%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG057+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 : n009.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 16:36:03 EDT 2023 % Result : Theorem 14.13s 2.63s % Output : Proof 131.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : ALG057+1 : TPTP v8.1.2. Released v2.7.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 04:46:35 EDT 2023 % 0.12/0.34 % CPUTime : % 0.52/0.61 ________ _____ % 0.52/0.61 ___ __ \_________(_)________________________________ % 0.52/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.61 % 0.52/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.61 (2023-06-19) % 0.52/0.61 % 0.52/0.61 (c) Philipp Rümmer, 2009-2023 % 0.52/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.61 Amanda Stjerna. % 0.52/0.61 Free software under BSD-3-Clause. % 0.52/0.61 % 0.52/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.61 % 0.52/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.62 Running up to 7 provers in parallel. % 0.52/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.71/1.48 Prover 4: Preprocessing ... % 5.71/1.48 Prover 1: Preprocessing ... % 5.71/1.51 Prover 3: Preprocessing ... % 5.71/1.51 Prover 2: Preprocessing ... % 5.71/1.51 Prover 6: Preprocessing ... % 5.71/1.51 Prover 5: Preprocessing ... % 5.71/1.52 Prover 0: Preprocessing ... % 10.28/2.08 Prover 1: Constructing countermodel ... % 10.28/2.09 Prover 4: Constructing countermodel ... % 10.28/2.09 Prover 2: Constructing countermodel ... % 10.67/2.13 Prover 6: Constructing countermodel ... % 10.67/2.14 Prover 3: Constructing countermodel ... % 10.90/2.17 Prover 0: Constructing countermodel ... % 14.13/2.63 Prover 6: proved (1995ms) % 14.13/2.63 % 14.13/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.13/2.63 % 14.13/2.63 Prover 0: stopped % 14.13/2.63 Prover 2: stopped % 14.13/2.63 Prover 3: stopped % 14.62/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.62/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.62/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.62/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.75/2.67 Prover 5: Constructing countermodel ... % 14.75/2.69 Prover 5: stopped % 14.75/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.84/2.94 Prover 7: Preprocessing ... % 16.97/2.96 Prover 8: Preprocessing ... % 16.97/2.98 Prover 11: Preprocessing ... % 17.48/3.03 Prover 10: Preprocessing ... % 17.48/3.05 Prover 13: Preprocessing ... % 18.47/3.15 Prover 8: Constructing countermodel ... % 19.13/3.24 Prover 11: Constructing countermodel ... % 19.36/3.30 Prover 7: Constructing countermodel ... % 19.36/3.32 Prover 13: Constructing countermodel ... % 19.94/3.35 Prover 10: Constructing countermodel ... % 63.47/8.96 Prover 13: stopped % 63.47/8.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 64.57/9.08 Prover 16: Preprocessing ... % 65.86/9.30 Prover 16: Constructing countermodel ... % 111.00/15.03 Prover 16: stopped % 111.00/15.04 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 112.15/15.24 Prover 19: Preprocessing ... % 113.55/15.38 Prover 19: Constructing countermodel ... % 118.12/15.97 Prover 1: stopped % 123.93/16.77 Prover 7: Found proof (size 448186) % 123.93/16.77 Prover 7: proved (14033ms) % 123.93/16.77 Prover 19: stopped % 123.93/16.77 Prover 10: stopped % 123.93/16.77 Prover 11: stopped % 123.93/16.77 Prover 8: stopped % 123.93/16.77 Prover 4: stopped % 123.93/16.77 % 123.93/16.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 123.93/16.77 % 125.20/16.98 % SZS output start Proof for theBenchmark % 125.44/17.01 Assumptions after simplification: % 125.44/17.01 --------------------------------- % 125.44/17.01 % 125.44/17.01 (ax1) % 125.44/17.07 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 125.44/17.07 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 125.44/17.07 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 125.44/17.07 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 125.44/17.07 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 125.44/17.07 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 125.44/17.07 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 125.44/17.07 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 125.44/17.07 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 125.44/17.07 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 125.44/17.07 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 125.44/17.07 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 125.44/17.07 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 125.44/17.07 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 125.44/17.07 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 125.44/17.07 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 125.44/17.07 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 125.44/17.07 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 125.44/17.07 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 125.44/17.07 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 125.44/17.07 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 125.44/17.07 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 125.44/17.07 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 125.44/17.07 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 125.44/17.07 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 125.44/17.07 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 125.44/17.07 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 125.44/17.07 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 125.44/17.07 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 125.44/17.07 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 125.44/17.07 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 125.44/17.07 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 125.44/17.07 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 125.44/17.07 | v0 = e0)) % 125.44/17.07 % 125.44/17.07 (ax2) % 125.44/17.07 op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 % 125.44/17.07 & op(unit, e0) = e0 & op(e4, unit) = e4 & op(e3, unit) = e3 & op(e2, unit) = % 125.44/17.07 e2 & op(e1, unit) = e1 & op(e0, unit) = e0 & $i(unit) & $i(e4) & $i(e3) & % 125.44/17.07 $i(e2) & $i(e1) & $i(e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | % 125.44/17.07 unit = e0) % 125.44/17.07 % 125.44/17.07 (ax3) % 125.80/17.11 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 125.80/17.11 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 125.80/17.11 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 125.80/17.11 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 125.80/17.11 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 