11/7.00 | | | | ALPHA: (53) implies: % 43.11/7.00 | | | | (54) all_52_15 = e1 % 43.11/7.00 | | | | % 43.11/7.00 | | | | COMBINE_EQS: (31), (54) imply: % 43.11/7.00 | | | | (55) all_4_2 = e1 % 43.11/7.00 | | | | % 43.11/7.00 | | | | SIMP: (55) implies: % 43.11/7.00 | | | | (56) all_4_2 = e1 % 43.11/7.00 | | | | % 43.11/7.00 | | | | REDUCE: (29), (56) imply: % 43.11/7.00 | | | | (57) ~ (all_52_2 = e1) % 43.11/7.00 | | | | % 43.11/7.00 | | | | BETA: splitting (15) gives: % 43.11/7.00 | | | | % 43.11/7.00 | | | | Case 1: % 43.11/7.00 | | | | | % 43.11/7.00 | | | | | (58) all_56_11 = e3 % 43.11/7.00 | | | | | % 43.11/7.00 | | | | | REF_CLOSE: (37), (48), (58) are inconsistent by sub-proof #24. % 43.11/7.00 | | | | | % 43.11/7.00 | | | | Case 2: % 43.11/7.00 | | | | | % 43.11/7.00 | | | | | (59) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 43.11/7.00 | | | | | % 43.11/7.00 | | | | | BETA: splitting (59) gives: % 43.11/7.00 | | | | | % 43.11/7.00 | | | | | Case 1: % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | | (60) all_56_11 = e2 % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | | REF_CLOSE: (37), (49), (60) are inconsistent by sub-proof #23. % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | Case 2: % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | | (61) ~ (all_56_11 = e2) % 43.11/7.00 | | | | | | (62) all_56_11 = e1 | all_56_11 = e0 % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | | BETA: splitting (62) gives: % 43.11/7.00 | | | | | | % 43.11/7.00 | | | | | | Case 1: % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | (63) all_56_11 = e1 % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | COMBINE_EQS: (37), (63) imply: % 43.11/7.00 | | | | | | | (64) all_8_1 = e1 % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | SIMP: (64) implies: % 43.11/7.00 | | | | | | | (65) all_8_1 = e1 % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | REDUCE: (45), (65) imply: % 43.11/7.00 | | | | | | | (66) ~ (all_52_12 = e1) % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | REDUCE: (49), (65) imply: % 43.11/7.00 | | | | | | | (67) ~ (e2 = e1) % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | SIMP: (67) implies: % 43.11/7.00 | | | | | | | (68) ~ (e2 = e1) % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | REDUCE: (34), (65) imply: % 43.11/7.00 | | | | | | | (69) ~ (e1 = e0) % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | BETA: splitting (3) gives: % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | (70) all_58_1 = e1 % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | COMBINE_EQS: (24), (70) imply: % 43.11/7.00 | | | | | | | | (71) all_52_2 = e1 % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | REDUCE: (57), (71) imply: % 43.11/7.00 | | | | | | | | (72) $false % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | CLOSE: (72) is inconsistent. % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | (73) all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | BETA: splitting (73) gives: % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | (74) all_58_2 = e1 % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | COMBINE_EQS: (17), (74) imply: % 43.11/7.00 | | | | | | | | | (75) all_6_2 = e1 % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | COMBINE_EQS: (16), (75) imply: % 43.11/7.00 | | | | | | | | | (76) all_52_13 = e1 % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | BETA: splitting (7) gives: % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | (77) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | ALPHA: (77) implies: % 43.11/7.00 | | | | | | | | | | (78) all_52_9 = e2 % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | COMBINE_EQS: (14), (78) imply: % 43.11/7.00 | | | | | | | | | | (79) all_10_2 = e2 % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | SIMP: (79) implies: % 43.11/7.00 | | | | | | | | | | (80) all_10_2 = e2 % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | BETA: splitting (8) gives: % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | (81) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | REF_CLOSE: (4), (78), (81) are inconsistent by sub-proof #64. % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | (82) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 % 43.11/7.00 | | | | | | | | | | | = e0 & ~ (all_52_2 = e1)) % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | BETA: splitting (82) gives: % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | (83) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | REF_CLOSE: (21), (22), (83) are inconsistent by sub-proof % 43.11/7.00 | | | | | | | | | | | | #22. % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | (84) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | ALPHA: (84) implies: % 43.11/7.00 | | | | | | | | | | | | (85) all_52_13 = e0 % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | COMBINE_EQS: (76), (85) imply: % 43.11/7.00 | | | | | | | | | | | | (86) e1 = e0 % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | SIMP: (86) implies: % 43.11/7.00 | | | | | | | | | | | | (87) e1 = e0 % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | COMBINE_EQS: (54), (87) imply: % 43.11/7.00 | | | | | | | | | | | | (88) all_52_15 = e0 % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | | REF_CLOSE: (4), (7), (22), (27), (43), (68), (69), (85), (88) % 43.11/7.00 | | | | | | | | | | | | are inconsistent by sub-proof #21. % 43.11/7.00 | | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | End of split % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | End of split % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | (89) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = % 43.11/7.00 | | | | | | | | | | e2 & ~ (all_52_8 = e0)) % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | BETA: splitting (89) gives: % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | Case 1: % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | (90) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | ALPHA: (90) implies: % 43.11/7.00 | | | | | | | | | | | (91) all_52_13 = e2 % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | COMBINE_EQS: (76), (91) imply: % 43.11/7.00 | | | | | | | | | | | (92) e2 = e1 % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | REDUCE: (68), (92) imply: % 43.11/7.00 | | | | | | | | | | | (93) $false % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | CLOSE: (93) is inconsistent. % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | (94) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | ALPHA: (94) implies: % 43.11/7.00 | | | | | | | | | | | (95) all_52_15 = e2 % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | COMBINE_EQS: (54), (95) imply: % 43.11/7.00 | | | | | | | | | | | (96) e2 = e1 % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | REDUCE: (68), (96) imply: % 43.11/7.00 | | | | | | | | | | | (97) $false % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | | CLOSE: (97) is inconsistent. % 43.11/7.00 | | | | | | | | | | | % 43.11/7.00 | | | | | | | | | | End of split % 43.11/7.00 | | | | | | | | | | % 43.11/7.00 | | | | | | | | | End of split % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | Case 2: % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | (98) all_58_7 = e1 | all_58_14 = e1 % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | | REF_CLOSE: (5), (18), (39), (66), (98) are inconsistent by % 43.11/7.00 | | | | | | | | | sub-proof #53. % 43.11/7.00 | | | | | | | | | % 43.11/7.00 | | | | | | | | End of split % 43.11/7.00 | | | | | | | | % 43.11/7.00 | | | | | | | End of split % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | Case 2: % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | (99) all_56_11 = e0 % 43.11/7.00 | | | | | | | % 43.11/7.00 | | | | | | | COMBINE_EQS: (37), (99) imply: % 43.11/7.01 | | | | | | | (100) all_8_1 = e0 % 43.11/7.01 | | | | | | | % 43.11/7.01 | | | | | | | SIMP: (100) implies: % 43.11/7.01 | | | | | | | (101) all_8_1 = e0 % 43.11/7.01 | | | | | | | % 43.11/7.01 | | | | | | | REDUCE: (34), (101) imply: % 43.11/7.01 | | | | | | | (102) $false % 43.11/7.01 | | | | | | | % 43.11/7.01 | | | | | | | CLOSE: (102) is inconsistent. % 43.11/7.01 | | | | | | | % 43.11/7.01 | | | | | | End of split % 43.11/7.01 | | | | | | % 43.11/7.01 | | | | | End of split % 43.11/7.01 | | | | | % 43.11/7.01 | | | | End of split % 43.11/7.01 | | | | % 43.11/7.01 | | | End of split % 43.11/7.01 | | | % 43.11/7.01 | | End of split % 43.11/7.01 | | % 43.11/7.01 | Case 2: % 43.11/7.01 | | % 43.11/7.01 | | (103) ~ (all_26_2 = e3) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (19), (103) imply: % 43.11/7.01 | | (104) $false % 43.11/7.01 | | % 43.11/7.01 | | CLOSE: (104) is inconsistent. % 43.11/7.01 | | % 43.11/7.01 | End of split % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #21 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) ~ (e2 = e0) % 43.11/7.01 (2) ~ (e3 = e1) % 43.11/7.01 (3) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.01 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.01 (4) all_52_13 = e0 % 43.11/7.01 (5) all_52_15 = e0 % 43.11/7.01 (6) all_52_11 = e3 % 43.11/7.01 (7) ~ (e2 = e1) % 43.11/7.01 (8) ~ (e1 = e0) % 43.11/7.01 (9) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.01 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | BETA: splitting (9) gives: % 43.11/7.01 | % 43.11/7.01 | Case 1: % 43.11/7.01 | | % 43.11/7.01 | | (10) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.11/7.01 | | % 43.11/7.01 | | ALPHA: (10) implies: % 43.11/7.01 | | (11) all_52_9 = e1 % 43.11/7.01 | | % 43.11/7.01 | | BETA: splitting (3) gives: % 43.11/7.01 | | % 43.11/7.01 | | Case 1: % 43.11/7.01 | | | % 43.11/7.01 | | | (12) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.11/7.01 | | | % 43.11/7.01 | | | ALPHA: (12) implies: % 43.11/7.01 | | | (13) all_52_9 = e2 % 43.11/7.01 | | | % 43.11/7.01 | | | COMBINE_EQS: (11), (13) imply: % 43.11/7.01 | | | (14) e2 = e1 % 43.11/7.01 | | | % 43.11/7.01 | | | REDUCE: (7), (14) imply: % 43.11/7.01 | | | (15) $false % 43.11/7.01 | | | % 43.11/7.01 | | | CLOSE: (15) is inconsistent. % 43.11/7.01 | | | % 43.11/7.01 | | Case 2: % 43.11/7.01 | | | % 43.11/7.01 | | | (16) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.11/7.01 | | | (all_52_8 = e0)) % 43.11/7.01 | | | % 43.11/7.01 | | | BETA: splitting (16) gives: % 43.11/7.01 | | | % 43.11/7.01 | | | Case 1: % 43.11/7.01 | | | | % 43.11/7.01 | | | | (17) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.11/7.01 | | | | % 43.11/7.01 | | | | REF_CLOSE: (1), (4), (17) are inconsistent by sub-proof #71. % 43.11/7.01 | | | | % 43.11/7.01 | | | Case 2: % 43.11/7.01 | | | | % 43.11/7.01 | | | | (18) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.11/7.01 | | | | % 43.11/7.01 | | | | REF_CLOSE: (1), (5), (18) are inconsistent by sub-proof #43. % 43.11/7.01 | | | | % 43.11/7.01 | | | End of split % 43.11/7.01 | | | % 43.11/7.01 | | End of split % 43.11/7.01 | | % 43.11/7.01 | Case 2: % 43.11/7.01 | | % 43.11/7.01 | | (19) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.11/7.01 | | (all_52_5 = e0)) % 43.11/7.01 | | % 43.11/7.01 | | BETA: splitting (19) gives: % 43.11/7.01 | | % 43.11/7.01 | | Case 1: % 43.11/7.01 | | | % 43.11/7.01 | | | (20) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.11/7.01 | | | % 43.11/7.01 | | | REF_CLOSE: (2), (6), (20) are inconsistent by sub-proof #69. % 43.11/7.01 | | | % 43.11/7.01 | | Case 2: % 43.11/7.01 | | | % 43.11/7.01 | | | (21) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.11/7.01 | | | % 43.11/7.01 | | | REF_CLOSE: (5), (8), (21) are inconsistent by sub-proof #44. % 43.11/7.01 | | | % 43.11/7.01 | | End of split % 43.11/7.01 | | % 43.11/7.01 | End of split % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #22 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.11/7.01 (2) all_52_11 = e3 % 43.11/7.01 (3) ~ (e3 = e0) % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | ALPHA: (1) implies: % 43.11/7.01 | (4) all_52_11 = e0 % 43.11/7.01 | % 43.11/7.01 | COMBINE_EQS: (2), (4) imply: % 43.11/7.01 | (5) e3 = e0 % 43.11/7.01 | % 43.11/7.01 | SIMP: (5) implies: % 43.11/7.01 | (6) e3 = e0 % 43.11/7.01 | % 43.11/7.01 | REDUCE: (3), (6) imply: % 43.11/7.01 | (7) $false % 43.11/7.01 | % 43.11/7.01 | CLOSE: (7) is inconsistent. % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #23 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) all_56_11 = all_8_1 % 43.11/7.01 (2) all_56_11 = e2 % 43.11/7.01 (3) ~ (all_8_1 = e2) % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | COMBINE_EQS: (1), (2) imply: % 43.11/7.01 | (4) all_8_1 = e2 % 43.11/7.01 | % 43.11/7.01 | SIMP: (4) implies: % 43.11/7.01 | (5) all_8_1 = e2 % 43.11/7.01 | % 43.11/7.01 | REDUCE: (3), (5) imply: % 43.11/7.01 | (6) $false % 43.11/7.01 | % 43.11/7.01 | CLOSE: (6) is inconsistent. % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #24 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) all_56_11 = all_8_1 % 43.11/7.01 (2) all_56_11 = e3 % 43.11/7.01 (3) ~ (all_8_1 = e3) % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | COMBINE_EQS: (1), (2) imply: % 43.11/7.01 | (4) all_8_1 = e3 % 43.11/7.01 | % 43.11/7.01 | SIMP: (4) implies: % 43.11/7.01 | (5) all_8_1 = e3 % 43.11/7.01 | % 43.11/7.01 | REDUCE: (3), (5) imply: % 43.11/7.01 | (6) $false % 43.11/7.01 | % 43.11/7.01 | CLOSE: (6) is inconsistent. % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #25 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) ~ (all_52_0 = all_52_3) % 43.11/7.01 (2) all_58_0 = all_4_2 % 43.11/7.01 (3) ~ (all_52_3 = all_6_2) % 43.11/7.01 (4) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0 % 43.11/7.01 (5) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.01 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.01 (6) all_52_11 = all_8_2 % 43.11/7.01 (7) op(all_6_2, e1) = e0 % 43.11/7.01 (8) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.01 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.01 (9) op(e1, all_6_2) = all_6_1 % 43.11/7.01 (10) all_58_5 = all_52_1 % 43.11/7.01 (11) ~ (all_52_3 = all_10_2) % 43.11/7.01 (12) all_34_2 = all_6_2 % 43.11/7.01 (13) all_58_11 = all_52_0 % 43.11/7.01 (14) all_52_9 = all_10_2 % 43.11/7.01 (15) all_52_13 = all_6_2 % 43.11/7.01 (16) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 43.11/7.01 (17) all_34_1 = all_6_1 % 43.11/7.01 (18) ~ (all_52_1 = all_8_2) % 43.11/7.01 (19) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/7.01 (20) ~ (all_52_12 = all_6_2) % 43.11/7.01 (21) all_58_1 = all_52_2 % 43.11/7.01 (22) op(e3, e1) = all_52_3 % 43.11/7.01 (23) ~ (e2 = e1) % 43.11/7.01 (24) ~ (all_52_2 = all_52_12) % 43.11/7.01 (25) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.01 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.01 (26) ~ (e3 = e2) % 43.11/7.01 (27) op(e1, e3) = all_52_12 % 43.11/7.01 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.01 (29) all_56_7 = all_52_12 % 43.11/7.01 (30) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.11/7.01 (31) all_52_15 = all_4_2 % 43.11/7.01 (32) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | ALPHA: (19) implies: % 43.11/7.01 | (33) all_52_13 = e3 % 43.11/7.01 | (34) ~ (all_52_12 = e1) % 43.11/7.01 | % 43.11/7.01 | COMBINE_EQS: (15), (33) imply: % 43.11/7.01 | (35) all_6_2 = e3 % 43.11/7.01 | % 43.11/7.01 | SIMP: (35) implies: % 43.11/7.01 | (36) all_6_2 = e3 % 43.11/7.01 | % 43.11/7.01 | COMBINE_EQS: (12), (36) imply: % 43.11/7.01 | (37) all_34_2 = e3 % 43.11/7.01 | % 43.11/7.01 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 43.11/7.01 | (14), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26), % 43.11/7.01 | (27), (28), (29), (30), (31), (32), (33), (34), (36), (37) are % 43.11/7.01 | inconsistent by sub-proof #26. % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #26 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) ~ (all_52_0 = all_52_3) % 43.11/7.01 (2) all_58_0 = all_4_2 % 43.11/7.01 (3) ~ (all_52_3 = all_6_2) % 43.11/7.01 (4) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0 % 43.11/7.01 (5) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.01 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.01 (6) all_52_11 = all_8_2 % 43.11/7.01 (7) op(all_6_2, e1) = e0 % 43.11/7.01 (8) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.01 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.01 (9) op(e1, all_6_2) = all_6_1 % 43.11/7.01 (10) all_58_5 = all_52_1 % 43.11/7.01 (11) ~ (all_52_3 = all_10_2) % 43.11/7.01 (12) ~ (all_52_12 = e1) % 43.11/7.01 (13) all_58_11 = all_52_0 % 43.11/7.01 (14) all_52_9 = all_10_2 % 43.11/7.01 (15) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 43.11/7.01 (16) all_34_1 = all_6_1 % 43.11/7.01 (17) ~ (all_52_1 = all_8_2) % 43.11/7.01 (18) all_6_2 = e3 % 43.11/7.01 (19) ~ (all_52_12 = all_6_2) % 43.11/7.01 (20) all_58_1 = all_52_2 % 43.11/7.01 (21) op(e3, e1) = all_52_3 % 43.11/7.01 (22) ~ (e2 = e1) % 43.11/7.01 (23) ~ (all_52_2 = all_52_12) % 43.11/7.01 (24) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.01 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.01 (25) all_34_2 = e3 % 43.11/7.01 (26) ~ (e3 = e2) % 43.11/7.01 (27) op(e1, e3) = all_52_12 % 43.11/7.01 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.01 (29) all_56_7 = all_52_12 % 43.11/7.01 (30) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.11/7.01 (31) all_52_13 = e3 % 43.11/7.01 (32) all_52_15 = all_4_2 % 43.11/7.01 (33) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | REDUCE: (3), (18) imply: % 43.11/7.01 | (34) ~ (all_52_3 = e3) % 43.11/7.01 | % 43.11/7.01 | REDUCE: (18), (19) imply: % 43.11/7.01 | (35) ~ (all_52_12 = e3) % 43.11/7.01 | % 43.11/7.01 | REDUCE: (7), (18) imply: % 43.11/7.01 | (36) op(e3, e1) = e0 % 43.11/7.01 | % 43.11/7.01 | REDUCE: (9), (18) imply: % 43.11/7.01 | (37) op(e1, e3) = all_6_1 % 43.11/7.01 | % 43.11/7.01 | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15), % 43.11/7.01 | (16), (17), (20), (21), (22), (23), (24), (25), (26), (27), (28), % 43.11/7.01 | (29), (30), (31), (32), (33), (34), (35), (36), (37) are % 43.11/7.01 | inconsistent by sub-proof #27. % 43.11/7.01 | % 43.11/7.01 End of proof % 43.11/7.01 % 43.11/7.01 Sub-proof #27 shows that the following formulas are inconsistent: % 43.11/7.01 ---------------------------------------------------------------- % 43.11/7.01 (1) ~ (all_52_0 = all_52_3) % 43.11/7.01 (2) all_58_0 = all_4_2 % 43.11/7.01 (3) op(e3, e1) = e0 % 43.11/7.01 (4) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0 % 43.11/7.01 (5) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.01 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.01 (6) all_52_11 = all_8_2 % 43.11/7.01 (7) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.01 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.01 (8) ~ (all_52_3 = e3) % 43.11/7.01 (9) all_58_5 = all_52_1 % 43.11/7.01 (10) ~ (all_52_12 = e3) % 43.11/7.01 (11) ~ (all_52_3 = all_10_2) % 43.11/7.01 (12) ~ (all_52_12 = e1) % 43.11/7.01 (13) all_58_11 = all_52_0 % 43.11/7.01 (14) all_52_9 = all_10_2 % 43.11/7.01 (15) op(e1, e3) = all_6_1 % 43.11/7.01 (16) ~ (all_34_1 = e2) | ~ (all_34_2 = e3) % 43.11/7.01 (17) all_34_1 = all_6_1 % 43.11/7.01 (18) ~ (all_52_1 = all_8_2) % 43.11/7.01 (19) all_58_1 = all_52_2 % 43.11/7.01 (20) op(e3, e1) = all_52_3 % 43.11/7.01 (21) ~ (e2 = e1) % 43.11/7.01 (22) ~ (all_52_2 = all_52_12) % 43.11/7.01 (23) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.01 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.01 (24) all_34_2 = e3 % 43.11/7.01 (25) ~ (e3 = e2) % 43.11/7.01 (26) op(e1, e3) = all_52_12 % 43.11/7.01 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.01 (28) all_56_7 = all_52_12 % 43.11/7.01 (29) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.11/7.01 (30) all_52_13 = e3 % 43.11/7.01 (31) all_52_15 = all_4_2 % 43.11/7.01 (32) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/7.01 % 43.11/7.01 Begin of proof % 43.11/7.01 | % 43.11/7.01 | BETA: splitting (16) gives: % 43.11/7.01 | % 43.11/7.01 | Case 1: % 43.11/7.01 | | % 43.11/7.01 | | (33) ~ (all_34_1 = e2) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (17), (33) imply: % 43.11/7.01 | | (34) ~ (all_6_1 = e2) % 43.11/7.01 | | % 43.11/7.01 | | GROUND_INST: instantiating (27) with all_52_12, all_6_1, e3, e1, simplifying % 43.11/7.01 | | with (15), (26) gives: % 43.11/7.01 | | (35) all_52_12 = all_6_1 % 43.11/7.01 | | % 43.11/7.01 | | GROUND_INST: instantiating (27) with all_52_3, e0, e1, e3, simplifying with % 43.11/7.01 | | (3), (20) gives: % 43.11/7.01 | | (36) all_52_3 = e0 % 43.11/7.01 | | % 43.11/7.01 | | COMBINE_EQS: (28), (35) imply: % 43.11/7.01 | | (37) all_56_7 = all_6_1 % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (1), (36) imply: % 43.11/7.01 | | (38) ~ (all_52_0 = e0) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (22), (35) imply: % 43.11/7.01 | | (39) ~ (all_52_2 = all_6_1) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (11), (36) imply: % 43.11/7.01 | | (40) ~ (all_10_2 = e0) % 43.11/7.01 | | % 43.11/7.01 | | SIMP: (40) implies: % 43.11/7.01 | | (41) ~ (all_10_2 = e0) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (8), (36) imply: % 43.11/7.01 | | (42) ~ (e3 = e0) % 43.11/7.01 | | % 43.11/7.01 | | SIMP: (42) implies: % 43.11/7.01 | | (43) ~ (e3 = e0) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (10), (35) imply: % 43.11/7.01 | | (44) ~ (all_6_1 = e3) % 43.11/7.01 | | % 43.11/7.01 | | REDUCE: (12), (35) imply: % 43.11/7.01 | | (45) ~ (all_6_1 = e1) % 43.11/7.01 | | % 43.11/7.01 | | BETA: splitting (7) gives: % 43.11/7.01 | | % 43.11/7.01 | | Case 1: % 43.11/7.01 | | | % 43.11/7.01 | | | (46) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.11/7.01 | | | % 43.11/7.01 | | | REF_CLOSE: (14), (41), (46) are inconsistent by sub-proof #29. % 43.11/7.01 | | | % 43.11/7.01 | | Case 2: % 43.11/7.01 | | | % 43.11/7.01 | | | (47) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.11/7.01 | | | (all_52_2 = e1)) % 43.11/7.01 | | | % 43.11/7.01 | | | BETA: splitting (47) gives: % 43.11/7.01 | | | % 43.11/7.01 | | | Case 1: % 43.11/7.01 | | | | % 43.11/7.01 | | | | (48) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.11/7.01 | | | | % 43.11/7.01 | | | | ALPHA: (48) implies: % 43.11/7.01 | | | | (49) all_52_11 = e0 % 43.11/7.01 | | | | % 43.11/7.01 | | | | COMBINE_EQS: (6), (49) imply: % 43.11/7.01 | | | | (50) all_8_2 = e0 % 43.11/7.01 | | | | % 43.11/7.01 | | | | SIMP: (50) implies: % 43.11/7.01 | | | | (51) all_8_2 = e0 % 43.11/7.01 | | | | % 43.11/7.02 | | | | REDUCE: (18), (51) imply: % 43.11/7.02 | | | | (52) ~ (all_52_1 = e0) % 43.11/7.02 | | | | % 43.11/7.02 | | | | BETA: splitting (29) gives: % 43.11/7.02 | | | | % 43.11/7.02 | | | | Case 1: % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | (53) all_56_7 = e3 % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | COMBINE_EQS: (37), (53) imply: % 43.11/7.02 | | | | | (54) all_6_1 = e3 % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | SIMP: (54) implies: % 43.11/7.02 | | | | | (55) all_6_1 = e3 % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | REDUCE: (44), (55) imply: % 43.11/7.02 | | | | | (56) $false % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | CLOSE: (56) is inconsistent. % 43.11/7.02 | | | | | % 43.11/7.02 | | | | Case 2: % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | (57) all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | BETA: splitting (57) gives: % 43.11/7.02 | | | | | % 43.11/7.02 | | | | | Case 1: % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | (58) all_56_7 = e2 % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | COMBINE_EQS: (37), (58) imply: % 43.11/7.02 | | | | | | (59) all_6_1 = e2 % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | SIMP: (59) implies: % 43.11/7.02 | | | | | | (60) all_6_1 = e2 % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | REDUCE: (34), (60) imply: % 43.11/7.02 | | | | | | (61) $false % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | CLOSE: (61) is inconsistent. % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | Case 2: % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | (62) ~ (all_56_7 = e2) % 43.11/7.02 | | | | | | (63) all_56_7 = e1 | all_56_7 = e0 % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | BETA: splitting (63) gives: % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | | Case 1: % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | (64) all_56_7 = e1 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | COMBINE_EQS: (37), (64) imply: % 43.11/7.02 | | | | | | | (65) all_6_1 = e1 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | SIMP: (65) implies: % 43.11/7.02 | | | | | | | (66) all_6_1 = e1 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | REDUCE: (45), (66) imply: % 43.11/7.02 | | | | | | | (67) $false % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | CLOSE: (67) is inconsistent. % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | Case 2: % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | (68) all_56_7 = e0 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | COMBINE_EQS: (37), (68) imply: % 43.11/7.02 | | | | | | | (69) all_6_1 = e0 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | SIMP: (69) implies: % 43.11/7.02 | | | | | | | (70) all_6_1 = e0 % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | REDUCE: (39), (70) imply: % 43.11/7.02 | | | | | | | (71) ~ (all_52_2 = e0) % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | REDUCE: (34), (70) imply: % 43.11/7.02 | | | | | | | (72) ~ (e2 = e0) % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | SIMP: (72) implies: % 43.11/7.02 | | | | | | | (73) ~ (e2 = e0) % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | REDUCE: (45), (70) imply: % 43.11/7.02 | | | | | | | (74) ~ (e1 = e0) % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | SIMP: (74) implies: % 43.11/7.02 | | | | | | | (75) ~ (e1 = e0) % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | BETA: splitting (4) gives: % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | | Case 1: % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | (76) all_58_0 = e0 % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | COMBINE_EQS: (2), (76) imply: % 43.11/7.02 | | | | | | | | (77) all_4_2 = e0 % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | COMBINE_EQS: (31), (77) imply: % 43.11/7.02 | | | | | | | | (78) all_52_15 = e0 % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | REF_CLOSE: (5), (21), (23), (25), (30), (49), (73), (75), (78) % 43.11/7.02 | | | | | | | | are inconsistent by sub-proof #42. % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | Case 2: % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | (79) ~ (all_58_0 = e0) % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | REDUCE: (2), (79) imply: % 43.11/7.02 | | | | | | | | (80) ~ (all_4_2 = e0) % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | BETA: splitting (32) gives: % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | | Case 1: % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | (81) all_58_0 = e0 % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | COMBINE_EQS: (2), (81) imply: % 43.11/7.02 | | | | | | | | | (82) all_4_2 = e0 % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | REDUCE: (80), (82) imply: % 43.11/7.02 | | | | | | | | | (83) $false % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | CLOSE: (83) is inconsistent. % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | Case 2: % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | (84) all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | | REF_CLOSE: (9), (13), (19), (38), (52), (71), (84) are % 43.11/7.02 | | | | | | | | | inconsistent by sub-proof #28. % 43.11/7.02 | | | | | | | | | % 43.11/7.02 | | | | | | | | End of split % 43.11/7.02 | | | | | | | | % 43.11/7.02 | | | | | | | End of split % 43.11/7.02 | | | | | | | % 43.11/7.02 | | | | | | End of split % 43.11/7.02 | | | | | | % 43.11/7.02 | | | | | End of split % 43.11/7.02 | | | | | % 43.11/7.02 | | | | End of split % 43.11/7.02 | | | | % 43.11/7.02 | | | Case 2: % 43.11/7.02 | | | | % 43.11/7.02 | | | | (85) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.11/7.02 | | | | % 43.11/7.02 | | | | REF_CLOSE: (30), (43), (85) are inconsistent by sub-proof #41. % 43.11/7.02 | | | | % 43.11/7.02 | | | End of split % 43.11/7.02 | | | % 43.11/7.02 | | End of split % 43.11/7.02 | | % 43.11/7.02 | Case 2: % 43.11/7.02 | | % 43.11/7.02 | | (86) ~ (all_34_2 = e3) % 43.11/7.02 | | % 43.11/7.02 | | REDUCE: (24), (86) imply: % 43.11/7.02 | | (87) $false % 43.11/7.02 | | % 43.11/7.02 | | CLOSE: (87) is inconsistent. % 43.11/7.02 | | % 43.11/7.02 | End of split % 43.11/7.02 | % 43.11/7.02 End of proof % 43.11/7.02 % 43.11/7.02 Sub-proof #28 shows that the following formulas are inconsistent: % 43.11/7.02 ---------------------------------------------------------------- % 43.11/7.02 (1) all_58_5 = all_52_1 % 43.11/7.02 (2) all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0 % 43.11/7.02 (3) all_58_11 = all_52_0 % 43.11/7.02 (4) ~ (all_52_0 = e0) % 43.11/7.02 (5) ~ (all_52_2 = e0) % 43.11/7.02 (6) all_58_1 = all_52_2 % 43.11/7.02 (7) ~ (all_52_1 = e0) % 43.11/7.02 % 43.11/7.02 Begin of proof % 43.11/7.02 | % 43.11/7.02 | BETA: splitting (2) gives: % 43.11/7.02 | % 43.11/7.02 | Case 1: % 43.11/7.02 | | % 43.11/7.02 | | (8) all_58_1 = e0 % 43.11/7.02 | | % 43.11/7.02 | | COMBINE_EQS: (6), (8) imply: % 43.11/7.02 | | (9) all_52_2 = e0 % 43.11/7.02 | | % 43.11/7.02 | | REDUCE: (5), (9) imply: % 43.11/7.02 | | (10) $false % 43.11/7.02 | | % 43.11/7.02 | | CLOSE: (10) is inconsistent. % 43.11/7.02 | | % 43.11/7.02 | Case 2: % 43.11/7.02 | | % 43.11/7.02 | | (11) all_58_5 = e0 | all_58_11 = e0 % 43.11/7.02 | | % 43.11/7.02 | | BETA: splitting (11) gives: % 43.11/7.02 | | % 43.11/7.02 | | Case 1: % 43.11/7.02 | | | % 43.11/7.02 | | | (12) all_58_5 = e0 % 43.11/7.02 | | | % 43.11/7.02 | | | COMBINE_EQS: (1), (12) imply: % 43.11/7.02 | | | (13) all_52_1 = e0 % 43.11/7.02 | | | % 43.11/7.02 | | | REDUCE: (7), (13) imply: % 43.11/7.02 | | | (14) $false % 43.11/7.02 | | | % 43.11/7.02 | | | CLOSE: (14) is inconsistent. % 43.11/7.02 | | | % 43.11/7.02 | | Case 2: % 43.11/7.02 | | | % 43.11/7.02 | | | (15) all_58_11 = e0 % 43.11/7.02 | | | % 43.11/7.02 | | | COMBINE_EQS: (3), (15) imply: % 43.11/7.02 | | | (16) all_52_0 = e0 % 43.11/7.02 | | | % 43.11/7.02 | | | REDUCE: (4), (16) imply: % 43.11/7.02 | | | (17) $false % 43.11/7.02 | | | % 43.11/7.02 | | | CLOSE: (17) is inconsistent. % 43.11/7.02 | | | % 43.11/7.02 | | End of split % 43.11/7.02 | | % 43.11/7.02 | End of split % 43.11/7.02 | % 43.11/7.02 End of proof % 43.11/7.02 % 43.11/7.02 Sub-proof #29 shows that the following formulas are inconsistent: % 43.11/7.02 ---------------------------------------------------------------- % 43.11/7.02 (1) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.11/7.02 (2) all_52_9 = all_10_2 % 43.11/7.02 (3) ~ (all_10_2 = e0) % 43.11/7.02 % 43.11/7.02 Begin of proof % 43.11/7.02 | % 43.11/7.02 | ALPHA: (1) implies: % 43.11/7.02 | (4) all_52_9 = e0 % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (2), (4) imply: % 43.11/7.02 | (5) all_10_2 = e0 % 43.11/7.02 | % 43.11/7.02 | SIMP: (5) implies: % 43.11/7.02 | (6) all_10_2 = e0 % 43.11/7.02 | % 43.11/7.02 | REDUCE: (3), (6) imply: % 43.11/7.02 | (7) $false % 43.11/7.02 | % 43.11/7.02 | CLOSE: (7) is inconsistent. % 43.11/7.02 | % 43.11/7.02 End of proof % 43.11/7.02 % 43.11/7.02 Sub-proof #30 shows that the following formulas are inconsistent: % 43.11/7.02 ---------------------------------------------------------------- % 43.11/7.02 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.02 (2) op(all_4_2, e0) = e1 % 43.11/7.02 (3) ~ (e2 = e0) % 43.11/7.02 (4) op(e0, all_4_2) = all_4_1 % 43.11/7.02 (5) ~ (all_52_0 = all_52_2) % 43.11/7.02 (6) ~ (all_52_14 = all_4_2) % 43.11/7.02 (7) all_58_7 = all_52_7 % 43.11/7.02 (8) all_40_2 = all_4_2 % 43.11/7.02 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.02 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.02 (10) op(e3, e0) = all_52_0 % 43.11/7.02 (11) all_52_11 = all_8_2 % 43.11/7.02 (12) op(e0, e3) = all_52_14 % 43.11/7.02 (13) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/7.02 (14) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.02 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.02 (15) all_56_3 = all_52_14 % 43.11/7.02 (16) ~ (all_52_7 = all_8_2) % 43.11/7.02 (17) all_40_1 = all_4_1 % 43.11/7.02 (18) ~ (all_52_12 = all_52_14) % 43.11/7.02 (19) all_52_9 = all_10_2 % 43.11/7.02 (20) all_52_13 = all_6_2 % 43.11/7.02 (21) ~ (all_52_0 = all_4_2) % 43.11/7.02 (22) all_58_2 = all_6_2 % 43.11/7.02 (23) all_58_14 = all_52_12 % 43.11/7.02 (24) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/7.02 (25) all_58_1 = all_52_2 % 43.11/7.02 (26) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.02 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.02 (27) ~ (all_52_0 = all_10_2) % 43.11/7.02 (28) ~ (e3 = e2) % 43.11/7.02 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.02 (30) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/7.02 (31) all_52_15 = all_4_2 % 43.11/7.02 % 43.11/7.02 Begin of proof % 43.11/7.02 | % 43.11/7.02 | ALPHA: (13) implies: % 43.11/7.02 | (32) all_52_15 = e3 % 43.11/7.02 | (33) ~ (all_52_14 = e0) % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (31), (32) imply: % 43.11/7.02 | (34) all_4_2 = e3 % 43.11/7.02 | % 43.11/7.02 | SIMP: (34) implies: % 43.11/7.02 | (35) all_4_2 = e3 % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (8), (35) imply: % 43.11/7.02 | (36) all_40_2 = e3 % 43.11/7.02 | % 43.11/7.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14), % 43.11/7.02 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 43.11/7.02 | (26), (27), (28), (29), (30), (32), (33), (35), (36) are % 43.11/7.02 | inconsistent by sub-proof #33. % 43.11/7.02 | % 43.11/7.02 End of proof % 43.11/7.02 % 43.11/7.02 Sub-proof #31 shows that the following formulas are inconsistent: % 43.11/7.02 ---------------------------------------------------------------- % 43.11/7.02 (1) all_58_0 = all_4_2 % 43.11/7.02 (2) ~ (all_52_12 = all_10_2) % 43.11/7.02 (3) all_58_9 = all_52_6 % 43.11/7.02 (4) all_42_2 = all_6_2 % 43.11/7.02 (5) all_58_7 = all_52_7 % 43.11/7.02 (6) ~ (all_52_3 = all_6_2) % 43.11/7.02 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.11/7.02 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.02 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.02 (9) all_52_11 = all_8_2 % 43.11/7.02 (10) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.02 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.02 (11) op(e1, all_6_2) = all_6_1 % 43.11/7.02 (12) all_58_5 = all_52_1 % 43.11/7.02 (13) ~ (all_52_3 = all_10_2) % 43.11/7.02 (14) all_58_11 = all_52_0 % 43.11/7.02 (15) all_52_9 = all_10_2 % 43.11/7.02 (16) all_42_1 = all_6_1 % 43.11/7.02 (17) all_52_13 = all_6_2 % 43.11/7.02 (18) ~ (all_52_0 = all_4_2) % 43.11/7.02 (19) ~ (all_52_1 = all_8_2) % 43.11/7.02 (20) ~ (e3 = e0) % 43.11/7.02 (21) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/7.02 (22) all_58_6 = all_8_2 % 43.11/7.02 (23) ~ (all_52_12 = all_6_2) % 43.11/7.02 (24) all_58_1 = all_52_2 % 43.11/7.02 (25) op(e3, e1) = all_52_3 % 43.11/7.02 (26) ~ (all_52_8 = all_4_2) % 43.11/7.02 (27) op(all_6_2, e1) = e2 % 43.11/7.02 (28) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.11/7.02 (29) ~ (all_52_2 = all_52_12) % 43.11/7.02 (30) ~ (e1 = e0) % 43.11/7.02 (31) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.02 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.02 (32) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 43.11/7.02 (33) ~ (all_52_7 = all_52_12) % 43.11/7.02 (34) all_58_8 = all_52_8 % 43.11/7.02 (35) op(e1, e3) = all_52_12 % 43.11/7.02 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.02 (37) all_56_7 = all_52_12 % 43.11/7.02 (38) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.11/7.02 (39) ~ (all_52_3 = all_52_6) % 43.11/7.02 (40) all_52_15 = all_4_2 % 43.11/7.02 % 43.11/7.02 Begin of proof % 43.11/7.02 | % 43.11/7.02 | ALPHA: (21) implies: % 43.11/7.02 | (41) all_52_13 = e3 % 43.11/7.02 | (42) ~ (all_52_12 = e1) % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (17), (41) imply: % 43.11/7.02 | (43) all_6_2 = e3 % 43.11/7.02 | % 43.11/7.02 | SIMP: (43) implies: % 43.11/7.02 | (44) all_6_2 = e3 % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (4), (44) imply: % 43.11/7.02 | (45) all_42_2 = e3 % 43.11/7.02 | % 43.11/7.02 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 43.11/7.02 | (14), (15), (16), (18), (19), (20), (22), (23), (24), (25), (26), % 43.11/7.02 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 43.11/7.02 | (38), (39), (40), (41), (42), (44), (45) are inconsistent by % 43.11/7.02 | sub-proof #38. % 43.11/7.02 | % 43.11/7.02 End of proof % 43.11/7.02 % 43.11/7.02 Sub-proof #32 shows that the following formulas are inconsistent: % 43.11/7.02 ---------------------------------------------------------------- % 43.11/7.02 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.02 (2) op(all_4_2, e0) = e1 % 43.11/7.02 (3) ~ (e2 = e0) % 43.11/7.02 (4) op(e0, all_4_2) = all_4_1 % 43.11/7.02 (5) ~ (all_52_0 = all_52_2) % 43.11/7.02 (6) ~ (all_52_14 = all_4_2) % 43.11/7.02 (7) all_58_7 = all_52_7 % 43.11/7.02 (8) all_40_2 = all_4_2 % 43.11/7.02 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.02 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.02 (10) op(e3, e0) = all_52_0 % 43.11/7.02 (11) all_52_11 = all_8_2 % 43.11/7.02 (12) op(e0, e3) = all_52_14 % 43.11/7.02 (13) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.11/7.02 (14) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.02 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.02 (15) all_56_3 = all_52_14 % 43.11/7.02 (16) ~ (all_52_7 = all_8_2) % 43.11/7.02 (17) all_40_1 = all_4_1 % 43.11/7.02 (18) ~ (all_52_12 = all_52_14) % 43.11/7.02 (19) all_52_9 = all_10_2 % 43.11/7.02 (20) all_52_13 = all_6_2 % 43.11/7.02 (21) ~ (all_52_0 = all_4_2) % 43.11/7.02 (22) all_58_2 = all_6_2 % 43.11/7.02 (23) all_58_14 = all_52_12 % 43.11/7.02 (24) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/7.02 (25) all_58_1 = all_52_2 % 43.11/7.02 (26) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.02 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.02 (27) ~ (all_52_0 = all_10_2) % 43.11/7.02 (28) ~ (e3 = e2) % 43.11/7.02 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.02 (30) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/7.02 (31) all_52_15 = all_4_2 % 43.11/7.02 % 43.11/7.02 Begin of proof % 43.11/7.02 | % 43.11/7.02 | ALPHA: (13) implies: % 43.11/7.02 | (32) all_52_15 = e3 % 43.11/7.02 | (33) ~ (all_52_14 = e0) % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (31), (32) imply: % 43.11/7.02 | (34) all_4_2 = e3 % 43.11/7.02 | % 43.11/7.02 | COMBINE_EQS: (8), (34) imply: % 43.11/7.03 | (35) all_40_2 = e3 % 43.11/7.03 | % 43.11/7.03 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14), % 43.11/7.03 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 43.11/7.03 | (26), (27), (28), (29), (30), (32), (33), (34), (35) are % 43.11/7.03 | inconsistent by sub-proof #33. % 43.11/7.03 | % 43.11/7.03 End of proof % 43.11/7.03 % 43.11/7.03 Sub-proof #33 shows that the following formulas are inconsistent: % 43.11/7.03 ---------------------------------------------------------------- % 43.11/7.03 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.03 (2) op(all_4_2, e0) = e1 % 43.11/7.03 (3) ~ (e2 = e0) % 43.11/7.03 (4) op(e0, all_4_2) = all_4_1 % 43.11/7.03 (5) ~ (all_52_0 = all_52_2) % 43.11/7.03 (6) ~ (all_52_14 = all_4_2) % 43.11/7.03 (7) all_58_7 = all_52_7 % 43.11/7.03 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.03 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.03 (9) op(e3, e0) = all_52_0 % 43.11/7.03 (10) all_52_11 = all_8_2 % 43.11/7.03 (11) op(e0, e3) = all_52_14 % 43.11/7.03 (12) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.03 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.03 (13) all_56_3 = all_52_14 % 43.11/7.03 (14) ~ (all_52_7 = all_8_2) % 43.11/7.03 (15) all_40_2 = e3 % 43.11/7.03 (16) all_40_1 = all_4_1 % 43.11/7.03 (17) ~ (all_52_12 = all_52_14) % 43.11/7.03 (18) all_52_9 = all_10_2 % 43.11/7.03 (19) all_52_13 = all_6_2 % 43.11/7.03 (20) ~ (all_52_0 = all_4_2) % 43.11/7.03 (21) all_58_2 = all_6_2 % 43.11/7.03 (22) all_58_14 = all_52_12 % 43.11/7.03 (23) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/7.03 (24) all_4_2 = e3 % 43.11/7.03 (25) all_58_1 = all_52_2 % 43.11/7.03 (26) ~ (all_52_14 = e0) % 43.11/7.03 (27) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.03 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.03 (28) ~ (all_52_0 = all_10_2) % 43.11/7.03 (29) all_52_15 = e3 % 43.11/7.03 (30) ~ (e3 = e2) % 43.11/7.03 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.03 (32) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/7.03 % 43.11/7.03 Begin of proof % 43.11/7.03 | % 43.11/7.03 | REDUCE: (20), (24) imply: % 43.11/7.03 | (33) ~ (all_52_0 = e3) % 43.11/7.03 | % 43.11/7.03 | REDUCE: (6), (24) imply: % 43.11/7.03 | (34) ~ (all_52_14 = e3) % 43.11/7.03 | % 43.11/7.03 | REDUCE: (2), (24) imply: % 43.11/7.03 | (35) op(e3, e0) = e1 % 43.11/7.03 | % 43.11/7.03 | REDUCE: (4), (24) imply: % 43.11/7.03 | (36) op(e0, e3) = all_4_1 % 43.11/7.03 | % 43.11/7.03 | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 43.11/7.03 | (16), (17), (18), (19), (21), (22), (23), (25), (26), (27), (28), % 43.11/7.03 | (29), (30), (31), (32), (33), (34), (35), (36) are inconsistent by % 43.11/7.03 | sub-proof #34. % 43.11/7.03 | % 43.11/7.03 End of proof % 43.11/7.03 % 43.11/7.03 Sub-proof #34 shows that the following formulas are inconsistent: % 43.11/7.03 ---------------------------------------------------------------- % 43.11/7.03 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.03 (2) ~ (e2 = e0) % 43.11/7.03 (3) ~ (all_52_0 = all_52_2) % 43.11/7.03 (4) all_58_7 = all_52_7 % 43.11/7.03 (5) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.03 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.03 (6) op(e3, e0) = all_52_0 % 43.11/7.03 (7) all_52_11 = all_8_2 % 43.11/7.03 (8) op(e0, e3) = all_52_14 % 43.11/7.03 (9) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.03 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.03 (10) all_56_3 = all_52_14 % 43.11/7.03 (11) ~ (all_52_7 = all_8_2) % 43.11/7.03 (12) all_40_2 = e3 % 43.11/7.03 (13) all_40_1 = all_4_1 % 43.11/7.03 (14) ~ (all_52_12 = all_52_14) % 43.11/7.03 (15) all_52_9 = all_10_2 % 43.11/7.03 (16) all_52_13 = all_6_2 % 43.11/7.03 (17) op(e3, e0) = e1 % 43.11/7.03 (18) all_58_2 = all_6_2 % 43.11/7.03 (19) all_58_14 = all_52_12 % 43.11/7.03 (20) ~ (all_40_1 = e2) | ~ (all_40_2 = e3) % 43.11/7.03 (21) ~ (all_52_0 = e3) % 43.11/7.03 (22) op(e0, e3) = all_4_1 % 43.11/7.03 (23) all_58_1 = all_52_2 % 43.11/7.03 (24) ~ (all_52_14 = e0) % 43.11/7.03 (25) ~ (all_52_14 = e3) % 43.11/7.03 (26) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.03 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.03 (27) ~ (all_52_0 = all_10_2) % 43.11/7.03 (28) all_52_15 = e3 % 43.11/7.03 (29) ~ (e3 = e2) % 43.11/7.03 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.03 (31) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.11/7.03 % 43.11/7.03 Begin of proof % 43.11/7.03 | % 43.11/7.03 | BETA: splitting (20) gives: % 43.11/7.03 | % 43.11/7.03 | Case 1: % 43.11/7.03 | | % 43.11/7.03 | | (32) ~ (all_40_1 = e2) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (13), (32) imply: % 43.11/7.03 | | (33) ~ (all_4_1 = e2) % 43.11/7.03 | | % 43.11/7.03 | | GROUND_INST: instantiating (30) with all_52_14, all_4_1, e3, e0, simplifying % 43.11/7.03 | | with (8), (22) gives: % 43.11/7.03 | | (34) all_52_14 = all_4_1 % 43.11/7.03 | | % 43.11/7.03 | | GROUND_INST: instantiating (30) with all_52_0, e1, e0, e3, simplifying with % 43.11/7.03 | | (6), (17) gives: % 43.11/7.03 | | (35) all_52_0 = e1 % 43.11/7.03 | | % 43.11/7.03 | | COMBINE_EQS: (10), (34) imply: % 43.11/7.03 | | (36) all_56_3 = all_4_1 % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (3), (35) imply: % 43.11/7.03 | | (37) ~ (all_52_2 = e1) % 43.11/7.03 | | % 43.11/7.03 | | SIMP: (37) implies: % 43.11/7.03 | | (38) ~ (all_52_2 = e1) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (27), (35) imply: % 43.11/7.03 | | (39) ~ (all_10_2 = e1) % 43.11/7.03 | | % 43.11/7.03 | | SIMP: (39) implies: % 