%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG067+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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:36:10 EDT 2023 % Result : Theorem 11.30s 2.31s % Output : Proof 23.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG067+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 02:50:29 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.12/1.45 Prover 1: Preprocessing ... % 5.12/1.47 Prover 4: Preprocessing ... % 5.12/1.49 Prover 2: Preprocessing ... % 5.12/1.49 Prover 0: Preprocessing ... % 5.12/1.50 Prover 3: Preprocessing ... % 5.12/1.50 Prover 5: Preprocessing ... % 5.12/1.50 Prover 6: Preprocessing ... % 8.99/1.99 Prover 3: Constructing countermodel ... % 8.99/1.99 Prover 1: Constructing countermodel ... % 8.99/1.99 Prover 4: Constructing countermodel ... % 8.99/1.99 Prover 2: Constructing countermodel ... % 9.69/2.06 Prover 6: Constructing countermodel ... % 10.26/2.10 Prover 0: Constructing countermodel ... % 11.30/2.31 Prover 2: proved (1683ms) % 11.30/2.31 % 11.30/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.30/2.31 % 11.30/2.31 Prover 0: stopped % 11.80/2.32 Prover 3: stopped % 11.80/2.32 Prover 6: stopped % 11.80/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.80/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.80/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.80/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.12/2.54 Prover 10: Preprocessing ... % 13.82/2.58 Prover 5: Constructing countermodel ... % 13.82/2.61 Prover 5: stopped % 14.08/2.62 Prover 8: Preprocessing ... % 14.08/2.62 Prover 11: Preprocessing ... % 14.08/2.62 Prover 7: Preprocessing ... % 14.08/2.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.25/2.72 Prover 13: Preprocessing ... % 14.90/2.72 Prover 8: Constructing countermodel ... % 14.90/2.77 Prover 7: Constructing countermodel ... % 15.35/2.78 Prover 10: Constructing countermodel ... % 15.35/2.80 Prover 11: Constructing countermodel ... % 16.33/2.97 Prover 13: Constructing countermodel ... % 20.98/3.63 Prover 8: Found proof (size 1856) % 20.98/3.63 Prover 8: proved (1303ms) % 20.98/3.63 Prover 10: stopped % 20.98/3.63 Prover 11: stopped % 20.98/3.63 Prover 4: stopped % 20.98/3.63 Prover 13: stopped % 20.98/3.63 Prover 1: stopped % 20.98/3.63 Prover 7: stopped % 20.98/3.63 % 20.98/3.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.98/3.63 % 21.96/3.71 % SZS output start Proof for theBenchmark % 21.96/3.71 Assumptions after simplification: % 21.96/3.71 --------------------------------- % 21.96/3.71 % 21.96/3.71 (ax1) % 22.11/3.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 22.11/3.77 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 22.11/3.77 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 22.11/3.77 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 22.11/3.77 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 22.11/3.77 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 22.11/3.77 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 22.11/3.77 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 22.11/3.77 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 22.11/3.77 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 22.11/3.77 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 22.11/3.77 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 22.11/3.77 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 22.11/3.77 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.11/3.77 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 22.11/3.77 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 22.11/3.77 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 22.11/3.77 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 22.11/3.77 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 22.11/3.77 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 22.11/3.77 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 22.11/3.77 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 22.11/3.77 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 22.11/3.77 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 22.11/3.77 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 22.11/3.77 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 22.11/3.77 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 22.11/3.77 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 22.11/3.77 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 22.11/3.77 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 22.11/3.77 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 22.11/3.77 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 22.11/3.77 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 22.11/3.77 | v0 = e0)) % 22.11/3.77 % 22.11/3.77 (ax3) % 22.11/3.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 22.11/3.79 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 22.11/3.79 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 22.11/3.79 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 22.11/3.79 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 22.11/3.79 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 22.11/3.79 v20 & op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 22.11/3.79 v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, e4) = % 22.11/3.79 v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 & op(e2, e0) = % 22.11/3.79 v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) = % 22.11/3.79 v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 22.11/3.79 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 22.11/3.79 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 22.11/3.79 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.11/3.79 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | % 22.11/3.79 v20 = e4 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = % 22.11/3.79 e4 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 22.11/3.79 (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | v23 = e2 % 22.11/3.79 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | v18 = e2 | v12 = % 22.11/3.79 e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | v15 = e1 | v8 = e1) & % 22.11/3.79 (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | v4 = e1) & (v24 = e0 | v23 = e0 % 22.11/3.79 | v20 = e0 | v15 = e0 | v8 = e0) & (v24 = e0 | v22 = e0 | v18 = e0 | v12 = % 22.11/3.79 e0 | v4 = e0) & (v23 = e4 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & % 22.11/3.79 (v23 = e3 | v21 = e3 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 % 22.11/3.79 | v17 = e2 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = % 22.11/3.79 e1 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 22.11/3.79 (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | v21 = e3 % 22.11/3.79 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | v19 = e2 | v14 = % 22.11/3.79 e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | v14 = e1 | v7 = e1) & % 22.11/3.79 (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | v7 = e0) & (v20 = e4 | v19 = e4 % 22.11/3.79 | v16 = e4 | v10 = e4 | v2 = e4) & (v20 = e3 | v19 = e3 | v16 = e3 | v10 = % 22.11/3.79 e3 | v2 = e3) & (v20 = e2 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & % 22.11/3.79 (v20 = e1 | v19 = e1 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 % 22.11/3.79 | v16 = e0 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = % 22.11/3.79 e4 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 22.11/3.79 (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | v17 = e1 % 22.11/3.79 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | v16 = e0 | v13 = % 22.11/3.79 e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | v9 = e4 | v1 = e4) & % 22.11/3.79 (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 = e3) & (v15 = e2 | v14 = e2 % 22.11/3.79 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v9 = % 22.11/3.79 e1 | v1 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v9 = e0 | v1 = e0) & % 22.11/3.79 (v12 = e4 | v11 = e4 | v10 = e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 % 22.11/3.79 | v10 = e3 | v9 = e3 | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = % 22.11/3.79 e2 | v5 = e2) & (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & % 22.11/3.79 (v12 = e0 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | % 22.11/3.79 v6 = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 | v0 % 22.11/3.79 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & (v8 = e1 | v7 % 22.11/3.79 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 = % 22.11/3.79 e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 = % 22.11/3.79 e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1 % 22.11/3.79 | v1 = e1 | v0 = e1) & (v0 = e0 | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) % 22.11/3.79 & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0)))) % 22.11/3.79 % 22.11/3.79 (ax4) % 22.47/3.81 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 22.47/3.81 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 22.47/3.81 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 22.47/3.81 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 22.47/3.81 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 22.47/3.81 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 22.47/3.81 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 22.47/3.81 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 22.47/3.81 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 22.47/3.81 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 22.47/3.81 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 22.47/3.81 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 22.47/3.81 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 22.47/3.81 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 22.47/3.81 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 22.47/3.81 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 22.47/3.81 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 22.47/3.81 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 22.47/3.81 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 22.47/3.81 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 22.47/3.81 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 22.47/3.81 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 22.47/3.81 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 22.47/3.81 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 22.47/3.81 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 22.47/3.81 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 22.47/3.81 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 22.47/3.81 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 22.47/3.81 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 22.47/3.81 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 22.47/3.81 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 22.47/3.81 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 22.47/3.81 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 22.47/3.81 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 22.47/3.81 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 22.47/3.81 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 22.47/3.81 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 22.47/3.81 % 22.47/3.81 (ax5) % 22.47/3.81 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 22.47/3.81 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 22.47/3.81 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 22.47/3.81 % 22.47/3.81 (ax6) % 22.47/3.81 op(e4, e2) = e1 & op(e2, e4) = e3 & op(e1, e1) = e0 & $i(e4) & $i(e3) & $i(e2) % 22.47/3.81 & $i(e1) & $i(e0) % 22.47/3.81 % 22.47/3.81 (co1) % 22.47/3.83 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 22.47/3.83 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 22.47/3.83 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 22.47/3.83 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 22.47/3.83 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 22.47/3.83 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v20 & op(e4, e3) = v24 & op(e4, e2) = % 22.47/3.83 v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v19 & op(e3, e3) = % 22.47/3.83 v15 & op(e3, e2) = v18 & op(e3, e1) = v17 & op(e3, e0) = v16 & op(e2, e4) = % 22.47/3.83 v14 & op(e2, e3) = v13 & op(e2, e2) = v10 & op(e2, e1) = v12 & op(e2, e0) = % 22.47/3.83 v11 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v5 % 22.47/3.83 & op(e1, e0) = v6 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 22.47/3.83 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 22.47/3.83 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 22.47/3.83 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.47/3.83 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v20 = e3) | v24 = % 22.47/3.83 e4) & ( ~ (v20 = e2) | v23 = e4) & ( ~ (v20 = e1) | v22 = e4) & ( ~ (v20 = % 22.47/3.83 e0) | v21 = e4) & ( ~ (v15 = e4) | v19 = e3) & ( ~ (v15 = e2) | v18 = % 22.47/3.83 e3) & ( ~ (v15 = e1) | v17 = e3) & ( ~ (v15 = e0) | v16 = e3) & ( ~ (v10 = % 22.47/3.83 e4) | v14 = e2) & ( ~ (v10 = e3) | v13 = e2) & ( ~ (v10 = e1) | v12 = % 22.47/3.83 e2) & ( ~ (v10 = e0) | v11 = e2) & ( ~ (v5 = e4) | v9 = e1) & ( ~ (v5 = % 22.47/3.83 e3) | v8 = e1) & ( ~ (v5 = e2) | v7 = e1) & ( ~ (v5 = e0) | v6 = e1) & ( % 22.47/3.83 ~ (v0 = e4) | v4 = e0) & ( ~ (v0 = e3) | v3 = e0) & ( ~ (v0 = e2) | v2 = % 22.47/3.83 e0) & ( ~ (v0 = e1) | v1 = e0) & ((v20 = e3 & v15 = e4 & ~ (v24 = e4)) | % 22.47/3.83 (v20 = e3 & v15 = e4 & ~ (v19 = e3)) | (v20 = e2 & v10 = e4 & ~ (v23 = % 22.47/3.83 e4)) | (v20 = e2 & v10 = e4 & ~ (v14 = e2)) | (v20 = e1 & v5 = e4 & % 22.47/3.83 ~ (v22 = e4)) | (v20 = e1 & v5 = e4 & ~ (v9 = e1)) | (v20 = e0 & v0 = % 22.47/3.83 e4 & ~ (v21 = e4)) | (v20 = e0 & v0 = e4 & ~ (v4 = e0)) | (v15 = e2 & % 22.47/3.83 v10 = e3 & ~ (v18 = e3)) | (v15 = e2 & v10 = e3 & ~ (v13 = e2)) | (v15 % 22.47/3.83 = e1 & v5 = e3 & ~ (v17 = e3)) | (v15 = e1 & v5 = e3 & ~ (v8 = e1)) | % 22.47/3.83 (v15 = e0 & v0 = e3 & ~ (v16 = e3)) | (v15 = e0 & v0 = e3 & ~ (v3 = e0)) % 22.47/3.83 | (v10 = e1 & v5 = e2 & ~ (v12 = e2)) | (v10 = e1 & v5 = e2 & ~ (v7 = % 22.47/3.83 e1)) | (v10 = e0 & v0 = e2 & ~ (v11 = e2)) | (v10 = e0 & v0 = e2 & ~ % 22.47/3.83 (v2 = e0)) | (v5 = e0 & v0 = e1 & ~ (v6 = e1)) | (v5 = e0 & v0 = e1 & % 22.47/3.83 ~ (v1 = e0)))) % 22.47/3.83 % 22.47/3.83 (function-axioms) % 22.47/3.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 22.47/3.83 v2) = v1) | ~ (op(v3, v2) = v0)) % 22.47/3.83 % 22.47/3.83 Further assumptions not needed in the proof: % 22.47/3.83 -------------------------------------------- % 22.47/3.83 ax2 % 22.47/3.83 % 22.47/3.83 Those formulas are unsatisfiable: % 22.47/3.83 --------------------------------- % 22.47/3.83 % 22.47/3.83 Begin of proof % 22.47/3.83 | % 22.47/3.83 | ALPHA: (ax1) implies: % 22.47/3.85 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.85 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 22.47/3.85 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 22.47/3.85 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 22.47/3.85 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 22.47/3.85 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 22.47/3.85 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 22.47/3.85 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 22.47/3.85 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 22.47/3.85 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 22.47/3.85 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 22.47/3.85 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 22.47/3.85 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 22.47/3.85 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 22.47/3.85 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 22.47/3.85 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 22.47/3.85 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 22.47/3.85 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 22.47/3.85 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 22.47/3.85 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 22.47/3.85 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 22.47/3.85 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 22.47/3.85 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 22.47/3.85 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 22.47/3.85 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 22.47/3.85 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 22.47/3.85 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 22.47/3.85 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 22.47/3.85 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 22.47/3.85 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 22.47/3.85 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 22.47/3.85 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 22.47/3.85 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 22.47/3.85 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 22.47/3.85 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 22.47/3.85 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 22.47/3.85 | % 22.47/3.85 | ALPHA: (ax3) implies: % 22.47/3.86 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.86 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 22.47/3.86 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 22.47/3.86 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 22.47/3.86 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 22.47/3.86 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v20 & % 22.47/3.86 | op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) = % 22.47/3.86 | v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, % 22.47/3.86 | e4) = v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 % 22.47/3.86 | & op(e2, e0) = v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) % 22.47/3.86 | = v10 & op(e1, e1) = v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, % 22.47/3.86 | e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & % 22.47/3.86 | $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 22.47/3.86 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 22.47/3.86 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 22.47/3.86 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | v20 = e4 | % 22.47/3.86 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = e4 | % 22.47/3.86 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) & % 22.47/3.86 | (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | % 22.47/3.86 | v23 = e2 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | % 22.47/3.86 | v18 = e2 | v12 = e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | % 22.47/3.86 | v15 = e1 | v8 = e1) & (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | % 22.47/3.86 | v4 = e1) & (v24 = e0 | v23 = e0 | v20 = e0 | v15 = e0 | v8 = e0) & % 22.47/3.86 | (v24 = e0 | v22 = e0 | v18 = e0 | v12 = e0 | v4 = e0) & (v23 = e4 | % 22.47/3.86 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & (v23 = e3 | v21 = e3 | % 22.47/3.86 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 | v17 = e2 | % 22.47/3.86 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = e1 | % 22.47/3.86 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) & % 22.47/3.86 | (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | % 22.47/3.86 | v21 = e3 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | % 22.47/3.86 | v19 = e2 | v14 = e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | % 22.47/3.86 | v14 = e1 | v7 = e1) & (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | % 22.47/3.86 | v7 = e0) & (v20 = e4 | v19 = e4 | v16 = e4 | v10 = e4 | v2 = e4) & % 22.47/3.86 | (v20 = e3 | v19 = e3 | v16 = e3 | v10 = e3 | v2 = e3) & (v20 = e2 | % 22.47/3.86 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & (v20 = e1 | v19 = e1 | % 22.47/3.86 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 | v16 = e0 | % 22.47/3.86 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = e4 | % 22.47/3.86 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) & % 22.47/3.86 | (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | % 22.47/3.86 | v17 = e1 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | % 22.47/3.86 | v16 = e0 | v13 = e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | % 22.47/3.86 | v9 = e4 | v1 = e4) & (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 % 22.47/3.86 | = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v9 = e2 | v1 = e2) & (v15 % 22.47/3.86 | = e1 | v14 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v15 = e0 | v14 = % 22.47/3.86 | e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v12 = e4 | v11 = e4 | v10 = % 22.47/3.86 | e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 | v10 = e3 | v9 = e3 % 22.47/3.86 | | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = e2 | v5 = e2) & % 22.47/3.86 | (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & (v12 = e0 | % 22.47/3.86 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | v6 % 22.47/3.86 | = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 % 22.47/3.86 | | v0 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & % 22.47/3.86 | (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = % 22.47/3.86 | e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | % 22.47/3.86 | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = % 22.47/3.86 | e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v0 = e0 % 22.47/3.86 | | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v4 = e0 | v3 = e0 | % 22.47/3.86 | v2 = e0 | v1 = e0)))) % 22.47/3.86 | % 22.47/3.86 | ALPHA: (ax4) implies: % 22.47/3.87 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.47/3.87 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 22.47/3.87 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 22.47/3.87 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 22.47/3.87 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 22.47/3.87 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24 % 22.47/3.87 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 % 22.47/3.87 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 % 22.47/3.87 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = % 22.47/3.87 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = % 22.47/3.87 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = % 22.47/3.87 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 = % 22.47/3.87 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 = % 22.47/3.87 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 = % 22.47/3.87 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = % 22.47/3.87 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 22.47/3.87 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = % 22.47/3.87 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = % 22.47/3.87 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = % 22.47/3.87 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = % 22.47/3.87 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 = % 22.47/3.87 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 = % 22.47/3.87 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 = % 22.47/3.87 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8) % 22.47/3.87 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8 % 22.47/3.87 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & % 22.47/3.87 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = % 22.47/3.87 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & % 22.47/3.87 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 22.47/3.87 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, % 22.47/3.87 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 & % 22.47/3.87 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) = % 22.47/3.87 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2, % 22.47/3.87 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 & % 22.47/3.87 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) = % 22.47/3.87 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0, % 22.47/3.87 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 22.47/3.87 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 22.47/3.87 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.47/3.87 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 22.47/3.87 | % 22.47/3.87 | ALPHA: (ax5) implies: % 22.47/3.87 | (4) ~ (e3 = e0) % 22.47/3.87 | (5) ~ (e3 = e2) % 22.47/3.87 | (6) ~ (e4 = e0) % 22.47/3.87 | (7) ~ (e4 = e1) % 22.47/3.87 | (8) ~ (e4 = e3) % 22.47/3.87 | % 22.47/3.87 | ALPHA: (ax6) implies: % 22.47/3.87 | (9) op(e1, e1) = e0 % 22.47/3.87 | (10) op(e2, e4) = e3 % 22.47/3.87 | (11) op(e4, e2) = e1 % 22.47/3.87 | % 22.47/3.87 | ALPHA: (co1) implies: % 22.79/3.88 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 22.79/3.88 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 22.79/3.88 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 22.79/3.88 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 22.79/3.88 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 22.79/3.88 | : ? [v24: $i] : (op(e4, e4) = v20 & op(e4, e3) = v24 & op(e4, e2) = % 22.79/3.88 | v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v19 & % 22.79/3.88 | op(e3, e3) = v15 & op(e3, e2) = v18 & op(e3, e1) = v17 & op(e3, e0) % 22.79/3.88 | = v16 & op(e2, e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v10 & % 22.79/3.88 | op(e2, e1) = v12 & op(e2, e0) = v11 & op(e1, e4) = v9 & op(e1, e3) = % 22.79/3.88 | v8 & op(e1, e2) = v7 & op(e1, e1) = v5 & op(e1, e0) = v6 & op(e0, % 22.79/3.88 | e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & % 22.79/3.88 | op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 22.79/3.88 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 22.79/3.88 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 22.79/3.88 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v20 = e3) % 22.79/3.88 | | v24 = e4) & ( ~ (v20 = e2) | v23 = e4) & ( ~ (v20 = e1) | v22 = % 22.79/3.88 | e4) & ( ~ (v20 = e0) | v21 = e4) & ( ~ (v15 = e4) | v19 = e3) & ( % 22.79/3.88 | ~ (v15 = e2) | v18 = e3) & ( ~ (v15 = e1) | v17 = e3) & ( ~ (v15 = % 22.79/3.88 | e0) | v16 = e3) & ( ~ (v10 = e4) | v14 = e2) & ( ~ (v10 = e3) | % 22.79/3.88 | v13 = e2) & ( ~ (v10 = e1) | v12 = e2) & ( ~ (v10 = e0) | v11 = % 22.79/3.88 | e2) & ( ~ (v5 = e4) | v9 = e1) & ( ~ (v5 = e3) | v8 = e1) & ( ~ % 22.79/3.88 | (v5 = e2) | v7 = e1) & ( ~ (v5 = e0) | v6 = e1) & ( ~ (v0 = e4) | % 22.79/3.88 | v4 = e0) & ( ~ (v0 = e3) | v3 = e0) & ( ~ (v0 = e2) | v2 = e0) & ( % 22.79/3.88 | ~ (v0 = e1) | v1 = e0) & ((v20 = e3 & v15 = e4 & ~ (v24 = e4)) | % 22.79/3.88 | (v20 = e3 & v15 = e4 & ~ (v19 = e3)) | (v20 = e2 & v10 = e4 & ~ % 22.79/3.88 | (v23 = e4)) | (v20 = e2 & v10 = e4 & ~ (v14 = e2)) | (v20 = e1 % 22.79/3.88 | & v5 = e4 & ~ (v22 = e4)) | (v20 = e1 & v5 = e4 & ~ (v9 = e1)) % 22.79/3.88 | | (v20 = e0 & v0 = e4 & ~ (v21 = e4)) | (v20 = e0 & v0 = e4 & ~ % 22.79/3.88 | (v4 = e0)) | (v15 = e2 & v10 = e3 & ~ (v18 = e3)) | (v15 = e2 & % 22.79/3.88 | v10 = e3 & ~ (v13 = e2)) | (v15 = e1 & v5 = e3 & ~ (v17 = e3)) % 22.79/3.88 | | (v15 = e1 & v5 = e3 & ~ (v8 = e1)) | (v15 = e0 & v0 = e3 & ~ % 22.79/3.88 | (v16 = e3)) | (v15 = e0 & v0 = e3 & ~ (v3 = e0)) | (v10 = e1 & % 22.79/3.88 | v5 = e2 & ~ (v12 = e2)) | (v10 = e1 & v5 = e2 & ~ (v7 = e1)) | % 22.79/3.88 | (v10 = e0 & v0 = e2 & ~ (v11 = e2)) | (v10 = e0 & v0 = e2 & ~ % 22.79/3.88 | (v2 = e0)) | (v5 = e0 & v0 = e1 & ~ (v6 = e1)) | (v5 = e0 & v0 % 22.79/3.88 | = e1 & ~ (v1 = e0)))) % 22.79/3.88 | % 22.79/3.88 | DELTA: instantiating (3) with fresh symbols all_4_0, all_4_1, all_4_2, % 22.79/3.88 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 22.79/3.88 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 22.79/3.88 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 22.79/3.88 | all_4_24 gives: % 22.79/3.89 | (13) ~ (all_4_0 = all_4_1) & ~ (all_4_0 = all_4_2) & ~ (all_4_0 = % 22.79/3.89 | all_4_3) & ~ (all_4_0 = all_4_4) & ~ (all_4_0 = all_4_5) & ~ % 22.79/3.89 | (all_4_0 = all_4_10) & ~ (all_4_0 = all_4_15) & ~ (all_4_0 = % 22.79/3.89 | all_4_20) & ~ (all_4_1 = all_4_2) & ~ (all_4_1 = all_4_3) & ~ % 22.79/3.89 | (all_4_1 = all_4_4) & ~ (all_4_1 = all_4_6) & ~ (all_4_1 = all_4_11) % 22.79/3.89 | & ~ (all_4_1 = all_4_16) & ~ (all_4_1 = all_4_21) & ~ (all_4_2 = % 22.79/3.89 | all_4_3) & ~ (all_4_2 = all_4_4) & ~ (all_4_2 = all_4_7) & ~ % 22.79/3.89 | (all_4_2 = all_4_12) & ~ (all_4_2 = all_4_17) & ~ (all_4_2 = % 22.79/3.89 | all_4_22) & ~ (all_4_3 = all_4_4) & ~ (all_4_3 = all_4_8) & ~ % 22.79/3.89 | (all_4_3 = all_4_13) & ~ (all_4_3 = all_4_18) & ~ (all_4_3 = % 22.79/3.89 | all_4_23) & ~ (all_4_4 = all_4_9) & ~ (all_4_4 = all_4_14) & ~ % 22.79/3.89 | (all_4_4 = all_4_19) & ~ (all_4_4 = all_4_24) & ~ (all_4_5 = % 22.79/3.89 | all_4_6) & ~ (all_4_5 = all_4_7) & ~ (all_4_5 = all_4_8) & ~ % 22.79/3.89 | (all_4_5 = all_4_9) & ~ (all_4_5 = all_4_10) & ~ (all_4_5 = % 22.79/3.89 | all_4_15) & ~ (all_4_5 = all_4_20) & ~ (all_4_6 = all_4_7) & ~ % 22.79/3.89 | (all_4_6 = all_4_8) & ~ (all_4_6 = all_4_9) & ~ (all_4_6 = all_4_11) % 22.79/3.89 | & ~ (all_4_6 = all_4_16) & ~ (all_4_6 = all_4_21) & ~ (all_4_7 = % 22.79/3.89 | all_4_8) & ~ (all_4_7 = all_4_9) & ~ (all_4_7 = all_4_12) & ~ % 22.79/3.89 | (all_4_7 = all_4_17) & ~ (all_4_7 = all_4_22) & ~ (all_4_8 = % 22.79/3.89 | all_4_9) & ~ (all_4_8 = all_4_13) & ~ (all_4_8 = all_4_18) & ~ % 22.79/3.89 | (all_4_8 = all_4_23) & ~ (all_4_9 = all_4_14) & ~ (all_4_9 = % 22.79/3.89 | all_4_19) & ~ (all_4_9 = all_4_24) & ~ (all_4_10 = all_4_11) & ~ % 22.79/3.89 | (all_4_10 = all_4_12) & ~ (all_4_10 = all_4_13) & ~ (all_4_10 = % 22.79/3.89 | all_4_14) & ~ (all_4_10 = all_4_15) & ~ (all_4_10 = all_4_20) & ~ % 22.79/3.89 | (all_4_11 = all_4_12) & ~ (all_4_11 = all_4_13) & ~ (all_4_11 = % 22.79/3.89 | all_4_14) & ~ (all_4_11 = all_4_16) & ~ (all_4_11 = all_4_21) & ~ % 22.79/3.89 | (all_4_12 = all_4_13) & ~ (all_4_12 = all_4_14) & ~ (all_4_12 = % 22.79/3.89 | all_4_17) & ~ (all_4_12 = all_4_22) & ~ (all_4_13 = all_4_14) & ~ % 22.79/3.89 | (all_4_13 = all_4_18) & ~ (all_4_13 = all_4_23) & ~ (all_4_14 = % 22.79/3.89 | all_4_19) & ~ (all_4_14 = all_4_24) & ~ (all_4_15 = all_4_16) & ~ % 22.79/3.89 | (all_4_15 = all_4_17) & ~ (all_4_15 = all_4_18) & ~ (all_4_15 = % 22.79/3.89 | all_4_19) & ~ (all_4_15 = all_4_20) & ~ (all_4_16 = all_4_17) & ~ % 22.79/3.89 | (all_4_16 = all_4_18) & ~ (all_4_16 = all_4_19) & ~ (all_4_16 = % 22.79/3.89 | all_4_21) & ~ (all_4_17 = all_4_18) & ~ (all_4_17 = all_4_19) & ~ % 22.79/3.89 | (all_4_17 = all_4_22) & ~ (all_4_18 = all_4_19) & ~ (all_4_18 = % 22.79/3.89 | all_4_23) & ~ (all_4_19 = all_4_24) & ~ (all_4_20 = all_4_21) & ~ % 22.79/3.89 | (all_4_20 = all_4_22) & ~ (all_4_20 = all_4_23) & ~ (all_4_20 = % 22.79/3.89 | all_4_24) & ~ (all_4_21 = all_4_22) & ~ (all_4_21 = all_4_23) & ~ % 22.79/3.89 | (all_4_21 = all_4_24) & ~ (all_4_22 = all_4_23) & ~ (all_4_22 = % 22.79/3.89 | all_4_24) & ~ (all_4_23 = all_4_24) & op(e4, e4) = all_4_0 & op(e4, % 22.79/3.89 | e3) = all_4_5 & op(e4, e2) = all_4_10 & op(e4, e1) = all_4_15 & % 22.79/3.89 | op(e4, e0) = all_4_20 & op(e3, e4) = all_4_1 & op(e3, e3) = all_4_6 & % 22.79/3.89 | op(e3, e2) = all_4_11 & op(e3, e1) = all_4_16 & op(e3, e0) = all_4_21 % 22.79/3.89 | & op(e2, e4) = all_4_2 & op(e2, e3) = all_4_7 & op(e2, e2) = all_4_12 % 22.79/3.89 | & op(e2, e1) = all_4_17 & op(e2, e0) = all_4_22 & op(e1, e4) = all_4_3 % 22.79/3.89 | & op(e1, e3) = all_4_8 & op(e1, e2) = all_4_13 & op(e1, e1) = all_4_18 % 22.79/3.89 | & op(e1, e0) = all_4_23 & op(e0, e4) = all_4_4 & op(e0, e3) = all_4_9 % 22.79/3.89 | & op(e0, e2) = all_4_14 & op(e0, e1) = all_4_19 & op(e0, e0) = % 22.79/3.89 | all_4_24 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & % 22.79/3.89 | $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & % 22.79/3.89 | $i(all_4_9) & $i(all_4_10) & $i(all_4_11) & $i(all_4_12) & % 22.79/3.89 | $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & $i(all_4_16) & % 22.79/3.89 | $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & $i(all_4_20) & % 22.79/3.89 | $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & $i(all_4_24) % 22.79/3.89 | % 22.79/3.89 | ALPHA: (13) implies: % 22.79/3.89 | (14) ~ (all_4_23 = all_4_24) % 22.79/3.89 | (15) ~ (all_4_22 = all_4_24) % 22.79/3.89 | (16) ~ (all_4_20 = all_4_24) % 22.79/3.89 | (17) ~ (all_4_18 = all_4_23) % 22.79/3.89 | (18) ~ (all_4_10 = all_4_12) % 22.79/3.89 | (19) ~ (all_4_9 = all_4_24) % 22.79/3.89 | (20) ~ (all_4_6 = all_4_9) % 22.79/3.89 | (21) ~ (all_4_4 = all_4_24) % 22.79/3.89 | (22) ~ (all_4_3 = all_4_23) % 22.79/3.89 | (23) ~ (all_4_3 = all_4_18) % 22.79/3.89 | (24) ~ (all_4_3 = all_4_4) % 22.79/3.89 | (25) ~ (all_4_2 = all_4_12) % 22.79/3.89 | (26) ~ (all_4_2 = all_4_4) % 22.79/3.89 | (27) ~ (all_4_2 = all_4_3) % 22.79/3.89 | (28) ~ (all_4_1 = all_4_2) % 22.79/3.89 | (29) ~ (all_4_0 = all_4_20) % 22.79/3.89 | (30) ~ (all_4_0 = all_4_10) % 22.79/3.89 | (31) ~ (all_4_0 = all_4_4) % 22.79/3.89 | (32) ~ (all_4_0 = all_4_3) % 22.79/3.89 | (33) ~ (all_4_0 = all_4_2) % 22.79/3.89 | (34) op(e0, e0) = all_4_24 % 22.79/3.89 | (35) op(e0, e3) = all_4_9 % 22.79/3.89 | (36) op(e0, e4) = all_4_4 % 22.79/3.89 | (37) op(e1, e0) = all_4_23 % 22.79/3.89 | (38) op(e1, e1) = all_4_18 % 22.79/3.89 | (39) op(e1, e4) = all_4_3 % 22.79/3.89 | (40) op(e2, e0) = all_4_22 % 22.79/3.89 | (41) op(e2, e2) = all_4_12 % 22.79/3.89 | (42) op(e2, e4) = all_4_2 % 22.79/3.89 | (43) op(e3, e0) = all_4_21 % 22.79/3.89 | (44) op(e3, e3) = all_4_6 % 22.79/3.89 | (45) op(e3, e4) = all_4_1 % 22.79/3.89 | (46) op(e4, e0) = all_4_20 % 22.79/3.89 | (47) op(e4, e2) = all_4_10 % 22.79/3.89 | (48) op(e4, e4) = all_4_0 % 22.79/3.89 | % 22.79/3.89 | DELTA: instantiating (12) with fresh symbols all_6_0, all_6_1, all_6_2, % 22.79/3.89 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 22.79/3.89 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 22.79/3.89 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 22.79/3.89 | all_6_24 gives: % 22.79/3.90 | (49) op(e4, e4) = all_6_4 & op(e4, e3) = all_6_0 & op(e4, e2) = all_6_1 & % 22.79/3.90 | op(e4, e1) = all_6_2 & op(e4, e0) = all_6_3 & op(e3, e4) = all_6_5 & % 22.79/3.90 | op(e3, e3) = all_6_9 & op(e3, e2) = all_6_6 & op(e3, e1) = all_6_7 & % 22.79/3.90 | op(e3, e0) = all_6_8 & op(e2, e4) = all_6_10 & op(e2, e3) = all_6_11 & % 22.79/3.90 | op(e2, e2) = all_6_14 & op(e2, e1) = all_6_12 & op(e2, e0) = all_6_13 % 22.79/3.90 | & op(e1, e4) = all_6_15 & op(e1, e3) = all_6_16 & op(e1, e2) = % 22.79/3.90 | all_6_17 & op(e1, e1) = all_6_19 & op(e1, e0) = all_6_18 & op(e0, e4) % 22.79/3.90 | = all_6_20 & op(e0, e3) = all_6_21 & op(e0, e2) = all_6_22 & op(e0, % 22.79/3.90 | e1) = all_6_23 & op(e0, e0) = all_6_24 & $i(all_6_0) & $i(all_6_1) & % 22.79/3.90 | $i(all_6_2) & $i(all_6_3) & $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & % 22.79/3.90 | $i(all_6_7) & $i(all_6_8) & $i(all_6_9) & $i(all_6_10) & $i(all_6_11) % 22.79/3.90 | & $i(all_6_12) & $i(all_6_13) & $i(all_6_14) & $i(all_6_15) & % 22.79/3.90 | $i(all_6_16) & $i(all_6_17) & $i(all_6_18) & $i(all_6_19) & % 22.79/3.90 | $i(all_6_20) & $i(all_6_21) & $i(all_6_22) & $i(all_6_23) & % 22.79/3.90 | $i(all_6_24) & ( ~ (all_6_4 = e3) | all_6_0 = e4) & ( ~ (all_6_4 = e2) % 22.79/3.90 | | all_6_1 = e4) & ( ~ (all_6_4 = e1) | all_6_2 = e4) & ( ~ (all_6_4 % 22.79/3.90 | = e0) | all_6_3 = e4) & ( ~ (all_6_9 = e4) | all_6_5 = e3) & ( ~ % 22.79/3.90 | (all_6_9 = e2) | all_6_6 = e3) & ( ~ (all_6_9 = e1) | all_6_7 = e3) % 22.79/3.90 | & ( ~ (all_6_9 = e0) | all_6_8 = e3) & ( ~ (all_6_14 = e4) | all_6_10 % 22.79/3.90 | = e2) & ( ~ (all_6_14 = e3) | all_6_11 = e2) & ( ~ (all_6_14 = e1) | % 22.79/3.90 | all_6_12 = e2) & ( ~ (all_6_14 = e0) | all_6_13 = e2) & ( ~ % 22.79/3.90 | (all_6_19 = e4) | all_6_15 = e1) & ( ~ (all_6_19 = e3) | all_6_16 = % 22.79/3.90 | e1) & ( ~ (all_6_19 = e2) | all_6_17 = e1) & ( ~ (all_6_19 = e0) | % 22.79/3.90 | all_6_18 = e1) & ( ~ (all_6_24 = e4) | all_6_20 = e0) & ( ~ % 22.79/3.90 | (all_6_24 = e3) | all_6_21 = e0) & ( ~ (all_6_24 = e2) | all_6_22 = % 22.79/3.90 | e0) & ( ~ (all_6_24 = e1) | all_6_23 = e0) & ((all_6_4 = e3 & % 22.79/3.90 | all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & all_6_9 = e4 & % 22.79/3.90 | ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = % 22.79/3.90 | e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 22.79/3.90 | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 22.79/3.90 | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & all_6_24 = % 22.79/3.90 | e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 22.79/3.90 | (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = % 22.79/3.90 | e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) | % 22.79/3.90 | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 & % 22.79/3.90 | all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 = % 22.79/3.90 | e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 22.79/3.90 | (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = % 22.79/3.90 | e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 22.79/3.90 | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = % 22.79/3.90 | e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 22.79/3.90 | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 22.79/3.90 | e1 & ~ (all_6_23 = e0))) % 22.79/3.90 | % 22.79/3.90 | ALPHA: (49) implies: % 22.79/3.90 | (50) op(e0, e0) = all_6_24 % 22.79/3.90 | (51) op(e0, e3) = all_6_21 % 22.79/3.90 | (52) op(e0, e4) = all_6_20 % 22.79/3.90 | (53) op(e1, e0) = all_6_18 % 22.79/3.90 | (54) op(e1, e1) = all_6_19 % 22.79/3.90 | (55) op(e2, e0) = all_6_13 % 22.79/3.90 | (56) op(e2, e2) = all_6_14 % 22.79/3.90 | (57) op(e2, e4) = all_6_10 % 22.79/3.90 | (58) op(e3, e0) = all_6_8 % 22.79/3.90 | (59) op(e3, e3) = all_6_9 % 22.79/3.90 | (60) op(e3, e4) = all_6_5 % 22.79/3.90 | (61) op(e4, e0) = all_6_3 % 22.79/3.90 | (62) op(e4, e2) = all_6_1 % 22.79/3.90 | (63) op(e4, e4) = all_6_4 % 22.79/3.91 | (64) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 22.79/3.91 | all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & % 22.79/3.91 | ~ (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 22.79/3.91 | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | % 22.79/3.91 | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & % 22.79/3.91 | all_6_24 = e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 & % 22.79/3.91 | ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = % 22.79/3.91 | e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) | % 22.79/3.91 | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 & % 22.79/3.91 | all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 = e3 % 22.79/3.91 | & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 % 22.79/3.91 | = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2)) | % 22.79/3.91 | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = e0 % 22.79/3.91 | & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 22.79/3.91 | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 22.79/3.91 | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = % 22.79/3.91 | e0)) % 22.79/3.91 | (65) ~ (all_6_24 = e3) | all_6_21 = e0 % 22.79/3.91 | (66) ~ (all_6_24 = e4) | all_6_20 = e0 % 22.79/3.91 | (67) ~ (all_6_19 = e0) | all_6_18 = e1 % 22.79/3.91 | (68) ~ (all_6_14 = e0) | all_6_13 = e2 % 22.79/3.91 | (69) ~ (all_6_14 = e4) | all_6_10 = e2 % 22.79/3.91 | (70) ~ (all_6_9 = e0) | all_6_8 = e3 % 22.79/3.91 | (71) ~ (all_6_9 = e4) | all_6_5 = e3 % 22.79/3.91 | (72) ~ (all_6_4 = e0) | all_6_3 = e4 % 22.79/3.91 | (73) ~ (all_6_4 = e2) | all_6_1 = e4 % 22.79/3.91 | % 22.79/3.91 | DELTA: instantiating (1) with fresh symbols all_8_0, all_8_1, all_8_2, % 22.79/3.91 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 22.79/3.91 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 22.79/3.91 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 22.79/3.91 | all_8_24 gives: % 22.79/3.91 | (74) op(e4, e4) = all_8_0 & op(e4, e3) = all_8_1 & op(e4, e2) = all_8_2 & % 22.79/3.91 | op(e4, e1) = all_8_3 & op(e4, e0) = all_8_4 & op(e3, e4) = all_8_5 & % 22.79/3.91 | op(e3, e3) = all_8_6 & op(e3, e2) = all_8_7 & op(e3, e1) = all_8_8 & % 22.79/3.91 | op(e3, e0) = all_8_9 & op(e2, e4) = all_8_10 & op(e2, e3) = all_8_11 & % 22.79/3.91 | op(e2, e2) = all_8_12 & op(e2, e1) = all_8_13 & op(e2, e0) = all_8_14 % 22.79/3.91 | & op(e1, e4) = all_8_15 & op(e1, e3) = all_8_16 & op(e1, e2) = % 22.79/3.91 | all_8_17 & op(e1, e1) = all_8_18 & op(e1, e0) = all_8_19 & op(e0, e4) % 22.79/3.91 | = all_8_20 & op(e0, e3) = all_8_21 & op(e0, e2) = all_8_22 & op(e0, % 22.79/3.91 | e1) = all_8_23 & op(e0, e0) = all_8_24 & $i(all_8_0) & $i(all_8_1) & % 22.79/3.91 | $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & % 22.79/3.91 | $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11) % 22.79/3.91 | & $i(all_8_12) & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & % 22.79/3.91 | $i(all_8_16) & $i(all_8_17) & $i(all_8_18) & $i(all_8_19) & % 22.79/3.91 | $i(all_8_20) & $i(all_8_21) & $i(all_8_22) & $i(all_8_23) & % 22.79/3.91 | $i(all_8_24) & (all_8_0 = e4 | all_8_0 = e3 | all_8_0 = e2 | all_8_0 = % 22.79/3.91 | e1 | all_8_0 = e0) & (all_8_1 = e4 | all_8_1 = e3 | all_8_1 = e2 | % 22.79/3.91 | all_8_1 = e1 | all_8_1 = e0) & (all_8_2 = e4 | all_8_2 = e3 | % 22.79/3.91 | all_8_2 = e2 | all_8_2 = e1 | all_8_2 = e0) & (all_8_3 = e4 | % 22.79/3.91 | all_8_3 = e3 | all_8_3 = e2 | all_8_3 = e1 | all_8_3 = e0) & % 22.79/3.91 | (all_8_4 = e4 | all_8_4 = e3 | all_8_4 = e2 | all_8_4 = e1 | all_8_4 = % 22.79/3.91 | e0) & (all_8_5 = e4 | all_8_5 = e3 | all_8_5 = e2 | all_8_5 = e1 | % 22.79/3.91 | all_8_5 = e0) & (all_8_6 = e4 | all_8_6 = e3 | all_8_6 = e2 | % 22.79/3.91 | all_8_6 = e1 | all_8_6 = e0) & (all_8_7 = e4 | all_8_7 = e3 | % 22.79/3.91 | all_8_7 = e2 | all_8_7 = e1 | all_8_7 = e0) & (all_8_8 = e4 | % 22.79/3.91 | all_8_8 = e3 | all_8_8 = e2 | all_8_8 = e1 | all_8_8 = e0) & % 22.79/3.91 | (all_8_9 = e4 | all_8_9 = e3 | all_8_9 = e2 | all_8_9 = e1 | all_8_9 = % 22.79/3.91 | e0) & (all_8_10 = e4 | all_8_10 = e3 | all_8_10 = e2 | all_8_10 = e1 % 22.79/3.91 | | all_8_10 = e0) & (all_8_11 = e4 | all_8_11 = e3 | all_8_11 = e2 | % 22.79/3.91 | all_8_11 = e1 | all_8_11 = e0) & (all_8_12 = e4 | all_8_12 = e3 | % 22.79/3.91 | all_8_12 = e2 | all_8_12 = e1 | all_8_12 = e0) & (all_8_13 = e4 | % 22.79/3.91 | all_8_13 = e3 | all_8_13 = e2 | all_8_13 = e1 | all_8_13 = e0) & % 22.79/3.91 | (all_8_14 = e4 | all_8_14 = e3 | all_8_14 = e2 | all_8_14 = e1 | % 22.79/3.91 | all_8_14 = e0) & (all_8_15 = e4 | all_8_15 = e3 | all_8_15 = e2 | % 22.79/3.91 | all_8_15 = e1 | all_8_15 = e0) & (all_8_16 = e4 | all_8_16 = e3 | % 22.79/3.91 | all_8_16 = e2 | all_8_16 = e1 | all_8_16 = e0) & (all_8_17 = e4 | % 22.79/3.91 | all_8_17 = e3 | all_8_17 = e2 | all_8_17 = e1 | all_8_17 = e0) & % 22.79/3.91 | (all_8_18 = e4 | all_8_18 = e3 | all_8_18 = e2 | all_8_18 = e1 | % 22.79/3.91 | all_8_18 = e0) & (all_8_19 = e4 | all_8_19 = e3 | all_8_19 = e2 | % 22.79/3.91 | all_8_19 = e1 | all_8_19 = e0) & (all_8_20 = e4 | all_8_20 = e3 | % 22.79/3.91 | all_8_20 = e2 | all_8_20 = e1 | all_8_20 = e0) & (all_8_21 = e4 | % 22.79/3.91 | all_8_21 = e3 | all_8_21 = e2 | all_8_21 = e1 | all_8_21 = e0) & % 22.79/3.92 | (all_8_22 = e4 | all_8_22 = e3 | all_8_22 = e2 | all_8_22 = e1 | % 22.79/3.92 | all_8_22 = e0) & (all_8_23 = e4 | all_8_23 = e3 | all_8_23 = e2 | % 22.79/3.92 | all_8_23 = e1 | all_8_23 = e0) & (all_8_24 = e4 | all_8_24 = e3 | % 22.79/3.92 | all_8_24 = e2 | all_8_24 = e1 | all_8_24 = e0) % 22.79/3.92 | % 22.79/3.92 | ALPHA: (74) implies: % 22.79/3.92 | (75) op(e0, e0) = all_8_24 % 22.79/3.92 | (76) op(e0, e3) = all_8_21 % 22.79/3.92 | (77) op(e0, e4) = all_8_20 % 22.79/3.92 | (78) op(e1, e0) = all_8_19 % 22.79/3.92 | (79) op(e1, e1) = all_8_18 % 22.79/3.92 | (80) op(e1, e4) = all_8_15 % 22.79/3.92 | (81) op(e2, e0) = all_8_14 % 22.79/3.92 | (82) op(e2, e2) = all_8_12 % 22.79/3.92 | (83) op(e2, e4) = all_8_10 % 22.79/3.92 | (84) op(e3, e0) = all_8_9 % 22.79/3.92 | (85) op(e3, e3) = all_8_6 % 22.79/3.92 | (86) op(e3, e4) = all_8_5 % 22.79/3.92 | (87) op(e4, e0) = all_8_4 % 22.79/3.92 | (88) op(e4, e2) = all_8_2 % 22.79/3.92 | (89) op(e4, e4) = all_8_0 % 22.79/3.92 | (90) all_8_15 = e4 | all_8_15 = e3 | all_8_15 = e2 | all_8_15 = e1 | % 22.79/3.92 | all_8_15 = e0 % 22.79/3.92 | (91) all_8_12 = e4 | all_8_12 = e3 | all_8_12 = e2 | all_8_12 = e1 | % 22.79/3.92 | all_8_12 = e0 % 22.79/3.92 | (92) all_8_0 = e4 | all_8_0 = e3 | all_8_0 = e2 | all_8_0 = e1 | all_8_0 = % 22.79/3.92 | e0 % 22.79/3.92 | % 22.79/3.92 | DELTA: instantiating (2) with fresh symbols all_10_0, all_10_1, all_10_2, % 22.79/3.92 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9, % 22.79/3.92 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15, % 22.79/3.92 | all_10_16, all_10_17, all_10_18, all_10_19, all_10_20, all_10_21, % 22.79/3.92 | all_10_22, all_10_23, all_10_24 gives: % 22.79/3.92 | (93) op(e4, e4) = all_10_0 & op(e4, e3) = all_10_1 & op(e4, e2) = all_10_4 % 22.79/3.92 | & op(e4, e1) = all_10_9 & op(e4, e0) = all_10_16 & op(e3, e4) = % 22.79/3.92 | all_10_2 & op(e3, e3) = all_10_3 & op(e3, e2) = all_10_5 & op(e3, e1) % 22.79/3.92 | = all_10_10 & op(e3, e0) = all_10_17 & op(e2, e4) = all_10_6 & op(e2, % 22.79/3.92 | e3) = all_10_7 & op(e2, e2) = all_10_8 & op(e2, e1) = all_10_11 & % 22.79/3.92 | op(e2, e0) = all_10_18 & op(e1, e4) = all_10_12 & op(e1, e3) = % 22.79/3.92 | all_10_13 & op(e1, e2) = all_10_14 & op(e1, e1) = all_10_15 & op(e1, % 22.79/3.92 | e0) = all_10_19 & op(e0, e4) = all_10_20 & op(e0, e3) = all_10_21 & % 22.79/3.92 | op(e0, e2) = all_10_22 & op(e0, e1) = all_10_23 & op(e0, e0) = % 22.79/3.92 | all_10_24 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & $i(all_10_3) % 22.79/3.92 | & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & % 22.79/3.92 | $i(all_10_8) & $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & % 22.79/3.93 | $i(all_10_12) & $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & % 22.79/3.93 | $i(all_10_16) & $i(all_10_17) & $i(all_10_18) & $i(all_10_19) & % 22.79/3.93 | $i(all_10_20) & $i(all_10_21) & $i(all_10_22) & $i(all_10_23) & % 22.79/3.93 | $i(all_10_24) & (all_10_0 = e4 | all_10_1 = e4 | all_10_4 = e4 | % 22.79/3.93 | all_10_9 = e4 | all_10_16 = e4) & (all_10_0 = e4 | all_10_2 = e4 | % 22.79/3.93 | all_10_6 = e4 | all_10_12 = e4 | all_10_20 = e4) & (all_10_0 = e3 | % 22.79/3.93 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3) & % 22.79/3.93 | (all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 | % 22.79/3.93 | all_10_20 = e3) & (all_10_0 = e2 | all_10_1 = e2 | all_10_4 = e2 | % 22.79/3.93 | all_10_9 = e2 | all_10_16 = e2) & (all_10_0 = e2 | all_10_2 = e2 | % 22.79/3.93 | all_10_6 = e2 | all_10_12 = e2 | all_10_20 = e2) & (all_10_0 = e1 | % 22.79/3.93 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1) & % 22.79/3.93 | (all_10_0 = e1 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 | % 22.79/3.93 | all_10_20 = e1) & (all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 | % 22.79/3.93 | all_10_9 = e0 | all_10_16 = e0) & (all_10_0 = e0 | all_10_2 = e0 | % 22.79/3.93 | all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0) & (all_10_1 = e4 | % 22.79/3.93 | all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4) & % 22.79/3.93 | (all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 | % 22.79/3.93 | all_10_21 = e3) & (all_10_1 = e2 | all_10_3 = e2 | all_10_7 = e2 | % 22.79/3.93 | all_10_13 = e2 | all_10_21 = e2) & (all_10_1 = e1 | all_10_3 = e1 | % 22.79/3.93 | all_10_7 = e1 | all_10_13 = e1 | all_10_21 = e1) & (all_10_1 = e0 | % 22.79/3.93 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | all_10_21 = e0) & % 22.79/3.93 | (all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 | % 22.79/3.93 | all_10_17 = e4) & (all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 | % 22.79/3.93 | all_10_10 = e3 | all_10_17 = e3) & (all_10_2 = e2 | all_10_3 = e2 | % 22.79/3.93 | all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2) & (all_10_2 = e1 | % 22.79/3.93 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | all_10_17 = e1) & % 22.79/3.93 | (all_10_2 = e0 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 | % 22.79/3.93 | all_10_17 = e0) & (all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 | % 22.79/3.93 | all_10_14 = e4 | all_10_22 = e4) & (all_10_4 = e3 | all_10_5 = e3 | % 22.79/3.93 | all_10_8 = e3 | all_10_14 = e3 | all_10_22 = e3) & (all_10_4 = e2 | % 22.79/3.93 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2) & % 22.79/3.93 | (all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 | % 22.79/3.93 | all_10_22 = e1) & (all_10_4 = e0 | all_10_5 = e0 | all_10_8 = e0 | % 22.79/3.93 | all_10_14 = e0 | all_10_22 = e0) & (all_10_6 = e4 | all_10_7 = e4 | % 22.79/3.93 | all_10_8 = e4 | all_10_11 = e4 | all_10_18 = e4) & (all_10_6 = e3 | % 22.79/3.93 | all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3 | all_10_18 = e3) & % 22.79/3.93 | (all_10_6 = e2 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 | % 22.79/3.93 | all_10_18 = e2) & (all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 | % 22.79/3.93 | all_10_11 = e1 | all_10_18 = e1) & (all_10_6 = e0 | all_10_7 = e0 | % 22.79/3.93 | all_10_8 = e0 | all_10_11 = e0 | all_10_18 = e0) & (all_10_9 = e4 | % 22.79/3.93 | all_10_10 = e4 | all_10_11 = e4 | all_10_15 = e4 | all_10_23 = e4) & % 22.79/3.93 | (all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 | % 22.79/3.93 | all_10_23 = e3) & (all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 | % 22.79/3.93 | all_10_15 = e2 | all_10_23 = e2) & (all_10_9 = e1 | all_10_10 = e1 | % 22.79/3.93 | all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1) & (all_10_9 = e0 | % 22.79/3.93 | all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0) & % 22.79/3.93 | (all_10_12 = e4 | all_10_13 = e4 | all_10_14 = e4 | all_10_15 = e4 | % 22.79/3.93 | all_10_19 = e4) & (all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3 % 22.79/3.93 | | all_10_15 = e3 | all_10_19 = e3) & (all_10_12 = e2 | all_10_13 = % 22.79/3.93 | e2 | all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2) & (all_10_12 % 22.79/3.93 | = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19 % 22.79/3.93 | = e1) & (all_10_12 = e0 | all_10_13 = e0 | all_10_14 = e0 | % 22.79/3.93 | all_10_15 = e0 | all_10_19 = e0) & (all_10_16 = e4 | all_10_17 = e4 % 22.79/3.93 | | all_10_18 = e4 | all_10_19 = e4 | all_10_24 = e4) & (all_10_16 = % 22.79/3.93 | e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | all_10_24 = % 22.79/3.93 | e3) & (all_10_16 = e2 | all_10_17 = e2 | all_10_18 = e2 | all_10_19 % 22.79/3.93 | = e2 | all_10_24 = e2) & (all_10_16 = e1 | all_10_17 = e1 | % 22.79/3.93 | all_10_18 = e1 | all_10_19 = e1 | all_10_24 = e1) & (all_10_20 = e4 % 22.79/3.93 | | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4) % 22.79/3.93 | & (all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 | % 22.79/3.93 | all_10_24 = e3) & (all_10_20 = e2 | all_10_21 = e2 | all_10_22 = e2 % 22.79/3.93 | | all_10_23 = e2 | all_10_24 = e2) & (all_10_20 = e1 | all_10_21 = % 22.79/3.93 | e1 | all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1) & (all_10_24 % 22.79/3.93 | = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 | % 22.79/3.93 | all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 = % 22.79/3.93 | e0 | all_10_23 = e0))) % 22.79/3.93 | % 22.79/3.93 | ALPHA: (93) implies: % 22.79/3.93 | (94) op(e0, e0) = all_10_24 % 22.79/3.93 | (95) op(e0, e3) = all_10_21 % 22.79/3.93 | (96) op(e0, e4) = all_10_20 % 22.79/3.93 | (97) op(e1, e0) = all_10_19 % 22.79/3.93 | (98) op(e1, e1) = all_10_15 % 22.79/3.93 | (99) op(e1, e4) = all_10_12 % 22.79/3.93 | (100) op(e2, e0) = all_10_18 % 22.79/3.93 | (101) op(e2, e2) = all_10_8 % 22.79/3.93 | (102) op(e2, e4) = all_10_6 % 22.79/3.93 | (103) op(e3, e0) = all_10_17 % 22.79/3.93 | (104) op(e3, e3) = all_10_3 % 22.79/3.93 | (105) op(e3, e4) = all_10_2 % 22.79/3.93 | (106) op(e4, e0) = all_10_16 % 22.79/3.93 | (107) op(e4, e2) = all_10_4 % 22.79/3.93 | (108) op(e4, e4) = all_10_0 % 22.79/3.93 | (109) all_10_16 = e4 | all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 22.79/3.93 | all_10_24 = e4 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_4_24, all_8_24, e0, e0, % 22.79/3.93 | simplifying with (34), (75) gives: % 22.79/3.93 | (110) all_8_24 = all_4_24 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_8_24, all_10_24, e0, e0, % 22.79/3.93 | simplifying with (75), (94) gives: % 22.79/3.93 | (111) all_10_24 = all_8_24 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_6_24, all_10_24, e0, e0, % 22.79/3.93 | simplifying with (50), (94) gives: % 22.79/3.93 | (112) all_10_24 = all_6_24 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_6_21, all_8_21, e3, e0, % 22.79/3.93 | simplifying with (51), (76) gives: % 22.79/3.93 | (113) all_8_21 = all_6_21 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_8_21, all_10_21, e3, e0, % 22.79/3.93 | simplifying with (76), (95) gives: % 22.79/3.93 | (114) all_10_21 = all_8_21 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_4_9, all_10_21, e3, e0, % 22.79/3.93 | simplifying with (35), (95) gives: % 22.79/3.93 | (115) all_10_21 = all_4_9 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_8_20, all_10_20, e4, e0, % 22.79/3.93 | simplifying with (77), (96) gives: % 22.79/3.93 | (116) all_10_20 = all_8_20 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_6_20, all_10_20, e4, e0, % 22.79/3.93 | simplifying with (52), (96) gives: % 22.79/3.93 | (117) all_10_20 = all_6_20 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_4_4, all_10_20, e4, e0, % 22.79/3.93 | simplifying with (36), (96) gives: % 22.79/3.93 | (118) all_10_20 = all_4_4 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_6_18, all_8_19, e0, e1, % 22.79/3.93 | simplifying with (53), (78) gives: % 22.79/3.93 | (119) all_8_19 = all_6_18 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_8_19, all_10_19, e0, e1, % 22.79/3.93 | simplifying with (78), (97) gives: % 22.79/3.93 | (120) all_10_19 = all_8_19 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_10_19, e0, e1, % 22.79/3.93 | simplifying with (37), (97) gives: % 22.79/3.93 | (121) all_10_19 = all_4_23 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_4_18, all_6_19, e1, e1, % 22.79/3.93 | simplifying with (38), (54) gives: % 22.79/3.93 | (122) all_6_19 = all_4_18 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_8_18, all_10_15, e1, e1, % 22.79/3.93 | simplifying with (79), (98) gives: % 22.79/3.93 | (123) all_10_15 = all_8_18 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with all_6_19, all_10_15, e1, e1, % 22.79/3.93 | simplifying with (54), (98) gives: % 22.79/3.93 | (124) all_10_15 = all_6_19 % 22.79/3.93 | % 22.79/3.93 | GROUND_INST: instantiating (function-axioms) with e0, all_10_15, e1, e1, % 22.79/3.94 | simplifying with (9), (98) gives: % 22.79/3.94 | (125) all_10_15 = e0 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_15, all_10_12, e4, e1, % 22.79/3.94 | simplifying with (80), (99) gives: % 22.79/3.94 | (126) all_10_12 = all_8_15 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_10_12, e4, e1, % 22.79/3.94 | simplifying with (39), (99) gives: % 22.79/3.94 | (127) all_10_12 = all_4_3 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_14, all_10_18, e0, e2, % 22.79/3.94 | simplifying with (81), (100) gives: % 22.79/3.94 | (128) all_10_18 = all_8_14 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_13, all_10_18, e0, e2, % 22.79/3.94 | simplifying with (55), (100) gives: % 22.79/3.94 | (129) all_10_18 = all_6_13 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_10_18, e0, e2, % 22.79/3.94 | simplifying with (40), (100) gives: % 22.79/3.94 | (130) all_10_18 = all_4_22 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_14, all_8_12, e2, e2, % 22.79/3.94 | simplifying with (56), (82) gives: % 22.79/3.94 | (131) all_8_12 = all_6_14 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_12, all_10_8, e2, e2, % 22.79/3.94 | simplifying with (82), (101) gives: % 22.79/3.94 | (132) all_10_8 = all_8_12 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_12, all_10_8, e2, e2, % 22.79/3.94 | simplifying with (41), (101) gives: % 22.79/3.94 | (133) all_10_8 = all_4_12 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_6_10, e4, e2, % 22.79/3.94 | simplifying with (42), (57) gives: % 22.79/3.94 | (134) all_6_10 = all_4_2 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_10, all_8_10, e4, e2, % 22.79/3.94 | simplifying with (57), (83) gives: % 22.79/3.94 | (135) all_8_10 = all_6_10 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_10, all_10_6, e4, e2, % 22.79/3.94 | simplifying with (83), (102) gives: % 22.79/3.94 | (136) all_10_6 = all_8_10 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with e3, all_10_6, e4, e2, % 22.79/3.94 | simplifying with (10), (102) gives: % 22.79/3.94 | (137) all_10_6 = e3 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_9, all_10_17, e0, e3, % 22.79/3.94 | simplifying with (84), (103) gives: % 22.79/3.94 | (138) all_10_17 = all_8_9 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_8, all_10_17, e0, e3, % 22.79/3.94 | simplifying with (58), (103) gives: % 22.79/3.94 | (139) all_10_17 = all_6_8 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_21, all_10_17, e0, e3, % 22.79/3.94 | simplifying with (43), (103) gives: % 22.79/3.94 | (140) all_10_17 = all_4_21 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_6, all_10_3, e3, e3, % 22.79/3.94 | simplifying with (85), (104) gives: % 22.79/3.94 | (141) all_10_3 = all_8_6 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_9, all_10_3, e3, e3, % 22.79/3.94 | simplifying with (59), (104) gives: % 22.79/3.94 | (142) all_10_3 = all_6_9 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_6, all_10_3, e3, e3, % 22.79/3.94 | simplifying with (44), (104) gives: % 22.79/3.94 | (143) all_10_3 = all_4_6 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_5, all_8_5, e4, e3, % 22.79/3.94 | simplifying with (60), (86) gives: % 22.79/3.94 | (144) all_8_5 = all_6_5 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_5, all_10_2, e4, e3, % 22.79/3.94 | simplifying with (86), (105) gives: % 22.79/3.94 | (145) all_10_2 = all_8_5 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_10_2, e4, e3, % 22.79/3.94 | simplifying with (45), (105) gives: % 22.79/3.94 | (146) all_10_2 = all_4_1 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_4, all_10_16, e0, e4, % 22.79/3.94 | simplifying with (87), (106) gives: % 22.79/3.94 | (147) all_10_16 = all_8_4 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_3, all_10_16, e0, e4, % 22.79/3.94 | simplifying with (61), (106) gives: % 22.79/3.94 | (148) all_10_16 = all_6_3 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_20, all_10_16, e0, e4, % 22.79/3.94 | simplifying with (46), (106) gives: % 22.79/3.94 | (149) all_10_16 = all_4_20 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_10, all_6_1, e2, e4, % 22.79/3.94 | simplifying with (47), (62) gives: % 22.79/3.94 | (150) all_6_1 = all_4_10 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_8_2, e2, e4, % 22.79/3.94 | simplifying with (62), (88) gives: % 22.79/3.94 | (151) all_8_2 = all_6_1 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_10_4, e2, e4, % 22.79/3.94 | simplifying with (88), (107) gives: % 22.79/3.94 | (152) all_10_4 = all_8_2 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with e1, all_10_4, e2, e4, % 22.79/3.94 | simplifying with (11), (107) gives: % 22.79/3.94 | (153) all_10_4 = e1 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_6_4, all_8_0, e4, e4, % 22.79/3.94 | simplifying with (63), (89) gives: % 22.79/3.94 | (154) all_8_0 = all_6_4 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_10_0, e4, e4, % 22.79/3.94 | simplifying with (89), (108) gives: % 22.79/3.94 | (155) all_10_0 = all_8_0 % 22.79/3.94 | % 22.79/3.94 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_10_0, e4, e4, % 22.79/3.94 | simplifying with (48), (108) gives: % 22.79/3.94 | (156) all_10_0 = all_4_0 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (155), (156) imply: % 22.79/3.94 | (157) all_8_0 = all_4_0 % 22.79/3.94 | % 22.79/3.94 | SIMP: (157) implies: % 22.79/3.94 | (158) all_8_0 = all_4_0 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (145), (146) imply: % 22.79/3.94 | (159) all_8_5 = all_4_1 % 22.79/3.94 | % 22.79/3.94 | SIMP: (159) implies: % 22.79/3.94 | (160) all_8_5 = all_4_1 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (141), (143) imply: % 22.79/3.94 | (161) all_8_6 = all_4_6 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (141), (142) imply: % 22.79/3.94 | (162) all_8_6 = all_6_9 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (152), (153) imply: % 22.79/3.94 | (163) all_8_2 = e1 % 22.79/3.94 | % 22.79/3.94 | SIMP: (163) implies: % 22.79/3.94 | (164) all_8_2 = e1 % 22.79/3.94 | % 22.79/3.94 | COMBINE_EQS: (136), (137) imply: % 22.79/3.94 | (165) all_8_10 = e3 % 22.79/3.94 | % 22.79/3.94 | SIMP: (165) implies: % 22.79/3.94 | (166) all_8_10 = e3 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (132), (133) imply: % 22.79/3.95 | (167) all_8_12 = all_4_12 % 22.79/3.95 | % 22.79/3.95 | SIMP: (167) implies: % 22.79/3.95 | (168) all_8_12 = all_4_12 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (126), (127) imply: % 22.79/3.95 | (169) all_8_15 = all_4_3 % 22.79/3.95 | % 22.79/3.95 | SIMP: (169) implies: % 22.79/3.95 | (170) all_8_15 = all_4_3 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (123), (125) imply: % 22.79/3.95 | (171) all_8_18 = e0 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (123), (124) imply: % 22.79/3.95 | (172) all_8_18 = all_6_19 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (147), (149) imply: % 22.79/3.95 | (173) all_8_4 = all_4_20 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (147), (148) imply: % 22.79/3.95 | (174) all_8_4 = all_6_3 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (138), (140) imply: % 22.79/3.95 | (175) all_8_9 = all_4_21 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (138), (139) imply: % 22.79/3.95 | (176) all_8_9 = all_6_8 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (128), (130) imply: % 22.79/3.95 | (177) all_8_14 = all_4_22 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (128), (129) imply: % 22.79/3.95 | (178) all_8_14 = all_6_13 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (120), (121) imply: % 22.79/3.95 | (179) all_8_19 = all_4_23 % 22.79/3.95 | % 22.79/3.95 | SIMP: (179) implies: % 22.79/3.95 | (180) all_8_19 = all_4_23 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (116), (118) imply: % 22.79/3.95 | (181) all_8_20 = all_4_4 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (116), (117) imply: % 22.79/3.95 | (182) all_8_20 = all_6_20 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (114), (115) imply: % 22.79/3.95 | (183) all_8_21 = all_4_9 % 22.79/3.95 | % 22.79/3.95 | SIMP: (183) implies: % 22.79/3.95 | (184) all_8_21 = all_4_9 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (111), (112) imply: % 22.79/3.95 | (185) all_8_24 = all_6_24 % 22.79/3.95 | % 22.79/3.95 | SIMP: (185) implies: % 22.79/3.95 | (186) all_8_24 = all_6_24 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (154), (158) imply: % 22.79/3.95 | (187) all_6_4 = all_4_0 % 22.79/3.95 | % 22.79/3.95 | SIMP: (187) implies: % 22.79/3.95 | (188) all_6_4 = all_4_0 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (151), (164) imply: % 22.79/3.95 | (189) all_6_1 = e1 % 22.79/3.95 | % 22.79/3.95 | SIMP: (189) implies: % 22.79/3.95 | (190) all_6_1 = e1 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (173), (174) imply: % 22.79/3.95 | (191) all_6_3 = all_4_20 % 22.79/3.95 | % 22.79/3.95 | SIMP: (191) implies: % 22.79/3.95 | (192) all_6_3 = all_4_20 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (144), (160) imply: % 22.79/3.95 | (193) all_6_5 = all_4_1 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (161), (162) imply: % 22.79/3.95 | (194) all_6_9 = all_4_6 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (175), (176) imply: % 22.79/3.95 | (195) all_6_8 = all_4_21 % 22.79/3.95 | % 22.79/3.95 | SIMP: (195) implies: % 22.79/3.95 | (196) all_6_8 = all_4_21 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (135), (166) imply: % 22.79/3.95 | (197) all_6_10 = e3 % 22.79/3.95 | % 22.79/3.95 | SIMP: (197) implies: % 22.79/3.95 | (198) all_6_10 = e3 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (131), (168) imply: % 22.79/3.95 | (199) all_6_14 = all_4_12 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (177), (178) imply: % 22.79/3.95 | (200) all_6_13 = all_4_22 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (171), (172) imply: % 22.79/3.95 | (201) all_6_19 = e0 % 22.79/3.95 | % 22.79/3.95 | SIMP: (201) implies: % 22.79/3.95 | (202) all_6_19 = e0 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (119), (180) imply: % 22.79/3.95 | (203) all_6_18 = all_4_23 % 22.79/3.95 | % 22.79/3.95 | SIMP: (203) implies: % 22.79/3.95 | (204) all_6_18 = all_4_23 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (181), (182) imply: % 22.79/3.95 | (205) all_6_20 = all_4_4 % 22.79/3.95 | % 22.79/3.95 | SIMP: (205) implies: % 22.79/3.95 | (206) all_6_20 = all_4_4 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (113), (184) imply: % 22.79/3.95 | (207) all_6_21 = all_4_9 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (110), (186) imply: % 22.79/3.95 | (208) all_6_24 = all_4_24 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (150), (190) imply: % 22.79/3.95 | (209) all_4_10 = e1 % 22.79/3.95 | % 22.79/3.95 | SIMP: (209) implies: % 22.79/3.95 | (210) all_4_10 = e1 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (134), (198) imply: % 22.79/3.95 | (211) all_4_2 = e3 % 22.79/3.95 | % 22.79/3.95 | SIMP: (211) implies: % 22.79/3.95 | (212) all_4_2 = e3 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (122), (202) imply: % 22.79/3.95 | (213) all_4_18 = e0 % 22.79/3.95 | % 22.79/3.95 | SIMP: (213) implies: % 22.79/3.95 | (214) all_4_18 = e0 % 22.79/3.95 | % 22.79/3.95 | COMBINE_EQS: (112), (208) imply: % 22.79/3.95 | (215) all_10_24 = all_4_24 % 22.79/3.95 | % 22.79/3.95 | REDUCE: (33), (212) imply: % 22.79/3.95 | (216) ~ (all_4_0 = e3) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (30), (210) imply: % 22.79/3.95 | (217) ~ (all_4_0 = e1) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (28), (212) imply: % 22.79/3.95 | (218) ~ (all_4_1 = e3) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (27), (212) imply: % 22.79/3.95 | (219) ~ (all_4_3 = e3) % 22.79/3.95 | % 22.79/3.95 | SIMP: (219) implies: % 22.79/3.95 | (220) ~ (all_4_3 = e3) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (26), (212) imply: % 22.79/3.95 | (221) ~ (all_4_4 = e3) % 22.79/3.95 | % 22.79/3.95 | SIMP: (221) implies: % 22.79/3.95 | (222) ~ (all_4_4 = e3) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (25), (212) imply: % 22.79/3.95 | (223) ~ (all_4_12 = e3) % 22.79/3.95 | % 22.79/3.95 | SIMP: (223) implies: % 22.79/3.95 | (224) ~ (all_4_12 = e3) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (23), (214) imply: % 22.79/3.95 | (225) ~ (all_4_3 = e0) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (18), (210) imply: % 22.79/3.95 | (226) ~ (all_4_12 = e1) % 22.79/3.95 | % 22.79/3.95 | SIMP: (226) implies: % 22.79/3.95 | (227) ~ (all_4_12 = e1) % 22.79/3.95 | % 22.79/3.95 | REDUCE: (17), (214) imply: % 22.79/3.95 | (228) ~ (all_4_23 = e0) % 22.79/3.95 | % 22.79/3.95 | SIMP: (228) implies: % 22.79/3.95 | (229) ~ (all_4_23 = e0) % 22.79/3.95 | % 22.79/3.95 | BETA: splitting (71) gives: % 22.79/3.95 | % 22.79/3.95 | Case 1: % 22.79/3.95 | | % 22.79/3.95 | | (230) ~ (all_6_9 = e4) % 22.79/3.95 | | % 22.79/3.95 | | REDUCE: (194), (230) imply: % 22.79/3.95 | | (231) ~ (all_4_6 = e4) % 22.79/3.95 | | % 22.79/3.95 | | BETA: splitting (73) gives: % 22.79/3.95 | | % 22.79/3.95 | | Case 1: % 22.79/3.95 | | | % 22.79/3.95 | | | (232) ~ (all_6_4 = e2) % 22.79/3.95 | | | % 22.79/3.95 | | | REDUCE: (188), (232) imply: % 22.79/3.95 | | | (233) ~ (all_4_0 = e2) % 22.79/3.95 | | | % 22.79/3.95 | | | BETA: splitting (67) gives: % 22.79/3.95 | | | % 22.79/3.95 | | | Case 1: % 22.79/3.95 | | | | % 22.79/3.95 | | | | (234) ~ (all_6_19 = e0) % 22.79/3.95 | | | | % 22.79/3.95 | | | | REDUCE: (202), (234) imply: % 22.79/3.95 | | | | (235) $false % 22.79/3.96 | | | | % 22.79/3.96 | | | | CLOSE: (235) is inconsistent. % 22.79/3.96 | | | | % 22.79/3.96 | | | Case 2: % 22.79/3.96 | | | | % 22.79/3.96 | | | | (236) all_6_18 = e1 % 22.79/3.96 | | | | % 22.79/3.96 | | | | COMBINE_EQS: (204), (236) imply: % 22.79/3.96 | | | | (237) all_4_23 = e1 % 22.79/3.96 | | | | % 22.79/3.96 | | | | COMBINE_EQS: (121), (237) imply: % 22.79/3.96 | | | | (238) all_10_19 = e1 % 22.79/3.96 | | | | % 22.79/3.96 | | | | REDUCE: (22), (237) imply: % 22.79/3.96 | | | | (239) ~ (all_4_3 = e1) % 22.79/3.96 | | | | % 22.79/3.96 | | | | REDUCE: (14), (237) imply: % 22.79/3.96 | | | | (240) ~ (all_4_24 = e1) % 22.79/3.96 | | | | % 22.79/3.96 | | | | SIMP: (240) implies: % 22.79/3.96 | | | | (241) ~ (all_4_24 = e1) % 22.79/3.96 | | | | % 22.79/3.96 | | | | REDUCE: (229), (237) imply: % 22.79/3.96 | | | | (242) ~ (e1 = e0) % 22.79/3.96 | | | | % 22.79/3.96 | | | | BETA: splitting (69) gives: % 22.79/3.96 | | | | % 22.79/3.96 | | | | Case 1: % 22.79/3.96 | | | | | % 22.79/3.96 | | | | | (243) ~ (all_6_14 = e4) % 22.79/3.96 | | | | | % 22.79/3.96 | | | | | REDUCE: (199), (243) imply: % 22.79/3.96 | | | | | (244) ~ (all_4_12 = e4) % 22.79/3.96 | | | | | % 22.79/3.96 | | | | | BETA: splitting (68) gives: % 22.79/3.96 | | | | | % 22.79/3.96 | | | | | Case 1: % 22.79/3.96 | | | | | | % 22.79/3.96 | | | | | | (245) ~ (all_6_14 = e0) % 22.79/3.96 | | | | | | % 22.79/3.96 | | | | | | REDUCE: (199), (245) imply: % 22.79/3.96 | | | | | | (246) ~ (all_4_12 = e0) % 22.79/3.96 | | | | | | % 22.79/3.96 | | | | | | BETA: splitting (91) gives: % 22.79/3.96 | | | | | | % 22.79/3.96 | | | | | | Case 1: % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | (247) all_8_12 = e1 % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | COMBINE_EQS: (168), (247) imply: % 22.79/3.96 | | | | | | | (248) all_4_12 = e1 % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | SIMP: (248) implies: % 22.79/3.96 | | | | | | | (249) all_4_12 = e1 % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | REDUCE: (227), (249) imply: % 22.79/3.96 | | | | | | | (250) $false % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | CLOSE: (250) is inconsistent. % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | Case 2: % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | (251) all_8_12 = e4 | all_8_12 = e3 | all_8_12 = e2 | all_8_12 % 22.79/3.96 | | | | | | | = e0 % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | BETA: splitting (251) gives: % 22.79/3.96 | | | | | | | % 22.79/3.96 | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | (252) all_8_12 = e4 % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | COMBINE_EQS: (168), (252) imply: % 22.79/3.96 | | | | | | | | (253) all_4_12 = e4 % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | SIMP: (253) implies: % 22.79/3.96 | | | | | | | | (254) all_4_12 = e4 % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | REDUCE: (244), (254) imply: % 22.79/3.96 | | | | | | | | (255) $false % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | CLOSE: (255) is inconsistent. % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | Case 2: % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | (256) ~ (all_8_12 = e4) % 22.79/3.96 | | | | | | | | (257) all_8_12 = e3 | all_8_12 = e2 | all_8_12 = e0 % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | BETA: splitting (257) gives: % 22.79/3.96 | | | | | | | | % 22.79/3.96 | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | (258) all_8_12 = e2 % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | COMBINE_EQS: (168), (258) imply: % 22.79/3.96 | | | | | | | | | (259) all_4_12 = e2 % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | SIMP: (259) implies: % 22.79/3.96 | | | | | | | | | (260) all_4_12 = e2 % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | COMBINE_EQS: (199), (260) imply: % 22.79/3.96 | | | | | | | | | (261) all_6_14 = e2 % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | REDUCE: (244), (260) imply: % 22.79/3.96 | | | | | | | | | (262) ~ (e4 = e2) % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | SIMP: (262) implies: % 22.79/3.96 | | | | | | | | | (263) ~ (e4 = e2) % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | REDUCE: (224), (260) imply: % 22.79/3.96 | | | | | | | | | (264) ~ (e3 = e2) % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | REDUCE: (246), (260) imply: % 22.79/3.96 | | | | | | | | | (265) ~ (e2 = e0) % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | BETA: splitting (65) gives: % 22.79/3.96 | | | | | | | | | % 22.79/3.96 | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | (266) ~ (all_6_24 = e3) % 22.79/3.96 | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | REDUCE: (208), (266) imply: % 22.79/3.96 | | | | | | | | | | (267) ~ (all_4_24 = e3) % 22.79/3.96 | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | BETA: splitting (66) gives: % 22.79/3.96 | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | (268) ~ (all_6_24 = e4) % 22.79/3.96 | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | REDUCE: (208), (268) imply: % 22.79/3.96 | | | | | | | | | | | (269) ~ (all_4_24 = e4) % 22.79/3.96 | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | BETA: splitting (64) gives: % 22.79/3.96 | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | (270) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 22.79/3.96 | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 22.79/3.96 | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 22.79/3.96 | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 22.79/3.96 | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 22.79/3.96 | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 22.79/3.96 | | | | | | | | | | | | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 22.79/3.96 | | | | | | | | | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 22.79/3.96 | | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 22.79/3.96 | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 22.79/3.96 | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 22.79/3.96 | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 22.79/3.96 | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | BETA: splitting (270) gives: % 22.79/3.96 | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | (271) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 22.79/3.96 | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 22.79/3.96 | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 22.79/3.96 | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 22.79/3.96 | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 22.79/3.96 | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | BETA: splitting (271) gives: % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | (272) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 22.79/3.96 | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 22.79/3.96 | | | | | | | | | | | | | | e3)) % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | REF_CLOSE: (194), (231), (272) are inconsistent by sub-proof % 22.79/3.96 | | | | | | | | | | | | | | #49. % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | Case 2: % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | (273) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 22.79/3.96 | | | | | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 22.79/3.96 | | | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 22.79/3.96 | | | | | | | | | | | | | | (all_6_2 = e4)) % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | REF_CLOSE: (6), (202), (261), (263), (273) are inconsistent % 22.79/3.96 | | | | | | | | | | | | | | by sub-proof #45. % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | End of split % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | Case 2: % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | (274) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 22.79/3.96 | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 22.79/3.96 | | | | | | | | | | | | | (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 % 22.79/3.96 | | | | | | | | | | | | | & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 % 22.79/3.96 | | | | | | | | | | | | | = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 22.79/3.96 | | | | | | | | | | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | BETA: splitting (274) gives: % 22.79/3.96 | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | (275) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 22.79/3.96 | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 22.79/3.96 | | | | | | | | | | | | | | (all_6_3 = e4)) % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | BETA: splitting (275) gives: % 22.79/3.96 | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | Case 1: % 22.79/3.96 | | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | | (276) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 22.79/3.96 | | | | | | | | | | | | | | | % 22.79/3.96 | | | | | | | | | | | | | | | ALPHA: (276) implies: % 22.79/3.96 | | | | | | | | | | | | | | | (277) all_6_19 = e4 % 22.79/3.96 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (6), (202), (277) are inconsistent by sub-proof % 22.79/3.97 | | | | | | | | | | | | | | | #46. % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | Case 2: % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | (278) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | ALPHA: (278) implies: % 22.79/3.97 | | | | | | | | | | | | | | | (279) all_6_24 = e4 % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (208), (269), (279) are inconsistent by sub-proof % 22.79/3.97 | | | | | | | | | | | | | | | #44. % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | End of split % 22.79/3.97 | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | Case 2: % 22.79/3.97 | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | (280) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 22.79/3.97 | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 22.79/3.97 | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 22.79/3.97 | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 22.79/3.97 | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | BETA: splitting (280) gives: % 22.79/3.97 | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | Case 1: % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | (281) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 22.79/3.97 | | | | | | | | | | | | | | | % 22.79/3.97 | | | | | | | | | | | | | | | ALPHA: (281) implies: % 22.79/3.97 | | | | | | | | | | | | | | | (282) all_6_24 = e4 % 22.79/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (208), (269), (282) are inconsistent by sub-proof % 23.25/3.97 | | | | | | | | | | | | | | | #44. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (283) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.25/3.97 | | | | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.25/3.97 | | | | | | | | | | | | | | | e2)) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (5), (261), (283) are inconsistent by sub-proof % 23.25/3.97 | | | | | | | | | | | | | | | #43. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | (284) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.97 | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.97 | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.25/3.97 | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.25/3.97 | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.25/3.97 | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) | (all_6_14 % 23.25/3.97 | | | | | | | | | | | | = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.25/3.97 | | | | | | | | | | | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = % 23.25/3.97 | | | | | | | | | | | | e2)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.97 | | | | | | | | | | | | (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.25/3.97 | | | | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.25/3.97 | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.25/3.97 | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | BETA: splitting (284) gives: % 23.25/3.97 | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | (285) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.97 | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.97 | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.25/3.97 | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.25/3.97 | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.25/3.97 | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | BETA: splitting (285) gives: % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | (286) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.97 | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.97 | | | | | | | | | | | | | | e1)) % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | BETA: splitting (286) gives: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (287) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | ALPHA: (287) implies: % 23.25/3.97 | | | | | | | | | | | | | | | (288) all_6_19 = e3 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (4), (202), (288) are inconsistent by sub-proof % 23.25/3.97 | | | | | | | | | | | | | | | #42. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (289) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | ALPHA: (289) implies: % 23.25/3.97 | | | | | | | | | | | | | | | (290) all_6_19 = e3 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (4), (202), (290) are inconsistent by sub-proof % 23.25/3.97 | | | | | | | | | | | | | | | #42. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | (291) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.25/3.97 | | | | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.25/3.97 | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.25/3.97 | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | BETA: splitting (291) gives: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (292) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | ALPHA: (292) implies: % 23.25/3.97 | | | | | | | | | | | | | | | (293) all_6_9 = e0 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (6), (64), (202), (208), (241), (242), (261), % 23.25/3.97 | | | | | | | | | | | | | | | (263), (265), (267), (269), (293) are inconsistent % 23.25/3.97 | | | | | | | | | | | | | | | by sub-proof #34. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (294) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.25/3.97 | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.25/3.97 | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | (295) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | ALPHA: (295) implies: % 23.25/3.97 | | | | | | | | | | | | | | | | (296) all_6_9 = e0 % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (64), (202), (208), (241), (242), (261), % 23.25/3.97 | | | | | | | | | | | | | | | | (263), (265), (267), (269), (296) are inconsistent % 23.25/3.97 | | | | | | | | | | | | | | | | by sub-proof #34. % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | (297) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | ALPHA: (297) implies: % 23.25/3.97 | | | | | | | | | | | | | | | | (298) all_6_19 = e2 % 23.25/3.97 | | | | | | | | | | | | | | | | (299) all_6_14 = e1 % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (298), (299) are inconsistent % 23.25/3.97 | | | | | | | | | | | | | | | | by sub-proof #32. % 23.25/3.97 | | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | End of split % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | (300) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.25/3.97 | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.97 | | | | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 23.25/3.97 | | | | | | | | | | | | | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.25/3.97 | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 % 23.25/3.97 | | | | | | | | | | | | | = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | BETA: splitting (300) gives: % 23.25/3.97 | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | (301) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.25/3.97 | | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.97 | | | | | | | | | | | | | | (all_6_13 = e2)) % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | BETA: splitting (301) gives: % 23.25/3.97 | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 1: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (302) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | ALPHA: (302) implies: % 23.25/3.97 | | | | | | | | | | | | | | | (303) all_6_19 = e2 % 23.25/3.97 | | | | | | | | | | | | | | | (304) all_6_14 = e1 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (303), (304) are inconsistent % 23.25/3.97 | | | | | | | | | | | | | | | by sub-proof #32. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | Case 2: % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | (305) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | ALPHA: (305) implies: % 23.25/3.97 | | | | | | | | | | | | | | | (306) all_6_14 = e0 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | COMBINE_EQS: (261), (306) imply: % 23.25/3.97 | | | | | | | | | | | | | | | (307) e2 = e0 % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | REDUCE: (265), (307) imply: % 23.25/3.97 | | | | | | | | | | | | | | | (308) $false % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.97 | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent. % 23.25/3.97 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | (309) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.25/3.98 | | | | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.25/3.98 | | | | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.25/3.98 | | | | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | BETA: splitting (309) gives: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (310) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | ALPHA: (310) implies: % 23.25/3.98 | | | | | | | | | | | | | | | (311) all_6_14 = e0 % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | COMBINE_EQS: (261), (311) imply: % 23.25/3.98 | | | | | | | | | | | | | | | (312) e2 = e0 % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REDUCE: (265), (312) imply: % 23.25/3.98 | | | | | | | | | | | | | | | (313) $false % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (314) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.25/3.98 | | | | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.25/3.98 | | | | | | | | | | | | | | | (all_6_23 = e0)) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (208), (241), (314) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #35. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | (315) all_6_24 = e4 % 23.25/3.98 | | | | | | | | | | | (316) all_6_20 = e0 % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | COMBINE_EQS: (206), (316) imply: % 23.25/3.98 | | | | | | | | | | | (317) all_4_4 = e0 % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | SIMP: (317) implies: % 23.25/3.98 | | | | | | | | | | | (318) all_4_4 = e0 % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | COMBINE_EQS: (208), (315) imply: % 23.25/3.98 | | | | | | | | | | | (319) all_4_24 = e4 % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | SIMP: (319) implies: % 23.25/3.98 | | | | | | | | | | | (320) all_4_24 = e4 % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | REDUCE: (31), (318) imply: % 23.25/3.98 | | | | | | | | | | | (321) ~ (all_4_0 = e0) % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | REDUCE: (21), (318), (320) imply: % 23.25/3.98 | | | | | | | | | | | (322) ~ (e4 = e0) % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | REDUCE: (222), (318) imply: % 23.25/3.98 | | | | | | | | | | | (323) ~ (e3 = e0) % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | BETA: splitting (64) gives: % 23.25/3.98 | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | (324) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.25/3.98 | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.25/3.98 | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.25/3.98 | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.25/3.98 | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.25/3.98 | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.25/3.98 | | | | | | | | | | | | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.25/3.98 | | | | | | | | | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.25/3.98 | | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.25/3.98 | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.25/3.98 | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.25/3.98 | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | BETA: splitting (324) gives: % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | (325) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.25/3.98 | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.25/3.98 | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.25/3.98 | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.25/3.98 | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.25/3.98 | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | REF_CLOSE: (6), (194), (202), (231), (261), (263), (325) are % 23.25/3.98 | | | | | | | | | | | | | inconsistent by sub-proof #31. % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | (326) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.25/3.98 | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.25/3.98 | | | | | | | | | | | | | (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 % 23.25/3.98 | | | | | | | | | | | | | & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 % 23.25/3.98 | | | | | | | | | | | | | = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.25/3.98 | | | | | | | | | | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | BETA: splitting (326) gives: % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | (327) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.25/3.98 | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.25/3.98 | | | | | | | | | | | | | | (all_6_3 = e4)) % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | BETA: splitting (327) gives: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (328) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (6), (202), (328) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #30. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (329) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | ALPHA: (329) implies: % 23.25/3.98 | | | | | | | | | | | | | | | (330) all_6_4 = e0 % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (188), (321), (330) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #29. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | (331) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.25/3.98 | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.25/3.98 | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.25/3.98 | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | BETA: splitting (331) gives: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (332) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | ALPHA: (332) implies: % 23.25/3.98 | | | | | | | | | | | | | | | (333) all_6_4 = e0 % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (188), (321), (333) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #29. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (334) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.25/3.98 | | | | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.25/3.98 | | | | | | | | | | | | | | | e2)) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (5), (261), (334) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #43. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | End of split % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | (335) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.98 | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.98 | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.25/3.98 | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.25/3.98 | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.25/3.98 | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) | (all_6_14 % 23.25/3.98 | | | | | | | | | | | | = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.25/3.98 | | | | | | | | | | | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = % 23.25/3.98 | | | | | | | | | | | | e2)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.98 | | | | | | | | | | | | (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.25/3.98 | | | | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.25/3.98 | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | BETA: splitting (335) gives: % 23.25/3.98 | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | (336) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.98 | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.98 | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.25/3.98 | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.25/3.98 | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.25/3.98 | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | BETA: splitting (336) gives: % 23.25/3.98 | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | (337) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.25/3.98 | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.25/3.98 | | | | | | | | | | | | | | e1)) % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | REF_CLOSE: (4), (202), (337) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | #28. % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | (338) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.25/3.98 | | | | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.25/3.98 | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.25/3.98 | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | BETA: splitting (338) gives: % 23.25/3.98 | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (339) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | ALPHA: (339) implies: % 23.25/3.98 | | | | | | | | | | | | | | | (340) all_6_24 = e3 % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | REF_CLOSE: (8), (315), (340) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | #27. % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | Case 2: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | (341) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.25/3.98 | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.25/3.98 | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 23.25/3.98 | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | Case 1: % 23.25/3.98 | | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | | (342) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.25/3.98 | | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | | ALPHA: (342) implies: % 23.25/3.98 | | | | | | | | | | | | | | | | (343) all_6_24 = e3 % 23.25/3.98 | | | | | | | | | | | | | | | | % 23.25/3.98 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (315), (343) are inconsistent by sub-proof % 23.25/3.98 | | | | | | | | | | | | | | | | #27. % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | (344) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 23.25/3.99 | | | | | | | | | | | | | | | | (345) all_6_19 = e2 % 23.25/3.99 | | | | | | | | | | | | | | | | (346) all_6_14 = e1 % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (345), (346) are inconsistent % 23.25/3.99 | | | | | | | | | | | | | | | | by sub-proof #26. % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | (347) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.25/3.99 | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.99 | | | | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 23.25/3.99 | | | | | | | | | | | | | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.25/3.99 | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 % 23.25/3.99 | | | | | | | | | | | | | = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.25/3.99 | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | BETA: splitting (347) gives: % 23.25/3.99 | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | Case 1: % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | (348) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.25/3.99 | | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.25/3.99 | | | | | | | | | | | | | | (all_6_13 = e2)) % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (265), (348) are inconsistent % 23.25/3.99 | | | | | | | | | | | | | | by sub-proof #25. % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | (349) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.25/3.99 | | | | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.25/3.99 | | | | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.25/3.99 | | | | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | BETA: splitting (349) gives: % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | Case 1: % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | (350) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | ALPHA: (350) implies: % 23.25/3.99 | | | | | | | | | | | | | | | (351) all_6_14 = e0 % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | REF_CLOSE: (261), (265), (351) are inconsistent by sub-proof % 23.25/3.99 | | | | | | | | | | | | | | | #36. % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | (352) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.25/3.99 | | | | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.25/3.99 | | | | | | | | | | | | | | | (all_6_23 = e0)) % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | Case 1: % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | (353) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | ALPHA: (353) implies: % 23.25/3.99 | | | | | | | | | | | | | | | | (354) all_6_24 = e1 % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (315), (354) are inconsistent by sub-proof % 23.25/3.99 | | | | | | | | | | | | | | | | #24. % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | (355) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | ALPHA: (355) implies: % 23.25/3.99 | | | | | | | | | | | | | | | | (356) all_6_24 = e1 % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (315), (356) are inconsistent by sub-proof % 23.25/3.99 | | | | | | | | | | | | | | | | #24. % 23.25/3.99 | | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | End of split % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | Case 2: % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | (357) all_6_24 = e3 % 23.25/3.99 | | | | | | | | | | (358) all_6_21 = e0 % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | COMBINE_EQS: (207), (358) imply: % 23.25/3.99 | | | | | | | | | | (359) all_4_9 = e0 % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | COMBINE_EQS: (208), (357) imply: % 23.25/3.99 | | | | | | | | | | (360) all_4_24 = e3 % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | REDUCE: (20), (359) imply: % 23.25/3.99 | | | | | | | | | | (361) ~ (all_4_6 = e0) % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | REDUCE: (19), (359), (360) imply: % 23.25/3.99 | | | | | | | | | | (362) ~ (e3 = e0) % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | REDUCE: (241), (360) imply: % 23.25/3.99 | | | | | | | | | | (363) ~ (e3 = e1) % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | BETA: splitting (64) gives: % 23.25/3.99 | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | Case 1: % 23.25/3.99 | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | (364) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.25/3.99 | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.25/3.99 | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.25/3.99 | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.25/3.99 | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.25/3.99 | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.25/3.99 | | | | | | | | | | | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.25/3.99 | | | | | | | | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.25/3.99 | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.25/3.99 | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.25/3.99 | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.25/3.99 | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.25/3.99 | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | BETA: splitting (364) gives: % 23.25/3.99 | | | | | | | | | | | % 23.25/3.99 | | | | | | | | | | | Case 1: % 23.25/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | (365) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.36/3.99 | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.36/3.99 | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.36/3.99 | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.36/3.99 | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.36/3.99 | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | REF_CLOSE: (6), (194), (202), (231), (261), (263), (365) are % 23.36/3.99 | | | | | | | | | | | | inconsistent by sub-proof #31. % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | Case 2: % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | (366) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.36/3.99 | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.36/3.99 | | | | | | | | | | | | (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 % 23.36/3.99 | | | | | | | | | | | | & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 % 23.36/3.99 | | | | | | | | | | | | = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.36/3.99 | | | | | | | | | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | BETA: splitting (366) gives: % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | Case 1: % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | (367) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.36/3.99 | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.36/3.99 | | | | | | | | | | | | | (all_6_3 = e4)) % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | BETA: splitting (367) gives: % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | Case 1: % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | (368) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | REF_CLOSE: (6), (202), (368) are inconsistent by sub-proof % 23.36/3.99 | | | | | | | | | | | | | | #30. % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | Case 2: % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | (369) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | ALPHA: (369) implies: % 23.36/3.99 | | | | | | | | | | | | | | (370) all_6_24 = e4 % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | COMBINE_EQS: (357), (370) imply: % 23.36/3.99 | | | | | | | | | | | | | | (371) e4 = e3 % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | REDUCE: (8), (371) imply: % 23.36/3.99 | | | | | | | | | | | | | | (372) $false % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | End of split % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | Case 2: % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | (373) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.36/3.99 | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.36/3.99 | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.36/3.99 | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | BETA: splitting (373) gives: % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | Case 1: % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | (374) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | ALPHA: (374) implies: % 23.36/3.99 | | | | | | | | | | | | | | (375) all_6_24 = e4 % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | COMBINE_EQS: (357), (375) imply: % 23.36/3.99 | | | | | | | | | | | | | | (376) e4 = e3 % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | REDUCE: (8), (376) imply: % 23.36/3.99 | | | | | | | | | | | | | | (377) $false % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | Case 2: % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | (378) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.36/3.99 | | | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.36/3.99 | | | | | | | | | | | | | | e2)) % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | | REF_CLOSE: (5), (261), (378) are inconsistent by sub-proof % 23.36/3.99 | | | | | | | | | | | | | | #43. % 23.36/3.99 | | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | | End of split % 23.36/3.99 | | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | | End of split % 23.36/3.99 | | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | | End of split % 23.36/3.99 | | | | | | | | | | | % 23.36/3.99 | | | | | | | | | | Case 2: % 23.36/3.99 | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | (379) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.00 | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.00 | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.36/4.00 | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.36/4.00 | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.36/4.00 | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) | (all_6_14 % 23.36/4.00 | | | | | | | | | | | = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.36/4.00 | | | | | | | | | | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = % 23.36/4.00 | | | | | | | | | | | e2)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.36/4.00 | | | | | | | | | | | (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.36/4.00 | | | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.36/4.00 | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.36/4.00 | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | BETA: splitting (379) gives: % 23.36/4.00 | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | (380) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.00 | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.00 | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.36/4.00 | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.36/4.00 | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.36/4.00 | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | BETA: splitting (380) gives: % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | (381) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.00 | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.00 | | | | | | | | | | | | | e1)) % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | REF_CLOSE: (4), (202), (381) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | #28. % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | (382) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.36/4.00 | | | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.36/4.00 | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.36/4.00 | | | | | | | | | | | | | (all_6_12 = e2)) % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | BETA: splitting (382) gives: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | (383) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | ALPHA: (383) implies: % 23.36/4.00 | | | | | | | | | | | | | | (384) all_6_9 = e0 % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | REF_CLOSE: (194), (361), (384) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | | #23. % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | (385) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.36/4.00 | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.36/4.00 | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | BETA: splitting (385) gives: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | (386) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | ALPHA: (386) implies: % 23.36/4.00 | | | | | | | | | | | | | | | (387) all_6_9 = e0 % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | REF_CLOSE: (194), (361), (387) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | | | #23. % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | (388) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | ALPHA: (388) implies: % 23.36/4.00 | | | | | | | | | | | | | | | (389) all_6_19 = e2 % 23.36/4.00 | | | | | | | | | | | | | | | (390) all_6_14 = e1 % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (389), (390) are inconsistent % 23.36/4.00 | | | | | | | | | | | | | | | by sub-proof #26. % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | (391) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.36/4.00 | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.36/4.00 | | | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 23.36/4.00 | | | | | | | | | | | | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.36/4.00 | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 % 23.36/4.00 | | | | | | | | | | | | = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | BETA: splitting (391) gives: % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | (392) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.36/4.00 | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.36/4.00 | | | | | | | | | | | | | (all_6_13 = e2)) % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | REF_CLOSE: (202), (242), (261), (265), (392) are inconsistent % 23.36/4.00 | | | | | | | | | | | | | by sub-proof #25. % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | (393) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.36/4.00 | | | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.36/4.00 | | | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.36/4.00 | | | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | BETA: splitting (393) gives: % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | (394) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | ALPHA: (394) implies: % 23.36/4.00 | | | | | | | | | | | | | | (395) all_6_14 = e0 % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | REF_CLOSE: (261), (265), (395) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | | #36. % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | (396) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.36/4.00 | | | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.36/4.00 | | | | | | | | | | | | | | (all_6_23 = e0)) % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | BETA: splitting (396) gives: % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | (397) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | ALPHA: (397) implies: % 23.36/4.00 | | | | | | | | | | | | | | | (398) all_6_24 = e1 % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | REF_CLOSE: (357), (363), (398) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | | | #22. % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | (399) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | ALPHA: (399) implies: % 23.36/4.00 | | | | | | | | | | | | | | | (400) all_6_24 = e1 % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | | REF_CLOSE: (357), (363), (400) are inconsistent by sub-proof % 23.36/4.00 | | | | | | | | | | | | | | | #22. % 23.36/4.00 | | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | (401) all_8_12 = e3 | all_8_12 = e0 % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | BETA: splitting (401) gives: % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | (402) all_8_12 = e3 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | COMBINE_EQS: (168), (402) imply: % 23.36/4.00 | | | | | | | | | | (403) all_4_12 = e3 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | SIMP: (403) implies: % 23.36/4.00 | | | | | | | | | | (404) all_4_12 = e3 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | REDUCE: (224), (404) imply: % 23.36/4.00 | | | | | | | | | | (405) $false % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | CLOSE: (405) is inconsistent. % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | (406) all_8_12 = e0 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | COMBINE_EQS: (168), (406) imply: % 23.36/4.00 | | | | | | | | | | (407) all_4_12 = e0 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | SIMP: (407) implies: % 23.36/4.00 | | | | | | | | | | (408) all_4_12 = e0 % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | REDUCE: (246), (408) imply: % 23.36/4.00 | | | | | | | | | | (409) $false % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | | CLOSE: (409) is inconsistent. % 23.36/4.00 | | | | | | | | | | % 23.36/4.00 | | | | | | | | | End of split % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | End of split % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | End of split % 23.36/4.00 | | | | | | | % 23.36/4.00 | | | | | | End of split % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | Case 2: % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | (410) all_6_14 = e0 % 23.36/4.00 | | | | | | (411) all_6_13 = e2 % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | COMBINE_EQS: (200), (411) imply: % 23.36/4.00 | | | | | | (412) all_4_22 = e2 % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | SIMP: (412) implies: % 23.36/4.00 | | | | | | (413) all_4_22 = e2 % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | COMBINE_EQS: (199), (410) imply: % 23.36/4.00 | | | | | | (414) all_4_12 = e0 % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | COMBINE_EQS: (130), (413) imply: % 23.36/4.00 | | | | | | (415) all_10_18 = e2 % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | REDUCE: (224), (414) imply: % 23.36/4.00 | | | | | | (416) ~ (e3 = e0) % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | REDUCE: (227), (414) imply: % 23.36/4.00 | | | | | | (417) ~ (e1 = e0) % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | REDUCE: (15), (413) imply: % 23.36/4.00 | | | | | | (418) ~ (all_4_24 = e2) % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | SIMP: (418) implies: % 23.36/4.00 | | | | | | (419) ~ (all_4_24 = e2) % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | BETA: splitting (72) gives: % 23.36/4.00 | | | | | | % 23.36/4.00 | | | | | | Case 1: % 23.36/4.00 | | | | | | | % 23.36/4.00 | | | | | | | (420) ~ (all_6_4 = e0) % 23.36/4.00 | | | | | | | % 23.36/4.00 | | | | | | | REDUCE: (188), (420) imply: % 23.36/4.00 | | | | | | | (421) ~ (all_4_0 = e0) % 23.36/4.00 | | | | | | | % 23.36/4.00 | | | | | | | BETA: splitting (92) gives: % 23.36/4.00 | | | | | | | % 23.36/4.00 | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | (422) all_8_0 = e1 % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | COMBINE_EQS: (158), (422) imply: % 23.36/4.00 | | | | | | | | (423) all_4_0 = e1 % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | SIMP: (423) implies: % 23.36/4.00 | | | | | | | | (424) all_4_0 = e1 % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | REDUCE: (217), (424) imply: % 23.36/4.00 | | | | | | | | (425) $false % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | CLOSE: (425) is inconsistent. % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | Case 2: % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | (426) ~ (all_8_0 = e1) % 23.36/4.00 | | | | | | | | (427) all_8_0 = e4 | all_8_0 = e3 | all_8_0 = e2 | all_8_0 = % 23.36/4.00 | | | | | | | | e0 % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | BETA: splitting (427) gives: % 23.36/4.00 | | | | | | | | % 23.36/4.00 | | | | | | | | Case 1: % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | (428) all_8_0 = e4 % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | COMBINE_EQS: (158), (428) imply: % 23.36/4.00 | | | | | | | | | (429) all_4_0 = e4 % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | SIMP: (429) implies: % 23.36/4.00 | | | | | | | | | (430) all_4_0 = e4 % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | COMBINE_EQS: (188), (430) imply: % 23.36/4.00 | | | | | | | | | (431) all_6_4 = e4 % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | REDUCE: (32), (430) imply: % 23.36/4.00 | | | | | | | | | (432) ~ (all_4_3 = e4) % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | SIMP: (432) implies: % 23.36/4.00 | | | | | | | | | (433) ~ (all_4_3 = e4) % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | REDUCE: (31), (430) imply: % 23.36/4.00 | | | | | | | | | (434) ~ (all_4_4 = e4) % 23.36/4.00 | | | | | | | | | % 23.36/4.00 | | | | | | | | | SIMP: (434) implies: % 23.36/4.00 | | | | | | | | | (435) ~ (all_4_4 = e4) % 23.36/4.00 | | | | | | | | | % 23.36/4.01 | | | | | | | | | REDUCE: (29), (430) imply: % 23.36/4.01 | | | | | | | | | (436) ~ (all_4_20 = e4) % 23.36/4.01 | | | | | | | | | % 23.36/4.01 | | | | | | | | | SIMP: (436) implies: % 23.36/4.01 | | | | | | | | | (437) ~ (all_4_20 = e4) % 23.36/4.01 | | | | | | | | | % 23.36/4.01 | | | | | | | | | BETA: splitting (90) gives: % 23.36/4.01 | | | | | | | | | % 23.36/4.01 | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | (438) all_8_15 = e1 % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | COMBINE_EQS: (170), (438) imply: % 23.36/4.01 | | | | | | | | | | (439) all_4_3 = e1 % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | SIMP: (439) implies: % 23.36/4.01 | | | | | | | | | | (440) all_4_3 = e1 % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | REDUCE: (239), (440) imply: % 23.36/4.01 | | | | | | | | | | (441) $false % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | CLOSE: (441) is inconsistent. % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | (442) ~ (all_8_15 = e1) % 23.36/4.01 | | | | | | | | | | (443) all_8_15 = e4 | all_8_15 = e3 | all_8_15 = e2 | % 23.36/4.01 | | | | | | | | | | all_8_15 = e0 % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | BETA: splitting (443) gives: % 23.36/4.01 | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | (444) all_8_15 = e4 % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | COMBINE_EQS: (170), (444) imply: % 23.36/4.01 | | | | | | | | | | | (445) all_4_3 = e4 % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | SIMP: (445) implies: % 23.36/4.01 | | | | | | | | | | | (446) all_4_3 = e4 % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | REDUCE: (433), (446) imply: % 23.36/4.01 | | | | | | | | | | | (447) $false % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | CLOSE: (447) is inconsistent. % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | (448) ~ (all_8_15 = e4) % 23.36/4.01 | | | | | | | | | | | (449) all_8_15 = e3 | all_8_15 = e2 | all_8_15 = e0 % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | BETA: splitting (449) gives: % 23.36/4.01 | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | (450) all_8_15 = e2 % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | COMBINE_EQS: (170), (450) imply: % 23.36/4.01 | | | | | | | | | | | | (451) all_4_3 = e2 % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | SIMP: (451) implies: % 23.36/4.01 | | | | | | | | | | | | (452) all_4_3 = e2 % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | REDUCE: (24), (452) imply: % 23.36/4.01 | | | | | | | | | | | | (453) ~ (all_4_4 = e2) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | SIMP: (453) implies: % 23.36/4.01 | | | | | | | | | | | | (454) ~ (all_4_4 = e2) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | REDUCE: (433), (452) imply: % 23.36/4.01 | | | | | | | | | | | | (455) ~ (e4 = e2) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | SIMP: (455) implies: % 23.36/4.01 | | | | | | | | | | | | (456) ~ (e4 = e2) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | REDUCE: (220), (452) imply: % 23.36/4.01 | | | | | | | | | | | | (457) ~ (e3 = e2) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | REDUCE: (239), (452) imply: % 23.36/4.01 | | | | | | | | | | | | (458) ~ (e2 = e1) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | REDUCE: (225), (452) imply: % 23.36/4.01 | | | | | | | | | | | | (459) ~ (e2 = e0) % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | BETA: splitting (66) gives: % 23.36/4.01 | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | (460) ~ (all_6_24 = e4) % 23.36/4.01 | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | REDUCE: (208), (460) imply: % 23.36/4.01 | | | | | | | | | | | | | (461) ~ (all_4_24 = e4) % 23.36/4.01 | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | BETA: splitting (109) gives: % 23.36/4.01 | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | (462) all_10_16 = e4 % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | COMBINE_EQS: (149), (462) imply: % 23.36/4.01 | | | | | | | | | | | | | | (463) all_4_20 = e4 % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | REDUCE: (437), (463) imply: % 23.36/4.01 | | | | | | | | | | | | | | (464) $false % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | CLOSE: (464) is inconsistent. % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | (465) all_10_17 = e4 | all_10_18 = e4 | all_10_19 = e4 | % 23.36/4.01 | | | | | | | | | | | | | | all_10_24 = e4 % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | BETA: splitting (465) gives: % 23.36/4.01 | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | (466) all_10_17 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | COMBINE_EQS: (140), (466) imply: % 23.36/4.01 | | | | | | | | | | | | | | | (467) all_4_21 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | SIMP: (467) implies: % 23.36/4.01 | | | | | | | | | | | | | | | (468) all_4_21 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | COMBINE_EQS: (196), (468) imply: % 23.36/4.01 | | | | | | | | | | | | | | | (469) all_6_8 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 23.36/4.01 | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | (470) ~ (all_6_9 = e0) % 23.36/4.01 | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | REDUCE: (194), (470) imply: % 23.36/4.01 | | | | | | | | | | | | | | | | (471) ~ (all_4_6 = e0) % 23.36/4.01 | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | (472) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.36/4.01 | | | | | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.36/4.01 | | | | | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.36/4.01 | | | | | | | | | | | | | | | | | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.36/4.01 | | | | | | | | | | | | | | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.36/4.01 | | | | | | | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.36/4.01 | | | | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.36/4.01 | | | | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.36/4.01 | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | BETA: splitting (472) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | (473) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.36/4.01 | | | | | | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (474) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | | e3)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (475) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (476) all_6_4 = e3 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (431), (476) are inconsistent by sub-proof % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | #21. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (477) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (478) all_6_4 = e3 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (431), (478) are inconsistent by sub-proof % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | #21. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (479) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (all_6_2 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (480) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (481) all_6_14 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (482) all_6_4 = e2 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (410), (431), (459), (481), (482) are inconsistent % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | by sub-proof #20. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (483) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (all_6_2 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (484) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (485) all_6_14 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (486) all_6_4 = e2 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (410), (431), (459), (485), (486) are inconsistent % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | by sub-proof #20. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (487) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (488) all_6_19 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (489) all_6_4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (489) imply: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (490) e4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | SIMP: (490) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | (491) e4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (488), (491) are inconsistent by % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | sub-proof #19. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | End of split % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | (492) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | | (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 % 23.36/4.01 | | | | | | | | | | | | | | | | | | = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.36/4.01 | | | | | | | | | | | | | | | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | BETA: splitting (492) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (493) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.36/4.01 | | | | | | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.36/4.01 | | | | | | | | | | | | | | | | | | | (all_6_3 = e4)) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (494) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (495) all_6_19 = e4 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (496) all_6_4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (496) imply: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (497) e4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | SIMP: (497) implies: % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | (498) e4 = e1 % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (495), (498) are inconsistent by % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | sub-proof #19. % 23.36/4.01 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (499) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (500) all_6_4 = e0 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (431), (500) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | #18. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (501) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (502) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (503) all_6_4 = e0 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (431), (503) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | #18. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (504) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | e2)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (64), (202), (208), (241), (242), % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (410), (419), (431), (458), (459), (504) are % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | (505) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.02 | | | | | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.36/4.02 | | | | | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) | (all_6_14 % 23.36/4.02 | | | | | | | | | | | | | | | | | = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.36/4.02 | | | | | | | | | | | | | | | | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = % 23.36/4.02 | | | | | | | | | | | | | | | | | e2)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.36/4.02 | | | | | | | | | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.36/4.02 | | | | | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.36/4.02 | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | BETA: splitting (505) gives: % 23.36/4.02 | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | (506) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.36/4.02 | | | | | | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | BETA: splitting (506) gives: % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (507) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | | e1)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (202), (507) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | #28. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (508) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (509) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (510) all_6_9 = e0 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (471), (510) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | #23. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (511) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | Case 1: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | (512) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | ALPHA: (512) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | (513) all_6_9 = e0 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (471), (513) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | #23. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | (514) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | ALPHA: (514) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | (515) all_6_14 = e1 % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (242), (410), (515) are inconsistent by sub-proof % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | #11. % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | (516) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.36/4.02 | | | | | | | | | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 23.36/4.02 | | | | | | | | | | | | | | | | | | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.36/4.02 | | | | | | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 % 23.36/4.02 | | | | | | | | | | | | | | | | | | = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (208), (241), (242), (410), (419), (516) are % 23.36/4.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 23.36/4.02 | | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | End of split % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | Case 2: % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | (517) all_6_8 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (517) imply: % 23.36/4.02 | | | | | | | | | | | | | | | | (518) e4 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | SIMP: (518) implies: % 23.36/4.02 | | | | | | | | | | | | | | | | (519) e4 = e3 % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | REDUCE: (8), (519) imply: % 23.36/4.02 | | | | | | | | | | | | | | | | (520) $false % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.36/4.02 | | | | | | | | | | | | | | | | CLOSE: (520) is inconsistent. % 23.36/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | End of split % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | Case 2: % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | (521) all_10_18 = e4 | all_10_19 = e4 | all_10_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | BETA: splitting (521) gives: % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | (522) all_10_18 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (522) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | (523) e4 = e2 % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | REDUCE: (456), (523) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | (524) $false % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | CLOSE: (524) is inconsistent. % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | Case 2: % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | (525) all_10_19 = e4 | all_10_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | BETA: splitting (525) gives: % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | (526) all_10_19 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (526) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | | (527) e4 = e1 % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | REDUCE: (7), (527) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | | (528) $false % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | CLOSE: (528) is inconsistent. % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | Case 2: % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | (529) all_10_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (529) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | | (530) all_4_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | SIMP: (530) implies: % 23.49/4.02 | | | | | | | | | | | | | | | | | (531) all_4_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | REDUCE: (461), (531) imply: % 23.49/4.02 | | | | | | | | | | | | | | | | | (532) $false % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | CLOSE: (532) is inconsistent. % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | End of split % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | End of split % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | End of split % 23.49/4.02 | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | End of split % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | Case 2: % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | (533) all_6_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | (534) all_6_20 = e0 % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | COMBINE_EQS: (206), (534) imply: % 23.49/4.02 | | | | | | | | | | | | | (535) all_4_4 = e0 % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | COMBINE_EQS: (208), (533) imply: % 23.49/4.02 | | | | | | | | | | | | | (536) all_4_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | SIMP: (536) implies: % 23.49/4.02 | | | | | | | | | | | | | (537) all_4_24 = e4 % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | REDUCE: (435), (535) imply: % 23.49/4.02 | | | | | | | | | | | | | (538) ~ (e4 = e0) % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | REDUCE: (454), (535) imply: % 23.49/4.02 | | | | | | | | | | | | | (539) ~ (e2 = e0) % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | BETA: splitting (64) gives: % 23.49/4.02 | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | (540) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.49/4.02 | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.49/4.02 | | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.49/4.02 | | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.49/4.02 | | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.49/4.02 | | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.49/4.02 | | | | | | | | | | | | | | all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.49/4.02 | | | | | | | | | | | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.49/4.02 | | | | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.49/4.02 | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.49/4.02 | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.49/4.02 | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.49/4.02 | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | BETA: splitting (540) gives: % 23.49/4.02 | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | (541) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.49/4.02 | | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.49/4.02 | | | | | | | | | | | | | | | e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.49/4.02 | | | | | | | | | | | | | | | (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 % 23.49/4.02 | | | | | | | | | | | | | | | & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 % 23.49/4.02 | | | | | | | | | | | | | | | = e4 & ~ (all_6_2 = e4)) % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | BETA: splitting (541) gives: % 23.49/4.02 | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | (542) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.49/4.02 | | | | | | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.49/4.02 | | | | | | | | | | | | | | | | e3)) % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | BETA: splitting (542) gives: % 23.49/4.02 | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | Case 1: % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | (543) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.49/4.02 | | | | | | | | | | | | | | | | | % 23.49/4.02 | | | | | | | | | | | | | | | | | ALPHA: (543) implies: % 23.49/4.03 | | | | | | | | | | | | | | | | | (544) all_6_4 = e3 % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (544) imply: % 23.49/4.03 | | | | | | | | | | | | | | | | | (545) e4 = e3 % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | REDUCE: (8), (545) imply: % 23.49/4.03 | | | | | | | | | | | | | | | | | (546) $false % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | CLOSE: (546) is inconsistent. % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | Case 2: % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | (547) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | ALPHA: (547) implies: % 23.49/4.03 | | | | | | | | | | | | | | | | | (548) all_6_4 = e3 % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (548) imply: % 23.49/4.03 | | | | | | | | | | | | | | | | | (549) e4 = e3 % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | REDUCE: (8), (549) imply: % 23.49/4.03 | | | | | | | | | | | | | | | | | (550) $false % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | | CLOSE: (550) is inconsistent. % 23.49/4.03 | | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | End of split % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | Case 2: % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | (551) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.49/4.03 | | | | | | | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.49/4.03 | | | | | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.49/4.03 | | | | | | | | | | | | | | | | (all_6_2 = e4)) % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | REF_CLOSE: (202), (242), (410), (431), (459), (551) are % 23.49/4.03 | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | End of split % 23.49/4.03 | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | Case 2: % 23.49/4.03 | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | (552) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.49/4.03 | | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.49/4.03 | | | | | | | | | | | | | | | (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 % 23.49/4.03 | | | | | | | | | | | | | | | & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 % 23.49/4.03 | | | | | | | | | | | | | | | = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.49/4.03 | | | | | | | | | | | | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.49/4.03 | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | BETA: splitting (552) gives: % 23.49/4.03 | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | Case 1: % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | (553) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.49/4.03 | | | | | | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.49/4.03 | | | | | | | | | | | | | | | | (all_6_3 = e4)) % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (202), (242), (431), (553) are inconsistent % 23.49/4.03 | | | | | | | | | | | | | | | | by sub-proof #14. % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.49/4.03 | | | | | | | | | | | | | | | Case 2: % 23.49/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | (554) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.52/4.03 | | | | | | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.52/4.03 | | | | | | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | BETA: splitting (554) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (555) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (431), (555) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | | #13. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (556) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.52/4.03 | | | | | | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.52/4.03 | | | | | | | | | | | | | | | | | e2)) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (64), (202), (208), (241), (242), % 23.52/4.03 | | | | | | | | | | | | | | | | | (410), (419), (431), (458), (459), (556) are % 23.52/4.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | (557) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.03 | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.03 | | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.03 | | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.52/4.03 | | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.52/4.03 | | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) | (all_6_14 % 23.52/4.03 | | | | | | | | | | | | | | = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.52/4.03 | | | | | | | | | | | | | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = % 23.52/4.03 | | | | | | | | | | | | | | e2)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.03 | | | | | | | | | | | | | | (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.03 | | | | | | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.03 | | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.03 | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | BETA: splitting (557) gives: % 23.52/4.03 | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | (558) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.03 | | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.03 | | | | | | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 % 23.52/4.03 | | | | | | | | | | | | | | | & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.52/4.03 | | | | | | | | | | | | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | BETA: splitting (558) gives: % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | (559) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.03 | | | | | | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.03 | | | | | | | | | | | | | | | | e1)) % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (202), (559) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | #28. % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | (560) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.52/4.03 | | | | | | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.03 | | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | BETA: splitting (560) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (561) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | ALPHA: (561) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | (562) all_6_24 = e3 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (533), (562) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | | #27. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (563) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.03 | | | | | | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | BETA: splitting (563) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | (564) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | ALPHA: (564) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (565) all_6_24 = e3 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (533), (565) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | | | #27. % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | (566) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (567) all_6_14 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (242), (410), (567) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | | | #11. % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | (568) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.03 | | | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = % 23.52/4.03 | | | | | | | | | | | | | | | e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.03 | | | | | | | | | | | | | | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 % 23.52/4.03 | | | | | | | | | | | | | | | = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | BETA: splitting (568) gives: % 23.52/4.03 | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | (569) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.03 | | | | | | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | (all_6_13 = e2)) % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | BETA: splitting (569) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (570) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | ALPHA: (570) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | (571) all_6_14 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (242), (410), (571) are inconsistent by sub-proof % 23.52/4.03 | | | | | | | | | | | | | | | | | #11. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (572) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | ALPHA: (572) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | (573) all_6_24 = e2 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (573) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | (574) e4 = e2 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REDUCE: (456), (574) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | (575) $false % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | CLOSE: (575) is inconsistent. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | End of split % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | (576) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.52/4.03 | | | | | | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.03 | | | | | | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (577) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | ALPHA: (577) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | (578) all_6_24 = e2 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (578) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | (579) e4 = e2 % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | REDUCE: (456), (579) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | (580) $false % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | CLOSE: (580) is inconsistent. % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | (581) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.52/4.03 | | | | | | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.03 | | | | | | | | | | | | | | | | | (all_6_23 = e0)) % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | BETA: splitting (581) gives: % 23.52/4.03 | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | Case 1: % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | (582) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | ALPHA: (582) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (583) all_6_24 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (583) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (584) e4 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | REDUCE: (7), (584) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (585) $false % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent. % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | Case 2: % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | (586) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | ALPHA: (586) implies: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (587) all_6_24 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (587) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (588) e4 = e1 % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | REDUCE: (7), (588) imply: % 23.52/4.03 | | | | | | | | | | | | | | | | | | (589) $false % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.03 | | | | | | | | | | | | | | | | | | CLOSE: (589) is inconsistent. % 23.52/4.03 | | | | | | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (590) all_8_15 = e3 | all_8_15 = e0 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | BETA: splitting (590) gives: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | (591) all_8_15 = e3 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | COMBINE_EQS: (170), (591) imply: % 23.52/4.04 | | | | | | | | | | | | | (592) all_4_3 = e3 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | SIMP: (592) implies: % 23.52/4.04 | | | | | | | | | | | | | (593) all_4_3 = e3 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | REDUCE: (220), (593) imply: % 23.52/4.04 | | | | | | | | | | | | | (594) $false % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | CLOSE: (594) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | (595) all_8_15 = e0 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | COMBINE_EQS: (170), (595) imply: % 23.52/4.04 | | | | | | | | | | | | | (596) all_4_3 = e0 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | SIMP: (596) implies: % 23.52/4.04 | | | | | | | | | | | | | (597) all_4_3 = e0 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | REDUCE: (225), (597) imply: % 23.52/4.04 | | | | | | | | | | | | | (598) $false % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | CLOSE: (598) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | (599) all_8_0 = e3 | all_8_0 = e2 | all_8_0 = e0 % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | BETA: splitting (599) gives: % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | (600) all_8_0 = e2 % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | COMBINE_EQS: (158), (600) imply: % 23.52/4.04 | | | | | | | | | | (601) all_4_0 = e2 % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | SIMP: (601) implies: % 23.52/4.04 | | | | | | | | | | (602) all_4_0 = e2 % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | REDUCE: (233), (602) imply: % 23.52/4.04 | | | | | | | | | | (603) $false % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | CLOSE: (603) is inconsistent. % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | (604) all_8_0 = e3 | all_8_0 = e0 % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | BETA: splitting (604) gives: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | (605) all_8_0 = e3 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | COMBINE_EQS: (158), (605) imply: % 23.52/4.04 | | | | | | | | | | | (606) all_4_0 = e3 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | SIMP: (606) implies: % 23.52/4.04 | | | | | | | | | | | (607) all_4_0 = e3 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | REDUCE: (216), (607) imply: % 23.52/4.04 | | | | | | | | | | | (608) $false % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | CLOSE: (608) is inconsistent. % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | (609) all_8_0 = e0 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | COMBINE_EQS: (158), (609) imply: % 23.52/4.04 | | | | | | | | | | | (610) all_4_0 = e0 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | SIMP: (610) implies: % 23.52/4.04 | | | | | | | | | | | (611) all_4_0 = e0 % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | REDUCE: (421), (611) imply: % 23.52/4.04 | | | | | | | | | | | (612) $false % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | CLOSE: (612) is inconsistent. % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | End of split % 23.52/4.04 | | | | | | | | % 23.52/4.04 | | | | | | | End of split % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | Case 2: % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | (613) all_6_4 = e0 % 23.52/4.04 | | | | | | | (614) all_6_3 = e4 % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | COMBINE_EQS: (192), (614) imply: % 23.52/4.04 | | | | | | | (615) all_4_20 = e4 % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | SIMP: (615) implies: % 23.52/4.04 | | | | | | | (616) all_4_20 = e4 % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | COMBINE_EQS: (188), (613) imply: % 23.52/4.04 | | | | | | | (617) all_4_0 = e0 % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | SIMP: (617) implies: % 23.52/4.04 | | | | | | | (618) all_4_0 = e0 % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | REDUCE: (233), (618) imply: % 23.52/4.04 | | | | | | | (619) ~ (e2 = e0) % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | SIMP: (619) implies: % 23.52/4.04 | | | | | | | (620) ~ (e2 = e0) % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | REDUCE: (16), (616) imply: % 23.52/4.04 | | | | | | | (621) ~ (all_4_24 = e4) % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | SIMP: (621) implies: % 23.52/4.04 | | | | | | | (622) ~ (all_4_24 = e4) % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | BETA: splitting (65) gives: % 23.52/4.04 | | | | | | | % 23.52/4.04 | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | % 23.52/4.04 | | | | | | | | (623) ~ (all_6_24 = e3) % 23.52/4.04 | | | | | | | | % 23.52/4.04 | | | | | | | | REDUCE: (208), (623) imply: % 23.52/4.04 | | | | | | | | (624) ~ (all_4_24 = e3) % 23.52/4.04 | | | | | | | | % 23.52/4.04 | | | | | | | | BETA: splitting (64) gives: % 23.52/4.04 | | | | | | | | % 23.52/4.04 | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | (625) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.52/4.04 | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) | % 23.52/4.04 | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | % 23.52/4.04 | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | BETA: splitting (625) gives: % 23.52/4.04 | | | | | | | | | % 23.52/4.04 | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | (626) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | % 23.52/4.04 | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) | % 23.52/4.04 | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.52/4.04 | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.04 | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.04 | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | BETA: splitting (626) gives: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | (627) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.52/4.04 | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.52/4.04 | | | | | | | | | | | e3)) % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | BETA: splitting (627) gives: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (628) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | ALPHA: (628) implies: % 23.52/4.04 | | | | | | | | | | | | (629) all_6_4 = e3 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | COMBINE_EQS: (613), (629) imply: % 23.52/4.04 | | | | | | | | | | | | (630) e3 = e0 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | REDUCE: (4), (630) imply: % 23.52/4.04 | | | | | | | | | | | | (631) $false % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | CLOSE: (631) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (632) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | ALPHA: (632) implies: % 23.52/4.04 | | | | | | | | | | | | (633) all_6_4 = e3 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | COMBINE_EQS: (613), (633) imply: % 23.52/4.04 | | | | | | | | | | | | (634) e3 = e0 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | REDUCE: (4), (634) imply: % 23.52/4.04 | | | | | | | | | | | | (635) $false % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | CLOSE: (635) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | (636) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.52/4.04 | | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.04 | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.04 | | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | BETA: splitting (636) gives: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (637) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | ALPHA: (637) implies: % 23.52/4.04 | | | | | | | | | | | | (638) all_6_4 = e2 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | COMBINE_EQS: (613), (638) imply: % 23.52/4.04 | | | | | | | | | | | | (639) e2 = e0 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | REDUCE: (620), (639) imply: % 23.52/4.04 | | | | | | | | | | | | (640) $false % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | CLOSE: (640) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (641) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.04 | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.04 | | | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | BETA: splitting (641) gives: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | (642) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | ALPHA: (642) implies: % 23.52/4.04 | | | | | | | | | | | | | (643) all_6_4 = e2 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | COMBINE_EQS: (613), (643) imply: % 23.52/4.04 | | | | | | | | | | | | | (644) e2 = e0 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | REDUCE: (620), (644) imply: % 23.52/4.04 | | | | | | | | | | | | | (645) $false % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | CLOSE: (645) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | (646) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | ALPHA: (646) implies: % 23.52/4.04 | | | | | | | | | | | | | (647) all_6_4 = e1 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | COMBINE_EQS: (613), (647) imply: % 23.52/4.04 | | | | | | | | | | | | | (648) e1 = e0 % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | REDUCE: (242), (648) imply: % 23.52/4.04 | | | | | | | | | | | | | (649) $false % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | | CLOSE: (649) is inconsistent. % 23.52/4.04 | | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | End of split % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | Case 2: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | (650) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) % 23.52/4.04 | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = % 23.52/4.04 | | | | | | | | | | e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.52/4.04 | | | | | | | | | | (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = e3 % 23.52/4.04 | | | | | | | | | | & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.04 | | | | | | | | | | e3 & ~ (all_6_11 = e2)) % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | BETA: splitting (650) gives: % 23.52/4.04 | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | (651) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.52/4.04 | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.52/4.04 | | | | | | | | | | | (all_6_3 = e4)) % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | BETA: splitting (651) gives: % 23.52/4.04 | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | Case 1: % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | (652) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | ALPHA: (652) implies: % 23.52/4.04 | | | | | | | | | | | | (653) all_6_4 = e1 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | COMBINE_EQS: (613), (653) imply: % 23.52/4.04 | | | | | | | | | | | | (654) e1 = e0 % 23.52/4.04 | | | | | | | | | | | | % 23.52/4.04 | | | | | | | | | | | | REDUCE: (242), (654) imply: % 23.52/4.05 | | | | | | | | | | | | (655) $false % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | CLOSE: (655) is inconsistent. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (656) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (208), (622), (656) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #41. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | (657) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.52/4.05 | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.05 | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.52/4.05 | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | BETA: splitting (657) gives: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (658) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (208), (622), (658) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #40. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (659) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.52/4.05 | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.52/4.05 | | | | | | | | | | | | e2)) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (4), (410), (659) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #12. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | (660) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | % 23.52/4.05 | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) | % 23.52/4.05 | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | % 23.52/4.05 | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | % 23.52/4.05 | | | | | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.05 | | | | | | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.05 | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.05 | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = e2 & % 23.52/4.05 | | | | | | | | | ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.05 | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.05 | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | BETA: splitting (660) gives: % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | (661) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.05 | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.05 | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.05 | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & % 23.52/4.05 | | | | | | | | | | ~ (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = % 23.52/4.05 | | | | | | | | | | e2 & ~ (all_6_12 = e2)) % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | BETA: splitting (661) gives: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | (662) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.05 | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.05 | | | | | | | | | | | e1)) % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | REF_CLOSE: (4), (202), (662) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | #28. % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | (663) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.52/4.05 | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.05 | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.05 | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | BETA: splitting (663) gives: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (664) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | ALPHA: (664) implies: % 23.52/4.05 | | | | | | | | | | | | (665) all_6_24 = e3 % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (208), (624), (665) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #5. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (666) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.05 | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.05 | | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | BETA: splitting (666) gives: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | (667) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | ALPHA: (667) implies: % 23.52/4.05 | | | | | | | | | | | | | (668) all_6_24 = e3 % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | REF_CLOSE: (208), (624), (668) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | | #5. % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | (669) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | ALPHA: (669) implies: % 23.52/4.05 | | | | | | | | | | | | | (670) all_6_14 = e1 % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | COMBINE_EQS: (410), (670) imply: % 23.52/4.05 | | | | | | | | | | | | | (671) e1 = e0 % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | REDUCE: (242), (671) imply: % 23.52/4.05 | | | | | | | | | | | | | (672) $false % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | CLOSE: (672) is inconsistent. % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | (673) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.05 | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.05 | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = e2 % 23.52/4.05 | | | | | | | | | | & ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 % 23.52/4.05 | | | | | | | | | | = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.05 | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | BETA: splitting (673) gives: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | (674) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.05 | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.05 | | | | | | | | | | | (all_6_13 = e2)) % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | BETA: splitting (674) gives: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (675) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | ALPHA: (675) implies: % 23.52/4.05 | | | | | | | | | | | | (676) all_6_14 = e1 % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | COMBINE_EQS: (410), (676) imply: % 23.52/4.05 | | | | | | | | | | | | (677) e1 = e0 % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REDUCE: (242), (677) imply: % 23.52/4.05 | | | | | | | | | | | | (678) $false % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | CLOSE: (678) is inconsistent. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (679) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (208), (419), (679) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #10. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | (680) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.52/4.05 | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.05 | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.05 | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | BETA: splitting (680) gives: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (681) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | REF_CLOSE: (208), (419), (681) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | #9. % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | (682) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.52/4.05 | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.05 | | | | | | | | | | | | (all_6_23 = e0)) % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | BETA: splitting (682) gives: % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | (683) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | ALPHA: (683) implies: % 23.52/4.05 | | | | | | | | | | | | | (684) all_6_24 = e1 % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | REF_CLOSE: (208), (241), (684) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | | #4. % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | (685) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | ALPHA: (685) implies: % 23.52/4.05 | | | | | | | | | | | | | (686) all_6_24 = e1 % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | | REF_CLOSE: (208), (241), (686) are inconsistent by sub-proof % 23.52/4.05 | | | | | | | | | | | | | #4. % 23.52/4.05 | | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | End of split % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | End of split % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | Case 2: % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | (687) all_6_24 = e3 % 23.52/4.05 | | | | | | | | (688) all_6_21 = e0 % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | COMBINE_EQS: (207), (688) imply: % 23.52/4.05 | | | | | | | | (689) all_4_9 = e0 % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | SIMP: (689) implies: % 23.52/4.05 | | | | | | | | (690) all_4_9 = e0 % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | COMBINE_EQS: (208), (687) imply: % 23.52/4.05 | | | | | | | | (691) all_4_24 = e3 % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | SIMP: (691) implies: % 23.52/4.05 | | | | | | | | (692) all_4_24 = e3 % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | REDUCE: (20), (690) imply: % 23.52/4.05 | | | | | | | | (693) ~ (all_4_6 = e0) % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | REDUCE: (622), (692) imply: % 23.52/4.05 | | | | | | | | (694) ~ (e4 = e3) % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | REDUCE: (241), (692) imply: % 23.52/4.05 | | | | | | | | (695) ~ (e3 = e1) % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | BETA: splitting (64) gives: % 23.52/4.05 | | | | | | | | % 23.52/4.05 | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | (696) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | % 23.52/4.05 | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) | % 23.52/4.05 | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | % 23.52/4.05 | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | BETA: splitting (696) gives: % 23.52/4.05 | | | | | | | | | % 23.52/4.05 | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | (697) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | % 23.52/4.05 | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) | % 23.52/4.05 | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.52/4.05 | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.05 | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.05 | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | BETA: splitting (697) gives: % 23.52/4.05 | | | | | | | | | | % 23.52/4.05 | | | | | | | | | | Case 1: % 23.52/4.05 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (698) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) % 23.52/4.06 | | | | | | | | | | | | (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = % 23.52/4.06 | | | | | | | | | | | e3)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (698) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (699) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (699) implies: % 23.52/4.06 | | | | | | | | | | | | (700) all_6_4 = e3 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (4), (613), (700) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #3. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (701) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (701) implies: % 23.52/4.06 | | | | | | | | | | | | (702) all_6_4 = e3 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (4), (613), (702) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #3. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (703) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) % 23.52/4.06 | | | | | | | | | | | | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.06 | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (703) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (704) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (704) implies: % 23.52/4.06 | | | | | | | | | | | | (705) all_6_4 = e2 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (613), (620), (705) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #2. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (706) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = % 23.52/4.06 | | | | | | | | | | | | e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ % 23.52/4.06 | | | | | | | | | | | | (all_6_2 = e4)) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | BETA: splitting (706) gives: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | (707) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | ALPHA: (707) implies: % 23.52/4.06 | | | | | | | | | | | | | (708) all_6_4 = e2 % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | REF_CLOSE: (613), (620), (708) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | | #2. % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | (709) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | ALPHA: (709) implies: % 23.52/4.06 | | | | | | | | | | | | | (710) all_6_4 = e1 % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | REF_CLOSE: (242), (613), (710) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | | #1. % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | (711) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) % 23.52/4.06 | | | | | | | | | | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = % 23.52/4.06 | | | | | | | | | | e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.52/4.06 | | | | | | | | | | (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = e3 % 23.52/4.06 | | | | | | | | | | & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.06 | | | | | | | | | | e3 & ~ (all_6_11 = e2)) % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | BETA: splitting (711) gives: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (712) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = % 23.52/4.06 | | | | | | | | | | | e1)) | (all_6_4 = e0 & all_6_24 = e4 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_3 = e4)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (712) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (713) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (713) implies: % 23.52/4.06 | | | | | | | | | | | | (714) all_6_4 = e1 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (242), (613), (714) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #1. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (715) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (715) implies: % 23.52/4.06 | | | | | | | | | | | | (716) all_6_24 = e4 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (8), (687), (716) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #27. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (717) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = % 23.52/4.06 | | | | | | | | | | | e0)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 % 23.52/4.06 | | | | | | | | | | | & ~ (all_6_11 = e2)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (717) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (718) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (718) implies: % 23.52/4.06 | | | | | | | | | | | | (719) all_6_24 = e4 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (8), (687), (719) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #27. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (720) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) % 23.52/4.06 | | | | | | | | | | | | | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = % 23.52/4.06 | | | | | | | | | | | | e2)) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (4), (410), (720) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #12. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | % 23.52/4.06 | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | % 23.52/4.06 | | | | | | | | | (721) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | % 23.52/4.06 | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) | % 23.52/4.06 | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | % 23.52/4.06 | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | % 23.52/4.06 | | | | | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.06 | | | | | | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.06 | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.06 | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = e2 & % 23.52/4.06 | | | | | | | | | ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.06 | | | | | | | | | e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.06 | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.06 | | | | | | | | | % 23.52/4.06 | | | | | | | | | BETA: splitting (721) gives: % 23.52/4.06 | | | | | | | | | % 23.52/4.06 | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | (722) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.06 | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.06 | | | | | | | | | | e1)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.06 | | | | | | | | | | (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & % 23.52/4.06 | | | | | | | | | | ~ (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = % 23.52/4.06 | | | | | | | | | | e2 & ~ (all_6_12 = e2)) % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | BETA: splitting (722) gives: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (723) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) % 23.52/4.06 | | | | | | | | | | | | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = % 23.52/4.06 | | | | | | | | | | | e1)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | REF_CLOSE: (4), (202), (723) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | #28. % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (724) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) % 23.52/4.06 | | | | | | | | | | | | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.06 | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (724) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (725) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (725) implies: % 23.52/4.06 | | | | | | | | | | | | (726) all_6_9 = e0 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | COMBINE_EQS: (194), (726) imply: % 23.52/4.06 | | | | | | | | | | | | (727) all_4_6 = e0 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REDUCE: (693), (727) imply: % 23.52/4.06 | | | | | | | | | | | | (728) $false % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | CLOSE: (728) is inconsistent. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (729) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = % 23.52/4.06 | | | | | | | | | | | | e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ % 23.52/4.06 | | | | | | | | | | | | (all_6_12 = e2)) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | BETA: splitting (729) gives: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | (730) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | ALPHA: (730) implies: % 23.52/4.06 | | | | | | | | | | | | | (731) all_6_9 = e0 % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | COMBINE_EQS: (194), (731) imply: % 23.52/4.06 | | | | | | | | | | | | | (732) all_4_6 = e0 % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | REDUCE: (693), (732) imply: % 23.52/4.06 | | | | | | | | | | | | | (733) $false % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | CLOSE: (733) is inconsistent. % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | (734) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | ALPHA: (734) implies: % 23.52/4.06 | | | | | | | | | | | | | (735) all_6_14 = e1 % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | | REF_CLOSE: (242), (410), (735) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | | #11. % 23.52/4.06 | | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | (736) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.06 | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.06 | | | | | | | | | | (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = e2 % 23.52/4.06 | | | | | | | | | | & ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 % 23.52/4.06 | | | | | | | | | | = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.06 | | | | | | | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | BETA: splitting (736) gives: % 23.52/4.06 | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (737) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.06 | | | | | | | | | | | e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_13 = e2)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (737) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (738) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (738) implies: % 23.52/4.06 | | | | | | | | | | | | (739) all_6_14 = e1 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REF_CLOSE: (242), (410), (739) are inconsistent by sub-proof % 23.52/4.06 | | | | | | | | | | | | #11. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | (740) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | ALPHA: (740) implies: % 23.52/4.06 | | | | | | | | | | | | (741) all_6_24 = e2 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | COMBINE_EQS: (687), (741) imply: % 23.52/4.06 | | | | | | | | | | | | (742) e3 = e2 % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | REDUCE: (5), (742) imply: % 23.52/4.06 | | | | | | | | | | | | (743) $false % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | | CLOSE: (743) is inconsistent. % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | End of split % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | Case 2: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | (744) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = % 23.52/4.06 | | | | | | | | | | | e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.06 | | | | | | | | | | | (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.06 | | | | | | | | | | | e1 & ~ (all_6_23 = e0)) % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | BETA: splitting (744) gives: % 23.52/4.06 | | | | | | | | | | | % 23.52/4.06 | | | | | | | | | | | Case 1: % 23.52/4.06 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | (745) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | ALPHA: (745) implies: % 23.52/4.07 | | | | | | | | | | | | (746) all_6_24 = e2 % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | COMBINE_EQS: (687), (746) imply: % 23.52/4.07 | | | | | | | | | | | | (747) e3 = e2 % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | REDUCE: (5), (747) imply: % 23.52/4.07 | | | | | | | | | | | | (748) $false % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | CLOSE: (748) is inconsistent. % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | Case 2: % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | (749) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.52/4.07 | | | | | | | | | | | | e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.07 | | | | | | | | | | | | (all_6_23 = e0)) % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | BETA: splitting (749) gives: % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | Case 1: % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | (750) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | ALPHA: (750) implies: % 23.52/4.07 | | | | | | | | | | | | | (751) all_6_24 = e1 % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | COMBINE_EQS: (687), (751) imply: % 23.52/4.07 | | | | | | | | | | | | | (752) e3 = e1 % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | REDUCE: (695), (752) imply: % 23.52/4.07 | | | | | | | | | | | | | (753) $false % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | CLOSE: (753) is inconsistent. % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | Case 2: % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | (754) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | ALPHA: (754) implies: % 23.52/4.07 | | | | | | | | | | | | | (755) all_6_24 = e1 % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | COMBINE_EQS: (687), (755) imply: % 23.52/4.07 | | | | | | | | | | | | | (756) e3 = e1 % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | REDUCE: (695), (756) imply: % 23.52/4.07 | | | | | | | | | | | | | (757) $false % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | | CLOSE: (757) is inconsistent. % 23.52/4.07 | | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | | End of split % 23.52/4.07 | | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | | End of split % 23.52/4.07 | | | | | | | | | | | % 23.52/4.07 | | | | | | | | | | End of split % 23.52/4.07 | | | | | | | | | | % 23.52/4.07 | | | | | | | | | End of split % 23.52/4.07 | | | | | | | | | % 23.52/4.07 | | | | | | | | End of split % 23.52/4.07 | | | | | | | | % 23.52/4.07 | | | | | | | End of split % 23.52/4.07 | | | | | | | % 23.52/4.07 | | | | | | End of split % 23.52/4.07 | | | | | | % 23.52/4.07 | | | | | End of split % 23.52/4.07 | | | | | % 23.52/4.07 | | | | Case 2: % 23.52/4.07 | | | | | % 23.52/4.07 | | | | | (758) all_6_10 = e2 % 23.52/4.07 | | | | | % 23.52/4.07 | | | | | COMBINE_EQS: (198), (758) imply: % 23.52/4.07 | | | | | (759) e3 = e2 % 23.52/4.07 | | | | | % 23.52/4.07 | | | | | SIMP: (759) implies: % 23.52/4.07 | | | | | (760) e3 = e2 % 23.52/4.07 | | | | | % 23.52/4.07 | | | | | REDUCE: (5), (760) imply: % 23.52/4.07 | | | | | (761) $false % 23.52/4.07 | | | | | % 23.52/4.07 | | | | | CLOSE: (761) is inconsistent. % 23.52/4.07 | | | | | % 23.52/4.07 | | | | End of split % 23.52/4.07 | | | | % 23.52/4.07 | | | End of split % 23.52/4.07 | | | % 23.52/4.07 | | Case 2: % 23.52/4.07 | | | % 23.52/4.07 | | | (762) all_6_1 = e4 % 23.52/4.07 | | | % 23.52/4.07 | | | COMBINE_EQS: (190), (762) imply: % 23.52/4.07 | | | (763) e4 = e1 % 23.52/4.07 | | | % 23.52/4.07 | | | REDUCE: (7), (763) imply: % 23.52/4.07 | | | (764) $false % 23.52/4.07 | | | % 23.52/4.07 | | | CLOSE: (764) is inconsistent. % 23.52/4.07 | | | % 23.52/4.07 | | End of split % 23.52/4.07 | | % 23.52/4.07 | Case 2: % 23.52/4.07 | | % 23.52/4.07 | | (765) all_6_5 = e3 % 23.52/4.07 | | % 23.52/4.07 | | COMBINE_EQS: (193), (765) imply: % 23.52/4.07 | | (766) all_4_1 = e3 % 23.52/4.07 | | % 23.52/4.07 | | SIMP: (766) implies: % 23.52/4.07 | | (767) all_4_1 = e3 % 23.52/4.07 | | % 23.52/4.07 | | REDUCE: (218), (767) imply: % 23.52/4.07 | | (768) $false % 23.52/4.07 | | % 23.52/4.07 | | CLOSE: (768) is inconsistent. % 23.52/4.07 | | % 23.52/4.07 | End of split % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #1 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) all_6_4 = e1 % 23.52/4.07 (2) all_6_4 = e0 % 23.52/4.07 (3) ~ (e1 = e0) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | COMBINE_EQS: (1), (2) imply: % 23.52/4.07 | (4) e1 = e0 % 23.52/4.07 | % 23.52/4.07 | SIMP: (4) implies: % 23.52/4.07 | (5) e1 = e0 % 23.52/4.07 | % 23.52/4.07 | REDUCE: (3), (5) imply: % 23.52/4.07 | (6) $false % 23.52/4.07 | % 23.52/4.07 | CLOSE: (6) is inconsistent. % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #2 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) all_6_4 = e2 % 23.52/4.07 (2) all_6_4 = e0 % 23.52/4.07 (3) ~ (e2 = e0) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | COMBINE_EQS: (1), (2) imply: % 23.52/4.07 | (4) e2 = e0 % 23.52/4.07 | % 23.52/4.07 | SIMP: (4) implies: % 23.52/4.07 | (5) e2 = e0 % 23.52/4.07 | % 23.52/4.07 | REDUCE: (3), (5) imply: % 23.52/4.07 | (6) $false % 23.52/4.07 | % 23.52/4.07 | CLOSE: (6) is inconsistent. % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #3 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) all_6_4 = e3 % 23.52/4.07 (2) all_6_4 = e0 % 23.52/4.07 (3) ~ (e3 = e0) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | COMBINE_EQS: (1), (2) imply: % 23.52/4.07 | (4) e3 = e0 % 23.52/4.07 | % 23.52/4.07 | SIMP: (4) implies: % 23.52/4.07 | (5) e3 = e0 % 23.52/4.07 | % 23.52/4.07 | REDUCE: (3), (5) imply: % 23.52/4.07 | (6) $false % 23.52/4.07 | % 23.52/4.07 | CLOSE: (6) is inconsistent. % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #4 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) all_6_24 = all_4_24 % 23.52/4.07 (2) all_6_24 = e1 % 23.52/4.07 (3) ~ (all_4_24 = e1) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | COMBINE_EQS: (1), (2) imply: % 23.52/4.07 | (4) all_4_24 = e1 % 23.52/4.07 | % 23.52/4.07 | SIMP: (4) implies: % 23.52/4.07 | (5) all_4_24 = e1 % 23.52/4.07 | % 23.52/4.07 | REDUCE: (3), (5) imply: % 23.52/4.07 | (6) $false % 23.52/4.07 | % 23.52/4.07 | CLOSE: (6) is inconsistent. % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #5 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) all_6_24 = all_4_24 % 23.52/4.07 (2) all_6_24 = e3 % 23.52/4.07 (3) ~ (all_4_24 = e3) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | COMBINE_EQS: (1), (2) imply: % 23.52/4.07 | (4) all_4_24 = e3 % 23.52/4.07 | % 23.52/4.07 | SIMP: (4) implies: % 23.52/4.07 | (5) all_4_24 = e3 % 23.52/4.07 | % 23.52/4.07 | REDUCE: (3), (5) imply: % 23.52/4.07 | (6) $false % 23.52/4.07 | % 23.52/4.07 | CLOSE: (6) is inconsistent. % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #6 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) ~ (e3 = e0) % 23.52/4.07 (2) ~ (all_4_24 = e2) % 23.52/4.07 (3) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.07 all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.07 (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.07 (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.52/4.07 all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & all_6_24 = e4 & % 23.52/4.07 ~ (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) % 23.52/4.07 | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.07 all_6_14 = e3 & ~ (all_6_11 = e2)) | (all_6_9 = e1 & all_6_19 = e3 & % 23.52/4.07 ~ (all_6_7 = e3)) | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.07 | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & % 23.52/4.07 all_6_24 = e3 & ~ (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & % 23.52/4.07 ~ (all_6_12 = e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.07 e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | % 23.52/4.07 (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.07 all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & % 23.52/4.07 ~ (all_6_23 = e0)) % 23.52/4.07 (4) all_6_24 = all_4_24 % 23.52/4.07 (5) ~ (all_4_24 = e1) % 23.52/4.07 (6) ~ (e3 = e2) % 23.52/4.07 (7) ~ (e4 = e0) % 23.52/4.07 (8) all_6_4 = e4 % 23.52/4.07 (9) all_6_19 = e0 % 23.52/4.07 (10) ~ (e2 = e1) % 23.52/4.07 (11) ~ (e2 = e0) % 23.52/4.07 (12) all_6_14 = e0 % 23.52/4.07 (13) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.07 all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.07 (14) ~ (e1 = e0) % 23.52/4.07 % 23.52/4.07 Begin of proof % 23.52/4.07 | % 23.52/4.07 | BETA: splitting (13) gives: % 23.52/4.07 | % 23.52/4.07 | Case 1: % 23.52/4.07 | | % 23.52/4.07 | | (15) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3) % 23.52/4.07 | | % 23.52/4.07 | | ALPHA: (15) implies: % 23.52/4.07 | | (16) all_6_9 = e2 % 23.52/4.07 | | % 23.52/4.