125.80/17.11 [v23: $i] : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, % 125.80/17.12 e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) = % 125.80/17.12 e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) | % 125.80/17.12 (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12 = e4 & % 125.80/17.12 op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 = e3 & op(e4, % 125.80/17.12 e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) = % 125.80/17.12 e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) & % 125.80/17.12 ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 & % 125.80/17.12 op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & op(e0, e4) % 125.80/17.12 = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) | % 125.80/17.12 (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 & % 125.80/17.12 op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 & op(e3, % 125.80/17.12 e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) = % 125.80/17.12 e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) | % 125.80/17.12 (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 & % 125.80/17.12 op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & op(e4, % 125.80/17.12 e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) = % 125.80/17.12 e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) & % 125.80/17.12 ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 & % 125.80/17.12 op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 & op(e4, e0) % 125.80/17.12 = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) | % 125.80/17.12 (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 & % 125.80/17.12 op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & op(e3, % 125.80/17.12 e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) = % 125.80/17.12 e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) | % 125.80/17.12 (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 & % 125.80/17.12 op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 & op(e4, % 125.80/17.12 e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) = % 125.80/17.12 e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & % 125.80/17.12 ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 & % 125.80/17.12 op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) % 125.80/17.12 = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 125.80/17.12 (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 & % 125.80/17.12 op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 & op(e3, % 125.80/17.12 e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) = % 125.80/17.12 e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) | % 125.80/17.12 (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 & % 125.80/17.12 op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & op(e3, % 125.80/17.12 e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) = % 125.80/17.12 e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) & % 125.80/17.12 ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 & % 125.80/17.12 op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 & op(e3, e0) % 125.80/17.12 = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 125.80/17.12 (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 & % 125.80/17.12 op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & op(e3, % 125.80/17.12 e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) = % 125.80/17.12 e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) | % 125.80/17.12 (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 125.80/17.12 op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 & op(e4, % 125.80/17.12 e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) = % 125.80/17.12 e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & % 125.80/17.12 ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 & % 125.80/17.12 op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) % 125.80/17.12 = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) | % 125.80/17.12 (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 125.80/17.12 op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 & op(e2, % 125.80/17.12 e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) = % 125.80/17.12 e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) | % 125.80/17.12 (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 & % 125.80/17.12 op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & op(e2, % 125.80/17.12 e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) = % 125.80/17.12 e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) & % 125.80/17.12 ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 & % 125.80/17.12 op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 & op(e2, e0) % 125.80/17.12 = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) | % 125.80/17.12 (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 & % 125.80/17.12 op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & op(e3, % 125.80/17.12 e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4) % 125.80/17.12 | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3 % 125.80/17.12 & op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 & op(e1, % 125.80/17.12 e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) = % 125.80/17.12 e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9 % 125.80/17.12 = e2 & op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 & % 125.80/17.12 op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & op(e2, e1) % 125.80/17.12 = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & % 125.80/17.12 ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 & % 125.80/17.12 op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = % 125.80/17.12 e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) | % 125.80/17.12 (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 & % 125.80/17.12 op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & op(e1, % 125.80/17.12 e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3) % 125.80/17.12 | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2 % 125.80/17.12 & op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 & op(e1, % 125.80/17.12 e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) = % 125.80/17.12 e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9 % 125.80/17.12 = e1 & op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 & % 125.80/17.12 op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & op(e1, e2) % 125.80/17.12 = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) & % 125.80/17.12 ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 & % 125.80/17.12 op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) = % 