43.11/7.03 | | (40) ~ (all_10_2 = e1) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (21), (35) imply: % 43.11/7.03 | | (41) ~ (e3 = e1) % 43.11/7.03 | | % 43.11/7.03 | | SIMP: (41) implies: % 43.11/7.03 | | (42) ~ (e3 = e1) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (14), (34) imply: % 43.11/7.03 | | (43) ~ (all_52_12 = all_4_1) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (25), (34) imply: % 43.11/7.03 | | (44) ~ (all_4_1 = e3) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (24), (34) imply: % 43.11/7.03 | | (45) ~ (all_4_1 = e0) % 43.11/7.03 | | % 43.11/7.03 | | BETA: splitting (26) gives: % 43.11/7.03 | | % 43.11/7.03 | | Case 1: % 43.11/7.03 | | | % 43.11/7.03 | | | (46) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.11/7.03 | | | % 43.11/7.03 | | | REF_CLOSE: (15), (40), (46) are inconsistent by sub-proof #58. % 43.11/7.03 | | | % 43.11/7.03 | | Case 2: % 43.11/7.03 | | | % 43.11/7.03 | | | (47) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.11/7.03 | | | (all_52_5 = e0)) % 43.11/7.03 | | | % 43.11/7.03 | | | BETA: splitting (47) gives: % 43.11/7.03 | | | % 43.11/7.03 | | | Case 1: % 43.11/7.03 | | | | % 43.11/7.03 | | | | (48) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.11/7.03 | | | | % 43.11/7.03 | | | | ALPHA: (48) implies: % 43.11/7.03 | | | | (49) all_52_11 = e1 % 43.11/7.03 | | | | % 43.11/7.03 | | | | COMBINE_EQS: (7), (49) imply: % 43.11/7.03 | | | | (50) all_8_2 = e1 % 43.11/7.03 | | | | % 43.11/7.03 | | | | SIMP: (50) implies: % 43.11/7.03 | | | | (51) all_8_2 = e1 % 43.11/7.03 | | | | % 43.11/7.03 | | | | REDUCE: (11), (51) imply: % 43.11/7.03 | | | | (52) ~ (all_52_7 = e1) % 43.11/7.03 | | | | % 43.11/7.03 | | | | REF_CLOSE: (1), (2), (4), (5), (9), (16), (18), (19), (23), (28), (29), % 43.11/7.03 | | | | (31), (33), (36), (38), (43), (44), (45), (49), (52) are % 43.11/7.03 | | | | inconsistent by sub-proof #52. % 43.11/7.03 | | | | % 43.11/7.03 | | | Case 2: % 43.11/7.03 | | | | % 43.11/7.03 | | | | (53) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.11/7.03 | | | | % 43.11/7.03 | | | | REF_CLOSE: (28), (42), (53) are inconsistent by sub-proof #51. % 43.11/7.03 | | | | % 43.11/7.03 | | | End of split % 43.11/7.03 | | | % 43.11/7.03 | | End of split % 43.11/7.03 | | % 43.11/7.03 | Case 2: % 43.11/7.03 | | % 43.11/7.03 | | (54) ~ (all_40_2 = e3) % 43.11/7.03 | | % 43.11/7.03 | | REDUCE: (12), (54) imply: % 43.11/7.03 | | (55) $false % 43.11/7.03 | | % 43.11/7.03 | | CLOSE: (55) is inconsistent. % 43.11/7.03 | | % 43.11/7.03 | End of split % 43.11/7.03 | % 43.11/7.03 End of proof % 43.11/7.03 % 43.11/7.03 Sub-proof #35 shows that the following formulas are inconsistent: % 43.11/7.03 ---------------------------------------------------------------- % 43.11/7.03 (1) ~ (all_52_0 = all_52_3) % 43.11/7.03 (2) all_58_0 = all_4_2 % 43.11/7.03 (3) ~ (all_52_4 = all_52_5) % 43.11/7.03 (4) ~ (e2 = e0) % 43.11/7.03 (5) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.11/7.03 (6) ~ (all_52_3 = all_6_2) % 43.11/7.03 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.11/7.03 (8) op(all_6_2, e1) = all_6_0 % 43.11/7.03 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.03 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.03 (10) all_52_11 = all_8_2 % 43.11/7.03 (11) ~ (all_52_5 = all_6_2) % 43.11/7.03 (12) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.03 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.03 (13) ~ (all_52_1 = all_4_2) % 43.11/7.03 (14) all_56_1 = all_52_5 % 43.11/7.03 (15) all_56_12 = all_52_0 % 43.11/7.03 (16) ~ (all_6_0 = e0) % 43.11/7.03 (17) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.11/7.03 (18) all_56_13 = all_52_3 % 43.11/7.03 (19) ~ (all_52_5 = all_4_2) % 43.11/7.03 (20) all_58_5 = all_52_1 % 43.11/7.03 (21) ~ (all_52_3 = all_10_2) % 43.11/7.03 (22) all_58_11 = all_52_0 % 43.11/7.03 (23) all_52_9 = all_10_2 % 43.11/7.03 (24) all_52_13 = all_6_2 % 43.11/7.03 (25) ~ (all_52_0 = all_4_2) % 43.11/7.03 (26) ~ (all_52_3 = all_52_4) % 43.11/7.03 (27) ~ (e3 = e0) % 43.11/7.03 (28) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.11/7.03 (29) ~ (all_52_4 = all_8_2) % 43.11/7.03 (30) ~ (all_52_4 = all_6_2) % 43.11/7.03 (31) all_58_1 = all_52_2 % 43.11/7.03 (32) op(e3, e1) = all_52_3 % 43.11/7.03 (33) ~ (all_6_0 = e2) % 43.11/7.03 (34) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 43.11/7.03 (35) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.11/7.03 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.11/7.03 (36) ~ (all_52_0 = all_10_2) % 43.11/7.03 (37) ~ (all_52_2 = all_4_2) % 43.11/7.03 (38) ~ (e3 = e2) % 43.11/7.03 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.11/7.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.11/7.03 (40) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 43.11/7.03 (41) all_56_9 = all_52_4 % 43.11/7.03 (42) all_52_15 = all_4_2 % 43.11/7.03 % 43.11/7.03 Begin of proof % 43.11/7.03 | % 43.11/7.03 | ALPHA: (28) implies: % 43.11/7.03 | (43) all_52_13 = e3 % 43.11/7.03 | % 43.11/7.03 | COMBINE_EQS: (24), (43) imply: % 43.11/7.03 | (44) all_6_2 = e3 % 43.11/7.03 | % 43.11/7.03 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.11/7.03 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 43.11/7.03 | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), % 43.11/7.03 | (37), (38), (39), (40), (41), (42), (43), (44) are inconsistent by % 43.11/7.03 | sub-proof #56. % 43.11/7.03 | % 43.11/7.03 End of proof % 43.11/7.03 % 43.11/7.03 Sub-proof #36 shows that the following formulas are inconsistent: % 43.11/7.03 ---------------------------------------------------------------- % 43.11/7.03 (1) ~ (all_52_0 = all_52_3) % 43.11/7.03 (2) all_58_0 = all_4_2 % 43.11/7.03 (3) ~ (all_4_0 = e2) % 43.11/7.03 (4) ~ (all_52_12 = all_10_2) % 43.11/7.03 (5) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.11/7.03 (6) all_58_9 = all_52_6 % 43.11/7.03 (7) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.11/7.03 (8) op(e0, all_4_2) = all_4_1 % 43.11/7.03 (9) all_42_2 = all_6_2 % 43.11/7.03 (10) ~ (all_52_14 = all_4_2) % 43.11/7.03 (11) all_58_7 = all_52_7 % 43.11/7.03 (12) ~ (all_52_3 = all_6_2) % 43.11/7.03 (13) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.11/7.03 (14) ~ (all_52_14 = all_10_2) % 43.11/7.03 (15) ~ (e3 = e1) % 43.11/7.03 (16) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.11/7.03 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.11/7.03 (17) op(e3, e0) = all_52_0 % 43.11/7.03 (18) all_52_11 = all_8_2 % 43.11/7.03 (19) op(e0, e3) = all_52_14 % 43.11/7.03 (20) op(all_4_2, e0) = all_4_0 % 43.11/7.03 (21) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.11/7.03 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.11/7.03 (22) all_56_3 = all_52_14 % 43.11/7.03 (23) ~ (all_4_0 = e1) % 43.52/7.03 (24) op(e1, all_6_2) = all_6_1 % 43.52/7.03 (25) all_56_12 = all_52_0 % 43.52/7.03 (26) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.03 (27) (all_52_13 = e3 & ~ (all_52_12 = e1)) | (all_52_15 = e3 & ~ (all_52_14 % 43.52/7.03 = e0)) % 43.52/7.03 (28) all_56_13 = all_52_3 % 43.52/7.03 (29) ~ (all_52_7 = all_8_2) % 43.52/7.03 (30) all_58_5 = all_52_1 % 43.52/7.03 (31) ~ (all_52_12 = all_52_14) % 43.52/7.03 (32) ~ (all_52_3 = all_10_2) % 43.52/7.03 (33) all_58_11 = all_52_0 % 43.52/7.03 (34) all_52_9 = all_10_2 % 43.52/7.03 (35) all_42_1 = all_6_1 % 43.52/7.03 (36) all_52_13 = all_6_2 % 43.52/7.03 (37) ~ (all_52_0 = all_4_2) % 43.52/7.03 (38) all_58_2 = all_6_2 % 43.52/7.04 (39) all_58_14 = all_52_12 % 43.52/7.04 (40) ~ (all_52_1 = all_8_2) % 43.52/7.04 (41) ~ (e3 = e0) % 43.52/7.04 (42) all_58_6 = all_8_2 % 43.52/7.04 (43) ~ (all_52_12 = all_6_2) % 43.52/7.04 (44) all_58_1 = all_52_2 % 43.52/7.04 (45) op(e3, e1) = all_52_3 % 43.52/7.04 (46) ~ (e2 = e1) % 43.52/7.04 (47) ~ (all_52_8 = all_4_2) % 43.52/7.04 (48) op(all_6_2, e1) = e2 % 43.52/7.04 (49) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.52/7.04 (50) ~ (all_52_2 = all_52_12) % 43.52/7.04 (51) ~ (e1 = e0) % 43.52/7.04 (52) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.04 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.04 (53) ~ (all_52_0 = all_10_2) % 43.52/7.04 (54) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 43.52/7.04 (55) ~ (all_52_7 = all_52_12) % 43.52/7.04 (56) all_58_8 = all_52_8 % 43.52/7.04 (57) ~ (e3 = e2) % 43.52/7.04 (58) op(e1, e3) = all_52_12 % 43.52/7.04 (59) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.04 (60) all_56_7 = all_52_12 % 43.52/7.04 (61) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.52/7.04 (62) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.04 (63) ~ (all_52_3 = all_52_6) % 43.52/7.04 (64) all_52_15 = all_4_2 % 43.52/7.04 % 43.52/7.04 Begin of proof % 43.52/7.04 | % 43.52/7.04 | BETA: splitting (27) gives: % 43.52/7.04 | % 43.52/7.04 | Case 1: % 43.52/7.04 | | % 43.52/7.04 | | (65) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.52/7.04 | | % 43.52/7.04 | | ALPHA: (65) implies: % 43.52/7.04 | | (66) all_52_13 = e3 % 43.52/7.04 | | (67) ~ (all_52_12 = e1) % 43.52/7.04 | | % 43.52/7.04 | | COMBINE_EQS: (36), (66) imply: % 43.52/7.04 | | (68) all_6_2 = e3 % 43.52/7.04 | | % 43.52/7.04 | | COMBINE_EQS: (9), (68) imply: % 43.52/7.04 | | (69) all_42_2 = e3 % 43.52/7.04 | | % 43.52/7.04 | | REF_CLOSE: (2), (4), (6), (11), (12), (13), (16), (18), (21), (24), (30), % 43.52/7.04 | | (32), (33), (34), (35), (37), (40), (41), (42), (43), (44), (45), % 43.52/7.04 | | (47), (48), (49), (50), (51), (52), (54), (55), (56), (58), (59), % 43.52/7.04 | | (60), (61), (63), (64), (66), (67), (68), (69) are inconsistent % 43.52/7.04 | | by sub-proof #38. % 43.52/7.04 | | % 43.52/7.04 | Case 2: % 43.52/7.04 | | % 43.52/7.04 | | (70) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.52/7.04 | | % 43.52/7.04 | | REF_CLOSE: (1), (3), (5), (7), (8), (10), (11), (12), (14), (15), (16), % 43.52/7.04 | | (17), (18), (19), (20), (21), (22), (23), (25), (26), (28), (29), % 43.52/7.04 | | (31), (32), (34), (36), (37), (38), (39), (44), (46), (52), (53), % 43.52/7.04 | | (57), (59), (62), (64), (70) are inconsistent by sub-proof #37. % 43.52/7.04 | | % 43.52/7.04 | End of split % 43.52/7.04 | % 43.52/7.04 End of proof % 43.52/7.04 % 43.52/7.04 Sub-proof #37 shows that the following formulas are inconsistent: % 43.52/7.04 ---------------------------------------------------------------- % 43.52/7.04 (1) ~ (all_52_0 = all_52_3) % 43.52/7.04 (2) ~ (all_4_0 = e2) % 43.52/7.04 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.04 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.04 (5) op(e0, all_4_2) = all_4_1 % 43.52/7.04 (6) ~ (all_52_14 = all_4_2) % 43.52/7.04 (7) all_58_7 = all_52_7 % 43.52/7.04 (8) ~ (all_52_3 = all_6_2) % 43.52/7.04 (9) ~ (all_52_14 = all_10_2) % 43.52/7.04 (10) ~ (e3 = e1) % 43.52/7.04 (11) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.04 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.04 (12) op(e3, e0) = all_52_0 % 43.52/7.04 (13) all_52_11 = all_8_2 % 43.52/7.04 (14) op(e0, e3) = all_52_14 % 43.52/7.04 (15) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.52/7.04 (16) op(all_4_2, e0) = all_4_0 % 43.52/7.04 (17) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.04 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.04 (18) all_56_3 = all_52_14 % 43.52/7.04 (19) ~ (all_4_0 = e1) % 43.52/7.04 (20) all_56_12 = all_52_0 % 43.52/7.04 (21) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.04 (22) all_56_13 = all_52_3 % 43.52/7.04 (23) ~ (all_52_7 = all_8_2) % 43.52/7.04 (24) ~ (all_52_12 = all_52_14) % 43.52/7.04 (25) ~ (all_52_3 = all_10_2) % 43.52/7.04 (26) all_52_9 = all_10_2 % 43.52/7.04 (27) all_52_13 = all_6_2 % 43.52/7.04 (28) ~ (all_52_0 = all_4_2) % 43.52/7.04 (29) all_58_2 = all_6_2 % 43.52/7.04 (30) all_58_14 = all_52_12 % 43.52/7.04 (31) all_58_1 = all_52_2 % 43.52/7.04 (32) ~ (e2 = e1) % 43.52/7.04 (33) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.04 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.04 (34) ~ (all_52_0 = all_10_2) % 43.52/7.04 (35) ~ (e3 = e2) % 43.52/7.04 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.04 (37) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.04 (38) all_52_15 = all_4_2 % 43.52/7.04 % 43.52/7.04 Begin of proof % 43.52/7.04 | % 43.52/7.04 | ALPHA: (15) implies: % 43.52/7.04 | (39) all_52_15 = e3 % 43.52/7.04 | (40) ~ (all_52_14 = e0) % 43.52/7.04 | % 43.52/7.04 | COMBINE_EQS: (38), (39) imply: % 43.52/7.04 | (41) all_4_2 = e3 % 43.52/7.04 | % 43.52/7.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.52/7.04 | (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.52/7.04 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 43.52/7.04 | (36), (37), (39), (40), (41) are inconsistent by sub-proof #47. % 43.52/7.04 | % 43.52/7.04 End of proof % 43.52/7.04 % 43.52/7.04 Sub-proof #38 shows that the following formulas are inconsistent: % 43.52/7.04 ---------------------------------------------------------------- % 43.52/7.04 (1) all_58_0 = all_4_2 % 43.52/7.04 (2) ~ (all_52_12 = all_10_2) % 43.52/7.04 (3) all_58_9 = all_52_6 % 43.52/7.04 (4) all_58_7 = all_52_7 % 43.52/7.04 (5) ~ (all_52_3 = all_6_2) % 43.52/7.04 (6) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.04 (7) all_42_2 = e3 % 43.52/7.04 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.04 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.04 (9) all_52_11 = all_8_2 % 43.52/7.04 (10) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.04 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.04 (11) op(e1, all_6_2) = all_6_1 % 43.52/7.04 (12) all_58_5 = all_52_1 % 43.52/7.04 (13) ~ (all_52_3 = all_10_2) % 43.52/7.04 (14) ~ (all_52_12 = e1) % 43.52/7.04 (15) all_58_11 = all_52_0 % 43.52/7.04 (16) all_52_9 = all_10_2 % 43.52/7.04 (17) all_42_1 = all_6_1 % 43.52/7.04 (18) ~ (all_52_0 = all_4_2) % 43.52/7.04 (19) ~ (all_52_1 = all_8_2) % 43.52/7.04 (20) ~ (e3 = e0) % 43.52/7.04 (21) all_6_2 = e3 % 43.52/7.04 (22) all_58_6 = all_8_2 % 43.52/7.04 (23) ~ (all_52_12 = all_6_2) % 43.52/7.04 (24) all_58_1 = all_52_2 % 43.52/7.04 (25) op(e3, e1) = all_52_3 % 43.52/7.04 (26) ~ (all_52_8 = all_4_2) % 43.52/7.04 (27) op(all_6_2, e1) = e2 % 43.52/7.04 (28) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.52/7.04 (29) ~ (all_52_2 = all_52_12) % 43.52/7.04 (30) ~ (e1 = e0) % 43.52/7.04 (31) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.04 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.04 (32) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 43.52/7.04 (33) ~ (all_52_7 = all_52_12) % 43.52/7.04 (34) all_58_8 = all_52_8 % 43.52/7.04 (35) op(e1, e3) = all_52_12 % 43.52/7.04 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.04 (37) all_56_7 = all_52_12 % 43.52/7.04 (38) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.52/7.04 (39) all_52_13 = e3 % 43.52/7.04 (40) ~ (all_52_3 = all_52_6) % 43.52/7.04 (41) all_52_15 = all_4_2 % 43.52/7.04 % 43.52/7.04 Begin of proof % 43.52/7.04 | % 43.52/7.04 | REDUCE: (5), (21) imply: % 43.52/7.04 | (42) ~ (all_52_3 = e3) % 43.52/7.04 | % 43.52/7.04 | REDUCE: (21), (23) imply: % 43.52/7.04 | (43) ~ (all_52_12 = e3) % 43.52/7.04 | % 43.52/7.04 | REDUCE: (21), (27) imply: % 43.52/7.04 | (44) op(e3, e1) = e2 % 43.52/7.04 | % 43.52/7.04 | REDUCE: (11), (21) imply: % 43.52/7.04 | (45) op(e1, e3) = all_6_1 % 43.52/7.04 | % 43.52/7.04 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), % 43.52/7.04 | (15), (16), (17), (18), (19), (20), (22), (24), (25), (26), (28), % 43.52/7.04 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 43.52/7.04 | (40), (41), (42), (43), (44), (45) are inconsistent by sub-proof % 43.52/7.04 | #39. % 43.52/7.04 | % 43.52/7.04 End of proof % 43.52/7.04 % 43.52/7.04 Sub-proof #39 shows that the following formulas are inconsistent: % 43.52/7.04 ---------------------------------------------------------------- % 43.52/7.04 (1) all_58_0 = all_4_2 % 43.52/7.04 (2) ~ (all_52_12 = all_10_2) % 43.52/7.04 (3) all_58_9 = all_52_6 % 43.52/7.04 (4) all_58_7 = all_52_7 % 43.52/7.04 (5) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.04 (6) all_42_2 = e3 % 43.52/7.04 (7) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.04 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.04 (8) all_52_11 = all_8_2 % 43.52/7.04 (9) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.04 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.04 (10) ~ (all_52_3 = e3) % 43.52/7.04 (11) all_58_5 = all_52_1 % 43.52/7.04 (12) ~ (all_52_12 = e3) % 43.52/7.04 (13) ~ (all_52_3 = all_10_2) % 43.52/7.04 (14) ~ (all_52_12 = e1) % 43.52/7.04 (15) all_58_11 = all_52_0 % 43.52/7.04 (16) all_52_9 = all_10_2 % 43.52/7.04 (17) all_42_1 = all_6_1 % 43.52/7.04 (18) op(e1, e3) = all_6_1 % 43.52/7.04 (19) ~ (all_52_0 = all_4_2) % 43.52/7.04 (20) ~ (all_52_1 = all_8_2) % 43.52/7.04 (21) ~ (e3 = e0) % 43.52/7.04 (22) all_58_6 = all_8_2 % 43.52/7.04 (23) all_58_1 = all_52_2 % 43.52/7.04 (24) op(e3, e1) = all_52_3 % 43.52/7.04 (25) ~ (all_52_8 = all_4_2) % 43.52/7.04 (26) op(e3, e1) = e2 % 43.52/7.04 (27) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.52/7.04 (28) ~ (all_52_2 = all_52_12) % 43.52/7.04 (29) ~ (e1 = e0) % 43.52/7.04 (30) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.04 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.04 (31) ~ (all_42_1 = e0) | ~ (all_42_2 = e3) % 43.52/7.04 (32) ~ (all_52_7 = all_52_12) % 43.52/7.04 (33) all_58_8 = all_52_8 % 43.52/7.04 (34) op(e1, e3) = all_52_12 % 43.52/7.04 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.04 (36) all_56_7 = all_52_12 % 43.52/7.04 (37) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.52/7.04 (38) all_52_13 = e3 % 43.52/7.04 (39) ~ (all_52_3 = all_52_6) % 43.52/7.04 (40) all_52_15 = all_4_2 % 43.52/7.04 % 43.52/7.04 Begin of proof % 43.52/7.04 | % 43.52/7.04 | BETA: splitting (31) gives: % 43.52/7.04 | % 43.52/7.04 | Case 1: % 43.52/7.04 | | % 43.52/7.04 | | (41) ~ (all_42_1 = e0) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (17), (41) imply: % 43.52/7.04 | | (42) ~ (all_6_1 = e0) % 43.52/7.04 | | % 43.52/7.04 | | GROUND_INST: instantiating (35) with all_52_12, all_6_1, e3, e1, simplifying % 43.52/7.04 | | with (18), (34) gives: % 43.52/7.04 | | (43) all_52_12 = all_6_1 % 43.52/7.04 | | % 43.52/7.04 | | GROUND_INST: instantiating (35) with all_52_3, e2, e1, e3, simplifying with % 43.52/7.04 | | (24), (26) gives: % 43.52/7.04 | | (44) all_52_3 = e2 % 43.52/7.04 | | % 43.52/7.04 | | COMBINE_EQS: (36), (43) imply: % 43.52/7.04 | | (45) all_56_7 = all_6_1 % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (28), (43) imply: % 43.52/7.04 | | (46) ~ (all_52_2 = all_6_1) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (39), (44) imply: % 43.52/7.04 | | (47) ~ (all_52_6 = e2) % 43.52/7.04 | | % 43.52/7.04 | | SIMP: (47) implies: % 43.52/7.04 | | (48) ~ (all_52_6 = e2) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (13), (44) imply: % 43.52/7.04 | | (49) ~ (all_10_2 = e2) % 43.52/7.04 | | % 43.52/7.04 | | SIMP: (49) implies: % 43.52/7.04 | | (50) ~ (all_10_2 = e2) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (10), (44) imply: % 43.52/7.04 | | (51) ~ (e3 = e2) % 43.52/7.04 | | % 43.52/7.04 | | SIMP: (51) implies: % 43.52/7.04 | | (52) ~ (e3 = e2) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (32), (43) imply: % 43.52/7.04 | | (53) ~ (all_52_7 = all_6_1) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (2), (43) imply: % 43.52/7.04 | | (54) ~ (all_10_2 = all_6_1) % 43.52/7.04 | | % 43.52/7.04 | | SIMP: (54) implies: % 43.52/7.04 | | (55) ~ (all_10_2 = all_6_1) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (12), (43) imply: % 43.52/7.04 | | (56) ~ (all_6_1 = e3) % 43.52/7.04 | | % 43.52/7.04 | | REDUCE: (14), (43) imply: % 43.52/7.04 | | (57) ~ (all_6_1 = e1) % 43.52/7.04 | | % 43.52/7.04 | | BETA: splitting (7) gives: % 43.52/7.04 | | % 43.52/7.04 | | Case 1: % 43.52/7.04 | | | % 43.52/7.04 | | | (58) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.52/7.04 | | | % 43.52/7.04 | | | ALPHA: (58) implies: % 43.52/7.04 | | | (59) all_52_9 = e2 % 43.52/7.04 | | | % 43.52/7.04 | | | COMBINE_EQS: (16), (59) imply: % 43.52/7.04 | | | (60) all_10_2 = e2 % 43.52/7.04 | | | % 43.52/7.04 | | | SIMP: (60) implies: % 43.52/7.04 | | | (61) all_10_2 = e2 % 43.52/7.04 | | | % 43.52/7.04 | | | REDUCE: (50), (61) imply: % 43.52/7.04 | | | (62) $false % 43.52/7.04 | | | % 43.52/7.04 | | | CLOSE: (62) is inconsistent. % 43.52/7.04 | | | % 43.52/7.04 | | Case 2: % 43.52/7.04 | | | % 43.52/7.04 | | | (63) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.52/7.04 | | | (all_52_8 = e0)) % 43.52/7.04 | | | % 43.52/7.04 | | | BETA: splitting (63) gives: % 43.52/7.04 | | | % 43.52/7.04 | | | Case 1: % 43.52/7.04 | | | | % 43.52/7.04 | | | | (64) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.04 | | | | % 43.52/7.04 | | | | ALPHA: (64) implies: % 43.52/7.04 | | | | (65) all_52_13 = e2 % 43.52/7.04 | | | | % 43.52/7.04 | | | | COMBINE_EQS: (38), (65) imply: % 43.52/7.04 | | | | (66) e3 = e2 % 43.52/7.04 | | | | % 43.52/7.04 | | | | SIMP: (66) implies: % 43.52/7.04 | | | | (67) e3 = e2 % 43.52/7.04 | | | | % 43.52/7.05 | | | | REDUCE: (52), (67) imply: % 43.52/7.05 | | | | (68) $false % 43.52/7.05 | | | | % 43.52/7.05 | | | | CLOSE: (68) is inconsistent. % 43.52/7.05 | | | | % 43.52/7.05 | | | Case 2: % 43.52/7.05 | | | | % 43.52/7.05 | | | | (69) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.05 | | | | % 43.52/7.05 | | | | ALPHA: (69) implies: % 43.52/7.05 | | | | (70) all_52_15 = e2 % 43.52/7.05 | | | | % 43.52/7.05 | | | | COMBINE_EQS: (40), (70) imply: % 43.52/7.05 | | | | (71) all_4_2 = e2 % 43.52/7.05 | | | | % 43.52/7.05 | | | | SIMP: (71) implies: % 43.52/7.05 | | | | (72) all_4_2 = e2 % 43.52/7.05 | | | | % 43.52/7.05 | | | | COMBINE_EQS: (1), (72) imply: % 43.52/7.05 | | | | (73) all_58_0 = e2 % 43.52/7.05 | | | | % 43.52/7.05 | | | | REDUCE: (19), (72) imply: % 43.52/7.05 | | | | (74) ~ (all_52_0 = e2) % 43.52/7.05 | | | | % 43.52/7.05 | | | | REDUCE: (25), (72) imply: % 43.52/7.05 | | | | (75) ~ (all_52_8 = e2) % 43.52/7.05 | | | | % 43.52/7.05 | | | | BETA: splitting (37) gives: % 43.52/7.05 | | | | % 43.52/7.05 | | | | Case 1: % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | (76) all_56_7 = e3 % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | COMBINE_EQS: (45), (76) imply: % 43.52/7.05 | | | | | (77) all_6_1 = e3 % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | REDUCE: (56), (77) imply: % 43.52/7.05 | | | | | (78) $false % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | CLOSE: (78) is inconsistent. % 43.52/7.05 | | | | | % 43.52/7.05 | | | | Case 2: % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | (79) all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0 % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | BETA: splitting (79) gives: % 43.52/7.05 | | | | | % 43.52/7.05 | | | | | Case 1: % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | (80) all_56_7 = e2 % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | COMBINE_EQS: (45), (80) imply: % 43.52/7.05 | | | | | | (81) all_6_1 = e2 % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | REDUCE: (46), (81) imply: % 43.52/7.05 | | | | | | (82) ~ (all_52_2 = e2) % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | REDUCE: (53), (81) imply: % 43.52/7.05 | | | | | | (83) ~ (all_52_7 = e2) % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | REDUCE: (57), (81) imply: % 43.52/7.05 | | | | | | (84) ~ (e2 = e1) % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | REDUCE: (42), (81) imply: % 43.52/7.05 | | | | | | (85) ~ (e2 = e0) % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | BETA: splitting (27) gives: % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | Case 1: % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | (86) all_58_6 = e2 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | COMBINE_EQS: (22), (86) imply: % 43.52/7.05 | | | | | | | (87) all_8_2 = e2 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | SIMP: (87) implies: % 43.52/7.05 | | | | | | | (88) all_8_2 = e2 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | COMBINE_EQS: (8), (88) imply: % 43.52/7.05 | | | | | | | (89) all_52_11 = e2 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | REDUCE: (20), (88) imply: % 43.52/7.05 | | | | | | | (90) ~ (all_52_1 = e2) % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | BETA: splitting (30) gives: % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | Case 1: % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | (91) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | ALPHA: (91) implies: % 43.52/7.05 | | | | | | | | (92) all_52_9 = e1 % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | COMBINE_EQS: (16), (92) imply: % 43.52/7.05 | | | | | | | | (93) all_10_2 = e1 % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | SIMP: (93) implies: % 43.52/7.05 | | | | | | | | (94) all_10_2 = e1 % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | REDUCE: (50), (94) imply: % 43.52/7.05 | | | | | | | | (95) ~ (e2 = e1) % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | BETA: splitting (9) gives: % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | Case 1: % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | (96) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | ALPHA: (96) implies: % 43.52/7.05 | | | | | | | | | (97) all_52_9 = e0 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | REF_CLOSE: (29), (92), (97) are inconsistent by sub-proof #75. % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | Case 2: % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | (98) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = % 43.52/7.05 | | | | | | | | | e0 & ~ (all_52_2 = e1)) % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | BETA: splitting (98) gives: % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | Case 1: % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | (99) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | ALPHA: (99) implies: % 43.52/7.05 | | | | | | | | | | (100) all_52_11 = e0 % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | COMBINE_EQS: (89), (100) imply: % 43.52/7.05 | | | | | | | | | | (101) e2 = e0 % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | SIMP: (101) implies: % 43.52/7.05 | | | | | | | | | | (102) e2 = e0 % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | COMBINE_EQS: (70), (102) imply: % 43.52/7.05 | | | | | | | | | | (103) all_52_15 = e0 % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | REF_CLOSE: (7), (29), (30), (38), (52), (84), (85), (100), % 43.52/7.05 | | | | | | | | | | (103) are inconsistent by sub-proof #42. % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | Case 2: % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | (104) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | | REF_CLOSE: (21), (38), (104) are inconsistent by sub-proof % 43.52/7.05 | | | | | | | | | | #41. % 43.52/7.05 | | | | | | | | | | % 43.52/7.05 | | | | | | | | | End of split % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | End of split % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | Case 2: % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | (105) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 % 43.52/7.05 | | | | | | | | & ~ (all_52_5 = e0)) % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | BETA: splitting (105) gives: % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | | Case 1: % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | (106) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | ALPHA: (106) implies: % 43.52/7.05 | | | | | | | | | (107) all_52_11 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | COMBINE_EQS: (89), (107) imply: % 43.52/7.05 | | | | | | | | | (108) e2 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | SIMP: (108) implies: % 43.52/7.05 | | | | | | | | | (109) e2 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | REF_CLOSE: (5), (11), (15), (23), (73), (74), (82), (84), % 43.52/7.05 | | | | | | | | | (90), (109) are inconsistent by sub-proof #68. % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | Case 2: % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | (110) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | ALPHA: (110) implies: % 43.52/7.05 | | | | | | | | | (111) all_52_15 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | COMBINE_EQS: (70), (111) imply: % 43.52/7.05 | | | | | | | | | (112) e2 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | SIMP: (112) implies: % 43.52/7.05 | | | | | | | | | (113) e2 = e1 % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | | REF_CLOSE: (5), (11), (15), (23), (73), (74), (82), (84), % 43.52/7.05 | | | | | | | | | (90), (113) are inconsistent by sub-proof #68. % 43.52/7.05 | | | | | | | | | % 43.52/7.05 | | | | | | | | End of split % 43.52/7.05 | | | | | | | | % 43.52/7.05 | | | | | | | End of split % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | Case 2: % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | (114) all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | REF_CLOSE: (3), (4), (33), (48), (75), (83), (114) are % 43.52/7.05 | | | | | | | inconsistent by sub-proof #40. % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | End of split % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | Case 2: % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | (115) all_56_7 = e1 | all_56_7 = e0 % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | BETA: splitting (115) gives: % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | | Case 1: % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | (116) all_56_7 = e1 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | COMBINE_EQS: (45), (116) imply: % 43.52/7.05 | | | | | | | (117) all_6_1 = e1 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | REDUCE: (57), (117) imply: % 43.52/7.05 | | | | | | | (118) $false % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | CLOSE: (118) is inconsistent. % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | Case 2: % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | (119) all_56_7 = e0 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | COMBINE_EQS: (45), (119) imply: % 43.52/7.05 | | | | | | | (120) all_6_1 = e0 % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | REDUCE: (42), (120) imply: % 43.52/7.05 | | | | | | | (121) $false % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | | CLOSE: (121) is inconsistent. % 43.52/7.05 | | | | | | | % 43.52/7.05 | | | | | | End of split % 43.52/7.05 | | | | | | % 43.52/7.05 | | | | | End of split % 43.52/7.05 | | | | | % 43.52/7.05 | | | | End of split % 43.52/7.05 | | | | % 43.52/7.05 | | | End of split % 43.52/7.05 | | | % 43.52/7.05 | | End of split % 43.52/7.05 | | % 43.52/7.05 | Case 2: % 43.52/7.05 | | % 43.52/7.05 | | (122) ~ (all_42_2 = e3) % 43.52/7.05 | | % 43.52/7.05 | | REDUCE: (6), (122) imply: % 43.52/7.05 | | (123) $false % 43.52/7.05 | | % 43.52/7.05 | | CLOSE: (123) is inconsistent. % 43.52/7.05 | | % 43.52/7.05 | End of split % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #40 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) ~ (all_52_7 = e2) % 43.52/7.05 (2) all_58_9 = all_52_6 % 43.52/7.05 (3) ~ (all_52_8 = e2) % 43.52/7.05 (4) ~ (all_52_6 = e2) % 43.52/7.05 (5) all_58_7 = all_52_7 % 43.52/7.05 (6) all_58_8 = all_52_8 % 43.52/7.05 (7) all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2 % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | BETA: splitting (7) gives: % 43.52/7.05 | % 43.52/7.05 | Case 1: % 43.52/7.05 | | % 43.52/7.05 | | (8) all_58_7 = e2 % 43.52/7.05 | | % 43.52/7.05 | | COMBINE_EQS: (5), (8) imply: % 43.52/7.05 | | (9) all_52_7 = e2 % 43.52/7.05 | | % 43.52/7.05 | | REDUCE: (1), (9) imply: % 43.52/7.05 | | (10) $false % 43.52/7.05 | | % 43.52/7.05 | | CLOSE: (10) is inconsistent. % 43.52/7.05 | | % 43.52/7.05 | Case 2: % 43.52/7.05 | | % 43.52/7.05 | | (11) all_58_8 = e2 | all_58_9 = e2 % 43.52/7.05 | | % 43.52/7.05 | | BETA: splitting (11) gives: % 43.52/7.05 | | % 43.52/7.05 | | Case 1: % 43.52/7.05 | | | % 43.52/7.05 | | | (12) all_58_8 = e2 % 43.52/7.05 | | | % 43.52/7.05 | | | COMBINE_EQS: (6), (12) imply: % 43.52/7.05 | | | (13) all_52_8 = e2 % 43.52/7.05 | | | % 43.52/7.05 | | | REDUCE: (3), (13) imply: % 43.52/7.05 | | | (14) $false % 43.52/7.05 | | | % 43.52/7.05 | | | CLOSE: (14) is inconsistent. % 43.52/7.05 | | | % 43.52/7.05 | | Case 2: % 43.52/7.05 | | | % 43.52/7.05 | | | (15) all_58_9 = e2 % 43.52/7.05 | | | % 43.52/7.05 | | | COMBINE_EQS: (2), (15) imply: % 43.52/7.05 | | | (16) all_52_6 = e2 % 43.52/7.05 | | | % 43.52/7.05 | | | REDUCE: (4), (16) imply: % 43.52/7.05 | | | (17) $false % 43.52/7.05 | | | % 43.52/7.05 | | | CLOSE: (17) is inconsistent. % 43.52/7.05 | | | % 43.52/7.05 | | End of split % 43.52/7.05 | | % 43.52/7.05 | End of split % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #41 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.05 (2) all_52_13 = e3 % 43.52/7.05 (3) ~ (e3 = e0) % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | ALPHA: (1) implies: % 43.52/7.05 | (4) all_52_13 = e0 % 43.52/7.05 | % 43.52/7.05 | COMBINE_EQS: (2), (4) imply: % 43.52/7.05 | (5) e3 = e0 % 43.52/7.05 | % 43.52/7.05 | SIMP: (5) implies: % 43.52/7.05 | (6) e3 = e0 % 43.52/7.05 | % 43.52/7.05 | REDUCE: (3), (6) imply: % 43.52/7.05 | (7) $false % 43.52/7.05 | % 43.52/7.05 | CLOSE: (7) is inconsistent. % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #42 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) ~ (e2 = e0) % 43.52/7.05 (2) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.05 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.05 (3) all_52_15 = e0 % 43.52/7.05 (4) ~ (e2 = e1) % 43.52/7.05 (5) all_52_11 = e0 % 43.52/7.05 (6) ~ (e1 = e0) % 43.52/7.05 (7) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.05 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.05 (8) ~ (e3 = e2) % 43.52/7.05 (9) all_52_13 = e3 % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | BETA: splitting (2) gives: % 43.52/7.05 | % 43.52/7.05 | Case 1: % 43.52/7.05 | | % 43.52/7.05 | | (10) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.52/7.05 | | % 43.52/7.05 | | ALPHA: (10) implies: % 43.52/7.05 | | (11) all_52_9 = e2 % 43.52/7.05 | | % 43.52/7.05 | | BETA: splitting (7) gives: % 43.52/7.05 | | % 43.52/7.05 | | Case 1: % 43.52/7.05 | | | % 43.52/7.05 | | | (12) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.05 | | | % 43.52/7.05 | | | REF_CLOSE: (4), (11), (12) are inconsistent by sub-proof #63. % 43.52/7.05 | | | % 43.52/7.05 | | Case 2: % 43.52/7.05 | | | % 43.52/7.05 | | | (13) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.52/7.05 | | | (all_52_5 = e0)) % 43.52/7.05 | | | % 43.52/7.05 | | | BETA: splitting (13) gives: % 43.52/7.05 | | | % 43.52/7.05 | | | Case 1: % 43.52/7.05 | | | | % 43.52/7.05 | | | | (14) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.05 | | | | % 43.52/7.05 | | | | ALPHA: (14) implies: % 43.52/7.05 | | | | (15) all_52_11 = e1 % 43.52/7.05 | | | | % 43.52/7.05 | | | | COMBINE_EQS: (5), (15) imply: % 43.52/7.05 | | | | (16) e1 = e0 % 43.52/7.05 | | | | % 43.52/7.05 | | | | REDUCE: (6), (16) imply: % 43.52/7.05 | | | | (17) $false % 43.52/7.05 | | | | % 43.52/7.05 | | | | CLOSE: (17) is inconsistent. % 43.52/7.05 | | | | % 43.52/7.05 | | | Case 2: % 43.52/7.05 | | | | % 43.52/7.05 | | | | (18) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.05 | | | | % 43.52/7.05 | | | | REF_CLOSE: (3), (6), (18) are inconsistent by sub-proof #44. % 43.52/7.05 | | | | % 43.52/7.05 | | | End of split % 43.52/7.05 | | | % 43.52/7.05 | | End of split % 43.52/7.05 | | % 43.52/7.05 | Case 2: % 43.52/7.05 | | % 43.52/7.05 | | (19) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.52/7.05 | | (all_52_8 = e0)) % 43.52/7.05 | | % 43.52/7.05 | | BETA: splitting (19) gives: % 43.52/7.05 | | % 43.52/7.05 | | Case 1: % 43.52/7.05 | | | % 43.52/7.05 | | | (20) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.05 | | | % 43.52/7.05 | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #59. % 43.52/7.05 | | | % 43.52/7.05 | | Case 2: % 43.52/7.05 | | | % 43.52/7.05 | | | (21) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.05 | | | % 43.52/7.05 | | | REF_CLOSE: (1), (3), (21) are inconsistent by sub-proof #43. % 43.52/7.05 | | | % 43.52/7.05 | | End of split % 43.52/7.05 | | % 43.52/7.05 | End of split % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #43 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.05 (2) all_52_15 = e0 % 43.52/7.05 (3) ~ (e2 = e0) % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | ALPHA: (1) implies: % 43.52/7.05 | (4) all_52_15 = e2 % 43.52/7.05 | % 43.52/7.05 | COMBINE_EQS: (2), (4) imply: % 43.52/7.05 | (5) e2 = e0 % 43.52/7.05 | % 43.52/7.05 | REDUCE: (3), (5) imply: % 43.52/7.05 | (6) $false % 43.52/7.05 | % 43.52/7.05 | CLOSE: (6) is inconsistent. % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #44 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.05 (2) all_52_15 = e0 % 43.52/7.05 (3) ~ (e1 = e0) % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | ALPHA: (1) implies: % 43.52/7.05 | (4) all_52_15 = e1 % 43.52/7.05 | % 43.52/7.05 | COMBINE_EQS: (2), (4) imply: % 43.52/7.05 | (5) e1 = e0 % 43.52/7.05 | % 43.52/7.05 | REDUCE: (3), (5) imply: % 43.52/7.05 | (6) $false % 43.52/7.05 | % 43.52/7.05 | CLOSE: (6) is inconsistent. % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #45 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) op(e3, e2) = all_52_6 % 43.52/7.05 (2) all_58_0 = all_4_2 % 43.52/7.05 (3) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.05 (4) ~ (all_52_0 = all_52_6) % 43.52/7.05 (5) ~ (all_52_3 = all_6_2) % 43.52/7.05 (6) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.05 (7) ~ (all_8_0 = e0) % 43.52/7.05 (8) ~ (e3 = e1) % 43.52/7.05 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.05 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.05 (10) all_52_11 = all_8_2 % 43.52/7.05 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.05 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.05 (12) ~ (all_52_1 = all_4_2) % 43.52/7.05 (13) all_56_12 = all_52_0 % 43.52/7.05 (14) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.05 (15) all_56_13 = all_52_3 % 43.52/7.05 (16) ~ (all_8_0 = e1) % 43.52/7.05 (17) ~ (all_52_6 = all_10_2) % 43.52/7.05 (18) all_58_5 = all_52_1 % 43.52/7.05 (19) ~ (all_52_3 = all_10_2) % 43.52/7.05 (20) all_58_11 = all_52_0 % 43.52/7.05 (21) all_52_9 = all_10_2 % 43.52/7.05 (22) all_52_13 = all_6_2 % 43.52/7.05 (23) ~ (all_52_0 = all_4_2) % 43.52/7.05 (24) ~ (e3 = e0) % 43.52/7.05 (25) op(all_8_2, e2) = all_8_0 % 43.52/7.05 (26) all_58_1 = all_52_2 % 43.52/7.05 (27) ~ (all_52_6 = all_8_2) % 43.52/7.05 (28) ~ (e1 = e0) % 43.52/7.05 (29) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.05 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.05 (30) ~ (all_52_0 = all_10_2) % 43.52/7.05 (31) ~ (all_52_2 = all_4_2) % 43.52/7.05 (32) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 43.52/7.05 (33) all_56_14 = all_52_6 % 43.52/7.05 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.05 (35) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.52/7.05 (36) ~ (all_52_3 = all_52_6) % 43.52/7.05 (37) all_52_15 = all_4_2 % 43.52/7.05 % 43.52/7.05 Begin of proof % 43.52/7.05 | % 43.52/7.05 | ALPHA: (35) implies: % 43.52/7.05 | (38) all_52_11 = e3 % 43.52/7.05 | % 43.52/7.05 | COMBINE_EQS: (10), (38) imply: % 43.52/7.05 | (39) all_8_2 = e3 % 43.52/7.05 | % 43.52/7.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 43.52/7.05 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.52/7.05 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), % 43.52/7.05 | (37), (38), (39) are inconsistent by sub-proof #66. % 43.52/7.05 | % 43.52/7.05 End of proof % 43.52/7.05 % 43.52/7.05 Sub-proof #46 shows that the following formulas are inconsistent: % 43.52/7.05 ---------------------------------------------------------------- % 43.52/7.05 (1) ~ (all_52_0 = all_52_3) % 43.52/7.05 (2) ~ (all_4_0 = e2) % 43.52/7.05 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.05 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.05 (5) op(e0, all_4_2) = all_4_1 % 43.52/7.05 (6) ~ (all_52_14 = all_4_2) % 43.52/7.05 (7) all_58_7 = all_52_7 % 43.52/7.06 (8) ~ (all_52_3 = all_6_2) % 43.52/7.06 (9) ~ (all_52_14 = all_10_2) % 43.52/7.06 (10) ~ (e3 = e1) % 43.52/7.06 (11) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.06 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.06 (12) op(e3, e0) = all_52_0 % 43.52/7.06 (13) all_52_11 = all_8_2 % 43.52/7.06 (14) op(e0, e3) = all_52_14 % 43.52/7.06 (15) all_52_15 = e3 & ~ (all_52_14 = e0) % 43.52/7.06 (16) op(all_4_2, e0) = all_4_0 % 43.52/7.06 (17) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.06 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.06 (18) all_56_3 = all_52_14 % 43.52/7.06 (19) ~ (all_4_0 = e1) % 43.52/7.06 (20) all_56_12 = all_52_0 % 43.52/7.06 (21) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.06 (22) all_56_13 = all_52_3 % 43.52/7.06 (23) ~ (all_52_7 = all_8_2) % 43.52/7.06 (24) ~ (all_52_12 = all_52_14) % 43.52/7.06 (25) ~ (all_52_3 = all_10_2) % 43.52/7.06 (26) all_52_9 = all_10_2 % 43.52/7.06 (27) all_52_13 = all_6_2 % 43.52/7.06 (28) ~ (all_52_0 = all_4_2) % 43.52/7.06 (29) all_58_2 = all_6_2 % 43.52/7.06 (30) all_58_14 = all_52_12 % 43.52/7.06 (31) all_58_1 = all_52_2 % 43.52/7.06 (32) ~ (e2 = e1) % 43.52/7.06 (33) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.06 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.06 (34) ~ (all_52_0 = all_10_2) % 43.52/7.06 (35) ~ (e3 = e2) % 43.52/7.06 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.06 (37) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.06 (38) all_52_15 = all_4_2 % 43.52/7.06 % 43.52/7.06 Begin of proof % 43.52/7.06 | % 43.52/7.06 | ALPHA: (15) implies: % 43.52/7.06 | (39) all_52_15 = e3 % 43.52/7.06 | (40) ~ (all_52_14 = e0) % 43.52/7.06 | % 43.52/7.06 | COMBINE_EQS: (38), (39) imply: % 43.52/7.06 | (41) all_4_2 = e3 % 43.52/7.06 | % 43.52/7.06 | SIMP: (41) implies: % 43.52/7.06 | (42) all_4_2 = e3 % 43.52/7.06 | % 43.52/7.