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 23.52/4.07 | | (14), (16) are inconsistent by sub-proof #7. % 23.52/4.07 | | % 23.52/4.07 | Case 2: % 23.52/4.07 | | % 23.52/4.07 | | (17) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2) % 23.52/4.07 | | % 23.52/4.07 | | ALPHA: (17) implies: % 23.52/4.07 | | (18) all_6_9 = e2 % 23.52/4.07 | | % 23.52/4.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 23.52/4.07 | | (14), (18) are inconsistent by sub-proof #7. % 23.52/4.07 | | % 23.52/4.07 | End of split % 23.52/4.07 | % 23.52/4.07 End of proof % 23.52/4.07 % 23.52/4.07 Sub-proof #7 shows that the following formulas are inconsistent: % 23.52/4.07 ---------------------------------------------------------------- % 23.52/4.07 (1) ~ (e3 = e0) % 23.52/4.07 (2) ~ (all_4_24 = e2) % 23.52/4.08 (3) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.08 all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.08 (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.08 (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.52/4.08 all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & all_6_24 = e4 & % 23.52/4.08 ~ (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) % 23.52/4.08 | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.08 all_6_14 = e3 & ~ (all_6_11 = e2)) | (all_6_9 = e1 & all_6_19 = e3 & % 23.52/4.08 ~ (all_6_7 = e3)) | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.08 | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & % 23.52/4.08 all_6_24 = e3 & ~ (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & % 23.52/4.08 ~ (all_6_12 = e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.08 e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | % 23.52/4.08 (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.08 all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & % 23.52/4.08 ~ (all_6_23 = e0)) % 23.52/4.08 (4) all_6_24 = all_4_24 % 23.52/4.08 (5) all_6_9 = e2 % 23.52/4.08 (6) ~ (all_4_24 = e1) % 23.52/4.08 (7) ~ (e3 = e2) % 23.52/4.08 (8) ~ (e4 = e0) % 23.52/4.08 (9) all_6_4 = e4 % 23.52/4.08 (10) all_6_19 = e0 % 23.52/4.08 (11) ~ (e2 = e1) % 23.52/4.08 (12) ~ (e2 = e0) % 23.52/4.08 (13) all_6_14 = e0 % 23.52/4.08 (14) ~ (e1 = e0) % 23.52/4.08 % 23.52/4.08 Begin of proof % 23.52/4.08 | % 23.52/4.08 | BETA: splitting (3) gives: % 23.52/4.08 | % 23.52/4.08 | Case 1: % 23.52/4.08 | | % 23.52/4.08 | | (15) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.08 | | all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 % 23.52/4.08 | | & ~ (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.08 | | (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = % 23.52/4.08 | | e4)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | % 23.52/4.08 | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & % 23.52/4.08 | | all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.08 | | e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.08 | | (all_6_11 = e2)) % 23.52/4.08 | | % 23.52/4.08 | | BETA: splitting (15) gives: % 23.52/4.08 | | % 23.52/4.08 | | Case 1: % 23.52/4.08 | | | % 23.52/4.08 | | | (16) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 % 23.52/4.08 | | | & all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = % 23.52/4.08 | | | e4 & ~ (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.08 | | | (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = % 23.52/4.08 | | | e4)) % 23.52/4.08 | | | % 23.52/4.08 | | | BETA: splitting (16) gives: % 23.52/4.08 | | | % 23.52/4.08 | | | Case 1: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (17) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = % 23.52/4.08 | | | | e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | BETA: splitting (17) gives: % 23.52/4.08 | | | | % 23.52/4.08 | | | | Case 1: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (18) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | ALPHA: (18) implies: % 23.52/4.08 | | | | | (19) all_6_9 = e4 % 23.52/4.08 | | | | | (20) all_6_4 = e3 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REF_CLOSE: (5), (7), (9), (19), (20) are inconsistent by sub-proof % 23.52/4.08 | | | | | #17. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | Case 2: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (21) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | ALPHA: (21) implies: % 23.52/4.08 | | | | | (22) all_6_9 = e4 % 23.52/4.08 | | | | | (23) all_6_4 = e3 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REF_CLOSE: (5), (7), (9), (22), (23) are inconsistent by sub-proof % 23.52/4.08 | | | | | #17. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | End of split % 23.52/4.08 | | | | % 23.52/4.08 | | | Case 2: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (24) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | (all_6_4 = % 23.52/4.08 | | | | e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & % 23.52/4.08 | | | | all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | REF_CLOSE: (9), (10), (12), (13), (14), (24) are inconsistent by % 23.52/4.08 | | | | sub-proof #15. % 23.52/4.08 | | | | % 23.52/4.08 | | | End of split % 23.52/4.08 | | | % 23.52/4.08 | | Case 2: % 23.52/4.08 | | | % 23.52/4.08 | | | (25) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.52/4.08 | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & % 23.52/4.08 | | | all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.08 | | | e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.08 | | | (all_6_11 = e2)) % 23.52/4.08 | | | % 23.52/4.08 | | | BETA: splitting (25) gives: % 23.52/4.08 | | | % 23.52/4.08 | | | Case 1: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (26) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.52/4.08 | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | REF_CLOSE: (8), (9), (10), (14), (26) are inconsistent by sub-proof #14. % 23.52/4.08 | | | | % 23.52/4.08 | | | Case 2: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (27) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = % 23.52/4.08 | | | | e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.08 | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | BETA: splitting (27) gives: % 23.52/4.08 | | | | % 23.52/4.08 | | | | Case 1: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (28) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REF_CLOSE: (8), (9), (28) are inconsistent by sub-proof #13. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | Case 2: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (29) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 % 23.52/4.08 | | | | | = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REF_CLOSE: (1), (13), (29) are inconsistent by sub-proof #12. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | End of split % 23.52/4.08 | | | | % 23.52/4.08 | | | End of split % 23.52/4.08 | | | % 23.52/4.08 | | End of split % 23.52/4.08 | | % 23.52/4.08 | Case 2: % 23.52/4.08 | | % 23.52/4.08 | | (30) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 & % 23.52/4.08 | | all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 = % 23.52/4.08 | | e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.08 | | (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = % 23.52/4.08 | | e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.52/4.08 | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = % 23.52/4.08 | | e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.08 | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.08 | | e1 & ~ (all_6_23 = e0)) % 23.52/4.08 | | % 23.52/4.08 | | BETA: splitting (30) gives: % 23.52/4.08 | | % 23.52/4.08 | | Case 1: % 23.52/4.08 | | | % 23.52/4.08 | | | (31) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 % 23.52/4.08 | | | & all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 % 23.52/4.08 | | | = e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.08 | | | (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 % 23.52/4.08 | | | = e2)) % 23.52/4.08 | | | % 23.52/4.08 | | | BETA: splitting (31) gives: % 23.52/4.08 | | | % 23.52/4.08 | | | Case 1: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (32) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = % 23.52/4.08 | | | | e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | BETA: splitting (32) gives: % 23.52/4.08 | | | | % 23.52/4.08 | | | | Case 1: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (33) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | ALPHA: (33) implies: % 23.52/4.08 | | | | | (34) all_6_9 = e1 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | COMBINE_EQS: (5), (34) imply: % 23.52/4.08 | | | | | (35) e2 = e1 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REDUCE: (11), (35) imply: % 23.52/4.08 | | | | | (36) $false % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | CLOSE: (36) is inconsistent. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | Case 2: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (37) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | ALPHA: (37) implies: % 23.52/4.08 | | | | | (38) all_6_9 = e1 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | COMBINE_EQS: (5), (38) imply: % 23.52/4.08 | | | | | (39) e2 = e1 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REDUCE: (11), (39) imply: % 23.52/4.08 | | | | | (40) $false % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | CLOSE: (40) is inconsistent. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | End of split % 23.52/4.08 | | | | % 23.52/4.08 | | | Case 2: % 23.52/4.08 | | | | % 23.52/4.08 | | | | (41) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | (all_6_9 = % 23.52/4.08 | | | | e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.52/4.08 | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.08 | | | | % 23.52/4.08 | | | | BETA: splitting (41) gives: % 23.52/4.08 | | | | % 23.52/4.08 | | | | Case 1: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (42) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | ALPHA: (42) implies: % 23.52/4.08 | | | | | (43) all_6_9 = e0 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | COMBINE_EQS: (5), (43) imply: % 23.52/4.08 | | | | | (44) e2 = e0 % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | REDUCE: (12), (44) imply: % 23.52/4.08 | | | | | (45) $false % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | CLOSE: (45) is inconsistent. % 23.52/4.08 | | | | | % 23.52/4.08 | | | | Case 2: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | (46) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | % 23.52/4.08 | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | BETA: splitting (46) gives: % 23.52/4.08 | | | | | % 23.52/4.08 | | | | | Case 1: % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | (47) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | ALPHA: (47) implies: % 23.52/4.08 | | | | | | (48) all_6_9 = e0 % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | COMBINE_EQS: (5), (48) imply: % 23.52/4.08 | | | | | | (49) e2 = e0 % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | REDUCE: (12), (49) imply: % 23.52/4.08 | | | | | | (50) $false % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | CLOSE: (50) is inconsistent. % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | Case 2: % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | (51) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | ALPHA: (51) implies: % 23.52/4.08 | | | | | | (52) all_6_14 = e1 % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | | REF_CLOSE: (13), (14), (52) are inconsistent by sub-proof #11. % 23.52/4.08 | | | | | | % 23.52/4.08 | | | | | End of split % 23.52/4.08 | | | | | % 23.52/4.08 | | | | End of split % 23.52/4.08 | | | | % 23.52/4.08 | | | End of split % 23.52/4.08 | | | % 23.52/4.08 | | Case 2: % 23.52/4.08 | | | % 23.52/4.08 | | | (53) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = % 23.52/4.08 | | | e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = e0 & % 23.52/4.08 | | | all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 % 23.52/4.08 | | | = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.08 | | | (all_6_23 = e0)) % 23.52/4.08 | | | % 23.52/4.08 | | | REF_CLOSE: (2), (4), (6), (13), (14), (53) are inconsistent by sub-proof % 23.52/4.08 | | | #8. % 23.52/4.08 | | | % 23.52/4.08 | | End of split % 23.52/4.08 | | % 23.52/4.08 | End of split % 23.52/4.08 | % 23.52/4.08 End of proof % 23.52/4.08 % 23.52/4.08 Sub-proof #8 shows that the following formulas are inconsistent: % 23.52/4.08 ---------------------------------------------------------------- % 23.52/4.08 (1) ~ (all_4_24 = e2) % 23.52/4.08 (2) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = e0 & % 23.52/4.08 all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = e0 & all_6_24 = e2 & % 23.52/4.08 ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = % 23.52/4.08 e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.08 (3) all_6_24 = all_4_24 % 23.52/4.08 (4) ~ (all_4_24 = e1) % 23.52/4.08 (5) all_6_14 = e0 % 23.52/4.08 (6) ~ (e1 = e0) % 23.52/4.08 % 23.52/4.08 Begin of proof % 23.52/4.08 | % 23.52/4.08 | BETA: splitting (2) gives: % 23.52/4.08 | % 23.52/4.08 | Case 1: % 23.52/4.08 | | % 23.52/4.08 | | (7) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = e0 % 23.52/4.08 | | & all_6_24 = e2 & ~ (all_6_13 = e2)) % 23.52/4.08 | | % 23.52/4.08 | | BETA: splitting (7) gives: % 23.52/4.08 | | % 23.52/4.08 | | Case 1: % 23.52/4.08 | | | % 23.52/4.08 | | | (8) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.08 | | | % 23.52/4.08 | | | ALPHA: (8) implies: % 23.52/4.08 | | | (9) all_6_14 = e1 % 23.52/4.08 | | | % 23.52/4.08 | | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #11. % 23.52/4.08 | | | % 23.52/4.08 | | Case 2: % 23.52/4.08 | | | % 23.52/4.08 | | | (10) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.08 | | | % 23.52/4.08 | | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #10. % 23.52/4.08 | | | % 23.52/4.08 | | End of split % 23.52/4.08 | | % 23.52/4.08 | Case 2: % 23.52/4.08 | | % 23.52/4.08 | | (11) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = % 23.52/4.08 | | e0 & all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.08 | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.08 | | % 23.52/4.08 | | BETA: splitting (11) gives: % 23.52/4.08 | | % 23.52/4.08 | | Case 1: % 23.52/4.08 | | | % 23.52/4.08 | | | (12) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.08 | | | % 23.52/4.08 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #9. % 23.52/4.08 | | | % 23.52/4.08 | | Case 2: % 23.52/4.08 | | | % 23.52/4.08 | | | (13) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = % 23.52/4.08 | | | e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.08 | | | % 23.52/4.08 | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #35. % 23.52/4.08 | | | % 23.52/4.08 | | End of split % 23.52/4.08 | | % 23.52/4.08 | End of split % 23.52/4.08 | % 23.52/4.08 End of proof % 23.52/4.08 % 23.52/4.08 Sub-proof #9 shows that the following formulas are inconsistent: % 23.52/4.08 ---------------------------------------------------------------- % 23.52/4.08 (1) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.08 (2) all_6_24 = all_4_24 % 23.52/4.08 (3) ~ (all_4_24 = e2) % 23.52/4.08 % 23.52/4.08 Begin of proof % 23.52/4.08 | % 23.52/4.08 | ALPHA: (1) implies: % 23.52/4.08 | (4) all_6_24 = e2 % 23.52/4.08 | % 23.52/4.08 | COMBINE_EQS: (2), (4) imply: % 23.52/4.08 | (5) all_4_24 = e2 % 23.52/4.08 | % 23.52/4.08 | REDUCE: (3), (5) imply: % 23.52/4.08 | (6) $false % 23.52/4.08 | % 23.52/4.08 | CLOSE: (6) is inconsistent. % 23.52/4.08 | % 23.52/4.08 End of proof % 23.52/4.08 % 23.52/4.08 Sub-proof #10 shows that the following formulas are inconsistent: % 23.52/4.08 ---------------------------------------------------------------- % 23.52/4.08 (1) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.08 (2) all_6_24 = all_4_24 % 23.52/4.08 (3) ~ (all_4_24 = e2) % 23.52/4.08 % 23.52/4.08 Begin of proof % 23.52/4.08 | % 23.52/4.08 | ALPHA: (1) implies: % 23.52/4.08 | (4) all_6_24 = e2 % 23.52/4.08 | % 23.52/4.08 | COMBINE_EQS: (2), (4) imply: % 23.52/4.08 | (5) all_4_24 = e2 % 23.52/4.08 | % 23.52/4.08 | REDUCE: (3), (5) imply: % 23.52/4.08 | (6) $false % 23.52/4.08 | % 23.52/4.08 | CLOSE: (6) is inconsistent. % 23.52/4.08 | % 23.52/4.08 End of proof % 23.52/4.08 % 23.52/4.08 Sub-proof #11 shows that the following formulas are inconsistent: % 23.52/4.08 ---------------------------------------------------------------- % 23.52/4.08 (1) all_6_14 = e1 % 23.52/4.08 (2) all_6_14 = e0 % 23.52/4.08 (3) ~ (e1 = e0) % 23.52/4.08 % 23.52/4.08 Begin of proof % 23.52/4.08 | % 23.52/4.08 | COMBINE_EQS: (1), (2) imply: % 23.52/4.08 | (4) e1 = e0 % 23.52/4.08 | % 23.52/4.08 | SIMP: (4) implies: % 23.52/4.08 | (5) e1 = e0 % 23.52/4.08 | % 23.52/4.08 | REDUCE: (3), (5) imply: % 23.52/4.08 | (6) $false % 23.52/4.08 | % 23.52/4.08 | CLOSE: (6) is inconsistent. % 23.52/4.08 | % 23.52/4.08 End of proof % 23.52/4.08 % 23.52/4.08 Sub-proof #12 shows that the following formulas are inconsistent: % 23.52/4.08 ---------------------------------------------------------------- % 23.52/4.09 (1) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.09 all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.09 (2) all_6_14 = e0 % 23.52/4.09 (3) ~ (e3 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | BETA: splitting (1) gives: % 23.52/4.09 | % 23.52/4.09 | Case 1: % 23.52/4.09 | | % 23.52/4.09 | | (4) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (4) implies: % 23.52/4.09 | | (5) all_6_14 = e3 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (2), (5) imply: % 23.52/4.09 | | (6) e3 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REDUCE: (3), (6) imply: % 23.52/4.09 | | (7) $false % 23.52/4.09 | | % 23.52/4.09 | | CLOSE: (7) is inconsistent. % 23.52/4.09 | | % 23.52/4.09 | Case 2: % 23.52/4.09 | | % 23.52/4.09 | | (8) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (8) implies: % 23.52/4.09 | | (9) all_6_14 = e3 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (2), (9) imply: % 23.52/4.09 | | (10) e3 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REDUCE: (3), (10) imply: % 23.52/4.09 | | (11) $false % 23.52/4.09 | | % 23.52/4.09 | | CLOSE: (11) is inconsistent. % 23.52/4.09 | | % 23.52/4.09 | End of split % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #13 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.09 (2) all_6_4 = e4 % 23.52/4.09 (3) ~ (e4 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | ALPHA: (1) implies: % 23.52/4.09 | (4) all_6_4 = e0 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (2), (4) imply: % 23.52/4.09 | (5) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #14 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & % 23.52/4.09 all_6_24 = e4 & ~ (all_6_3 = e4)) % 23.52/4.09 (2) ~ (e4 = e0) % 23.52/4.09 (3) all_6_4 = e4 % 23.52/4.09 (4) all_6_19 = e0 % 23.52/4.09 (5) ~ (e1 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | BETA: splitting (1) gives: % 23.52/4.09 | % 23.52/4.09 | Case 1: % 23.52/4.09 | | % 23.52/4.09 | | (6) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (6) implies: % 23.52/4.09 | | (7) all_6_19 = e4 % 23.52/4.09 | | (8) all_6_4 = e1 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (3), (8) imply: % 23.52/4.09 | | (9) e4 = e1 % 23.52/4.09 | | % 23.52/4.09 | | REF_CLOSE: (4), (5), (7), (9) are inconsistent by sub-proof #19. % 23.52/4.09 | | % 23.52/4.09 | Case 2: % 23.52/4.09 | | % 23.52/4.09 | | (10) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (10) implies: % 23.52/4.09 | | (11) all_6_4 = e0 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (3), (11) imply: % 23.52/4.09 | | (12) e4 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REDUCE: (2), (12) imply: % 23.52/4.09 | | (13) $false % 23.52/4.09 | | % 23.52/4.09 | | CLOSE: (13) is inconsistent. % 23.52/4.09 | | % 23.52/4.09 | End of split % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #15 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e4 % 23.52/4.09 (2) all_6_19 = e0 % 23.52/4.09 (3) ~ (e2 = e0) % 23.52/4.09 (4) all_6_14 = e0 % 23.52/4.09 (5) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | (all_6_4 = e2 & % 23.52/4.09 all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & % 23.52/4.09 ~ (all_6_2 = e4)) % 23.52/4.09 (6) ~ (e1 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | BETA: splitting (5) gives: % 23.52/4.09 | % 23.52/4.09 | Case 1: % 23.52/4.09 | | % 23.52/4.09 | | (7) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (7) implies: % 23.52/4.09 | | (8) all_6_14 = e4 % 23.52/4.09 | | (9) all_6_4 = e2 % 23.52/4.09 | | % 23.52/4.09 | | REF_CLOSE: (1), (3), (4), (8), (9) are inconsistent by sub-proof #16. % 23.52/4.09 | | % 23.52/4.09 | Case 2: % 23.52/4.09 | | % 23.52/4.09 | | (10) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 % 23.52/4.09 | | & all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.09 | | % 23.52/4.09 | | BETA: splitting (10) gives: % 23.52/4.09 | | % 23.52/4.09 | | Case 1: % 23.52/4.09 | | | % 23.52/4.09 | | | (11) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.09 | | | % 23.52/4.09 | | | ALPHA: (11) implies: % 23.52/4.09 | | | (12) all_6_14 = e4 % 23.52/4.09 | | | (13) all_6_4 = e2 % 23.52/4.09 | | | % 23.52/4.09 | | | REF_CLOSE: (1), (3), (4), (12), (13) are inconsistent by sub-proof #16. % 23.52/4.09 | | | % 23.52/4.09 | | Case 2: % 23.52/4.09 | | | % 23.52/4.09 | | | (14) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.52/4.09 | | | % 23.52/4.09 | | | ALPHA: (14) implies: % 23.52/4.09 | | | (15) all_6_19 = e4 % 23.52/4.09 | | | (16) all_6_4 = e1 % 23.52/4.09 | | | % 23.52/4.09 | | | COMBINE_EQS: (1), (16) imply: % 23.52/4.09 | | | (17) e4 = e1 % 23.52/4.09 | | | % 23.52/4.09 | | | REF_CLOSE: (2), (6), (15), (17) are inconsistent by sub-proof #19. % 23.52/4.09 | | | % 23.52/4.09 | | End of split % 23.52/4.09 | | % 23.52/4.09 | End of split % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #16 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e2 % 23.52/4.09 (2) all_6_4 = e4 % 23.52/4.09 (3) ~ (e2 = e0) % 23.52/4.09 (4) all_6_14 = e0 % 23.52/4.09 (5) all_6_14 = e4 % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (6) e4 = e2 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (4), (5) imply: % 23.52/4.09 | (7) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (6), (7) imply: % 23.52/4.09 | (8) e2 = e0 % 23.52/4.09 | % 23.52/4.09 | SIMP: (8) implies: % 23.52/4.09 | (9) e2 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (9) imply: % 23.52/4.09 | (10) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (10) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #17 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_9 = e2 % 23.52/4.09 (2) ~ (e3 = e2) % 23.52/4.09 (3) all_6_4 = e3 % 23.52/4.09 (4) all_6_4 = e4 % 23.52/4.09 (5) all_6_9 = e4 % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (3), (4) imply: % 23.52/4.09 | (6) e4 = e3 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (5) imply: % 23.52/4.09 | (7) e4 = e2 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (6), (7) imply: % 23.52/4.09 | (8) e3 = e2 % 23.52/4.09 | % 23.52/4.09 | SIMP: (8) implies: % 23.52/4.09 | (9) e3 = e2 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (2), (9) imply: % 23.52/4.09 | (10) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (10) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #18 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e4 % 23.52/4.09 (2) all_6_4 = e0 % 23.52/4.09 (3) ~ (e4 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #19 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_19 = e0 % 23.52/4.09 (2) all_6_19 = e4 % 23.52/4.09 (3) e4 = e1 % 23.52/4.09 (4) ~ (e1 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (5) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (3), (5) imply: % 23.52/4.09 | (6) e1 = e0 % 23.52/4.09 | % 23.52/4.09 | SIMP: (6) implies: % 23.52/4.09 | (7) e1 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (4), (7) imply: % 23.52/4.09 | (8) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (8) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #20 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e2 % 23.52/4.09 (2) all_6_4 = e4 % 23.52/4.09 (3) ~ (e2 = e0) % 23.52/4.09 (4) all_6_14 = e0 % 23.52/4.09 (5) all_6_14 = e4 % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (6) e4 = e2 % 23.52/4.09 | % 23.52/4.09 | SIMP: (6) implies: % 23.52/4.09 | (7) e4 = e2 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (4), (5) imply: % 23.52/4.09 | (8) e4 = e0 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (7), (8) imply: % 23.52/4.09 | (9) e2 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (9) imply: % 23.52/4.09 | (10) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (10) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #21 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = e4 % 23.52/4.09 (2) all_6_4 = e3 % 23.52/4.09 (3) ~ (e4 = e3) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) e4 = e3 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) e4 = e3 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #22 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_24 = e3 % 23.52/4.09 (2) all_6_24 = e1 % 23.52/4.09 (3) ~ (e3 = e1) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) e3 = e1 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) e3 = e1 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #23 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_9 = all_4_6 % 23.52/4.09 (2) all_6_9 = e0 % 23.52/4.09 (3) ~ (all_4_6 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) all_4_6 = e0 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) all_4_6 = e0 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #24 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_24 = e4 % 23.52/4.09 (2) all_6_24 = e1 % 23.52/4.09 (3) ~ (e4 = e1) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) e4 = e1 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) e4 = e1 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #25 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = e0 & % 23.52/4.09 all_6_24 = e2 & ~ (all_6_13 = e2)) % 23.52/4.09 (2) all_6_14 = e2 % 23.52/4.09 (3) all_6_19 = e0 % 23.52/4.09 (4) ~ (e2 = e0) % 23.52/4.09 (5) ~ (e1 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | BETA: splitting (1) gives: % 23.52/4.09 | % 23.52/4.09 | Case 1: % 23.52/4.09 | | % 23.52/4.09 | | (6) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (6) implies: % 23.52/4.09 | | (7) all_6_19 = e2 % 23.52/4.09 | | (8) all_6_14 = e1 % 23.52/4.09 | | % 23.52/4.09 | | REF_CLOSE: (2), (3), (5), (7), (8) are inconsistent by sub-proof #26. % 23.52/4.09 | | % 23.52/4.09 | Case 2: % 23.52/4.09 | | % 23.52/4.09 | | (9) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (9) implies: % 23.52/4.09 | | (10) all_6_14 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #36. % 23.52/4.09 | | % 23.52/4.09 | End of split % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #26 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_19 = e2 % 23.52/4.09 (2) all_6_14 = e2 % 23.52/4.09 (3) all_6_19 = e0 % 23.52/4.09 (4) ~ (e1 = e0) % 23.52/4.09 (5) all_6_14 = e1 % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (2), (5) imply: % 23.52/4.09 | (6) e2 = e1 % 23.52/4.09 | % 23.52/4.09 | SIMP: (6) implies: % 23.52/4.09 | (7) e2 = e1 % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (3) imply: % 23.52/4.09 | (8) e2 = e0 % 23.52/4.09 | % 23.52/4.09 | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #33. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #27 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_24 = e4 % 23.52/4.09 (2) all_6_24 = e3 % 23.52/4.09 (3) ~ (e4 = e3) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | COMBINE_EQS: (1), (2) imply: % 23.52/4.09 | (4) e4 = e3 % 23.52/4.09 | % 23.52/4.09 | SIMP: (4) implies: % 23.52/4.09 | (5) e4 = e3 % 23.52/4.09 | % 23.52/4.09 | REDUCE: (3), (5) imply: % 23.52/4.09 | (6) $false % 23.52/4.09 | % 23.52/4.09 | CLOSE: (6) is inconsistent. % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #28 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 & % 23.52/4.09 all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.09 (2) all_6_19 = e0 % 23.52/4.09 (3) ~ (e3 = e0) % 23.52/4.09 % 23.52/4.09 Begin of proof % 23.52/4.09 | % 23.52/4.09 | BETA: splitting (1) gives: % 23.52/4.09 | % 23.52/4.09 | Case 1: % 23.52/4.09 | | % 23.52/4.09 | | (4) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (4) implies: % 23.52/4.09 | | (5) all_6_19 = e3 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (2), (5) imply: % 23.52/4.09 | | (6) e3 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REDUCE: (3), (6) imply: % 23.52/4.09 | | (7) $false % 23.52/4.09 | | % 23.52/4.09 | | CLOSE: (7) is inconsistent. % 23.52/4.09 | | % 23.52/4.09 | Case 2: % 23.52/4.09 | | % 23.52/4.09 | | (8) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1) % 23.52/4.09 | | % 23.52/4.09 | | ALPHA: (8) implies: % 23.52/4.09 | | (9) all_6_19 = e3 % 23.52/4.09 | | % 23.52/4.09 | | COMBINE_EQS: (2), (9) imply: % 23.52/4.09 | | (10) e3 = e0 % 23.52/4.09 | | % 23.52/4.09 | | REDUCE: (3), (10) imply: % 23.52/4.09 | | (11) $false % 23.52/4.09 | | % 23.52/4.09 | | CLOSE: (11) is inconsistent. % 23.52/4.09 | | % 23.52/4.09 | End of split % 23.52/4.09 | % 23.52/4.09 End of proof % 23.52/4.09 % 23.52/4.09 Sub-proof #29 shows that the following formulas are inconsistent: % 23.52/4.09 ---------------------------------------------------------------- % 23.52/4.09 (1) all_6_4 = all_4_0 % 23.52/4.10 (2) all_6_4 = e0 % 23.52/4.10 (3) ~ (all_4_0 = e0) % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | COMBINE_EQS: (1), (2) imply: % 23.52/4.10 | (4) all_4_0 = e0 % 23.52/4.10 | % 23.52/4.10 | SIMP: (4) implies: % 23.52/4.10 | (5) all_4_0 = e0 % 23.52/4.10 | % 23.52/4.10 | REDUCE: (3), (5) imply: % 23.52/4.10 | (6) $false % 23.52/4.10 | % 23.52/4.10 | CLOSE: (6) is inconsistent. % 23.52/4.10 | % 23.52/4.10 End of proof % 23.52/4.10 % 23.52/4.10 Sub-proof #30 shows that the following formulas are inconsistent: % 23.52/4.10 ---------------------------------------------------------------- % 23.52/4.10 (1) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.52/4.10 (2) all_6_19 = e0 % 23.52/4.10 (3) ~ (e4 = e0) % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | ALPHA: (1) implies: % 23.52/4.10 | (4) all_6_19 = e4 % 23.52/4.10 | % 23.52/4.10 | COMBINE_EQS: (2), (4) imply: % 23.52/4.10 | (5) e4 = e0 % 23.52/4.10 | % 23.52/4.10 | REDUCE: (3), (5) imply: % 23.52/4.10 | (6) $false % 23.52/4.10 | % 23.52/4.10 | CLOSE: (6) is inconsistent. % 23.52/4.10 | % 23.52/4.10 End of proof % 23.52/4.10 % 23.52/4.10 Sub-proof #31 shows that the following formulas are inconsistent: % 23.52/4.10 ---------------------------------------------------------------- % 23.52/4.10 (1) all_6_9 = all_4_6 % 23.52/4.10 (2) ~ (e4 = e0) % 23.52/4.10 (3) all_6_14 = e2 % 23.52/4.10 (4) ~ (all_4_6 = e4) % 23.52/4.10 (5) all_6_19 = e0 % 23.52/4.10 (6) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.10 all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.10 (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.10 (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.10 (7) ~ (e4 = e2) % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | BETA: splitting (6) gives: % 23.52/4.10 | % 23.52/4.10 | Case 1: % 23.52/4.10 | | % 23.52/4.10 | | (8) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.10 | | all_6_9 = e4 & ~ (all_6_5 = e3)) % 23.52/4.10 | | % 23.52/4.10 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #49. % 23.52/4.10 | | % 23.52/4.10 | Case 2: % 23.52/4.10 | | % 23.52/4.10 | | (9) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | (all_6_4 = e2 & % 23.52/4.10 | | all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 % 23.52/4.10 | | & ~ (all_6_2 = e4)) % 23.52/4.10 | | % 23.52/4.10 | | BETA: splitting (9) gives: % 23.52/4.10 | | % 23.52/4.10 | | Case 1: % 23.52/4.10 | | | % 23.52/4.10 | | | (10) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.10 | | | % 23.52/4.10 | | | REF_CLOSE: (3), (7), (10) are inconsistent by sub-proof #48. % 23.52/4.10 | | | % 23.52/4.10 | | Case 2: % 23.52/4.10 | | | % 23.52/4.10 | | | (11) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = % 23.52/4.10 | | | e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.10 | | | % 23.52/4.10 | | | BETA: splitting (11) gives: % 23.52/4.10 | | | % 23.52/4.10 | | | Case 1: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (12) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.10 | | | | % 23.52/4.10 | | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #47. % 23.52/4.10 | | | | % 23.52/4.10 | | | Case 2: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (13) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.52/4.10 | | | | % 23.52/4.10 | | | | ALPHA: (13) implies: % 23.52/4.10 | | | | (14) all_6_19 = e4 % 23.52/4.10 | | | | % 23.52/4.10 | | | | COMBINE_EQS: (5), (14) imply: % 23.52/4.10 | | | | (15) e4 = e0 % 23.52/4.10 | | | | % 23.52/4.10 | | | | REDUCE: (2), (15) imply: % 23.52/4.10 | | | | (16) $false % 23.52/4.10 | | | | % 23.52/4.10 | | | | CLOSE: (16) is inconsistent. % 23.52/4.10 | | | | % 23.52/4.10 | | | End of split % 23.52/4.10 | | | % 23.52/4.10 | | End of split % 23.52/4.10 | | % 23.52/4.10 | End of split % 23.52/4.10 | % 23.52/4.10 End of proof % 23.52/4.10 % 23.52/4.10 Sub-proof #32 shows that the following formulas are inconsistent: % 23.52/4.10 ---------------------------------------------------------------- % 23.52/4.10 (1) all_6_19 = e2 % 23.52/4.10 (2) all_6_14 = e2 % 23.52/4.10 (3) all_6_19 = e0 % 23.52/4.10 (4) ~ (e1 = e0) % 23.52/4.10 (5) all_6_14 = e1 % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | COMBINE_EQS: (2), (5) imply: % 23.52/4.10 | (6) e2 = e1 % 23.52/4.10 | % 23.52/4.10 | COMBINE_EQS: (1), (3) imply: % 23.52/4.10 | (7) e2 = e0 % 23.52/4.10 | % 23.52/4.10 | SIMP: (7) implies: % 23.52/4.10 | (8) e2 = e0 % 23.52/4.10 | % 23.52/4.10 | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #33. % 23.52/4.10 | % 23.52/4.10 End of proof % 23.52/4.10 % 23.52/4.10 Sub-proof #33 shows that the following formulas are inconsistent: % 23.52/4.10 ---------------------------------------------------------------- % 23.52/4.10 (1) e2 = e1 % 23.52/4.10 (2) e2 = e0 % 23.52/4.10 (3) ~ (e1 = e0) % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | COMBINE_EQS: (1), (2) imply: % 23.52/4.10 | (4) e1 = e0 % 23.52/4.10 | % 23.52/4.10 | SIMP: (4) implies: % 23.52/4.10 | (5) e1 = e0 % 23.52/4.10 | % 23.52/4.10 | REDUCE: (3), (5) imply: % 23.52/4.10 | (6) $false % 23.52/4.10 | % 23.52/4.10 | CLOSE: (6) is inconsistent. % 23.52/4.10 | % 23.52/4.10 End of proof % 23.52/4.10 % 23.52/4.10 Sub-proof #34 shows that the following formulas are inconsistent: % 23.52/4.10 ---------------------------------------------------------------- % 23.52/4.10 (1) all_6_9 = e0 % 23.52/4.10 (2) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.10 all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.10 (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | % 23.52/4.10 (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4)) | (all_6_4 = e1 & % 23.52/4.10 all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = e0 & all_6_24 = e4 & % 23.52/4.10 ~ (all_6_3 = e4)) | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) % 23.52/4.10 | (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.10 all_6_14 = e3 & ~ (all_6_11 = e2)) | (all_6_9 = e1 & all_6_19 = e3 & % 23.52/4.10 ~ (all_6_7 = e3)) | (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.10 | (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & % 23.52/4.10 all_6_24 = e3 & ~ (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & % 23.52/4.10 ~ (all_6_12 = e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = % 23.52/4.10 e1)) | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | % 23.52/4.10 (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.10 all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & % 23.52/4.10 ~ (all_6_23 = e0)) % 23.52/4.10 (3) all_6_24 = all_4_24 % 23.52/4.10 (4) ~ (all_4_24 = e1) % 23.52/4.10 (5) ~ (e4 = e0) % 23.52/4.10 (6) all_6_14 = e2 % 23.52/4.10 (7) all_6_19 = e0 % 23.52/4.10 (8) ~ (e2 = e0) % 23.52/4.10 (9) ~ (e4 = e2) % 23.52/4.10 (10) ~ (all_4_24 = e4) % 23.52/4.10 (11) ~ (all_4_24 = e3) % 23.52/4.10 (12) ~ (e1 = e0) % 23.52/4.10 % 23.52/4.10 Begin of proof % 23.52/4.10 | % 23.52/4.10 | BETA: splitting (2) gives: % 23.52/4.10 | % 23.52/4.10 | Case 1: % 23.52/4.10 | | % 23.52/4.10 | | (13) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.10 | | all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = e4 % 23.52/4.10 | | & ~ (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.10 | | (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = % 23.52/4.10 | | e4)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | % 23.52/4.10 | | (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & % 23.52/4.10 | | all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.10 | | e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.10 | | (all_6_11 = e2)) % 23.52/4.10 | | % 23.52/4.10 | | BETA: splitting (13) gives: % 23.52/4.10 | | % 23.52/4.10 | | Case 1: % 23.52/4.10 | | | % 23.52/4.10 | | | (14) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 % 23.52/4.10 | | | & all_6_9 = e4 & ~ (all_6_5 = e3)) | (all_6_4 = e2 & all_6_14 = % 23.52/4.10 | | | e4 & ~ (all_6_1 = e4)) | (all_6_4 = e2 & all_6_14 = e4 & ~ % 23.52/4.10 | | | (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = % 23.52/4.10 | | | e4)) % 23.52/4.10 | | | % 23.52/4.10 | | | BETA: splitting (14) gives: % 23.52/4.10 | | | % 23.52/4.10 | | | Case 1: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (15) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = % 23.52/4.10 | | | | e3 & all_6_9 = e4 & ~ (all_6_5 = e3)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (15) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (16) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (16) implies: % 23.52/4.10 | | | | | (17) all_6_9 = e4 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | COMBINE_EQS: (1), (17) imply: % 23.52/4.10 | | | | | (18) e4 = e0 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REDUCE: (5), (18) imply: % 23.52/4.10 | | | | | (19) $false % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | CLOSE: (19) is inconsistent. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | Case 2: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (20) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (20) implies: % 23.52/4.10 | | | | | (21) all_6_9 = e4 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | COMBINE_EQS: (1), (21) imply: % 23.52/4.10 | | | | | (22) e4 = e0 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REDUCE: (5), (22) imply: % 23.52/4.10 | | | | | (23) $false % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | CLOSE: (23) is inconsistent. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | End of split % 23.52/4.10 | | | | % 23.52/4.10 | | | Case 2: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (24) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | (all_6_4 = % 23.52/4.10 | | | | e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & % 23.52/4.10 | | | | all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | REF_CLOSE: (5), (6), (7), (9), (24) are inconsistent by sub-proof #45. % 23.52/4.10 | | | | % 23.52/4.10 | | | End of split % 23.52/4.10 | | | % 23.52/4.10 | | Case 2: % 23.52/4.10 | | | % 23.52/4.10 | | | (25) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.52/4.10 | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) | (all_6_4 = e0 & % 23.52/4.10 | | | all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = e2 & all_6_14 = % 23.52/4.10 | | | e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & all_6_14 = e3 & ~ % 23.52/4.10 | | | (all_6_11 = e2)) % 23.52/4.10 | | | % 23.52/4.10 | | | BETA: splitting (25) gives: % 23.52/4.10 | | | % 23.52/4.10 | | | Case 1: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (26) (all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1)) | (all_6_4 = % 23.52/4.10 | | | | e0 & all_6_24 = e4 & ~ (all_6_3 = e4)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (26) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (27) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_15 = e1) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (27) implies: % 23.52/4.10 | | | | | (28) all_6_19 = e4 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REF_CLOSE: (5), (7), (28) are inconsistent by sub-proof #46. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | Case 2: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (29) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REF_CLOSE: (3), (10), (29) are inconsistent by sub-proof #41. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | End of split % 23.52/4.10 | | | | % 23.52/4.10 | | | Case 2: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (30) (all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0)) | (all_6_9 = % 23.52/4.10 | | | | e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.10 | | | | all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (30) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (31) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REF_CLOSE: (3), (10), (31) are inconsistent by sub-proof #40. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | Case 2: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (32) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 % 23.52/4.10 | | | | | = e2 & all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | BETA: splitting (32) gives: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | Case 1: % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | (33) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3) % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | ALPHA: (33) implies: % 23.52/4.10 | | | | | | (34) all_6_9 = e2 % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | REF_CLOSE: (1), (8), (34) are inconsistent by sub-proof #39. % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | Case 2: % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | (35) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2) % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | ALPHA: (35) implies: % 23.52/4.10 | | | | | | (36) all_6_9 = e2 % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | REF_CLOSE: (1), (8), (36) are inconsistent by sub-proof #39. % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | End of split % 23.52/4.10 | | | | | % 23.52/4.10 | | | | End of split % 23.52/4.10 | | | | % 23.52/4.10 | | | End of split % 23.52/4.10 | | | % 23.52/4.10 | | End of split % 23.52/4.10 | | % 23.52/4.10 | Case 2: % 23.52/4.10 | | % 23.52/4.10 | | (37) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 & % 23.52/4.10 | | all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 = % 23.52/4.10 | | e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.10 | | (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = % 23.52/4.10 | | e2)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | % 23.52/4.10 | | (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = % 23.52/4.10 | | e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & % 23.52/4.10 | | all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = % 23.52/4.10 | | e1 & ~ (all_6_23 = e0)) % 23.52/4.10 | | % 23.52/4.10 | | BETA: splitting (37) gives: % 23.52/4.10 | | % 23.52/4.10 | | Case 1: % 23.52/4.10 | | | % 23.52/4.10 | | | (38) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = e1 % 23.52/4.10 | | | & all_6_19 = e3 & ~ (all_6_16 = e1)) | (all_6_9 = e0 & all_6_24 % 23.52/4.10 | | | = e3 & ~ (all_6_8 = e3)) | (all_6_9 = e0 & all_6_24 = e3 & ~ % 23.52/4.10 | | | (all_6_21 = e0)) | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 % 23.52/4.10 | | | = e2)) % 23.52/4.10 | | | % 23.52/4.10 | | | BETA: splitting (38) gives: % 23.52/4.10 | | | % 23.52/4.10 | | | Case 1: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (39) (all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3)) | (all_6_9 = % 23.52/4.10 | | | | e1 & all_6_19 = e3 & ~ (all_6_16 = e1)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (39) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (40) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_7 = e3) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (40) implies: % 23.52/4.10 | | | | | (41) all_6_9 = e1 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REF_CLOSE: (1), (12), (41) are inconsistent by sub-proof #38. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | Case 2: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (42) all_6_9 = e1 & all_6_19 = e3 & ~ (all_6_16 = e1) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (42) implies: % 23.52/4.10 | | | | | (43) all_6_9 = e1 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REF_CLOSE: (1), (12), (43) are inconsistent by sub-proof #38. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | End of split % 23.52/4.10 | | | | % 23.52/4.10 | | | Case 2: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (44) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3)) | (all_6_9 = % 23.52/4.10 | | | | e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | (all_6_14 = e1 & % 23.52/4.10 | | | | all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (44) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (45) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_8 = e3) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (45) implies: % 23.52/4.10 | | | | | (46) all_6_24 = e3 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | COMBINE_EQS: (3), (46) imply: % 23.52/4.10 | | | | | (47) all_4_24 = e3 % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | REDUCE: (11), (47) imply: % 23.52/4.10 | | | | | (48) $false % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | CLOSE: (48) is inconsistent. % 23.52/4.10 | | | | | % 23.52/4.10 | | | | Case 2: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (49) (all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0)) | % 23.52/4.10 | | | | | (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2)) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | BETA: splitting (49) gives: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | Case 1: % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | (50) all_6_9 = e0 & all_6_24 = e3 & ~ (all_6_21 = e0) % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | ALPHA: (50) implies: % 23.52/4.10 | | | | | | (51) all_6_24 = e3 % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | COMBINE_EQS: (3), (51) imply: % 23.52/4.10 | | | | | | (52) all_4_24 = e3 % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | REDUCE: (11), (52) imply: % 23.52/4.10 | | | | | | (53) $false % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | CLOSE: (53) is inconsistent. % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | Case 2: % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | (54) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_12 = e2) % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | ALPHA: (54) implies: % 23.52/4.10 | | | | | | (55) all_6_19 = e2 % 23.52/4.10 | | | | | | (56) all_6_14 = e1 % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | | REF_CLOSE: (6), (7), (12), (55), (56) are inconsistent by sub-proof % 23.52/4.10 | | | | | | #37. % 23.52/4.10 | | | | | | % 23.52/4.10 | | | | | End of split % 23.52/4.10 | | | | | % 23.52/4.10 | | | | End of split % 23.52/4.10 | | | | % 23.52/4.10 | | | End of split % 23.52/4.10 | | | % 23.52/4.10 | | Case 2: % 23.52/4.10 | | | % 23.52/4.10 | | | (57) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 = % 23.52/4.10 | | | e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) | (all_6_14 = e0 & % 23.52/4.10 | | | all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 = e0 & all_6_24 % 23.52/4.10 | | | = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & all_6_24 = e1 & ~ % 23.52/4.10 | | | (all_6_23 = e0)) % 23.52/4.10 | | | % 23.52/4.10 | | | BETA: splitting (57) gives: % 23.52/4.10 | | | % 23.52/4.10 | | | Case 1: % 23.52/4.10 | | | | % 23.52/4.10 | | | | (58) (all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1)) | (all_6_14 % 23.52/4.10 | | | | = e0 & all_6_24 = e2 & ~ (all_6_13 = e2)) % 23.52/4.10 | | | | % 23.52/4.10 | | | | BETA: splitting (58) gives: % 23.52/4.10 | | | | % 23.52/4.10 | | | | Case 1: % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | (59) all_6_14 = e1 & all_6_19 = e2 & ~ (all_6_17 = e1) % 23.52/4.10 | | | | | % 23.52/4.10 | | | | | ALPHA: (59) implies: % 23.52/4.10 | | | | | (60) all_6_19 = e2 % 23.52/4.10 | | | | | (61) all_6_14 = e1 % 23.52/4.10 | | | | | % 23.52/4.11 | | | | | REF_CLOSE: (6), (7), (12), (60), (61) are inconsistent by sub-proof % 23.52/4.11 | | | | | #37. % 23.52/4.11 | | | | | % 23.52/4.11 | | | | Case 2: % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | (62) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_13 = e2) % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | ALPHA: (62) implies: % 23.52/4.11 | | | | | (63) all_6_14 = e0 % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | REF_CLOSE: (6), (8), (63) are inconsistent by sub-proof #36. % 23.52/4.11 | | | | | % 23.52/4.11 | | | | End of split % 23.52/4.11 | | | | % 23.52/4.11 | | | Case 2: % 23.52/4.11 | | | | % 23.52/4.11 | | | | (64) (all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0)) | (all_6_19 % 23.52/4.11 | | | | = e0 & all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.11 | | | | all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.11 | | | | % 23.52/4.11 | | | | BETA: splitting (64) gives: % 23.52/4.11 | | | | % 23.52/4.11 | | | | Case 1: % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | (65) all_6_14 = e0 & all_6_24 = e2 & ~ (all_6_22 = e0) % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | ALPHA: (65) implies: % 23.52/4.11 | | | | | (66) all_6_14 = e0 % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | REF_CLOSE: (6), (8), (66) are inconsistent by sub-proof #36. % 23.52/4.11 | | | | | % 23.52/4.11 | | | | Case 2: % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | (67) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1)) | % 23.52/4.11 | | | | | (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.11 | | | | | % 23.52/4.11 | | | | | REF_CLOSE: (3), (4), (67) are inconsistent by sub-proof #35. % 23.52/4.11 | | | | | % 23.52/4.11 | | | | End of split % 23.52/4.11 | | | | % 23.52/4.11 | | | End of split % 23.52/4.11 | | | % 23.52/4.11 | | End of split % 23.52/4.11 | | % 23.52/4.11 | End of split % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #35 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) (all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1)) | (all_6_19 = e0 & % 23.52/4.11 all_6_24 = e1 & ~ (all_6_23 = e0)) % 23.52/4.11 (2) all_6_24 = all_4_24 % 23.52/4.11 (3) ~ (all_4_24 = e1) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | BETA: splitting (1) gives: % 23.52/4.11 | % 23.52/4.11 | Case 1: % 23.52/4.11 | | % 23.52/4.11 | | (4) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_18 = e1) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (4) implies: % 23.52/4.11 | | (5) all_6_24 = e1 % 23.52/4.11 | | % 23.52/4.11 | | COMBINE_EQS: (2), (5) imply: % 23.52/4.11 | | (6) all_4_24 = e1 % 23.52/4.11 | | % 23.52/4.11 | | REDUCE: (3), (6) imply: % 23.52/4.11 | | (7) $false % 23.52/4.11 | | % 23.52/4.11 | | CLOSE: (7) is inconsistent. % 23.52/4.11 | | % 23.52/4.11 | Case 2: % 23.52/4.11 | | % 23.52/4.11 | | (8) all_6_19 = e0 & all_6_24 = e1 & ~ (all_6_23 = e0) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (8) implies: % 23.52/4.11 | | (9) all_6_24 = e1 % 23.52/4.11 | | % 23.52/4.11 | | COMBINE_EQS: (2), (9) imply: % 23.52/4.11 | | (10) all_4_24 = e1 % 23.52/4.11 | | % 23.52/4.11 | | REDUCE: (3), (10) imply: % 23.52/4.11 | | (11) $false % 23.52/4.11 | | % 23.52/4.11 | | CLOSE: (11) is inconsistent. % 23.52/4.11 | | % 23.52/4.11 | End of split % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #36 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_14 = e2 % 23.52/4.11 (2) all_6_14 = e0 % 23.52/4.11 (3) ~ (e2 = e0) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #37 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_19 = e2 % 23.52/4.11 (2) all_6_14 = e2 % 23.52/4.11 (3) all_6_19 = e0 % 23.52/4.11 (4) ~ (e1 = e0) % 23.52/4.11 (5) all_6_14 = e1 % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (2), (5) imply: % 23.52/4.11 | (6) e2 = e1 % 23.52/4.11 | % 23.52/4.11 | SIMP: (6) implies: % 23.52/4.11 | (7) e2 = e1 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (3) imply: % 23.52/4.11 | (8) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (8) implies: % 23.52/4.11 | (9) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (7), (9) imply: % 23.52/4.11 | (10) e1 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (4), (10) imply: % 23.52/4.11 | (11) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (11) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #38 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_9 = e1 % 23.52/4.11 (2) all_6_9 = e0 % 23.52/4.11 (3) ~ (e1 = e0) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) e1 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) e1 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #39 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_9 = e2 % 23.52/4.11 (2) all_6_9 = e0 % 23.52/4.11 (3) ~ (e2 = e0) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) e2 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #40 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_20 = e0) % 23.52/4.11 (2) all_6_24 = all_4_24 % 23.52/4.11 (3) ~ (all_4_24 = e4) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | ALPHA: (1) implies: % 23.52/4.11 | (4) all_6_24 = e4 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (2), (4) imply: % 23.52/4.11 | (5) all_4_24 = e4 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #41 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_4 = e0 & all_6_24 = e4 & ~ (all_6_3 = e4) % 23.52/4.11 (2) all_6_24 = all_4_24 % 23.52/4.11 (3) ~ (all_4_24 = e4) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | ALPHA: (1) implies: % 23.52/4.11 | (4) all_6_24 = e4 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (2), (4) imply: % 23.52/4.11 | (5) all_4_24 = e4 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #42 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_19 = e3 % 23.52/4.11 (2) all_6_19 = e0 % 23.52/4.11 (3) ~ (e3 = e0) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) e3 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) e3 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #43 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) (all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3)) | (all_6_9 = e2 & % 23.52/4.11 all_6_14 = e3 & ~ (all_6_11 = e2)) % 23.52/4.11 (2) all_6_14 = e2 % 23.52/4.11 (3) ~ (e3 = e2) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | BETA: splitting (1) gives: % 23.52/4.11 | % 23.52/4.11 | Case 1: % 23.52/4.11 | | % 23.52/4.11 | | (4) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_6 = e3) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (4) implies: % 23.52/4.11 | | (5) all_6_14 = e3 % 23.52/4.11 | | % 23.52/4.11 | | COMBINE_EQS: (2), (5) imply: % 23.52/4.11 | | (6) e3 = e2 % 23.52/4.11 | | % 23.52/4.11 | | REDUCE: (3), (6) imply: % 23.52/4.11 | | (7) $false % 23.52/4.11 | | % 23.52/4.11 | | CLOSE: (7) is inconsistent. % 23.52/4.11 | | % 23.52/4.11 | Case 2: % 23.52/4.11 | | % 23.52/4.11 | | (8) all_6_9 = e2 & all_6_14 = e3 & ~ (all_6_11 = e2) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (8) implies: % 23.52/4.11 | | (9) all_6_14 = e3 % 23.52/4.11 | | % 23.52/4.11 | | COMBINE_EQS: (2), (9) imply: % 23.52/4.11 | | (10) e3 = e2 % 23.52/4.11 | | % 23.52/4.11 | | REDUCE: (3), (10) imply: % 23.52/4.11 | | (11) $false % 23.52/4.11 | | % 23.52/4.11 | | CLOSE: (11) is inconsistent. % 23.52/4.11 | | % 23.52/4.11 | End of split % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #44 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_24 = all_4_24 % 23.52/4.11 (2) all_6_24 = e4 % 23.52/4.11 (3) ~ (all_4_24 = e4) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) all_4_24 = e4 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) all_4_24 = e4 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #45 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) ~ (e4 = e0) % 23.52/4.11 (2) all_6_14 = e2 % 23.52/4.11 (3) all_6_19 = e0 % 23.52/4.11 (4) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4)) | (all_6_4 = e2 & % 23.52/4.11 all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & all_6_19 = e4 & % 23.52/4.11 ~ (all_6_2 = e4)) % 23.52/4.11 (5) ~ (e4 = e2) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | BETA: splitting (4) gives: % 23.52/4.11 | % 23.52/4.11 | Case 1: % 23.52/4.11 | | % 23.52/4.11 | | (6) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.11 | | % 23.52/4.11 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #48. % 23.52/4.11 | | % 23.52/4.11 | Case 2: % 23.52/4.11 | | % 23.52/4.11 | | (7) (all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2)) | (all_6_4 = e1 & % 23.52/4.11 | | all_6_19 = e4 & ~ (all_6_2 = e4)) % 23.52/4.11 | | % 23.52/4.11 | | BETA: splitting (7) gives: % 23.52/4.11 | | % 23.52/4.11 | | Case 1: % 23.52/4.11 | | | % 23.52/4.11 | | | (8) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.11 | | | % 23.52/4.11 | | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #47. % 23.52/4.11 | | | % 23.52/4.11 | | Case 2: % 23.52/4.11 | | | % 23.52/4.11 | | | (9) all_6_4 = e1 & all_6_19 = e4 & ~ (all_6_2 = e4) % 23.52/4.11 | | | % 23.52/4.11 | | | ALPHA: (9) implies: % 23.52/4.11 | | | (10) all_6_19 = e4 % 23.52/4.11 | | | % 23.52/4.11 | | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #46. % 23.52/4.11 | | | % 23.52/4.11 | | End of split % 23.52/4.11 | | % 23.52/4.11 | End of split % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #46 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_19 = e4 % 23.52/4.11 (2) all_6_19 = e0 % 23.52/4.11 (3) ~ (e4 = e0) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) e4 = e0 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) e4 = e0 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #47 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_10 = e2) % 23.52/4.11 (2) all_6_14 = e2 % 23.52/4.11 (3) ~ (e4 = e2) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | ALPHA: (1) implies: % 23.52/4.11 | (4) all_6_14 = e4 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (2), (4) imply: % 23.52/4.11 | (5) e4 = e2 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #48 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_4 = e2 & all_6_14 = e4 & ~ (all_6_1 = e4) % 23.52/4.11 (2) all_6_14 = e2 % 23.52/4.11 (3) ~ (e4 = e2) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | ALPHA: (1) implies: % 23.52/4.11 | (4) all_6_14 = e4 % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (2), (4) imply: % 23.52/4.11 | (5) e4 = e2 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #49 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) (all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4)) | (all_6_4 = e3 & % 23.52/4.11 all_6_9 = e4 & ~ (all_6_5 = e3)) % 23.52/4.11 (2) all_6_9 = all_4_6 % 23.52/4.11 (3) ~ (all_4_6 = e4) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | BETA: splitting (1) gives: % 23.52/4.11 | % 23.52/4.11 | Case 1: % 23.52/4.11 | | % 23.52/4.11 | | (4) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_0 = e4) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (4) implies: % 23.52/4.11 | | (5) all_6_9 = e4 % 23.52/4.11 | | % 23.52/4.11 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #50. % 23.52/4.11 | | % 23.52/4.11 | Case 2: % 23.52/4.11 | | % 23.52/4.11 | | (6) all_6_4 = e3 & all_6_9 = e4 & ~ (all_6_5 = e3) % 23.52/4.11 | | % 23.52/4.11 | | ALPHA: (6) implies: % 23.52/4.11 | | (7) all_6_9 = e4 % 23.52/4.11 | | % 23.52/4.11 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #50. % 23.52/4.11 | | % 23.52/4.11 | End of split % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % 23.52/4.11 Sub-proof #50 shows that the following formulas are inconsistent: % 23.52/4.11 ---------------------------------------------------------------- % 23.52/4.11 (1) all_6_9 = all_4_6 % 23.52/4.11 (2) all_6_9 = e4 % 23.52/4.11 (3) ~ (all_4_6 = e4) % 23.52/4.11 % 23.52/4.11 Begin of proof % 23.52/4.11 | % 23.52/4.11 | COMBINE_EQS: (1), (2) imply: % 23.52/4.11 | (4) all_4_6 = e4 % 23.52/4.11 | % 23.52/4.11 | SIMP: (4) implies: % 23.52/4.11 | (5) all_4_6 = e4 % 23.52/4.11 | % 23.52/4.11 | REDUCE: (3), (5) imply: % 23.52/4.11 | (6) $false % 23.52/4.11 | % 23.52/4.11 | CLOSE: (6) is inconsistent. % 23.52/4.11 | % 23.52/4.11 End of proof % 23.52/4.11 % SZS output end Proof for theBenchmark % 23.52/4.11 % 23.52/4.11 3512ms %------------------------------------------------------------------------------