125.80/17.12 e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6 % 125.80/17.12 = e3 & op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 125.80/17.12 op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & op(e3, e0) % 125.80/17.12 = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0 % 125.80/17.12 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 & % 125.80/17.12 op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) = % 125.80/17.12 e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3 % 125.80/17.12 = e4 & op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 & % 125.80/17.12 op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4) % 125.80/17.12 = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 125.80/17.12 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 & % 125.80/17.12 op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = % 125.80/17.12 e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4 % 125.80/17.12 = e1 & op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 125.80/17.12 op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = % 125.80/17.12 e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) | % 125.80/17.12 (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 & % 125.80/17.12 op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 & op(e0, % 125.80/17.12 e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = % 125.80/17.12 e0))))) % 125.80/17.12 % 125.80/17.12 (ax4) % 125.89/17.13 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 125.89/17.13 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 125.89/17.13 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 125.89/17.13 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 125.89/17.13 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 125.89/17.13 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 125.89/17.13 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 125.89/17.13 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 125.89/17.13 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 125.89/17.13 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 125.89/17.13 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 125.89/17.13 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 125.89/17.13 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 125.89/17.13 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 125.89/17.13 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 125.89/17.13 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 125.89/17.13 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 125.89/17.13 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 125.89/17.13 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 125.89/17.13 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 125.89/17.13 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 125.89/17.13 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 125.89/17.13 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 125.89/17.13 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 125.89/17.13 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 125.89/17.13 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 125.89/17.13 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 125.89/17.13 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 125.89/17.13 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 125.89/17.13 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 125.89/17.13 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 125.89/17.13 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 125.89/17.13 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 125.89/17.13 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 125.89/17.13 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 125.89/17.13 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 125.89/17.13 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 125.89/17.13 % 125.89/17.13 (ax5) % 125.89/17.13 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 125.89/17.13 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 125.89/17.13 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 125.89/17.13 % 125.89/17.13 (ax6) % 125.89/17.13 op(e4, e4) = e0 & op(e3, e4) = e1 & op(e2, e4) = e3 & op(e2, e2) = e4 & $i(e4) % 125.89/17.13 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 125.89/17.13 % 125.89/17.13 (co1) % 125.89/17.16 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 125.89/17.16 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 125.89/17.16 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 125.89/17.16 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 125.89/17.16 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 125.89/17.16 [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? % 125.89/17.16 [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 125.89/17.16 [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? % 125.89/17.16 [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? % 125.89/17.16 [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? % 125.89/17.16 [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? % 125.89/17.16 [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? % 125.89/17.16 [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? % 125.89/17.16 [v63: $i] : ? [v64: $i] : ? [v65: $i] : ? [v66: $i] : ? [v67: $i] : ? % 125.89/17.16 [v68: $i] : ? [v69: $i] : ? [v70: $i] : ? [v71: $i] : ? [v72: $i] : ? % 125.89/17.16 [v73: $i] : ? [v74: $i] : ? [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? % 125.89/17.16 [v78: $i] : ? [v79: $i] : ? [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? % 125.89/17.16 [v83: $i] : ? [v84: $i] : ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? % 125.89/17.16 [v88: $i] : ? [v89: $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? % 125.89/17.16 [v93: $i] : ? [v94: $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? % 125.89/17.16 [v98: $i] : ? [v99: $i] : (((v98 = e4 & ~ (v99 = e3) & ~ (v57 = v45) & % 125.89/17.16 op(v45, e4) = v99 & op(v45, e3) = e4 & op(e4, e3) = v45 & op(e3, e4) = % 125.89/17.16 v57 & $i(v99) & $i(v57) & $i(v45)) | (v96 = e4 & ~ (v97 = e2) & ~ (v54 % 125.89/17.16 = v33) & op(v33, e4) = v97 & op(v33, e2) = e4 & op(e4, e2) = v33 & % 125.89/17.16 op(e2, e4) = v54 & $i(v97) & $i(v54) & $i(v33)) | (v94 = e4 & ~ (v95 = % 125.89/17.16 e1) & ~ (v51 = v21) & op(v21, e4) = v95 & op(v21, e1) = e4 & op(e4, % 125.89/17.16 e1) = v21 & op(e1, e4) = v51 & $i(v95) & $i(v51) & $i(v21)) | (v92 = % 125.89/17.16 e4 & ~ (v93 = e0) & ~ (v48 = v9) & op(v9, e4) = v93 & op(v9, e0) = e4 % 125.89/17.16 & op(e4, e0) = v9 & op(e0, e4) = v48 & $i(v93) & $i(v48) & $i(v9)) | % 125.89/17.16 (v90 = e3 & ~ (v91 = e4) & ~ (v57 = v45) & op(v57, e4) = e3 & op(v57, % 125.89/17.16 e3) = v91 & op(e4, e3) = v45 & op(e3, e4) = v57 & $i(v91) & $i(v57) & % 125.89/17.16 $i(v45)) | (v88 = e3 & ~ (v89 = e2) & ~ (v42 = v30) & op(v30, e3) = % 125.89/17.16 v89 & op(v30, e2) = e3 & op(e3, e2) = v30 & op(e2, e3) = v42 & $i(v89) & % 125.89/17.16 $i(v42) & $i(v30)) | (v86 = e3 & ~ (v87 = e1) & ~ (v39 = v18) & % 125.89/17.16 op(v18, e3) = v87 & op(v18, e1) = e3 & op(e3, e1) = v18 & op(e1, e3) = % 125.89/17.16 v39 & $i(v87) & $i(v39) & $i(v18)) | (v84 = e3 & ~ (v85 = e0) & ~ (v36 % 125.89/17.16 = v6) & op(v6, e3) = v85 & op(v6, e0) = e3 & op(e3, e0) = v6 & op(e0, % 125.89/17.16 e3) = v36 & $i(v85) & $i(v36) & $i(v6)) | (v82 = e2 & ~ (v83 = e4) & % 125.89/17.16 ~ (v54 = v33) & op(v54, e4) = e2 & op(v54, e2) = v83 & op(e4, e2) = v33 % 125.89/17.16 & op(e2, e4) = v54 & $i(v83) & $i(v54) & $i(v33)) | (v80 = e2 & ~ (v81 % 125.89/17.16 = e3) & ~ (v42 = v30) & op(v42, e3) = e2 & op(v42, e2) = v81 & op(e3, % 125.89/17.16 e2) = v30 & op(e2, e3) = v42 & $i(v81) & $i(v42) & $i(v30)) | (v78 = % 125.89/17.16 e2 & ~ (v79 = e1) & ~ (v27 = v15) & op(v15, e2) = v79 & op(v15, e1) = % 125.89/17.16 e2 & op(e2, e1) = v15 & op(e1, e2) = v27 & $i(v79) & $i(v27) & $i(v15)) % 125.89/17.16 | (v76 = e2 & ~ (v77 = e0) & ~ (v24 = v3) & op(v3, e2) = v77 & op(v3, % 125.89/17.16 e0) = e2 & op(e2, e0) = v3 & op(e0, e2) = v24 & $i(v77) & $i(v24) & % 125.89/17.16 $i(v3)) | (v74 = e1 & ~ (v75 = e4) & ~ (v51 = v21) & op(v51, e4) = e1 % 125.89/17.16 & op(v51, e1) = v75 & op(e4, e1) = v21 & op(e1, e4) = v51 & $i(v75) & % 125.89/17.16 $i(v51) & $i(v21)) | (v72 = e1 & ~ (v73 = e3) & ~ (v39 = v18) & % 125.89/17.16 op(v39, e3) = e1 & op(v39, e1) = v73 & op(e3, e1) = v18 & op(e1, e3) = % 125.89/17.16 v39 & $i(v73) & $i(v39) & $i(v18)) | (v70 = e1 & ~ (v71 = e2) & ~ (v27 % 125.89/17.16 = v15) & op(v27, e2) = e1 & op(v27, e1) = v71 & op(e2, e1) = v15 & % 125.89/17.16 op(e1, e2) = v27 & $i(v71) & $i(v27) & $i(v15)) | (v68 = e1 & ~ (v69 = % 125.89/17.16 e0) & ~ (v12 = v0) & op(v0, e1) = v69 & op(v0, e0) = e1 & op(e1, e0) % 125.89/17.16 = v0 & op(e0, e1) = v12 & $i(v69) & $i(v12) & $i(v0)) | (v66 = e0 & ~ % 125.89/17.16 (v67 = e4) & ~ (v48 = v9) & op(v48, e4) = e0 & op(v48, e0) = v67 & % 125.89/17.16 op(e4, e0) = v9 & op(e0, e4) = v48 & $i(v67) & $i(v48) & $i(v9)) | (v64 % 125.89/17.16 = e0 & ~ (v65 = e3) & ~ (v36 = v6) & op(v36, e3) = e0 & op(v36, e0) = % 125.89/17.16 v65 & op(e3, e0) = v6 & op(e0, e3) = v36 & $i(v65) & $i(v36) & $i(v6)) | % 125.89/17.16 (v62 = e0 & ~ (v63 = e2) & ~ (v24 = v3) & op(v24, e2) = e0 & op(v24, e0) % 125.89/17.16 = v63 & op(e2, e0) = v3 & op(e0, e2) = v24 & $i(v63) & $i(v24) & $i(v3)) % 125.89/17.16 | (v60 = e0 & ~ (v61 = e1) & ~ (v12 = v0) & op(v12, e1) = e0 & op(v12, % 125.89/17.16 e0) = v61 & op(e1, e0) = v0 & op(e0, e1) = v12 & $i(v61) & $i(v12) & % 125.89/17.16 $i(v0))) & ((v59 = e3 & ~ (v58 = e4) & op(e4, v57) = e3 & op(e3, v57) = % 125.89/17.16 v58 & op(e3, e4) = v57 & $i(v58) & $i(v57)) | (v56 = e2 & ~ (v55 = e4) % 125.89/17.16 & op(e4, v54) = e2 & op(e2, v54) = v55 & op(e2, e4) = v54 & $i(v55) & % 125.89/17.16 $i(v54)) | (v53 = e1 & ~ (v52 = e4) & op(e4, v51) = e1 & op(e1, v51) = % 125.89/17.16 v52 & op(e1, e4) = v51 & $i(v52) & $i(v51)) | (v50 = e0 & ~ (v49 = e4) % 125.89/17.16 & op(e4, v48) = e0 & op(e0, v48) = v49 & op(e0, e4) = v48 & $i(v49) & % 125.89/17.16 $i(v48))) & ((v47 = e4 & ~ (v46 = e3) & op(e4, v45) = v46 & op(e4, e3) % 125.89/17.16 = v45 & op(e3, v45) = e4 & $i(v46) & $i(v45)) | (v44 = e2 & ~ (v43 = % 125.89/17.16 e3) & op(e3, v42) = e2 & op(e2, v42) = v43 & op(e2, e3) = v42 & % 125.89/17.16 $i(v43) & $i(v42)) | (v41 = e1 & ~ (v40 = e3) & op(e3, v39) = e1 & % 125.89/17.16 op(e1, v39) = v40 & op(e1, e3) = v39 & $i(v40) & $i(v39)) | (v38 = e0 & % 125.89/17.16 ~ (v37 = e3) & op(e3, v36) = e0 & op(e0, v36) = v37 & op(e0, e3) = v36 & % 125.89/17.16 $i(v37) & $i(v36))) & ((v35 = e4 & ~ (v34 = e2) & op(e4, v33) = v34 & % 125.89/17.16 op(e4, e2) = v33 & op(e2, v33) = e4 & $i(v34) & $i(v33)) | (v32 = e3 & % 125.89/17.16 ~ (v31 = e2) & op(e3, v30) = v31 & op(e3, e2) = v30 & op(e2, v30) = e3 & % 125.89/17.16 $i(v31) & $i(v30)) | (v29 = e1 & ~ (v28 = e2) & op(e2, v27) = e1 & % 125.89/17.16 op(e1, v27) = v28 & op(e1, e2) = v27 & $i(v28) & $i(v27)) | (v26 = e0 & % 125.89/17.16 ~ (v25 = e2) & op(e2, v24) = e0 & op(e0, v24) = v25 & op(e0, e2) = v24 & % 125.89/17.16 $i(v25) & $i(v24))) & ((v23 = e4 & ~ (v22 = e1) & op(e4, v21) = v22 & % 125.89/17.16 op(e4, e1) = v21 & op(e1, v21) = e4 & $i(v22) & $i(v21)) | (v20 = e3 & % 125.89/17.16 ~ (v19 = e1) & op(e3, v18) = v19 & op(e3, e1) = v18 & op(e1, v18) = e3 & % 125.89/17.16 $i(v19) & $i(v18)) | (v17 = e2 & ~ (v16 = e1) & op(e2, v15) = v16 & % 125.89/17.16 op(e2, e1) = v15 & op(e1, v15) = e2 & $i(v16) & $i(v15)) | (v14 = e0 & % 125.89/17.16 ~ (v13 = e1) & op(e1, v12) = e0 & op(e0, v12) = v13 & op(e0, e1) = v12 & % 125.89/17.16 $i(v13) & $i(v12))) & ((v11 = e4 & ~ (v10 = e0) & op(e4, v9) = v10 & % 125.89/17.16 op(e4, e0) = v9 & op(e0, v9) = e4 & $i(v10) & $i(v9)) | (v8 = e3 & ~ % 125.89/17.16 (v7 = e0) & op(e3, v6) = v7 & op(e3, e0) = v6 & op(e0, v6) = e3 & $i(v7) % 125.89/17.16 & $i(v6)) | (v5 = e2 & ~ (v4 = e0) & op(e2, v3) = v4 & op(e2, e0) = v3 % 125.89/17.16 & op(e0, v3) = e2 & $i(v4) & $i(v3)) | (v2 = e1 & ~ (v1 = e0) & op(e1, % 125.89/17.16 v0) = v1 & op(e1, e0) = v0 & op(e0, v0) = e1 & $i(v1) & $i(v0)))) % 125.89/17.16 % 125.89/17.16 (function-axioms) % 125.89/17.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 125.89/17.16 v2) = v1) | ~ (op(v3, v2) = v0)) % 125.89/17.16 % 125.89/17.16 Those formulas are unsatisfiable: % 125.89/17.16 --------------------------------- % 125.89/17.16 % 125.89/17.16 Begin of proof % 125.89/17.16 | % 125.89/17.16 | ALPHA: (ax1) implies: % 125.89/17.17 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 125.89/17.