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.52/7.06 | (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.52/7.06 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 43.52/7.06 | (36), (37), (39), (40), (42) are inconsistent by sub-proof #47. % 43.52/7.06 | % 43.52/7.06 End of proof % 43.52/7.06 % 43.52/7.06 Sub-proof #47 shows that the following formulas are inconsistent: % 43.52/7.06 ---------------------------------------------------------------- % 43.52/7.06 (1) ~ (all_52_0 = all_52_3) % 43.52/7.06 (2) ~ (all_4_0 = e2) % 43.52/7.06 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.06 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.06 (5) op(e0, all_4_2) = all_4_1 % 43.52/7.06 (6) ~ (all_52_14 = all_4_2) % 43.52/7.06 (7) all_58_7 = all_52_7 % 43.52/7.06 (8) ~ (all_52_3 = all_6_2) % 43.52/7.06 (9) ~ (all_52_14 = all_10_2) % 43.52/7.06 (10) ~ (e3 = e1) % 43.52/7.06 (11) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.06 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.06 (12) op(e3, e0) = all_52_0 % 43.52/7.06 (13) all_52_11 = all_8_2 % 43.52/7.06 (14) op(e0, e3) = all_52_14 % 43.52/7.06 (15) op(all_4_2, e0) = all_4_0 % 43.52/7.06 (16) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.06 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.06 (17) all_56_3 = all_52_14 % 43.52/7.06 (18) ~ (all_4_0 = e1) % 43.52/7.06 (19) all_56_12 = all_52_0 % 43.52/7.06 (20) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.06 (21) all_56_13 = all_52_3 % 43.52/7.06 (22) ~ (all_52_7 = all_8_2) % 43.52/7.06 (23) ~ (all_52_12 = all_52_14) % 43.52/7.06 (24) ~ (all_52_3 = all_10_2) % 43.52/7.06 (25) all_52_9 = all_10_2 % 43.52/7.06 (26) all_52_13 = all_6_2 % 43.52/7.06 (27) ~ (all_52_0 = all_4_2) % 43.52/7.06 (28) all_58_2 = all_6_2 % 43.52/7.06 (29) all_58_14 = all_52_12 % 43.52/7.06 (30) all_4_2 = e3 % 43.52/7.06 (31) all_58_1 = all_52_2 % 43.52/7.06 (32) ~ (e2 = e1) % 43.52/7.06 (33) ~ (all_52_14 = e0) % 43.52/7.06 (34) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.06 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.06 (35) ~ (all_52_0 = all_10_2) % 43.52/7.06 (36) all_52_15 = e3 % 43.52/7.06 (37) ~ (e3 = e2) % 43.52/7.06 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.06 (39) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.06 % 43.52/7.06 Begin of proof % 43.52/7.06 | % 43.52/7.06 | REDUCE: (27), (30) imply: % 43.52/7.06 | (40) ~ (all_52_0 = e3) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (6), (30) imply: % 43.52/7.06 | (41) ~ (all_52_14 = e3) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (15), (30) imply: % 43.52/7.06 | (42) op(e3, e0) = all_4_0 % 43.52/7.06 | % 43.52/7.06 | REDUCE: (5), (30) imply: % 43.52/7.06 | (43) op(e0, e3) = all_4_1 % 43.52/7.06 | % 43.52/7.06 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), % 43.52/7.06 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 43.52/7.06 | (28), (29), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 43.52/7.06 | (40), (41), (42), (43) are inconsistent by sub-proof #48. % 43.52/7.06 | % 43.52/7.06 End of proof % 43.52/7.06 % 43.52/7.06 Sub-proof #48 shows that the following formulas are inconsistent: % 43.52/7.06 ---------------------------------------------------------------- % 43.52/7.06 (1) ~ (all_52_0 = all_52_3) % 43.52/7.06 (2) ~ (all_4_0 = e2) % 43.52/7.06 (3) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.06 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.06 (5) all_58_7 = all_52_7 % 43.52/7.06 (6) ~ (all_52_3 = all_6_2) % 43.52/7.06 (7) ~ (all_52_14 = all_10_2) % 43.52/7.06 (8) ~ (e3 = e1) % 43.52/7.06 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.06 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.06 (10) op(e3, e0) = all_52_0 % 43.52/7.06 (11) all_52_11 = all_8_2 % 43.52/7.06 (12) op(e0, e3) = all_52_14 % 43.52/7.06 (13) op(e3, e0) = all_4_0 % 43.52/7.06 (14) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.06 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.06 (15) all_56_3 = all_52_14 % 43.52/7.06 (16) ~ (all_4_0 = e1) % 43.52/7.06 (17) all_56_12 = all_52_0 % 43.52/7.06 (18) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.06 (19) all_56_13 = all_52_3 % 43.52/7.06 (20) ~ (all_52_7 = all_8_2) % 43.52/7.06 (21) ~ (all_52_12 = all_52_14) % 43.52/7.06 (22) ~ (all_52_3 = all_10_2) % 43.52/7.06 (23) all_52_9 = all_10_2 % 43.52/7.06 (24) all_52_13 = all_6_2 % 43.52/7.06 (25) all_58_2 = all_6_2 % 43.52/7.06 (26) all_58_14 = all_52_12 % 43.52/7.06 (27) ~ (all_52_0 = e3) % 43.52/7.06 (28) op(e0, e3) = all_4_1 % 43.52/7.06 (29) all_58_1 = all_52_2 % 43.52/7.06 (30) ~ (e2 = e1) % 43.52/7.06 (31) ~ (all_52_14 = e0) % 43.52/7.06 (32) ~ (all_52_14 = e3) % 43.52/7.06 (33) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.06 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.06 (34) ~ (all_52_0 = all_10_2) % 43.52/7.06 (35) all_52_15 = e3 % 43.52/7.06 (36) ~ (e3 = e2) % 43.52/7.06 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.06 (38) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.06 % 43.52/7.06 Begin of proof % 43.52/7.06 | % 43.52/7.06 | GROUND_INST: instantiating (37) with all_52_14, all_4_1, e3, e0, simplifying % 43.52/7.06 | with (12), (28) gives: % 43.52/7.06 | (39) all_52_14 = all_4_1 % 43.52/7.06 | % 43.52/7.06 | GROUND_INST: instantiating (37) with all_52_0, all_4_0, e0, e3, simplifying % 43.52/7.06 | with (10), (13) gives: % 43.52/7.06 | (40) all_52_0 = all_4_0 % 43.52/7.06 | % 43.52/7.06 | COMBINE_EQS: (17), (40) imply: % 43.52/7.06 | (41) all_56_12 = all_4_0 % 43.52/7.06 | % 43.52/7.06 | COMBINE_EQS: (15), (39) imply: % 43.52/7.06 | (42) all_56_3 = all_4_1 % 43.52/7.06 | % 43.52/7.06 | REDUCE: (1), (40) imply: % 43.52/7.06 | (43) ~ (all_52_3 = all_4_0) % 43.52/7.06 | % 43.52/7.06 | SIMP: (43) implies: % 43.52/7.06 | (44) ~ (all_52_3 = all_4_0) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (34), (40) imply: % 43.52/7.06 | (45) ~ (all_10_2 = all_4_0) % 43.52/7.06 | % 43.52/7.06 | SIMP: (45) implies: % 43.52/7.06 | (46) ~ (all_10_2 = all_4_0) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (27), (40) imply: % 43.52/7.06 | (47) ~ (all_4_0 = e3) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (21), (39) imply: % 43.52/7.06 | (48) ~ (all_52_12 = all_4_1) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (7), (39) imply: % 43.52/7.06 | (49) ~ (all_10_2 = all_4_1) % 43.52/7.06 | % 43.52/7.06 | SIMP: (49) implies: % 43.52/7.06 | (50) ~ (all_10_2 = all_4_1) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (32), (39) imply: % 43.52/7.06 | (51) ~ (all_4_1 = e3) % 43.52/7.06 | % 43.52/7.06 | REDUCE: (31), (39) imply: % 43.52/7.06 | (52) ~ (all_4_1 = e0) % 43.52/7.06 | % 43.52/7.06 | BETA: splitting (18) gives: % 43.52/7.06 | % 43.52/7.06 | Case 1: % 43.52/7.06 | | % 43.52/7.06 | | (53) all_56_12 = e3 % 43.52/7.06 | | % 43.52/7.06 | | COMBINE_EQS: (41), (53) imply: % 43.52/7.06 | | (54) all_4_0 = e3 % 43.52/7.06 | | % 43.52/7.06 | | SIMP: (54) implies: % 43.52/7.06 | | (55) all_4_0 = e3 % 43.52/7.06 | | % 43.52/7.06 | | REDUCE: (47), (55) imply: % 43.52/7.06 | | (56) $false % 43.52/7.06 | | % 43.52/7.06 | | CLOSE: (56) is inconsistent. % 43.52/7.06 | | % 43.52/7.06 | Case 2: % 43.52/7.06 | | % 43.52/7.06 | | (57) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.06 | | % 43.52/7.06 | | BETA: splitting (57) gives: % 43.52/7.06 | | % 43.52/7.06 | | Case 1: % 43.52/7.06 | | | % 43.52/7.06 | | | (58) all_56_12 = e2 % 43.52/7.06 | | | % 43.52/7.06 | | | COMBINE_EQS: (41), (58) imply: % 43.52/7.06 | | | (59) all_4_0 = e2 % 43.52/7.06 | | | % 43.52/7.06 | | | SIMP: (59) implies: % 43.52/7.06 | | | (60) all_4_0 = e2 % 43.52/7.06 | | | % 43.52/7.06 | | | REDUCE: (2), (60) imply: % 43.52/7.06 | | | (61) $false % 43.52/7.06 | | | % 43.52/7.06 | | | CLOSE: (61) is inconsistent. % 43.52/7.06 | | | % 43.52/7.06 | | Case 2: % 43.52/7.06 | | | % 43.52/7.06 | | | (62) ~ (all_56_12 = e2) % 43.52/7.06 | | | (63) all_56_12 = e1 | all_56_12 = e0 % 43.52/7.06 | | | % 43.52/7.06 | | | BETA: splitting (63) gives: % 43.52/7.06 | | | % 43.52/7.06 | | | Case 1: % 43.52/7.06 | | | | % 43.52/7.06 | | | | (64) all_56_12 = e1 % 43.52/7.06 | | | | % 43.52/7.06 | | | | COMBINE_EQS: (41), (64) imply: % 43.52/7.06 | | | | (65) all_4_0 = e1 % 43.52/7.06 | | | | % 43.52/7.06 | | | | SIMP: (65) implies: % 43.52/7.06 | | | | (66) all_4_0 = e1 % 43.52/7.06 | | | | % 43.52/7.06 | | | | REDUCE: (16), (66) imply: % 43.52/7.06 | | | | (67) $false % 43.52/7.06 | | | | % 43.52/7.06 | | | | CLOSE: (67) is inconsistent. % 43.52/7.06 | | | | % 43.52/7.06 | | | Case 2: % 43.52/7.06 | | | | % 43.52/7.06 | | | | (68) all_56_12 = e0 % 43.52/7.06 | | | | % 43.52/7.06 | | | | COMBINE_EQS: (41), (68) imply: % 43.52/7.06 | | | | (69) all_4_0 = e0 % 43.52/7.06 | | | | % 43.52/7.06 | | | | SIMP: (69) implies: % 43.52/7.06 | | | | (70) all_4_0 = e0 % 43.52/7.06 | | | | % 43.52/7.06 | | | | REDUCE: (44), (70) imply: % 43.52/7.06 | | | | (71) ~ (all_52_3 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | REDUCE: (46), (70) imply: % 43.52/7.06 | | | | (72) ~ (all_10_2 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | REDUCE: (2), (70) imply: % 43.52/7.06 | | | | (73) ~ (e2 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | SIMP: (73) implies: % 43.52/7.06 | | | | (74) ~ (e2 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | REDUCE: (16), (70) imply: % 43.52/7.06 | | | | (75) ~ (e1 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | SIMP: (75) implies: % 43.52/7.06 | | | | (76) ~ (e1 = e0) % 43.52/7.06 | | | | % 43.52/7.06 | | | | BETA: splitting (9) gives: % 43.52/7.06 | | | | % 43.52/7.06 | | | | Case 1: % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | (77) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | ALPHA: (77) implies: % 43.52/7.06 | | | | | (78) all_52_9 = e2 % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | COMBINE_EQS: (23), (78) imply: % 43.52/7.06 | | | | | (79) all_10_2 = e2 % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | SIMP: (79) implies: % 43.52/7.06 | | | | | (80) all_10_2 = e2 % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | REDUCE: (50), (80) imply: % 43.52/7.06 | | | | | (81) ~ (all_4_1 = e2) % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | SIMP: (81) implies: % 43.52/7.06 | | | | | (82) ~ (all_4_1 = e2) % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | BETA: splitting (33) gives: % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | Case 1: % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | (83) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | ALPHA: (83) implies: % 43.52/7.06 | | | | | | (84) all_52_9 = e1 % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | COMBINE_EQS: (78), (84) imply: % 43.52/7.06 | | | | | | (85) e2 = e1 % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | REDUCE: (30), (85) imply: % 43.52/7.06 | | | | | | (86) $false % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | CLOSE: (86) is inconsistent. % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | Case 2: % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | (87) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.52/7.06 | | | | | | (all_52_5 = e0)) % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | BETA: splitting (87) gives: % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | Case 1: % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | (88) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | ALPHA: (88) implies: % 43.52/7.06 | | | | | | | (89) all_52_11 = e1 % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | COMBINE_EQS: (11), (89) imply: % 43.52/7.06 | | | | | | | (90) all_8_2 = e1 % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | SIMP: (90) implies: % 43.52/7.06 | | | | | | | (91) all_8_2 = e1 % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | REDUCE: (20), (91) imply: % 43.52/7.06 | | | | | | | (92) ~ (all_52_7 = e1) % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | BETA: splitting (14) gives: % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | Case 1: % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | | (93) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | | REF_CLOSE: (74), (78), (93) are inconsistent by sub-proof #64. % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | Case 2: % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | | (94) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 % 43.52/7.06 | | | | | | | | & ~ (all_52_2 = e1)) % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | | BETA: splitting (94) gives: % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | | Case 1: % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | (95) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | ALPHA: (95) implies: % 43.52/7.06 | | | | | | | | | (96) all_52_11 = e0 % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | COMBINE_EQS: (89), (96) imply: % 43.52/7.06 | | | | | | | | | (97) e1 = e0 % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | REDUCE: (76), (97) imply: % 43.52/7.06 | | | | | | | | | (98) $false % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | CLOSE: (98) is inconsistent. % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | Case 2: % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | (99) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | ALPHA: (99) implies: % 43.52/7.06 | | | | | | | | | (100) ~ (all_52_2 = e1) % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | | REF_CLOSE: (3), (5), (9), (14), (24), (25), (26), (29), (35), % 43.52/7.06 | | | | | | | | | (36), (38), (42), (48), (51), (52), (74), (82), % 43.52/7.06 | | | | | | | | | (89), (92), (100) are inconsistent by sub-proof % 43.52/7.06 | | | | | | | | | #52. % 43.52/7.06 | | | | | | | | | % 43.52/7.06 | | | | | | | | End of split % 43.52/7.06 | | | | | | | | % 43.52/7.06 | | | | | | | End of split % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | Case 2: % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | (101) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | | REF_CLOSE: (8), (35), (101) are inconsistent by sub-proof #51. % 43.52/7.06 | | | | | | | % 43.52/7.06 | | | | | | End of split % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | End of split % 43.52/7.06 | | | | | % 43.52/7.06 | | | | Case 2: % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | (102) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.52/7.06 | | | | | (all_52_8 = e0)) % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | BETA: splitting (102) gives: % 43.52/7.06 | | | | | % 43.52/7.06 | | | | | Case 1: % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | (103) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | ALPHA: (103) implies: % 43.52/7.06 | | | | | | (104) all_52_13 = e2 % 43.52/7.06 | | | | | | % 43.52/7.06 | | | | | | COMBINE_EQS: (24), (104) imply: % 43.52/7.07 | | | | | | (105) all_6_2 = e2 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | SIMP: (105) implies: % 43.52/7.07 | | | | | | (106) all_6_2 = e2 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | REDUCE: (6), (106) imply: % 43.52/7.07 | | | | | | (107) ~ (all_52_3 = e2) % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | BETA: splitting (14) gives: % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | Case 1: % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | (108) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | ALPHA: (108) implies: % 43.52/7.07 | | | | | | | (109) all_52_9 = e0 % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | COMBINE_EQS: (23), (109) imply: % 43.52/7.07 | | | | | | | (110) all_10_2 = e0 % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | REDUCE: (72), (110) imply: % 43.52/7.07 | | | | | | | (111) $false % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | CLOSE: (111) is inconsistent. % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | Case 2: % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | (112) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & % 43.52/7.07 | | | | | | | ~ (all_52_2 = e1)) % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | BETA: splitting (112) gives: % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | | Case 1: % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | (113) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | ALPHA: (113) implies: % 43.52/7.07 | | | | | | | | (114) all_52_11 = e0 % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | BETA: splitting (33) gives: % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | Case 1: % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | | (115) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | | REF_CLOSE: (4), (19), (22), (23), (71), (107), (115) are % 43.52/7.07 | | | | | | | | | inconsistent by sub-proof #70. % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | Case 2: % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | | (116) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = % 43.52/7.07 | | | | | | | | | e1 & ~ (all_52_5 = e0)) % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | | BETA: splitting (116) gives: % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | | Case 1: % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | (117) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | ALPHA: (117) implies: % 43.52/7.07 | | | | | | | | | | (118) all_52_11 = e1 % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | REF_CLOSE: (76), (114), (118) are inconsistent by sub-proof % 43.52/7.07 | | | | | | | | | | #62. % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | Case 2: % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | (119) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | ALPHA: (119) implies: % 43.52/7.07 | | | | | | | | | | (120) all_52_15 = e1 % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | COMBINE_EQS: (35), (120) imply: % 43.52/7.07 | | | | | | | | | | (121) e3 = e1 % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | REDUCE: (8), (121) imply: % 43.52/7.07 | | | | | | | | | | (122) $false % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | | CLOSE: (122) is inconsistent. % 43.52/7.07 | | | | | | | | | | % 43.52/7.07 | | | | | | | | | End of split % 43.52/7.07 | | | | | | | | | % 43.52/7.07 | | | | | | | | End of split % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | Case 2: % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | (123) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | | REF_CLOSE: (74), (104), (123) are inconsistent by sub-proof #50. % 43.52/7.07 | | | | | | | | % 43.52/7.07 | | | | | | | End of split % 43.52/7.07 | | | | | | | % 43.52/7.07 | | | | | | End of split % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | Case 2: % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | (124) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | REF_CLOSE: (35), (36), (124) are inconsistent by sub-proof #49. % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | End of split % 43.52/7.07 | | | | | % 43.52/7.07 | | | | End of split % 43.52/7.07 | | | | % 43.52/7.07 | | | End of split % 43.52/7.07 | | | % 43.52/7.07 | | End of split % 43.52/7.07 | | % 43.52/7.07 | End of split % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #49 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.07 (2) all_52_15 = e3 % 43.52/7.07 (3) ~ (e3 = e2) % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | ALPHA: (1) implies: % 43.52/7.07 | (4) all_52_15 = e2 % 43.52/7.07 | % 43.52/7.07 | COMBINE_EQS: (2), (4) imply: % 43.52/7.07 | (5) e3 = e2 % 43.52/7.07 | % 43.52/7.07 | REDUCE: (3), (5) imply: % 43.52/7.07 | (6) $false % 43.52/7.07 | % 43.52/7.07 | CLOSE: (6) is inconsistent. % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #50 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.07 (2) all_52_13 = e2 % 43.52/7.07 (3) ~ (e2 = e0) % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | ALPHA: (1) implies: % 43.52/7.07 | (4) all_52_13 = e0 % 43.52/7.07 | % 43.52/7.07 | COMBINE_EQS: (2), (4) imply: % 43.52/7.07 | (5) e2 = e0 % 43.52/7.07 | % 43.52/7.07 | SIMP: (5) implies: % 43.52/7.07 | (6) e2 = e0 % 43.52/7.07 | % 43.52/7.07 | REDUCE: (3), (6) imply: % 43.52/7.07 | (7) $false % 43.52/7.07 | % 43.52/7.07 | CLOSE: (7) is inconsistent. % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #51 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.07 (2) all_52_15 = e3 % 43.52/7.07 (3) ~ (e3 = e1) % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | ALPHA: (1) implies: % 43.52/7.07 | (4) all_52_15 = e1 % 43.52/7.07 | % 43.52/7.07 | COMBINE_EQS: (2), (4) imply: % 43.52/7.07 | (5) e3 = e1 % 43.52/7.07 | % 43.52/7.07 | SIMP: (5) implies: % 43.52/7.07 | (6) e3 = e1 % 43.52/7.07 | % 43.52/7.07 | REDUCE: (3), (6) imply: % 43.52/7.07 | (7) $false % 43.52/7.07 | % 43.52/7.07 | CLOSE: (7) is inconsistent. % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #52 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.07 (2) ~ (e2 = e0) % 43.52/7.07 (3) all_58_7 = all_52_7 % 43.52/7.07 (4) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.07 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.07 (5) ~ (all_52_12 = all_4_1) % 43.52/7.07 (6) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.07 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.07 (7) all_52_11 = e1 % 43.52/7.07 (8) ~ (all_4_1 = e0) % 43.52/7.07 (9) all_52_13 = all_6_2 % 43.52/7.07 (10) all_58_2 = all_6_2 % 43.52/7.07 (11) all_58_14 = all_52_12 % 43.52/7.07 (12) ~ (all_4_1 = e2) % 43.52/7.07 (13) ~ (all_52_2 = e1) % 43.52/7.07 (14) all_58_1 = all_52_2 % 43.52/7.07 (15) all_52_15 = e3 % 43.52/7.07 (16) ~ (e3 = e2) % 43.52/7.07 (17) all_56_3 = all_4_1 % 43.52/7.07 (18) ~ (all_52_7 = e1) % 43.52/7.07 (19) ~ (all_4_1 = e3) % 43.52/7.07 (20) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | BETA: splitting (20) gives: % 43.52/7.07 | % 43.52/7.07 | Case 1: % 43.52/7.07 | | % 43.52/7.07 | | (21) all_56_3 = e3 % 43.52/7.07 | | % 43.52/7.07 | | COMBINE_EQS: (17), (21) imply: % 43.52/7.07 | | (22) all_4_1 = e3 % 43.52/7.07 | | % 43.52/7.07 | | REDUCE: (19), (22) imply: % 43.52/7.07 | | (23) $false % 43.52/7.07 | | % 43.52/7.07 | | CLOSE: (23) is inconsistent. % 43.52/7.07 | | % 43.52/7.07 | Case 2: % 43.52/7.07 | | % 43.52/7.07 | | (24) all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0 % 43.52/7.07 | | % 43.52/7.07 | | BETA: splitting (24) gives: % 43.52/7.07 | | % 43.52/7.07 | | Case 1: % 43.52/7.07 | | | % 43.52/7.07 | | | (25) all_56_3 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | COMBINE_EQS: (17), (25) imply: % 43.52/7.07 | | | (26) all_4_1 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | REDUCE: (12), (26) imply: % 43.52/7.07 | | | (27) $false % 43.52/7.07 | | | % 43.52/7.07 | | | CLOSE: (27) is inconsistent. % 43.52/7.07 | | | % 43.52/7.07 | | Case 2: % 43.52/7.07 | | | % 43.52/7.07 | | | (28) ~ (all_56_3 = e2) % 43.52/7.07 | | | (29) all_56_3 = e1 | all_56_3 = e0 % 43.52/7.07 | | | % 43.52/7.07 | | | BETA: splitting (29) gives: % 43.52/7.07 | | | % 43.52/7.07 | | | Case 1: % 43.52/7.07 | | | | % 43.52/7.07 | | | | (30) all_56_3 = e1 % 43.52/7.07 | | | | % 43.52/7.07 | | | | COMBINE_EQS: (17), (30) imply: % 43.52/7.07 | | | | (31) all_4_1 = e1 % 43.52/7.07 | | | | % 43.52/7.07 | | | | REDUCE: (5), (31) imply: % 43.52/7.07 | | | | (32) ~ (all_52_12 = e1) % 43.52/7.07 | | | | % 43.52/7.07 | | | | REDUCE: (12), (31) imply: % 43.52/7.07 | | | | (33) ~ (e2 = e1) % 43.52/7.07 | | | | % 43.52/7.07 | | | | SIMP: (33) implies: % 43.52/7.07 | | | | (34) ~ (e2 = e1) % 43.52/7.07 | | | | % 43.52/7.07 | | | | REDUCE: (8), (31) imply: % 43.52/7.07 | | | | (35) ~ (e1 = e0) % 43.52/7.07 | | | | % 43.52/7.07 | | | | BETA: splitting (1) gives: % 43.52/7.07 | | | | % 43.52/7.07 | | | | Case 1: % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | (36) all_58_1 = e1 % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | COMBINE_EQS: (14), (36) imply: % 43.52/7.07 | | | | | (37) all_52_2 = e1 % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | REDUCE: (13), (37) imply: % 43.52/7.07 | | | | | (38) $false % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | CLOSE: (38) is inconsistent. % 43.52/7.07 | | | | | % 43.52/7.07 | | | | Case 2: % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | (39) all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1 % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | BETA: splitting (39) gives: % 43.52/7.07 | | | | | % 43.52/7.07 | | | | | Case 1: % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | (40) all_58_2 = e1 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | COMBINE_EQS: (10), (40) imply: % 43.52/7.07 | | | | | | (41) all_6_2 = e1 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | COMBINE_EQS: (9), (41) imply: % 43.52/7.07 | | | | | | (42) all_52_13 = e1 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | REF_CLOSE: (2), (4), (6), (7), (15), (16), (34), (35), (42) are % 43.52/7.07 | | | | | | inconsistent by sub-proof #54. % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | Case 2: % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | (43) all_58_7 = e1 | all_58_14 = e1 % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | | REF_CLOSE: (3), (11), (18), (32), (43) are inconsistent by sub-proof % 43.52/7.07 | | | | | | #53. % 43.52/7.07 | | | | | | % 43.52/7.07 | | | | | End of split % 43.52/7.07 | | | | | % 43.52/7.07 | | | | End of split % 43.52/7.07 | | | | % 43.52/7.07 | | | Case 2: % 43.52/7.07 | | | | % 43.52/7.07 | | | | (44) all_56_3 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | COMBINE_EQS: (17), (44) imply: % 43.52/7.07 | | | | (45) all_4_1 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | REDUCE: (8), (45) imply: % 43.52/7.07 | | | | (46) $false % 43.52/7.07 | | | | % 43.52/7.07 | | | | CLOSE: (46) is inconsistent. % 43.52/7.07 | | | | % 43.52/7.07 | | | End of split % 43.52/7.07 | | | % 43.52/7.07 | | End of split % 43.52/7.07 | | % 43.52/7.07 | End of split % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #53 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_58_7 = all_52_7 % 43.52/7.07 (2) all_58_7 = e1 | all_58_14 = e1 % 43.52/7.07 (3) ~ (all_52_12 = e1) % 43.52/7.07 (4) all_58_14 = all_52_12 % 43.52/7.07 (5) ~ (all_52_7 = e1) % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | BETA: splitting (2) gives: % 43.52/7.07 | % 43.52/7.07 | Case 1: % 43.52/7.07 | | % 43.52/7.07 | | (6) all_58_7 = e1 % 43.52/7.07 | | % 43.52/7.07 | | COMBINE_EQS: (1), (6) imply: % 43.52/7.07 | | (7) all_52_7 = e1 % 43.52/7.07 | | % 43.52/7.07 | | REDUCE: (5), (7) imply: % 43.52/7.07 | | (8) $false % 43.52/7.07 | | % 43.52/7.07 | | CLOSE: (8) is inconsistent. % 43.52/7.07 | | % 43.52/7.07 | Case 2: % 43.52/7.07 | | % 43.52/7.07 | | (9) all_58_14 = e1 % 43.52/7.07 | | % 43.52/7.07 | | COMBINE_EQS: (4), (9) imply: % 43.52/7.07 | | (10) all_52_12 = e1 % 43.52/7.07 | | % 43.52/7.07 | | SIMP: (10) implies: % 43.52/7.07 | | (11) all_52_12 = e1 % 43.52/7.07 | | % 43.52/7.07 | | REDUCE: (3), (11) imply: % 43.52/7.07 | | (12) $false % 43.52/7.07 | | % 43.52/7.07 | | CLOSE: (12) is inconsistent. % 43.52/7.07 | | % 43.52/7.07 | End of split % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #54 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) all_52_13 = e1 % 43.52/7.07 (2) ~ (e2 = e0) % 43.52/7.07 (3) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.07 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.07 (4) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.07 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.07 (5) all_52_11 = e1 % 43.52/7.07 (6) ~ (e2 = e1) % 43.52/7.07 (7) ~ (e1 = e0) % 43.52/7.07 (8) all_52_15 = e3 % 43.52/7.07 (9) ~ (e3 = e2) % 43.52/7.07 % 43.52/7.07 Begin of proof % 43.52/7.07 | % 43.52/7.07 | BETA: splitting (3) gives: % 43.52/7.07 | % 43.52/7.07 | Case 1: % 43.52/7.07 | | % 43.52/7.07 | | (10) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.52/7.07 | | % 43.52/7.07 | | ALPHA: (10) implies: % 43.52/7.07 | | (11) all_52_9 = e2 % 43.52/7.07 | | % 43.52/7.07 | | BETA: splitting (4) gives: % 43.52/7.07 | | % 43.52/7.07 | | Case 1: % 43.52/7.07 | | | % 43.52/7.07 | | | (12) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.07 | | | % 43.52/7.07 | | | REF_CLOSE: (2), (11), (12) are inconsistent by sub-proof #64. % 43.52/7.07 | | | % 43.52/7.07 | | Case 2: % 43.52/7.07 | | | % 43.52/7.07 | | | (13) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.52/7.07 | | | (all_52_2 = e1)) % 43.52/7.07 | | | % 43.52/7.07 | | | BETA: splitting (13) gives: % 43.52/7.07 | | | % 43.52/7.07 | | | Case 1: % 43.52/7.07 | | | | % 43.52/7.07 | | | | (14) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.07 | | | | % 43.52/7.07 | | | | ALPHA: (14) implies: % 43.52/7.07 | | | | (15) all_52_11 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #62. % 43.52/7.07 | | | | % 43.52/7.07 | | | Case 2: % 43.52/7.07 | | | | % 43.52/7.07 | | | | (16) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.07 | | | | % 43.52/7.07 | | | | ALPHA: (16) implies: % 43.52/7.07 | | | | (17) all_52_13 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | COMBINE_EQS: (1), (17) imply: % 43.52/7.07 | | | | (18) e1 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | SIMP: (18) implies: % 43.52/7.07 | | | | (19) e1 = e0 % 43.52/7.07 | | | | % 43.52/7.07 | | | | REDUCE: (7), (19) imply: % 43.52/7.07 | | | | (20) $false % 43.52/7.07 | | | | % 43.52/7.07 | | | | CLOSE: (20) is inconsistent. % 43.52/7.07 | | | | % 43.52/7.07 | | | End of split % 43.52/7.07 | | | % 43.52/7.07 | | End of split % 43.52/7.07 | | % 43.52/7.07 | Case 2: % 43.52/7.07 | | % 43.52/7.07 | | (21) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.52/7.07 | | (all_52_8 = e0)) % 43.52/7.07 | | % 43.52/7.07 | | BETA: splitting (21) gives: % 43.52/7.07 | | % 43.52/7.07 | | Case 1: % 43.52/7.07 | | | % 43.52/7.07 | | | (22) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.07 | | | % 43.52/7.07 | | | ALPHA: (22) implies: % 43.52/7.07 | | | (23) all_52_13 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | COMBINE_EQS: (1), (23) imply: % 43.52/7.07 | | | (24) e2 = e1 % 43.52/7.07 | | | % 43.52/7.07 | | | SIMP: (24) implies: % 43.52/7.07 | | | (25) e2 = e1 % 43.52/7.07 | | | % 43.52/7.07 | | | REDUCE: (6), (25) imply: % 43.52/7.07 | | | (26) $false % 43.52/7.07 | | | % 43.52/7.07 | | | CLOSE: (26) is inconsistent. % 43.52/7.07 | | | % 43.52/7.07 | | Case 2: % 43.52/7.07 | | | % 43.52/7.07 | | | (27) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.07 | | | % 43.52/7.07 | | | ALPHA: (27) implies: % 43.52/7.07 | | | (28) all_52_15 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | COMBINE_EQS: (8), (28) imply: % 43.52/7.07 | | | (29) e3 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | SIMP: (29) implies: % 43.52/7.07 | | | (30) e3 = e2 % 43.52/7.07 | | | % 43.52/7.07 | | | REDUCE: (9), (30) imply: % 43.52/7.07 | | | (31) $false % 43.52/7.07 | | | % 43.52/7.07 | | | CLOSE: (31) is inconsistent. % 43.52/7.07 | | | % 43.52/7.07 | | End of split % 43.52/7.07 | | % 43.52/7.07 | End of split % 43.52/7.07 | % 43.52/7.07 End of proof % 43.52/7.07 % 43.52/7.07 Sub-proof #55 shows that the following formulas are inconsistent: % 43.52/7.07 ---------------------------------------------------------------- % 43.52/7.07 (1) ~ (all_52_0 = all_52_3) % 43.52/7.07 (2) all_58_0 = all_4_2 % 43.52/7.07 (3) ~ (all_52_4 = all_52_5) % 43.52/7.07 (4) ~ (e2 = e0) % 43.52/7.07 (5) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.07 (6) ~ (all_52_3 = all_6_2) % 43.52/7.07 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.07 (8) op(all_6_2, e1) = all_6_0 % 43.52/7.07 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.07 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.07 (10) all_52_11 = all_8_2 % 43.52/7.07 (11) ~ (all_52_5 = all_6_2) % 43.52/7.07 (12) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.07 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.07 (13) ~ (all_52_1 = all_4_2) % 43.52/7.07 (14) all_56_1 = all_52_5 % 43.52/7.07 (15) all_56_12 = all_52_0 % 43.52/7.07 (16) ~ (all_6_0 = e0) % 43.52/7.07 (17) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.07 (18) all_56_13 = all_52_3 % 43.52/7.07 (19) ~ (all_52_5 = all_4_2) % 43.52/7.07 (20) all_58_5 = all_52_1 % 43.52/7.07 (21) ~ (all_52_3 = all_10_2) % 43.52/7.07 (22) all_58_11 = all_52_0 % 43.52/7.07 (23) all_52_9 = all_10_2 % 43.52/7.07 (24) all_52_13 = all_6_2 % 43.52/7.07 (25) ~ (all_52_0 = all_4_2) % 43.52/7.07 (26) ~ (all_52_3 = all_52_4) % 43.52/7.07 (27) ~ (e3 = e0) % 43.52/7.07 (28) all_52_13 = e3 & ~ (all_52_12 = e1) % 43.52/7.07 (29) ~ (all_52_4 = all_8_2) % 43.52/7.07 (30) ~ (all_52_4 = all_6_2) % 43.52/7.07 (31) all_58_1 = all_52_2 % 43.52/7.07 (32) op(e3, e1) = all_52_3 % 43.52/7.07 (33) ~ (all_6_0 = e2) % 43.52/7.07 (34) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 43.52/7.07 (35) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.07 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.07 (36) ~ (all_52_0 = all_10_2) % 43.52/7.07 (37) ~ (all_52_2 = all_4_2) % 43.52/7.07 (38) ~ (e3 = e2) % 43.52/7.07 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.07 (40) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 43.52/7.07 (41) all_56_9 = all_52_4 % 43.52/7.08 (42) all_52_15 = all_4_2 % 43.52/7.08 % 43.52/7.08 Begin of proof % 43.52/7.08 | % 43.52/7.08 | ALPHA: (28) implies: % 43.52/7.08 | (43) all_52_13 = e3 % 43.52/7.08 | % 43.52/7.08 | COMBINE_EQS: (24), (43) imply: % 43.52/7.08 | (44) all_6_2 = e3 % 43.52/7.08 | % 43.52/7.08 | SIMP: (44) implies: % 43.52/7.08 | (45) all_6_2 = e3 % 43.52/7.08 | % 43.52/7.08 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 43.52/7.08 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 43.52/7.08 | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), % 43.52/7.08 | (37), (38), (39), (40), (41), (42), (43), (45) are inconsistent by % 43.52/7.08 | sub-proof #56. % 43.52/7.08 | % 43.52/7.08 End of proof % 43.52/7.08 % 43.52/7.08 Sub-proof #56 shows that the following formulas are inconsistent: % 43.52/7.08 ---------------------------------------------------------------- % 43.52/7.08 (1) ~ (all_52_0 = all_52_3) % 43.52/7.08 (2) all_58_0 = all_4_2 % 43.52/7.08 (3) ~ (all_52_4 = all_52_5) % 43.52/7.08 (4) ~ (e2 = e0) % 43.52/7.08 (5) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.08 (6) ~ (all_52_3 = all_6_2) % 43.52/7.08 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.08 (8) op(all_6_2, e1) = all_6_0 % 43.52/7.08 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.08 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.08 (10) all_52_11 = all_8_2 % 43.52/7.08 (11) ~ (all_52_5 = all_6_2) % 43.52/7.08 (12) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.08 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.08 (13) ~ (all_52_1 = all_4_2) % 43.52/7.08 (14) all_56_1 = all_52_5 % 43.52/7.08 (15) all_56_12 = all_52_0 % 43.52/7.08 (16) ~ (all_6_0 = e0) % 43.52/7.08 (17) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.08 (18) all_56_13 = all_52_3 % 43.52/7.08 (19) ~ (all_52_5 = all_4_2) % 43.52/7.08 (20) all_58_5 = all_52_1 % 43.52/7.08 (21) ~ (all_52_3 = all_10_2) % 43.52/7.08 (22) all_58_11 = all_52_0 % 43.52/7.08 (23) all_52_9 = all_10_2 % 43.52/7.08 (24) ~ (all_52_0 = all_4_2) % 43.52/7.08 (25) ~ (all_52_3 = all_52_4) % 43.52/7.08 (26) ~ (e3 = e0) % 43.52/7.08 (27) all_6_2 = e3 % 43.52/7.08 (28) ~ (all_52_4 = all_8_2) % 43.52/7.08 (29) ~ (all_52_4 = all_6_2) % 43.52/7.08 (30) all_58_1 = all_52_2 % 43.52/7.08 (31) op(e3, e1) = all_52_3 % 43.52/7.08 (32) ~ (all_6_0 = e2) % 43.52/7.08 (33) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 43.52/7.08 (34) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.08 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.08 (35) ~ (all_52_0 = all_10_2) % 43.52/7.08 (36) ~ (all_52_2 = all_4_2) % 43.52/7.08 (37) ~ (e3 = e2) % 43.52/7.08 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.08 (39) all_52_13 = e3 % 43.52/7.08 (40) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 43.52/7.08 (41) all_56_9 = all_52_4 % 43.52/7.08 (42) all_52_15 = all_4_2 % 43.52/7.08 % 43.52/7.08 Begin of proof % 43.52/7.08 | % 43.52/7.08 | REDUCE: (6), (27) imply: % 43.52/7.08 | (43) ~ (all_52_3 = e3) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (27), (29) imply: % 43.52/7.08 | (44) ~ (all_52_4 = e3) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (11), (27) imply: % 43.52/7.08 | (45) ~ (all_52_5 = e3) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (8), (27) imply: % 43.52/7.08 | (46) op(e3, e1) = all_6_0 % 43.52/7.08 | % 43.52/7.08 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (13), (14), (15), % 43.52/7.08 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 43.52/7.08 | (28), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 43.52/7.08 | (40), (41), (42), (43), (44), (45), (46) are inconsistent by % 43.52/7.08 | sub-proof #57. % 43.52/7.08 | % 43.52/7.08 End of proof % 43.52/7.08 % 43.52/7.08 Sub-proof #57 shows that the following formulas are inconsistent: % 43.52/7.08 ---------------------------------------------------------------- % 43.52/7.08 (1) ~ (all_52_0 = all_52_3) % 43.52/7.08 (2) all_58_0 = all_4_2 % 43.52/7.08 (3) ~ (all_52_4 = all_52_5) % 43.52/7.08 (4) ~ (all_52_4 = e3) % 43.52/7.08 (5) ~ (e2 = e0) % 43.52/7.08 (6) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.08 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.08 (8) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.08 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.08 (9) all_52_11 = all_8_2 % 43.52/7.08 (10) ~ (all_52_5 = e3) % 43.52/7.08 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.08 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.08 (12) ~ (all_52_1 = all_4_2) % 43.52/7.08 (13) all_56_1 = all_52_5 % 43.52/7.08 (14) op(e3, e1) = all_6_0 % 43.52/7.08 (15) all_56_12 = all_52_0 % 43.52/7.08 (16) ~ (all_6_0 = e0) % 43.52/7.08 (17) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.08 (18) all_56_13 = all_52_3 % 43.52/7.08 (19) ~ (all_52_3 = e3) % 43.52/7.08 (20) ~ (all_52_5 = all_4_2) % 43.52/7.08 (21) all_58_5 = all_52_1 % 43.52/7.08 (22) ~ (all_52_3 = all_10_2) % 43.52/7.08 (23) all_58_11 = all_52_0 % 43.52/7.08 (24) all_52_9 = all_10_2 % 43.52/7.08 (25) ~ (all_52_0 = all_4_2) % 43.52/7.08 (26) ~ (all_52_3 = all_52_4) % 43.52/7.08 (27) ~ (e3 = e0) % 43.52/7.08 (28) ~ (all_52_4 = all_8_2) % 43.52/7.08 (29) all_58_1 = all_52_2 % 43.52/7.08 (30) op(e3, e1) = all_52_3 % 43.52/7.08 (31) ~ (all_6_0 = e2) % 43.52/7.08 (32) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 43.52/7.08 (33) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.08 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.08 (34) ~ (all_52_0 = all_10_2) % 43.52/7.08 (35) ~ (all_52_2 = all_4_2) % 43.52/7.08 (36) ~ (e3 = e2) % 43.52/7.08 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.08 (38) all_52_13 = e3 % 43.52/7.08 (39) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 43.52/7.08 (40) all_56_9 = all_52_4 % 43.52/7.08 (41) all_52_15 = all_4_2 % 43.52/7.08 % 43.52/7.08 Begin of proof % 43.52/7.08 | % 43.52/7.08 | GROUND_INST: instantiating (37) with all_52_3, all_6_0, e1, e3, simplifying % 43.52/7.08 | with (14), (30) gives: % 43.52/7.08 | (42) all_52_3 = all_6_0 % 43.52/7.08 | % 43.52/7.08 | COMBINE_EQS: (18), (42) imply: % 43.52/7.08 | (43) all_56_13 = all_6_0 % 43.52/7.08 | % 43.52/7.08 | REDUCE: (1), (42) imply: % 43.52/7.08 | (44) ~ (all_52_0 = all_6_0) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (26), (42) imply: % 43.52/7.08 | (45) ~ (all_52_4 = all_6_0) % 43.52/7.08 | % 43.52/7.08 | SIMP: (45) implies: % 43.52/7.08 | (46) ~ (all_52_4 = all_6_0) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (22), (42) imply: % 43.52/7.08 | (47) ~ (all_10_2 = all_6_0) % 43.52/7.08 | % 43.52/7.08 | SIMP: (47) implies: % 43.52/7.08 | (48) ~ (all_10_2 = all_6_0) % 43.52/7.08 | % 43.52/7.08 | REDUCE: (19), (42) imply: % 43.52/7.08 | (49) ~ (all_6_0 = e3) % 43.52/7.08 | % 43.52/7.08 | BETA: splitting (6) gives: % 43.52/7.08 | % 43.52/7.08 | Case 1: % 43.52/7.08 | | % 43.52/7.08 | | (50) all_56_13 = e3 % 43.52/7.08 | | % 43.52/7.08 | | COMBINE_EQS: (43), (50) imply: % 43.52/7.08 | | (51) all_6_0 = e3 % 43.52/7.08 | | % 43.52/7.08 | | SIMP: (51) implies: % 43.52/7.08 | | (52) all_6_0 = e3 % 43.52/7.08 | | % 43.52/7.08 | | REDUCE: (49), (52) imply: % 43.52/7.08 | | (53) $false % 43.52/7.08 | | % 43.52/7.08 | | CLOSE: (53) is inconsistent. % 43.52/7.08 | | % 43.52/7.08 | Case 2: % 43.52/7.08 | | % 43.52/7.08 | | (54) all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.08 | | % 43.52/7.08 | | BETA: splitting (54) gives: % 43.52/7.08 | | % 43.52/7.08 | | Case 1: % 43.52/7.08 | | | % 43.52/7.08 | | | (55) all_56_13 = e2 % 43.52/7.08 | | | % 43.52/7.08 | | | COMBINE_EQS: (43), (55) imply: % 43.52/7.08 | | | (56) all_6_0 = e2 % 43.52/7.08 | | | % 43.52/7.08 | | | SIMP: (56) implies: % 43.52/7.08 | | | (57) all_6_0 = e2 % 43.52/7.08 | | | % 43.52/7.08 | | | REDUCE: (31), (57) imply: % 43.52/7.08 | | | (58) $false % 43.52/7.08 | | | % 43.52/7.08 | | | CLOSE: (58) is inconsistent. % 43.52/7.08 | | | % 43.52/7.08 | | Case 2: % 43.52/7.08 | | | % 43.52/7.08 | | | (59) ~ (all_56_13 = e2) % 43.52/7.08 | | | (60) all_56_13 = e1 | all_56_13 = e0 % 43.52/7.08 | | | % 43.52/7.08 | | | BETA: splitting (60) gives: % 43.52/7.08 | | | % 43.52/7.08 | | | Case 1: % 43.52/7.08 | | | | % 43.52/7.08 | | | | (61) all_56_13 = e1 % 43.52/7.08 | | | | % 43.52/7.08 | | | | COMBINE_EQS: (43), (61) imply: % 43.52/7.08 | | | | (62) all_6_0 = e1 % 43.52/7.08 | | | | % 43.52/7.08 | | | | SIMP: (62) implies: % 43.52/7.08 | | | | (63) all_6_0 = e1 % 43.52/7.08 | | | | % 43.52/7.08 | | | | REDUCE: (44), (63) imply: % 43.52/7.08 | | | | (64) ~ (all_52_0 = e1) % 43.52/7.08 | | | | % 43.52/7.08 | | | | REDUCE: (46), (63) imply: % 43.52/7.08 | | | | (65) ~ (all_52_4 = e1) % 43.52/7.08 | | | | % 43.52/7.08 | | | | REDUCE: (48), (63) imply: % 43.52/7.08 | | | | (66) ~ (all_10_2 = e1) % 43.52/7.08 | | | | % 43.52/7.08 | | | | REDUCE: (31), (63) imply: % 43.52/7.08 | | | | (67) ~ (e2 = e1) % 43.52/7.08 | | | | % 43.52/7.08 | | | | SIMP: (67) implies: % 43.52/7.08 | | | | (68) ~ (e2 = e1) % 43.52/7.08 | | | | % 43.52/7.08 | | | | REDUCE: (16), (63) imply: % 43.52/7.08 | | | | (69) ~ (e1 = e0) % 43.52/7.08 | | | | % 43.52/7.08 | | | | BETA: splitting (8) gives: % 43.52/7.08 | | | | % 43.52/7.08 | | | | Case 1: % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | (70) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | ALPHA: (70) implies: % 43.52/7.08 | | | | | (71) all_52_9 = e2 % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | COMBINE_EQS: (24), (71) imply: % 43.52/7.08 | | | | | (72) all_10_2 = e2 % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | SIMP: (72) implies: % 43.52/7.08 | | | | | (73) all_10_2 = e2 % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | REDUCE: (34), (73) imply: % 43.52/7.08 | | | | | (74) ~ (all_52_0 = e2) % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | BETA: splitting (11) gives: % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | Case 1: % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | (75) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | REF_CLOSE: (5), (71), (75) are inconsistent by sub-proof #64. % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | Case 2: % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | (76) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.52/7.08 | | | | | | (all_52_2 = e1)) % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | BETA: splitting (76) gives: % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | Case 1: % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | (77) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | ALPHA: (77) implies: % 43.52/7.08 | | | | | | | (78) all_52_11 = e0 % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | COMBINE_EQS: (9), (78) imply: % 43.52/7.08 | | | | | | | (79) all_8_2 = e0 % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | SIMP: (79) implies: % 43.52/7.08 | | | | | | | (80) all_8_2 = e0 % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | REDUCE: (28), (80) imply: % 43.52/7.08 | | | | | | | (81) ~ (all_52_4 = e0) % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | BETA: splitting (33) gives: % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | | (82) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | | REF_CLOSE: (68), (71), (82) are inconsistent by sub-proof #63. % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | | (83) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 % 43.52/7.08 | | | | | | | | & ~ (all_52_5 = e0)) % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | | BETA: splitting (83) gives: % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | (84) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | ALPHA: (84) implies: % 43.52/7.08 | | | | | | | | | (85) all_52_11 = e1 % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | REF_CLOSE: (11), (15), (17), (24), (27), (34), (38), (64), % 43.52/7.08 | | | | | | | | | (69), (74), (85) are inconsistent by sub-proof #60. % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | (86) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | ALPHA: (86) implies: % 43.52/7.08 | | | | | | | | | (87) all_52_15 = e1 % 43.52/7.08 | | | | | | | | | (88) ~ (all_52_5 = e0) % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | COMBINE_EQS: (41), (87) imply: % 43.52/7.08 | | | | | | | | | (89) all_4_2 = e1 % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | REDUCE: (20), (89) imply: % 43.52/7.08 | | | | | | | | | (90) ~ (all_52_5 = e1) % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | BETA: splitting (39) gives: % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | (91) all_56_9 = e3 % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | COMBINE_EQS: (40), (91) imply: % 43.52/7.08 | | | | | | | | | | (92) all_52_4 = e3 % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | SIMP: (92) implies: % 43.52/7.08 | | | | | | | | | | (93) all_52_4 = e3 % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | REDUCE: (4), (93) imply: % 43.52/7.08 | | | | | | | | | | (94) $false % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | CLOSE: (94) is inconsistent. % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | (95) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0 % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | BETA: splitting (32) gives: % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | (96) all_56_1 = e3 % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | COMBINE_EQS: (13), (96) imply: % 43.52/7.08 | | | | | | | | | | | (97) all_52_5 = e3 % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | REDUCE: (10), (97) imply: % 43.52/7.08 | | | | | | | | | | | (98) $false % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | CLOSE: (98) is inconsistent. % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | (99) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | BETA: splitting (95) gives: % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | (100) all_56_9 = e2 % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | COMBINE_EQS: (40), (100) imply: % 43.52/7.08 | | | | | | | | | | | | (101) all_52_4 = e2 % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | SIMP: (101) implies: % 43.52/7.08 | | | | | | | | | | | | (102) all_52_4 = e2 % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | REDUCE: (3), (102) imply: % 43.52/7.08 | | | | | | | | | | | | (103) ~ (all_52_5 = e2) % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | SIMP: (103) implies: % 43.52/7.08 | | | | | | | | | | | | (104) ~ (all_52_5 = e2) % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | BETA: splitting (99) gives: % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | (105) all_56_1 = e2 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | COMBINE_EQS: (13), (105) imply: % 43.52/7.08 | | | | | | | | | | | | | (106) all_52_5 = e2 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | REDUCE: (104), (106) imply: % 43.52/7.08 | | | | | | | | | | | | | (107) $false % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | (108) all_56_1 = e1 | all_56_1 = e0 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | BETA: splitting (108) gives: % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | (109) all_56_1 = e1 % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | COMBINE_EQS: (13), (109) imply: % 43.52/7.08 | | | | | | | | | | | | | | (110) all_52_5 = e1 % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | REDUCE: (90), (110) imply: % 43.52/7.08 | | | | | | | | | | | | | | (111) $false % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | (112) all_56_1 = e0 % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | COMBINE_EQS: (13), (112) imply: % 43.52/7.08 | | | | | | | | | | | | | | (113) all_52_5 = e0 % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | REDUCE: (88), (113) imply: % 43.52/7.08 | | | | | | | | | | | | | | (114) $false % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | | CLOSE: (114) is inconsistent. % 43.52/7.08 | | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | (115) all_56_9 = e1 | all_56_9 = e0 % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | BETA: splitting (115) gives: % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | Case 1: % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | (116) all_56_9 = e1 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | COMBINE_EQS: (40), (116) imply: % 43.52/7.08 | | | | | | | | | | | | | (117) all_52_4 = e1 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | SIMP: (117) implies: % 43.52/7.08 | | | | | | | | | | | | | (118) all_52_4 = e1 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | REDUCE: (65), (118) imply: % 43.52/7.08 | | | | | | | | | | | | | (119) $false % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | Case 2: % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | (120) all_56_9 = e0 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | COMBINE_EQS: (40), (120) imply: % 43.52/7.08 | | | | | | | | | | | | | (121) all_52_4 = e0 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | SIMP: (121) implies: % 43.52/7.08 | | | | | | | | | | | | | (122) all_52_4 = e0 % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | REDUCE: (81), (122) imply: % 43.52/7.08 | | | | | | | | | | | | | (123) $false % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | | CLOSE: (123) is inconsistent. % 43.52/7.08 | | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | | | % 43.52/7.08 | | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | | % 43.52/7.08 | | | | | | | | | End of split % 43.52/7.08 | | | | | | | | | % 43.52/7.08 | | | | | | | | End of split % 43.52/7.08 | | | | | | | | % 43.52/7.08 | | | | | | | End of split % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | Case 2: % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | (124) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | | REF_CLOSE: (27), (38), (124) are inconsistent by sub-proof #61. % 43.52/7.08 | | | | | | | % 43.52/7.08 | | | | | | End of split % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | End of split % 43.52/7.08 | | | | | % 43.52/7.08 | | | | Case 2: % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | (125) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.52/7.08 | | | | | (all_52_8 = e0)) % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | BETA: splitting (125) gives: % 43.52/7.08 | | | | | % 43.52/7.08 | | | | | Case 1: % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | (126) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | REF_CLOSE: (36), (38), (126) are inconsistent by sub-proof #59. % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | Case 2: % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | (127) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | ALPHA: (127) implies: % 43.52/7.08 | | | | | | (128) all_52_15 = e2 % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | COMBINE_EQS: (41), (128) imply: % 43.52/7.08 | | | | | | (129) all_4_2 = e2 % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | SIMP: (129) implies: % 43.52/7.08 | | | | | | (130) all_4_2 = e2 % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | COMBINE_EQS: (2), (130) imply: % 43.52/7.08 | | | | | | (131) all_58_0 = e2 % 43.52/7.08 | | | | | | % 43.52/7.08 | | | | | | REDUCE: (25), (130) imply: % 43.52/7.09 | | | | | | (132) ~ (all_52_0 = e2) % 43.52/7.09 | | | | | | % 43.52/7.09 | | | | | | REDUCE: (12), (130) imply: % 43.52/7.09 | | | | | | (133) ~ (all_52_1 = e2) % 43.52/7.09 | | | | | | % 43.52/7.09 | | | | | | REDUCE: (35), (130) imply: % 43.52/7.09 | | | | | | (134) ~ (all_52_2 = e2) % 43.52/7.09 | | | | | | % 43.52/7.09 | | | | | | BETA: splitting (33) gives: % 43.52/7.09 | | | | | | % 43.52/7.09 | | | | | | Case 1: % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | | (135) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | | REF_CLOSE: (24), (66), (135) are inconsistent by sub-proof #58. % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | Case 2: % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | | (136) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & % 43.52/7.09 | | | | | | | ~ (all_52_5 = e0)) % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | | BETA: splitting (136) gives: % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | | Case 1: % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | (137) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | ALPHA: (137) implies: % 43.52/7.09 | | | | | | | | (138) all_52_11 = e1 % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | REF_CLOSE: (11), (15), (17), (24), (27), (34), (38), (64), (69), % 43.52/7.09 | | | | | | | | (132), (138) are inconsistent by sub-proof #60. % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | Case 2: % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | (139) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | ALPHA: (139) implies: % 43.52/7.09 | | | | | | | | (140) all_52_15 = e1 % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | COMBINE_EQS: (128), (140) imply: % 43.52/7.09 | | | | | | | | (141) e2 = e1 % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | | REF_CLOSE: (7), (21), (23), (29), (68), (131), (132), (133), % 43.52/7.09 | | | | | | | | (134), (141) are inconsistent by sub-proof #68. % 43.52/7.09 | | | | | | | | % 43.52/7.09 | | | | | | | End of split % 43.52/7.09 | | | | | | | % 43.52/7.09 | | | | | | End of split % 43.52/7.09 | | | | | | % 43.52/7.09 | | | | | End of split % 43.52/7.09 | | | | | % 43.52/7.09 | | | | End of split % 43.52/7.09 | | | | % 43.52/7.09 | | | Case 2: % 43.52/7.09 | | | | % 43.52/7.09 | | | | (142) all_56_13 = e0 % 43.52/7.09 | | | | % 43.52/7.09 | | | | COMBINE_EQS: (43), (142) imply: % 43.52/7.09 | | | | (143) all_6_0 = e0 % 43.52/7.09 | | | | % 43.52/7.09 | | | | SIMP: (143) implies: % 43.52/7.09 | | | | (144) all_6_0 = e0 % 43.52/7.09 | | | | % 43.52/7.09 | | | | REDUCE: (16), (144) imply: % 43.52/7.09 | | | | (145) $false % 43.52/7.09 | | | | % 43.52/7.09 | | | | CLOSE: (145) is inconsistent. % 43.52/7.09 | | | | % 43.52/7.09 | | | End of split % 43.52/7.09 | | | % 43.52/7.09 | | End of split % 43.52/7.09 | | % 43.52/7.09 | End of split % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #58 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.09 (2) all_52_9 = all_10_2 % 43.52/7.09 (3) ~ (all_10_2 = e1) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (1) implies: % 43.52/7.09 | (4) all_52_9 = e1 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (2), (4) imply: % 43.52/7.09 | (5) all_10_2 = e1 % 43.52/7.09 | % 43.52/7.09 | SIMP: (5) implies: % 43.52/7.09 | (6) all_10_2 = e1 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (6) imply: % 43.52/7.09 | (7) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (7) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #59 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.52/7.09 (2) all_52_13 = e3 % 43.52/7.09 (3) ~ (e3 = e2) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (1) implies: % 43.52/7.09 | (4) all_52_13 = e2 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (2), (4) imply: % 43.52/7.09 | (5) e3 = e2 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (5) imply: % 43.52/7.09 | (6) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (6) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #60 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) ~ (all_52_0 = e1) % 43.52/7.09 (2) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.09 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.09 (3) all_56_12 = all_52_0 % 43.52/7.09 (4) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.09 (5) all_52_11 = e1 % 43.52/7.09 (6) all_52_9 = all_10_2 % 43.52/7.09 (7) ~ (all_52_0 = e2) % 43.52/7.09 (8) ~ (e3 = e0) % 43.52/7.09 (9) ~ (e1 = e0) % 43.52/7.09 (10) ~ (all_52_0 = all_10_2) % 43.52/7.09 (11) all_52_13 = e3 % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | BETA: splitting (2) gives: % 43.52/7.09 | % 43.52/7.09 | Case 1: % 43.52/7.09 | | % 43.52/7.09 | | (12) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.09 | | % 43.52/7.09 | | ALPHA: (12) implies: % 43.52/7.09 | | (13) all_52_9 = e0 % 43.52/7.09 | | (14) ~ (all_52_0 = e3) % 43.52/7.09 | | % 43.52/7.09 | | COMBINE_EQS: (6), (13) imply: % 43.52/7.09 | | (15) all_10_2 = e0 % 43.52/7.09 | | % 43.52/7.09 | | SIMP: (15) implies: % 43.52/7.09 | | (16) all_10_2 = e0 % 43.52/7.09 | | % 43.52/7.09 | | REDUCE: (10), (16) imply: % 43.52/7.09 | | (17) ~ (all_52_0 = e0) % 43.52/7.09 | | % 43.52/7.09 | | REF_CLOSE: (1), (3), (4), (7), (14), (17) are inconsistent by sub-proof #73. % 43.52/7.09 | | % 43.52/7.09 | Case 2: % 43.52/7.09 | | % 43.52/7.09 | | (18) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.52/7.09 | | (all_52_2 = e1)) % 43.52/7.09 | | % 43.52/7.09 | | BETA: splitting (18) gives: % 43.52/7.09 | | % 43.52/7.09 | | Case 1: % 43.52/7.09 | | | % 43.52/7.09 | | | (19) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.52/7.09 | | | % 43.52/7.09 | | | ALPHA: (19) implies: % 43.52/7.09 | | | (20) all_52_11 = e0 % 43.52/7.09 | | | % 43.52/7.09 | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #62. % 43.52/7.09 | | | % 43.52/7.09 | | Case 2: % 43.52/7.09 | | | % 43.52/7.09 | | | (21) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.09 | | | % 43.52/7.09 | | | REF_CLOSE: (8), (11), (21) are inconsistent by sub-proof #61. % 43.52/7.09 | | | % 43.52/7.09 | | End of split % 43.52/7.09 | | % 43.52/7.09 | End of split % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #61 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.52/7.09 (2) all_52_13 = e3 % 43.52/7.09 (3) ~ (e3 = e0) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (1) implies: % 43.52/7.09 | (4) all_52_13 = e0 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (2), (4) imply: % 43.52/7.09 | (5) e3 = e0 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (5) imply: % 43.52/7.09 | (6) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (6) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #62 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_11 = e1 % 43.52/7.09 (2) all_52_11 = e0 % 43.52/7.09 (3) ~ (e1 = e0) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (1), (2) imply: % 43.52/7.09 | (4) e1 = e0 % 43.52/7.09 | % 43.52/7.09 | SIMP: (4) implies: % 43.52/7.09 | (5) e1 = e0 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (5) imply: % 43.52/7.09 | (6) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (6) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #63 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.52/7.09 (2) all_52_9 = e2 % 43.52/7.09 (3) ~ (e2 = e1) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (1) implies: % 43.52/7.09 | (4) all_52_9 = e1 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (2), (4) imply: % 43.52/7.09 | (5) e2 = e1 % 43.52/7.09 | % 43.52/7.09 | SIMP: (5) implies: % 43.52/7.09 | (6) e2 = e1 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (6) imply: % 43.52/7.09 | (7) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (7) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #64 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.52/7.09 (2) all_52_9 = e2 % 43.52/7.09 (3) ~ (e2 = e0) % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (1) implies: % 43.52/7.09 | (4) all_52_9 = e0 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (2), (4) imply: % 43.52/7.09 | (5) e2 = e0 % 43.52/7.09 | % 43.52/7.09 | SIMP: (5) implies: % 43.52/7.09 | (6) e2 = e0 % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (6) imply: % 43.52/7.09 | (7) $false % 43.52/7.09 | % 43.52/7.09 | CLOSE: (7) is inconsistent. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #65 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) op(e3, e2) = all_52_6 % 43.52/7.09 (2) all_58_0 = all_4_2 % 43.52/7.09 (3) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.09 (4) ~ (all_52_0 = all_52_6) % 43.52/7.09 (5) ~ (all_52_3 = all_6_2) % 43.52/7.09 (6) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.09 (7) ~ (all_8_0 = e0) % 43.52/7.09 (8) ~ (e3 = e1) % 43.52/7.09 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.09 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.09 (10) all_52_11 = all_8_2 % 43.52/7.09 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.09 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.09 (12) ~ (all_52_1 = all_4_2) % 43.52/7.09 (13) all_56_12 = all_52_0 % 43.52/7.09 (14) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.09 (15) all_56_13 = all_52_3 % 43.52/7.09 (16) ~ (all_8_0 = e1) % 43.52/7.09 (17) ~ (all_52_6 = all_10_2) % 43.52/7.09 (18) all_58_5 = all_52_1 % 43.52/7.09 (19) ~ (all_52_3 = all_10_2) % 43.52/7.09 (20) all_58_11 = all_52_0 % 43.52/7.09 (21) all_52_9 = all_10_2 % 43.52/7.09 (22) all_52_13 = all_6_2 % 43.52/7.09 (23) ~ (all_52_0 = all_4_2) % 43.52/7.09 (24) ~ (e3 = e0) % 43.52/7.09 (25) op(all_8_2, e2) = all_8_0 % 43.52/7.09 (26) all_58_1 = all_52_2 % 43.52/7.09 (27) ~ (all_52_6 = all_8_2) % 43.52/7.09 (28) ~ (e1 = e0) % 43.52/7.09 (29) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.09 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.09 (30) ~ (all_52_0 = all_10_2) % 43.52/7.09 (31) ~ (all_52_2 = all_4_2) % 43.52/7.09 (32) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 43.52/7.09 (33) all_56_14 = all_52_6 % 43.52/7.09 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.09 (35) all_52_11 = e3 & ~ (all_52_10 = e2) % 43.52/7.09 (36) ~ (all_52_3 = all_52_6) % 43.52/7.09 (37) all_52_15 = all_4_2 % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | ALPHA: (35) implies: % 43.52/7.09 | (38) all_52_11 = e3 % 43.52/7.09 | % 43.52/7.09 | COMBINE_EQS: (10), (38) imply: % 43.52/7.09 | (39) all_8_2 = e3 % 43.52/7.09 | % 43.52/7.09 | SIMP: (39) implies: % 43.52/7.09 | (40) all_8_2 = e3 % 43.52/7.09 | % 43.52/7.09 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 43.52/7.09 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.52/7.09 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), % 43.52/7.09 | (37), (38), (40) are inconsistent by sub-proof #66. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #66 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) op(e3, e2) = all_52_6 % 43.52/7.09 (2) all_58_0 = all_4_2 % 43.52/7.09 (3) all_8_2 = e3 % 43.52/7.09 (4) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.09 (5) ~ (all_52_0 = all_52_6) % 43.52/7.09 (6) ~ (all_52_3 = all_6_2) % 43.52/7.09 (7) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.52/7.09 (8) ~ (all_8_0 = e0) % 43.52/7.09 (9) ~ (e3 = e1) % 43.52/7.09 (10) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.52/7.09 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.52/7.09 (11) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.52/7.09 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.52/7.09 (12) ~ (all_52_1 = all_4_2) % 43.52/7.09 (13) all_56_12 = all_52_0 % 43.52/7.09 (14) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.52/7.09 (15) all_56_13 = all_52_3 % 43.52/7.09 (16) ~ (all_8_0 = e1) % 43.52/7.09 (17) ~ (all_52_6 = all_10_2) % 43.52/7.09 (18) all_58_5 = all_52_1 % 43.52/7.09 (19) ~ (all_52_3 = all_10_2) % 43.52/7.09 (20) all_58_11 = all_52_0 % 43.52/7.09 (21) all_52_9 = all_10_2 % 43.52/7.09 (22) all_52_13 = all_6_2 % 43.52/7.09 (23) ~ (all_52_0 = all_4_2) % 43.52/7.09 (24) ~ (e3 = e0) % 43.52/7.09 (25) op(all_8_2, e2) = all_8_0 % 43.52/7.09 (26) all_52_11 = e3 % 43.52/7.09 (27) all_58_1 = all_52_2 % 43.52/7.09 (28) ~ (all_52_6 = all_8_2) % 43.52/7.09 (29) ~ (e1 = e0) % 43.52/7.09 (30) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.52/7.09 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.52/7.09 (31) ~ (all_52_0 = all_10_2) % 43.52/7.09 (32) ~ (all_52_2 = all_4_2) % 43.52/7.09 (33) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 43.52/7.09 (34) all_56_14 = all_52_6 % 43.52/7.09 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.52/7.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.52/7.09 (36) ~ (all_52_3 = all_52_6) % 43.52/7.09 (37) all_52_15 = all_4_2 % 43.52/7.09 % 43.52/7.09 Begin of proof % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (28) imply: % 43.52/7.09 | (38) ~ (all_52_6 = e3) % 43.52/7.09 | % 43.52/7.09 | REDUCE: (3), (25) imply: % 43.52/7.09 | (39) op(e3, e2) = all_8_0 % 43.52/7.09 | % 43.52/7.09 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 43.52/7.09 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 43.52/7.09 | (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 43.52/7.09 | (38), (39) are inconsistent by sub-proof #67. % 43.52/7.09 | % 43.52/7.09 End of proof % 43.52/7.09 % 43.52/7.09 Sub-proof #67 shows that the following formulas are inconsistent: % 43.52/7.09 ---------------------------------------------------------------- % 43.52/7.09 (1) op(e3, e2) = all_52_6 % 43.52/7.09 (2) all_58_0 = all_4_2 % 43.52/7.09 (3) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.52/7.09 (4) ~ (all_52_0 = all_52_6) % 43.78/7.09 (5) ~ (all_52_3 = all_6_2) % 43.78/7.09 (6) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.78/7.09 (7) ~ (all_8_0 = e0) % 43.78/7.09 (8) ~ (e3 = e1) % 43.78/7.09 (9) (all_52_9 = e2 & ~ (all_52_6 = e3)) | (all_52_13 = e2 & ~ (all_52_7 = % 43.78/7.09 e1)) | (all_52_15 = e2 & ~ (all_52_8 = e0)) % 43.78/7.09 (10) (all_52_9 = e0 & ~ (all_52_0 = e3)) | (all_52_11 = e0 & ~ (all_52_1 = % 43.78/7.09 e2)) | (all_52_13 = e0 & ~ (all_52_2 = e1)) % 43.78/7.09 (11) ~ (all_52_1 = all_4_2) % 43.78/7.09 (12) op(e3, e2) = all_8_0 % 43.78/7.09 (13) all_56_12 = all_52_0 % 43.78/7.09 (14) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.78/7.09 (15) all_56_13 = all_52_3 % 43.78/7.09 (16) ~ (all_8_0 = e1) % 43.78/7.09 (17) ~ (all_52_6 = all_10_2) % 43.78/7.09 (18) all_58_5 = all_52_1 % 43.78/7.09 (19) ~ (all_52_3 = all_10_2) % 43.78/7.09 (20) all_58_11 = all_52_0 % 43.78/7.09 (21) all_52_9 = all_10_2 % 43.78/7.09 (22) all_52_13 = all_6_2 % 43.78/7.09 (23) ~ (all_52_0 = all_4_2) % 43.78/7.09 (24) ~ (all_52_6 = e3) % 43.78/7.09 (25) ~ (e3 = e0) % 43.78/7.09 (26) all_52_11 = e3 % 43.78/7.09 (27) all_58_1 = all_52_2 % 43.78/7.09 (28) ~ (e1 = e0) % 43.78/7.09 (29) (all_52_9 = e1 & ~ (all_52_3 = e3)) | (all_52_11 = e1 & ~ (all_52_4 = % 43.78/7.09 e2)) | (all_52_15 = e1 & ~ (all_52_5 = e0)) % 43.78/7.09 (30) ~ (all_52_0 = all_10_2) % 43.78/7.09 (31) ~ (all_52_2 = all_4_2) % 43.78/7.09 (32) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 43.78/7.09 (33) all_56_14 = all_52_6 % 43.78/7.09 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.78/7.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 43.78/7.09 (35) ~ (all_52_3 = all_52_6) % 43.78/7.09 (36) all_52_15 = all_4_2 % 43.78/7.09 % 43.78/7.09 Begin of proof % 43.78/7.09 | % 43.78/7.09 | GROUND_INST: instantiating (34) with all_52_6, all_8_0, e2, e3, simplifying % 43.78/7.09 | with (1), (12) gives: % 43.78/7.09 | (37) all_52_6 = all_8_0 % 43.78/7.09 | % 43.78/7.09 | COMBINE_EQS: (33), (37) imply: % 43.78/7.09 | (38) all_56_14 = all_8_0 % 43.78/7.10 | % 43.78/7.10 | REDUCE: (4), (37) imply: % 43.78/7.10 | (39) ~ (all_52_0 = all_8_0) % 43.78/7.10 | % 43.78/7.10 | REDUCE: (35), (37) imply: % 43.78/7.10 | (40) ~ (all_52_3 = all_8_0) % 43.78/7.10 | % 43.78/7.10 | REDUCE: (17), (37) imply: % 43.78/7.10 | (41) ~ (all_10_2 = all_8_0) % 43.78/7.10 | % 43.78/7.10 | SIMP: (41) implies: % 43.78/7.10 | (42) ~ (all_10_2 = all_8_0) % 43.78/7.10 | % 43.78/7.10 | REDUCE: (24), (37) imply: % 43.78/7.10 | (43) ~ (all_8_0 = e3) % 43.78/7.10 | % 43.78/7.10 | BETA: splitting (32) gives: % 43.78/7.10 | % 43.78/7.10 | Case 1: % 43.78/7.10 | | % 43.78/7.10 | | (44) all_56_14 = e3 % 43.78/7.10 | | % 43.78/7.10 | | COMBINE_EQS: (38), (44) imply: % 43.78/7.10 | | (45) all_8_0 = e3 % 43.78/7.10 | | % 43.78/7.10 | | SIMP: (45) implies: % 43.78/7.10 | | (46) all_8_0 = e3 % 43.78/7.10 | | % 43.78/7.10 | | REDUCE: (43), (46) imply: % 43.78/7.10 | | (47) $false % 43.78/7.10 | | % 43.78/7.10 | | CLOSE: (47) is inconsistent. % 43.78/7.10 | | % 43.78/7.10 | Case 2: % 43.78/7.10 | | % 43.78/7.10 | | (48) all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0 % 43.78/7.10 | | % 43.78/7.10 | | BETA: splitting (48) gives: % 43.78/7.10 | | % 43.78/7.10 | | Case 1: % 43.78/7.10 | | | % 43.78/7.10 | | | (49) all_56_14 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | COMBINE_EQS: (38), (49) imply: % 43.78/7.10 | | | (50) all_8_0 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | SIMP: (50) implies: % 43.78/7.10 | | | (51) all_8_0 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (39), (51) imply: % 43.78/7.10 | | | (52) ~ (all_52_0 = e2) % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (40), (51) imply: % 43.78/7.10 | | | (53) ~ (all_52_3 = e2) % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (42), (51) imply: % 43.78/7.10 | | | (54) ~ (all_10_2 = e2) % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (16), (51) imply: % 43.78/7.10 | | | (55) ~ (e2 = e1) % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (7), (51) imply: % 43.78/7.10 | | | (56) ~ (e2 = e0) % 43.78/7.10 | | | % 43.78/7.10 | | | BETA: splitting (10) gives: % 43.78/7.10 | | | % 43.78/7.10 | | | Case 1: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (57) all_52_9 = e0 & ~ (all_52_0 = e3) % 43.78/7.10 | | | | % 43.78/7.10 | | | | ALPHA: (57) implies: % 43.78/7.10 | | | | (58) all_52_9 = e0 % 43.78/7.10 | | | | (59) ~ (all_52_0 = e3) % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (21), (58) imply: % 43.78/7.10 | | | | (60) all_10_2 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (60) implies: % 43.78/7.10 | | | | (61) all_10_2 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (30), (61) imply: % 43.78/7.10 | | | | (62) ~ (all_52_0 = e0) % 43.78/7.10 | | | | % 43.78/7.10 | | | | BETA: splitting (29) gives: % 43.78/7.10 | | | | % 43.78/7.10 | | | | Case 1: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | (63) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | ALPHA: (63) implies: % 43.78/7.10 | | | | | (64) all_52_9 = e1 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | REF_CLOSE: (28), (58), (64) are inconsistent by sub-proof #75. % 43.78/7.10 | | | | | % 43.78/7.10 | | | | Case 2: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | (65) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 & ~ % 43.78/7.10 | | | | | (all_52_5 = e0)) % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | BETA: splitting (65) gives: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | Case 1: % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | (66) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | REF_CLOSE: (8), (26), (66) are inconsistent by sub-proof #74. % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | Case 2: % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | (67) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | ALPHA: (67) implies: % 43.78/7.10 | | | | | | (68) all_52_15 = e1 % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | COMBINE_EQS: (36), (68) imply: % 43.78/7.10 | | | | | | (69) all_4_2 = e1 % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | SIMP: (69) implies: % 43.78/7.10 | | | | | | (70) all_4_2 = e1 % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | REDUCE: (23), (70) imply: % 43.78/7.10 | | | | | | (71) ~ (all_52_0 = e1) % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | REF_CLOSE: (13), (14), (52), (59), (62), (71) are inconsistent by % 43.78/7.10 | | | | | | sub-proof #73. % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | End of split % 43.78/7.10 | | | | | % 43.78/7.10 | | | | End of split % 43.78/7.10 | | | | % 43.78/7.10 | | | Case 2: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (72) (all_52_11 = e0 & ~ (all_52_1 = e2)) | (all_52_13 = e0 & ~ % 43.78/7.10 | | | | (all_52_2 = e1)) % 43.78/7.10 | | | | % 43.78/7.10 | | | | BETA: splitting (72) gives: % 43.78/7.10 | | | | % 43.78/7.10 | | | | Case 1: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | (73) all_52_11 = e0 & ~ (all_52_1 = e2) % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | ALPHA: (73) implies: % 43.78/7.10 | | | | | (74) all_52_11 = e0 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | COMBINE_EQS: (26), (74) imply: % 43.78/7.10 | | | | | (75) e3 = e0 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | REDUCE: (25), (75) imply: % 43.78/7.10 | | | | | (76) $false % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | CLOSE: (76) is inconsistent. % 43.78/7.10 | | | | | % 43.78/7.10 | | | | Case 2: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | (77) all_52_13 = e0 & ~ (all_52_2 = e1) % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | ALPHA: (77) implies: % 43.78/7.10 | | | | | (78) all_52_13 = e0 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | COMBINE_EQS: (22), (78) imply: % 43.78/7.10 | | | | | (79) all_6_2 = e0 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | SIMP: (79) implies: % 43.78/7.10 | | | | | (80) all_6_2 = e0 % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | REDUCE: (5), (80) imply: % 43.78/7.10 | | | | | (81) ~ (all_52_3 = e0) % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | BETA: splitting (9) gives: % 43.78/7.10 | | | | | % 43.78/7.10 | | | | | Case 1: % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | (82) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | REF_CLOSE: (21), (54), (82) are inconsistent by sub-proof #72. % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | Case 2: % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | (83) (all_52_13 = e2 & ~ (all_52_7 = e1)) | (all_52_15 = e2 & ~ % 43.78/7.10 | | | | | | (all_52_8 = e0)) % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | BETA: splitting (83) gives: % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | | Case 1: % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | (84) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | REF_CLOSE: (56), (78), (84) are inconsistent by sub-proof #71. % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | Case 2: % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | (85) all_52_15 = e2 & ~ (all_52_8 = e0) % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | ALPHA: (85) implies: % 43.78/7.10 | | | | | | | (86) all_52_15 = e2 % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | COMBINE_EQS: (36), (86) imply: % 43.78/7.10 | | | | | | | (87) all_4_2 = e2 % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | SIMP: (87) implies: % 43.78/7.10 | | | | | | | (88) all_4_2 = e2 % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | COMBINE_EQS: (2), (88) imply: % 43.78/7.10 | | | | | | | (89) all_58_0 = e2 % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | REDUCE: (11), (88) imply: % 43.78/7.10 | | | | | | | (90) ~ (all_52_1 = e2) % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | REDUCE: (31), (88) imply: % 43.78/7.10 | | | | | | | (91) ~ (all_52_2 = e2) % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | BETA: splitting (29) gives: % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | | Case 1: % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | | (92) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | | REF_CLOSE: (3), (15), (19), (21), (53), (81), (92) are % 43.78/7.10 | | | | | | | | inconsistent by sub-proof #70. % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | Case 2: % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | | (93) (all_52_11 = e1 & ~ (all_52_4 = e2)) | (all_52_15 = e1 % 43.78/7.10 | | | | | | | | & ~ (all_52_5 = e0)) % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | | BETA: splitting (93) gives: % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | | Case 1: % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | (94) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | REF_CLOSE: (8), (26), (94) are inconsistent by sub-proof #69. % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | Case 2: % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | (95) all_52_15 = e1 & ~ (all_52_5 = e0) % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | ALPHA: (95) implies: % 43.78/7.10 | | | | | | | | | (96) all_52_15 = e1 % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | COMBINE_EQS: (86), (96) imply: % 43.78/7.10 | | | | | | | | | (97) e2 = e1 % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | | REF_CLOSE: (6), (18), (20), (27), (52), (55), (89), (90), % 43.78/7.10 | | | | | | | | | (91), (97) are inconsistent by sub-proof #68. % 43.78/7.10 | | | | | | | | | % 43.78/7.10 | | | | | | | | End of split % 43.78/7.10 | | | | | | | | % 43.78/7.10 | | | | | | | End of split % 43.78/7.10 | | | | | | | % 43.78/7.10 | | | | | | End of split % 43.78/7.10 | | | | | | % 43.78/7.10 | | | | | End of split % 43.78/7.10 | | | | | % 43.78/7.10 | | | | End of split % 43.78/7.10 | | | | % 43.78/7.10 | | | End of split % 43.78/7.10 | | | % 43.78/7.10 | | Case 2: % 43.78/7.10 | | | % 43.78/7.10 | | | (98) all_56_14 = e1 | all_56_14 = e0 % 43.78/7.10 | | | % 43.78/7.10 | | | BETA: splitting (98) gives: % 43.78/7.10 | | | % 43.78/7.10 | | | Case 1: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (99) all_56_14 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (38), (99) imply: % 43.78/7.10 | | | | (100) all_8_0 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (100) implies: % 43.78/7.10 | | | | (101) all_8_0 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (16), (101) imply: % 43.78/7.10 | | | | (102) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (102) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | Case 2: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (103) all_56_14 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (38), (103) imply: % 43.78/7.10 | | | | (104) all_8_0 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (104) implies: % 43.78/7.10 | | | | (105) all_8_0 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (7), (105) imply: % 43.78/7.10 | | | | (106) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (106) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | End of split % 43.78/7.10 | | | % 43.78/7.10 | | End of split % 43.78/7.10 | | % 43.78/7.10 | End of split % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #68 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.78/7.10 (2) all_58_5 = all_52_1 % 43.78/7.10 (3) all_58_11 = all_52_0 % 43.78/7.10 (4) ~ (all_52_0 = e2) % 43.78/7.10 (5) all_58_1 = all_52_2 % 43.78/7.10 (6) ~ (all_52_2 = e2) % 43.78/7.10 (7) ~ (e2 = e1) % 43.78/7.10 (8) e2 = e1 % 43.78/7.10 (9) ~ (all_52_1 = e2) % 43.78/7.10 (10) all_58_0 = e2 % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | COMBINE_EQS: (8), (10) imply: % 43.78/7.10 | (11) all_58_0 = e1 % 43.78/7.10 | % 43.78/7.10 | BETA: splitting (1) gives: % 43.78/7.10 | % 43.78/7.10 | Case 1: % 43.78/7.10 | | % 43.78/7.10 | | % 43.78/7.10 | | COMBINE_EQS: (10), (11) imply: % 43.78/7.10 | | (12) e2 = e1 % 43.78/7.10 | | % 43.78/7.10 | | REDUCE: (7), (8) imply: % 43.78/7.10 | | (13) $false % 43.78/7.10 | | % 43.78/7.10 | | CLOSE: (13) is inconsistent. % 43.78/7.10 | | % 43.78/7.10 | Case 2: % 43.78/7.10 | | % 43.78/7.10 | | (14) all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2 % 43.78/7.10 | | % 43.78/7.10 | | BETA: splitting (14) gives: % 43.78/7.10 | | % 43.78/7.10 | | Case 1: % 43.78/7.10 | | | % 43.78/7.10 | | | (15) all_58_1 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | COMBINE_EQS: (5), (15) imply: % 43.78/7.10 | | | (16) all_52_2 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (6), (16) imply: % 43.78/7.10 | | | (17) $false % 43.78/7.10 | | | % 43.78/7.10 | | | CLOSE: (17) is inconsistent. % 43.78/7.10 | | | % 43.78/7.10 | | Case 2: % 43.78/7.10 | | | % 43.78/7.10 | | | (18) all_58_5 = e2 | all_58_11 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | BETA: splitting (18) gives: % 43.78/7.10 | | | % 43.78/7.10 | | | Case 1: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (19) all_58_5 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (2), (19) imply: % 43.78/7.10 | | | | (20) all_52_1 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (20) implies: % 43.78/7.10 | | | | (21) all_52_1 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (9), (21) imply: % 43.78/7.10 | | | | (22) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (22) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | Case 2: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (23) all_58_11 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (3), (23) imply: % 43.78/7.10 | | | | (24) all_52_0 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (24) implies: % 43.78/7.10 | | | | (25) all_52_0 = e2 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (4), (25) imply: % 43.78/7.10 | | | | (26) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (26) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | End of split % 43.78/7.10 | | | % 43.78/7.10 | | End of split % 43.78/7.10 | | % 43.78/7.10 | End of split % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #69 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.78/7.10 (2) all_52_11 = e3 % 43.78/7.10 (3) ~ (e3 = e1) % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | ALPHA: (1) implies: % 43.78/7.10 | (4) all_52_11 = e1 % 43.78/7.10 | % 43.78/7.10 | COMBINE_EQS: (2), (4) imply: % 43.78/7.10 | (5) e3 = e1 % 43.78/7.10 | % 43.78/7.10 | REDUCE: (3), (5) imply: % 43.78/7.10 | (6) $false % 43.78/7.10 | % 43.78/7.10 | CLOSE: (6) is inconsistent. % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #70 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.78/7.10 (2) all_52_9 = e1 & ~ (all_52_3 = e3) % 43.78/7.10 (3) all_56_13 = all_52_3 % 43.78/7.10 (4) ~ (all_52_3 = all_10_2) % 43.78/7.10 (5) all_52_9 = all_10_2 % 43.78/7.10 (6) ~ (all_52_3 = e2) % 43.78/7.10 (7) ~ (all_52_3 = e0) % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | ALPHA: (2) implies: % 43.78/7.10 | (8) all_52_9 = e1 % 43.78/7.10 | (9) ~ (all_52_3 = e3) % 43.78/7.10 | % 43.78/7.10 | COMBINE_EQS: (5), (8) imply: % 43.78/7.10 | (10) all_10_2 = e1 % 43.78/7.10 | % 43.78/7.10 | SIMP: (10) implies: % 43.78/7.10 | (11) all_10_2 = e1 % 43.78/7.10 | % 43.78/7.10 | REDUCE: (4), (11) imply: % 43.78/7.10 | (12) ~ (all_52_3 = e1) % 43.78/7.10 | % 43.78/7.10 | BETA: splitting (1) gives: % 43.78/7.10 | % 43.78/7.10 | Case 1: % 43.78/7.10 | | % 43.78/7.10 | | (13) all_56_13 = e3 % 43.78/7.10 | | % 43.78/7.10 | | COMBINE_EQS: (3), (13) imply: % 43.78/7.10 | | (14) all_52_3 = e3 % 43.78/7.10 | | % 43.78/7.10 | | SIMP: (14) implies: % 43.78/7.10 | | (15) all_52_3 = e3 % 43.78/7.10 | | % 43.78/7.10 | | REDUCE: (9), (15) imply: % 43.78/7.10 | | (16) $false % 43.78/7.10 | | % 43.78/7.10 | | CLOSE: (16) is inconsistent. % 43.78/7.10 | | % 43.78/7.10 | Case 2: % 43.78/7.10 | | % 43.78/7.10 | | (17) all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 43.78/7.10 | | % 43.78/7.10 | | BETA: splitting (17) gives: % 43.78/7.10 | | % 43.78/7.10 | | Case 1: % 43.78/7.10 | | | % 43.78/7.10 | | | (18) all_56_13 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | COMBINE_EQS: (3), (18) imply: % 43.78/7.10 | | | (19) all_52_3 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | SIMP: (19) implies: % 43.78/7.10 | | | (20) all_52_3 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (6), (20) imply: % 43.78/7.10 | | | (21) $false % 43.78/7.10 | | | % 43.78/7.10 | | | CLOSE: (21) is inconsistent. % 43.78/7.10 | | | % 43.78/7.10 | | Case 2: % 43.78/7.10 | | | % 43.78/7.10 | | | (22) all_56_13 = e1 | all_56_13 = e0 % 43.78/7.10 | | | % 43.78/7.10 | | | BETA: splitting (22) gives: % 43.78/7.10 | | | % 43.78/7.10 | | | Case 1: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (23) all_56_13 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (3), (23) imply: % 43.78/7.10 | | | | (24) all_52_3 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (24) implies: % 43.78/7.10 | | | | (25) all_52_3 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (12), (25) imply: % 43.78/7.10 | | | | (26) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (26) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | Case 2: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (27) all_56_13 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (3), (27) imply: % 43.78/7.10 | | | | (28) all_52_3 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (28) implies: % 43.78/7.10 | | | | (29) all_52_3 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (7), (29) imply: % 43.78/7.10 | | | | (30) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (30) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | End of split % 43.78/7.10 | | | % 43.78/7.10 | | End of split % 43.78/7.10 | | % 43.78/7.10 | End of split % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #71 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) all_52_13 = e2 & ~ (all_52_7 = e1) % 43.78/7.10 (2) all_52_13 = e0 % 43.78/7.10 (3) ~ (e2 = e0) % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | ALPHA: (1) implies: % 43.78/7.10 | (4) all_52_13 = e2 % 43.78/7.10 | % 43.78/7.10 | COMBINE_EQS: (2), (4) imply: % 43.78/7.10 | (5) e2 = e0 % 43.78/7.10 | % 43.78/7.10 | REDUCE: (3), (5) imply: % 43.78/7.10 | (6) $false % 43.78/7.10 | % 43.78/7.10 | CLOSE: (6) is inconsistent. % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #72 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) all_52_9 = e2 & ~ (all_52_6 = e3) % 43.78/7.10 (2) all_52_9 = all_10_2 % 43.78/7.10 (3) ~ (all_10_2 = e2) % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | ALPHA: (1) implies: % 43.78/7.10 | (4) all_52_9 = e2 % 43.78/7.10 | % 43.78/7.10 | COMBINE_EQS: (2), (4) imply: % 43.78/7.10 | (5) all_10_2 = e2 % 43.78/7.10 | % 43.78/7.10 | REDUCE: (3), (5) imply: % 43.78/7.10 | (6) $false % 43.78/7.10 | % 43.78/7.10 | CLOSE: (6) is inconsistent. % 43.78/7.10 | % 43.78/7.10 End of proof % 43.78/7.10 % 43.78/7.10 Sub-proof #73 shows that the following formulas are inconsistent: % 43.78/7.10 ---------------------------------------------------------------- % 43.78/7.10 (1) ~ (all_52_0 = e1) % 43.78/7.10 (2) all_56_12 = all_52_0 % 43.78/7.10 (3) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.78/7.10 (4) ~ (all_52_0 = e2) % 43.78/7.10 (5) ~ (all_52_0 = e3) % 43.78/7.10 (6) ~ (all_52_0 = e0) % 43.78/7.10 % 43.78/7.10 Begin of proof % 43.78/7.10 | % 43.78/7.10 | BETA: splitting (3) gives: % 43.78/7.10 | % 43.78/7.10 | Case 1: % 43.78/7.10 | | % 43.78/7.10 | | (7) all_56_12 = e3 % 43.78/7.10 | | % 43.78/7.10 | | COMBINE_EQS: (2), (7) imply: % 43.78/7.10 | | (8) all_52_0 = e3 % 43.78/7.10 | | % 43.78/7.10 | | SIMP: (8) implies: % 43.78/7.10 | | (9) all_52_0 = e3 % 43.78/7.10 | | % 43.78/7.10 | | REDUCE: (5), (9) imply: % 43.78/7.10 | | (10) $false % 43.78/7.10 | | % 43.78/7.10 | | CLOSE: (10) is inconsistent. % 43.78/7.10 | | % 43.78/7.10 | Case 2: % 43.78/7.10 | | % 43.78/7.10 | | (11) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 43.78/7.10 | | % 43.78/7.10 | | BETA: splitting (11) gives: % 43.78/7.10 | | % 43.78/7.10 | | Case 1: % 43.78/7.10 | | | % 43.78/7.10 | | | (12) all_56_12 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | COMBINE_EQS: (2), (12) imply: % 43.78/7.10 | | | (13) all_52_0 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | SIMP: (13) implies: % 43.78/7.10 | | | (14) all_52_0 = e2 % 43.78/7.10 | | | % 43.78/7.10 | | | REDUCE: (4), (14) imply: % 43.78/7.10 | | | (15) $false % 43.78/7.10 | | | % 43.78/7.10 | | | CLOSE: (15) is inconsistent. % 43.78/7.10 | | | % 43.78/7.10 | | Case 2: % 43.78/7.10 | | | % 43.78/7.10 | | | (16) all_56_12 = e1 | all_56_12 = e0 % 43.78/7.10 | | | % 43.78/7.10 | | | BETA: splitting (16) gives: % 43.78/7.10 | | | % 43.78/7.10 | | | Case 1: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (17) all_56_12 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (2), (17) imply: % 43.78/7.10 | | | | (18) all_52_0 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (18) implies: % 43.78/7.10 | | | | (19) all_52_0 = e1 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (1), (19) imply: % 43.78/7.10 | | | | (20) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (20) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | Case 2: % 43.78/7.10 | | | | % 43.78/7.10 | | | | (21) all_56_12 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | COMBINE_EQS: (2), (21) imply: % 43.78/7.10 | | | | (22) all_52_0 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | SIMP: (22) implies: % 43.78/7.10 | | | | (23) all_52_0 = e0 % 43.78/7.10 | | | | % 43.78/7.10 | | | | REDUCE: (6), (23) imply: % 43.78/7.10 | | | | (24) $false % 43.78/7.10 | | | | % 43.78/7.10 | | | | CLOSE: (24) is inconsistent. % 43.78/7.10 | | | | % 43.78/7.10 | | | End of split % 43.78/7.10 | | | % 43.78/7.10 | | End of split % 43.78/7.10 | | % 43.78/7.10 | End of split % 43.78/7.10 | % 43.78/7.11 End of proof % 43.78/7.11 % 43.78/7.11 Sub-proof #74 shows that the following formulas are inconsistent: % 43.78/7.11 ---------------------------------------------------------------- % 43.78/7.11 (1) all_52_11 = e1 & ~ (all_52_4 = e2) % 43.78/7.11 (2) all_52_11 = e3 % 43.78/7.11 (3) ~ (e3 = e1) % 43.78/7.11 % 43.78/7.11 Begin of proof % 43.78/7.11 | % 43.78/7.11 | ALPHA: (1) implies: % 43.78/7.11 | (4) all_52_11 = e1 % 43.78/7.11 | % 43.78/7.11 | COMBINE_EQS: (2), (4) imply: % 43.78/7.11 | (5) e3 = e1 % 43.78/7.11 | % 43.78/7.11 | SIMP: (5) implies: % 43.78/7.11 | (6) e3 = e1 % 43.78/7.11 | % 43.78/7.11 | REDUCE: (3), (6) imply: % 43.78/7.11 | (7) $false % 43.78/7.11 | % 43.78/7.11 | CLOSE: (7) is inconsistent. % 43.78/7.11 | % 43.78/7.11 End of proof % 43.78/7.11 % 43.78/7.11 Sub-proof #75 shows that the following formulas are inconsistent: % 43.78/7.11 ---------------------------------------------------------------- % 43.78/7.11 (1) all_52_9 = e1 % 43.78/7.11 (2) all_52_9 = e0 % 43.78/7.11 (3) ~ (e1 = e0) % 43.78/7.11 % 43.78/7.11 Begin of proof % 43.78/7.11 | % 43.78/7.11 | COMBINE_EQS: (1), (2) imply: % 43.78/7.11 | (4) e1 = e0 % 43.78/7.11 | % 43.78/7.11 | SIMP: (4) implies: % 43.78/7.11 | (5) e1 = e0 % 43.78/7.11 | % 43.78/7.11 | REDUCE: (3), (5) imply: % 43.78/7.11 | (6) $false % 43.78/7.11 | % 43.78/7.11 | CLOSE: (6) is inconsistent. % 43.78/7.11 | % 43.78/7.11 End of proof % 43.78/7.11 % SZS output end Proof for theBenchmark % 43.78/7.11 % 43.78/7.11 6495ms %------------------------------------------------------------------------------