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 125.89/17.17 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 125.89/17.17 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 125.89/17.17 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 125.89/17.17 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 125.89/17.17 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 125.89/17.17 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 125.89/17.17 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 125.89/17.17 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 125.89/17.17 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 125.89/17.17 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 125.89/17.17 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 125.89/17.17 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 125.89/17.17 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 125.89/17.17 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 125.89/17.17 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 125.89/17.17 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 125.89/17.17 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 125.89/17.17 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 125.89/17.17 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 125.89/17.17 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 125.89/17.17 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 125.89/17.17 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 125.89/17.17 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 125.89/17.17 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 125.89/17.17 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 125.89/17.17 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 125.89/17.17 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 125.89/17.17 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 125.89/17.17 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 125.89/17.17 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 125.89/17.17 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 125.89/17.17 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 125.89/17.17 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 125.89/17.17 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 125.89/17.17 | % 125.89/17.17 | ALPHA: (ax2) implies: % 125.89/17.17 | (2) op(e0, unit) = e0 % 125.89/17.17 | (3) op(e1, unit) = e1 % 125.89/17.17 | (4) op(e2, unit) = e2 % 125.89/17.17 | (5) op(e3, unit) = e3 % 125.89/17.17 | (6) op(e4, unit) = e4 % 125.89/17.18 | (7) op(unit, e0) = e0 % 125.89/17.18 | (8) op(unit, e1) = e1 % 125.89/17.18 | (9) op(unit, e2) = e2 % 125.89/17.18 | (10) op(unit, e3) = e3 % 125.89/17.18 | (11) op(unit, e4) = e4 % 125.89/17.18 | (12) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 125.89/17.18 | % 125.89/17.18 | ALPHA: (ax3) implies: % 125.89/17.20 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 125.89/17.20 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 125.89/17.20 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 125.89/17.20 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 125.89/17.20 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 125.89/17.20 | : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, % 125.89/17.20 | e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, % 125.89/17.20 | e1) = e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, % 125.89/17.20 | e4) = e4) | (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, % 125.89/17.20 | e4) = e4) | (v12 = e4 & op(e1, e4) = e4) | (v4 = e4 & op(e0, % 125.89/17.20 | e4) = e4)) & ((v24 = e3 & op(e4, e4) = e3) | (v23 = e3 & % 125.89/17.20 | op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) = e3) | (v15 = e3 & % 125.89/17.20 | op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) & ((v24 = e3 & % 125.89/17.20 | op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 & % 125.89/17.20 | op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & % 125.89/17.20 | op(e0, e4) = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & % 125.89/17.20 | op(e4, e3) = e2) | (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & % 125.89/17.20 | op(e4, e1) = e2) | (v8 = e2 & op(e4, e0) = e2)) & ((v24 = e2 & % 125.89/17.20 | op(e4, e4) = e2) | (v22 = e2 & op(e3, e4) = e2) | (v18 = e2 & % 125.89/17.20 | op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) = e2) | (v4 = e2 & % 125.89/17.20 | op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) | (v23 = e1 & % 125.89/17.20 | op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 & % 125.89/17.20 | op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & % 125.89/17.20 | op(e4, e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & % 125.89/17.20 | op(e2, e4) = e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & % 125.89/17.20 | op(e0, e4) = e1)) & ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & % 125.89/17.20 | op(e4, e3) = e0) | (v20 = e0 & op(e4, e2) = e0) | (v15 = e0 & % 125.89/17.20 | op(e4, e1) = e0) | (v8 = e0 & op(e4, e0) = e0)) & ((v24 = e0 & % 125.89/17.20 | op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) | (v18 = e0 & % 125.89/17.20 | op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 & % 125.89/17.20 | op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & % 125.89/17.20 | op(e3, e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & % 125.89/17.20 | op(e1, e3) = e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & % 125.89/17.20 | op(e4, e3) = e3) | (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & % 125.89/17.20 | op(e2, e3) = e3) | (v11 = e3 & op(e1, e3) = e3) | (v3 = e3 & % 125.89/17.20 | op(e0, e3) = e3)) & ((v23 = e2 & op(e4, e3) = e2) | (v21 = e2 & % 125.89/17.20 | op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v11 = e2 & % 125.89/17.20 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v23 = e1 & % 125.89/17.20 | op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 & % 125.89/17.20 | op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & % 125.89/17.20 | op(e0, e3) = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & % 125.89/17.20 | op(e3, e3) = e0) | (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & % 125.89/17.20 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v22 = e4 & % 125.89/17.20 | op(e3, e4) = e4) | (v21 = e4 & op(e3, e3) = e4) | (v19 = e4 & % 125.89/17.20 | op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) = e4) | (v7 = e4 & % 125.89/17.20 | op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) | (v21 = e3 & % 125.89/17.20 | op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 & % 125.89/17.20 | op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & % 125.89/17.20 | op(e3, e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & % 125.89/17.20 | op(e3, e2) = e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & % 125.89/17.20 | op(e3, e0) = e2)) & ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & % 125.89/17.20 | op(e3, e3) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v14 = e1 & % 125.89/17.20 | op(e3, e1) = e1) | (v7 = e1 & op(e3, e0) = e1)) & ((v22 = e0 & % 125.89/17.20 | op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) | (v19 = e0 & % 125.89/17.20 | op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 & % 125.89/17.20 | op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & % 125.89/17.20 | op(e3, e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & % 125.89/17.20 | op(e1, e2) = e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & % 125.89/17.20 | op(e4, e2) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & % 125.89/17.20 | op(e2, e2) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v2 = e3 & % 125.89/17.20 | op(e0, e2) = e3)) & ((v20 = e2 & op(e4, e2) = e2) | (v19 = e2 & % 125.89/17.20 | op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) = e2) | (v10 = e2 & % 125.89/17.20 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v20 = e1 & % 125.89/17.20 | op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 & % 125.89/17.20 | op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & % 125.89/17.20 | op(e0, e2) = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & % 125.89/17.20 | op(e3, e2) = e0) | (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & % 125.89/17.20 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v18 = e4 & % 125.89/17.20 | op(e2, e4) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v16 = e4 & % 125.89/17.20 | op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v6 = e4 & % 125.89/17.20 | op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) | (v17 = e3 & % 125.89/17.20 | op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 & % 125.89/17.20 | op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & % 125.89/17.20 | op(e2, e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & % 125.89/17.20 | op(e2, e2) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & % 125.89/17.20 | op(e2, e0) = e2)) & ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & % 125.89/17.20 | op(e2, e3) = e1) | (v16 = e1 & op(e2, e2) = e1) | (v13 = e1 & % 125.89/17.20 | op(e2, e1) = e1) | (v6 = e1 & op(e2, e0) = e1)) & ((v18 = e0 & % 125.89/17.20 | op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) | (v16 = e0 & % 125.89/17.20 | op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 & % 125.89/17.20 | op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & % 125.89/17.20 | op(e3, e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & % 125.89/17.20 | op(e1, e1) = e4) | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & % 125.89/17.20 | op(e4, e1) = e3) | (v14 = e3 & op(e3, e1) = e3) | (v13 = e3 & % 125.89/17.20 | op(e2, e1) = e3) | (v9 = e3 & op(e1, e1) = e3) | (v1 = e3 & % 125.89/17.20 | op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) = e2) | (v14 = e2 & % 125.89/17.20 | op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9 = e2 & % 125.89/17.20 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 & % 125.89/17.20 | op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & % 125.89/17.20 | op(e2, e1) = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & % 125.89/17.20 | op(e0, e1) = e1)) & ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & % 125.89/17.20 | op(e3, e1) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v9 = e0 & % 125.89/17.20 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v12 = e4 & % 125.89/17.20 | op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) | (v10 = e4 & % 125.89/17.20 | op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 & % 125.89/17.20 | op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & % 125.89/17.20 | op(e1, e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & % 125.89/17.20 | op(e1, e1) = e3) | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & % 125.89/17.20 | op(e1, e4) = e2) | (v11 = e2 & op(e1, e3) = e2) | (v10 = e2 & % 125.89/17.20 | op(e1, e2) = e2) | (v9 = e2 & op(e1, e1) = e2) | (v5 = e2 & % 125.89/17.20 | op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) = e1) | (v11 = e1 & % 125.89/17.20 | op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9 = e1 & % 125.89/17.20 | op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 & % 125.89/17.20 | op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & % 125.89/17.20 | op(e1, e2) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & % 125.89/17.20 | op(e1, e0) = e0)) & ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & % 125.89/17.20 | op(e3, e0) = e4) | (v6 = e4 & op(e2, e0) = e4) | (v5 = e4 & % 125.89/17.20 | op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v8 = e3 & % 125.89/17.20 | op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6 = e3 & % 125.89/17.20 | op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 125.89/17.20 | op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & % 125.89/17.20 | op(e3, e0) = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & % 125.89/17.20 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & % 125.89/17.20 | op(e4, e0) = e1) | (v7 = e1 & op(e3, e0) = e1) | (v6 = e1 & % 125.89/17.20 | op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) = e1) | (v0 = e1 & % 125.89/17.20 | op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3 = e4 & % 125.89/17.20 | op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 & % 125.89/17.20 | op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & % 125.89/17.20 | op(e0, e4) = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & % 125.89/17.20 | op(e0, e2) = e3) | (v1 = e3 & op(e0, e1) = e3) | (v0 = e3 & % 125.89/17.20 | op(e0, e0) = e3)) & ((v4 = e2 & op(e0, e4) = e2) | (v3 = e2 & % 125.89/17.20 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & % 125.89/17.20 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4 = e1 & % 125.89/17.20 | op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 125.89/17.20 | op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 125.89/17.20 | op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & % 125.89/17.20 | op(e4, e0) = e0) | (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & % 125.89/17.20 | op(e2, e0) = e0) | (v5 = e0 & op(e1, e0) = e0)) & ((v4 = e0 % 125.89/17.20 | & op(e0, e4) = e0) | (v3 = e0 & op(e0, e3) = e0) | (v2 = e0 % 125.89/17.20 | & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = e0))))) % 125.89/17.20 | % 125.89/17.20 | ALPHA: (ax4) implies: % 125.89/17.21 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 125.89/17.21 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 125.89/17.21 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 125.89/17.21 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 125.89/17.21 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 125.89/17.21 | : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 125.89/17.21 | ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ % 125.89/17.21 | (v24 = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ % 125.89/17.21 | (v23 = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ % 125.89/17.21 | (v22 = v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ % 125.89/17.21 | (v22 = v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ % 125.89/17.21 | (v21 = v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ % 125.89/17.21 | (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ % 125.89/17.21 | (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ % 125.89/17.21 | (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ % 125.89/17.21 | (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ % 125.89/17.21 | (v17 = v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ % 125.89/17.21 | (v17 = v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ % 125.89/17.21 | (v16 = v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ % 125.89/17.21 | (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ % 125.89/17.21 | (v14 = v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ % 125.89/17.21 | (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ % 125.89/17.21 | (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ % 125.89/17.21 | (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 % 125.89/17.21 | = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) % 125.89/17.21 | & ~ (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 % 125.89/17.21 | = v6) & ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) % 125.89/17.21 | & ~ (v5 = v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 % 125.89/17.21 | = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) % 125.89/17.21 | & ~ (v2 = v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 % 125.89/17.21 | & op(e4, e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) % 125.89/17.21 | = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & % 125.89/17.21 | op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = % 125.89/17.21 | v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, % 125.89/17.21 | e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 125.89/17.21 | op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) % 125.89/17.21 | = v5 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 125.89/17.21 | $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) % 125.89/17.21 | & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 125.89/17.21 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 125.89/17.21 | % 125.89/17.21 | ALPHA: (ax5) implies: % 125.89/17.21 | (15) ~ (e2 = e0) % 125.89/17.21 | (16) ~ (e2 = e1) % 125.89/17.21 | (17) ~ (e3 = e2) % 125.89/17.21 | (18) ~ (e4 = e0) % 125.89/17.21 | (19) ~ (e4 = e1) % 125.89/17.21 | (20) ~ (e4 = e2) % 125.89/17.21 | % 125.89/17.21 | ALPHA: (ax6) implies: % 125.89/17.21 | (21) op(e2, e2) = e4 % 125.89/17.21 | (22) op(e2, e4) = e3 % 125.89/17.21 | (23) op(e3, e4) = e1 % 125.89/17.21 | (24) op(e4, e4) = e0 % 125.89/17.21 | % 125.89/17.21 | ALPHA: (co1) implies: % 126.35/17.23 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 126.35/17.23 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 126.35/17.23 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 126.35/17.23 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 126.35/17.23 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 126.35/17.23 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 126.35/17.23 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 126.35/17.23 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] % 126.35/17.23 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: % 126.35/17.23 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? % 126.35/17.23 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] % 126.35/17.23 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: % 126.35/17.23 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? % 126.35/17.23 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] % 126.35/17.23 | : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: % 126.35/17.23 | $i] : ? [v71: $i] : ? [v72: $i] : ? [v73: $i] : ? [v74: $i] : ? % 126.35/17.23 | [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: $i] : ? [v79: $i] % 126.35/17.23 | : ? [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? [v83: $i] : ? [v84: % 126.35/17.23 | $i] : ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? [v88: $i] : ? % 126.35/17.23 | [v89: $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? [v93: $i] % 126.35/17.23 | : ? [v94: $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? [v98: % 126.35/17.23 | $i] : ? [v99: $i] : (((v98 = e4 & ~ (v99 = e3) & ~ (v57 = v45) & % 126.35/17.23 | op(v45, e4) = v99 & op(v45, e3) = e4 & op(e4, e3) = v45 & op(e3, % 126.35/17.23 | e4) = v57 & $i(v99) & $i(v57) & $i(v45)) | (v96 = e4 & ~ (v97 % 126.35/17.23 | = e2) & ~ (v54 = v33) & op(v33, e4) = v97 & op(v33, e2) = e4 % 126.35/17.23 | & op(e4, e2) = v33 & op(e2, e4) = v54 & $i(v97) & $i(v54) & % 126.35/17.23 | $i(v33)) | (v94 = e4 & ~ (v95 = e1) & ~ (v51 = v21) & op(v21, % 126.35/17.23 | e4) = v95 & op(v21, e1) = e4 & op(e4, e1) = v21 & op(e1, e4) = % 126.35/17.23 | v51 & $i(v95) & $i(v51) & $i(v21)) | (v92 = e4 & ~ (v93 = e0) & % 126.35/17.23 | ~ (v48 = v9) & op(v9, e4) = v93 & op(v9, e0) = e4 & op(e4, e0) % 126.35/17.23 | = v9 & op(e0, e4) = v48 & $i(v93) & $i(v48) & $i(v9)) | (v90 = % 126.35/17.23 | e3 & ~ (v91 = e4) & ~ (v57 = v45) & op(v57, e4) = e3 & op(v57, % 126.35/17.23 | e3) = v91 & op(e4, e3) = v45 & op(e3, e4) = v57 & $i(v91) & % 126.35/17.23 | $i(v57) & $i(v45)) | (v88 = e3 & ~ (v89 = e2) & ~ (v42 = v30) % 126.35/17.23 | & op(v30, e3) = v89 & op(v30, e2) = e3 & op(e3, e2) = v30 & % 126.35/17.23 | op(e2, e3) = v42 & $i(v89) & $i(v42) & $i(v30)) | (v86 = e3 & ~ % 126.35/17.23 | (v87 = e1) & ~ (v39 = v18) & op(v18, e3) = v87 & op(v18, e1) = % 126.35/17.23 | e3 & op(e3, e1) = v18 & op(e1, e3) = v39 & $i(v87) & $i(v39) & % 126.35/17.23 | $i(v18)) | (v84 = e3 & ~ (v85 = e0) & ~ (v36 = v6) & op(v6, % 126.35/17.23 | e3) = v85 & op(v6, e0) = e3 & op(e3, e0) = v6 & op(e0, e3) = % 126.35/17.23 | v36 & $i(v85) & $i(v36) & $i(v6)) | (v82 = e2 & ~ (v83 = e4) & % 126.35/17.23 | ~ (v54 = v33) & op(v54, e4) = e2 & op(v54, e2) = v83 & op(e4, % 126.35/17.23 | e2) = v33 & op(e2, e4) = v54 & $i(v83) & $i(v54) & $i(v33)) | % 126.35/17.23 | (v80 = e2 & ~ (v81 = e3) & ~ (v42 = v30) & op(v42, e3) = e2 & % 126.35/17.23 | op(v42, e2) = v81 & op(e3, e2) = v30 & op(e2, e3) = v42 & % 126.35/17.23 | $i(v81) & $i(v42) & $i(v30)) | (v78 = e2 & ~ (v79 = e1) & ~ % 126.35/17.23 | (v27 = v15) & op(v15, e2) = v79 & op(v15, e1) = e2 & op(e2, e1) % 126.35/17.23 | = v15 & op(e1, e2) = v27 & $i(v79) & $i(v27) & $i(v15)) | (v76 = % 126.35/17.23 | e2 & ~ (v77 = e0) & ~ (v24 = v3) & op(v3, e2) = v77 & op(v3, % 126.35/17.23 | e0) = e2 & op(e2, e0) = v3 & op(e0, e2) = v24 & $i(v77) & % 126.35/17.23 | $i(v24) & $i(v3)) | (v74 = e1 & ~ (v75 = e4) & ~ (v51 = v21) & % 126.35/17.23 | op(v51, e4) = e1 & op(v51, e1) = v75 & op(e4, e1) = v21 & op(e1, % 126.35/17.23 | e4) = v51 & $i(v75) & $i(v51) & $i(v21)) | (v72 = e1 & ~ (v73 % 126.35/17.23 | = e3) & ~ (v39 = v18) & op(v39, e3) = e1 & op(v39, e1) = v73 % 126.35/17.23 | & op(e3, e1) = v18 & op(e1, e3) = v39 & $i(v73) & $i(v39) & % 126.35/17.23 | $i(v18)) | (v70 = e1 & ~ (v71 = e2) & ~ (v27 = v15) & op(v27, % 126.35/17.23 | e2) = e1 & op(v27, e1) = v71 & op(e2, e1) = v15 & op(e1, e2) = % 126.35/17.23 | v27 & $i(v71) & $i(v27) & $i(v15)) | (v68 = e1 & ~ (v69 = e0) & % 126.35/17.23 | ~ (v12 = v0) & op(v0, e1) = v69 & op(v0, e0) = e1 & op(e1, e0) % 126.35/17.23 | = v0 & op(e0, e1) = v12 & $i(v69) & $i(v12) & $i(v0)) | (v66 = % 126.35/17.23 | e0 & ~ (v67 = e4) & ~ (v48 = v9) & op(v48, e4) = e0 & op(v48, % 126.35/17.23 | e0) = v67 & op(e4, e0) = v9 & op(e0, e4) = v48 & $i(v67) & % 126.35/17.23 | $i(v48) & $i(v9)) | (v64 = e0 & ~ (v65 = e3) & ~ (v36 = v6) & % 126.35/17.23 | op(v36, e3) = e0 & op(v36, e0) = v65 & op(e3, e0) = v6 & op(e0, % 126.35/17.23 | e3) = v36 & $i(v65) & $i(v36) & $i(v6)) | (v62 = e0 & ~ (v63 % 126.35/17.23 | = e2) & ~ (v24 = v3) & op(v24, e2) = e0 & op(v24, e0) = v63 & % 126.35/17.23 | op(e2, e0) = v3 & op(e0, e2) = v24 & $i(v63) & $i(v24) & $i(v3)) % 126.35/17.23 | | (v60 = e0 & ~ (v61 = e1) & ~ (v12 = v0) & op(v12, e1) = e0 & % 126.35/17.23 | op(v12, e0) = v61 & op(e1, e0) = v0 & op(e0, e1) = v12 & $i(v61) % 126.35/17.23 | & $i(v12) & $i(v0))) & ((v59 = e3 & ~ (v58 = e4) & op(e4, v57) % 126.35/17.23 | = e3 & op(e3, v57) = v58 & op(e3, e4) = v57 & $i(v58) & $i(v57)) % 126.35/17.23 | | (v56 = e2 & ~ (v55 = e4) & op(e4, v54) = e2 & op(e2, v54) = v55 % 126.35/17.23 | & op(e2, e4) = v54 & $i(v55) & $i(v54)) | (v53 = e1 & ~ (v52 = % 126.35/17.23 | e4) & op(e4, v51) = e1 & op(e1, v51) = v52 & op(e1, e4) = v51 % 126.35/17.23 | & $i(v52) & $i(v51)) | (v50 = e0 & ~ (v49 = e4) & op(e4, v48) = % 126.35/17.23 | e0 & op(e0, v48) = v49 & op(e0, e4) = v48 & $i(v49) & $i(v48))) % 126.35/17.23 | & ((v47 = e4 & ~ (v46 = e3) & op(e4, v45) = v46 & op(e4, e3) = v45 % 126.35/17.23 | & op(e3, v45) = e4 & $i(v46) & $i(v45)) | (v44 = e2 & ~ (v43 = % 126.35/17.23 | e3) & op(e3, v42) = e2 & op(e2, v42) = v43 & op(e2, e3) = v42 % 126.35/17.23 | & $i(v43) & $i(v42)) | (v41 = e1 & ~ (v40 = e3) & op(e3, v39) = % 126.35/17.23 | e1 & op(e1, v39) = v40 & op(e1, e3) = v39 & $i(v40) & $i(v39)) | % 126.35/17.23 | (v38 = e0 & ~ (v37 = e3) & op(e3, v36) = e0 & op(e0, v36) = v37 & % 126.35/17.23 | op(e0, e3) = v36 & $i(v37) & $i(v36))) & ((v35 = e4 & ~ (v34 = % 126.35/17.23 | e2) & op(e4, v33) = v34 & op(e4, e2) = v33 & op(e2, v33) = e4 % 126.35/17.23 | & $i(v34) & $i(v33)) | (v32 = e3 & ~ (v31 = e2) & op(e3, v30) = % 126.35/17.23 | v31 & op(e3, e2) = v30 & op(e2, v30) = e3 & $i(v31) & $i(v30)) | % 126.35/17.23 | (v29 = e1 & ~ (v28 = e2) & op(e2, v27) = e1 & op(e1, v27) = v28 & % 126.35/17.23 | op(e1, e2) = v27 & $i(v28) & $i(v27)) | (v26 = e0 & ~ (v25 = % 126.35/17.23 | e2) & op(e2, v24) = e0 & op(e0, v24) = v25 & op(e0, e2) = v24 % 126.35/17.23 | & $i(v25) & $i(v24))) & ((v23 = e4 & ~ (v22 = e1) & op(e4, v21) % 126.35/17.23 | = v22 & op(e4, e1) = v21 & op(e1, v21) = e4 & $i(v22) & $i(v21)) % 126.35/17.23 | | (v20 = e3 & ~ (v19 = e1) & op(e3, v18) = v19 & op(e3, e1) = v18 % 126.35/17.23 | & op(e1, v18) = e3 & $i(v19) & $i(v18)) | (v17 = e2 & ~ (v16 = % 126.35/17.23 | e1) & op(e2, v15) = v16 & op(e2, e1) = v15 & op(e1, v15) = e2 % 126.35/17.23 | & $i(v16) & $i(v15)) | (v14 = e0 & ~ (v13 = e1) & op(e1, v12) = % 126.35/17.23 | e0 & op(e0, v12) = v13 & op(e0, e1) = v12 & $i(v13) & $i(v12))) % 126.35/17.23 | & ((v11 = e4 & ~ (v10 = e0) & op(e4, v9) = v10 & op(e4, e0) = v9 & % 126.35/17.23 | op(e0, v9) = e4 & $i(v10) & $i(v9)) | (v8 = e3 & ~ (v7 = e0) & % 126.35/17.23 | op(e3, v6) = v7 & op(e3, e0) = v6 & op(e0, v6) = e3 & $i(v7) & % 126.35/17.23 | $i(v6)) | (v5 = e2 & ~ (v4 = e0) & op(e2, v3) = v4 & op(e2, e0) % 126.35/17.23 | = v3 & op(e0, v3) = e2 & $i(v4) & $i(v3)) | (v2 = e1 & ~ (v1 = % 126.35/17.23 | e0) & op(e1, v0) = v1 & op(e1, e0) = v0 & op(e0, v0) = e1 & % 126.35/17.23 | $i(v1) & $i(v0)))) % 126.35/17.23 | % 126.35/17.23 | DELTA: instantiating (14) with fresh symbols all_4_0, all_4_1, all_4_2, % 126.35/17.23 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 126.35/17.23 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 126.35/17.23 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 126.35/17.23 | all_4_24 gives: % 126.35/17.23 | (26) ~ (all_4_0 = all_4_1) & ~ (all_4_0 = all_4_2) & ~ (all_4_0 = % 126.35/17.23 | all_4_3) & ~ (all_4_0 = all_4_4) & ~ (all_4_0 = all_4_5) & ~ % 126.35/17.23 | (all_4_0 = all_4_10) & ~ (all_4_0 = all_4_15) & ~ (all_4_0 = % 126.35/17.23 | all_4_20) & ~ (all_4_1 = all_4_2) & ~ (all_4_1 = all_4_3) & ~ % 126.35/17.23 | (all_4_1 = all_4_4) & ~ (all_4_1 = all_4_6) & ~ (all_4_1 = all_4_11) % 126.35/17.23 | & ~ (all_4_1 = all_4_16) & ~ (all_4_1 = all_4_21) & ~ (all_4_2 = % 126.35/17.23 | all_4_3) & ~ (all_4_2 = all_4_4) & ~ (all_4_2 = all_4_7) & ~ % 126.35/17.23 | (all_4_2 = all_4_12) & ~ (all_4_2 = all_4_17) & ~ (all_4_2 = % 126.35/17.23 | all_4_22) & ~ (all_4_3 = all_4_4) & ~ (all_4_3 = all_4_8) & ~ % 126.35/17.23 | (all_4_3 = all_4_13) & ~ (all_4_3 = all_4_18) & ~ (all_4_3 = % 126.35/17.23 | all_4_23) & ~ (all_4_4 = all_4_9) & ~ (all_4_4 = all_4_14) & ~ % 126.35/17.23 | (all_4_4 = all_4_19) & ~ (all_4_4 = all_4_24) & ~ (all_4_5 = % 126.35/17.23 | all_4_6) & ~ (all_4_5 = all_4_7) & ~ (all_4_5 = all_4_8) & ~ % 126.35/17.23 | (all_4_5 = all_4_9) & ~ (all_4_5 = all_4_10) & ~ (all_4_5 = % 126.35/17.23 | all_4_15) & ~ (all_4_5 = all_4_20) & ~ (all_4_6 = all_4_7) & ~ % 126.35/17.23 | (all_4_6 = all_4_8) & ~ (all_4_6 = all_4_9) & ~ (all_4_6 = all_4_11) % 126.35/17.23 | & ~ (all_4_6 = all_4_16) & ~ (all_4_6 = all_4_21) & ~ (all_4_7 = % 126.35/17.23 | all_4_8) & ~ (all_4_7 = all_4_9) & ~ (all_4_7 = all_4_12) & ~ % 126.35/17.23 | (all_4_7 = all_4_17) & ~ (all_4_7 = all_4_22) & ~ (all_4_8 = % 126.35/17.23 | all_4_9) & ~ (all_4_8 = all_4_13) & ~ (all_4_8 = all_4_18) & ~ % 126.35/17.23 | (all_4_8 = all_4_23) & ~ (all_4_9 = all_4_14) & ~ (all_4_9 = % 126.35/17.23 | all_4_19) & ~ (all_4_9 = all_4_24) & ~ (all_4_10 = all_4_11) & ~ % 126.35/17.23 | (all_4_10 = all_4_12) & ~ (all_4_10 = all_4_13) & ~ (all_4_10 = % 126.35/17.23 | all_4_14) & ~ (all_4_10 = all_4_15) & ~ (all_4_10 = all_4_20) & ~ % 126.35/17.23 | (all_4_11 = all_4_12) & ~ (all_4_11 = all_4_13) & ~ (all_4_11 = % 126.35/17.23 | all_4_14) & ~ (all_4_11 = all_4_16) & ~ (all_4_11 = all_4_21) & ~ % 126.35/17.23 | (all_4_12 = all_4_13) & ~ (all_4_12 = all_4_14) & ~ (all_4_12 = % 126.35/17.23 | all_4_17) & ~ (all_4_12 = all_4_22) & ~ (all_4_13 = all_4_14) & ~ % 126.35/17.23 | (all_4_13 = all_4_18) & ~ (all_4_13 = all_4_23) & ~ (all_4_14 = % 126.35/17.23 | all_4_19) & ~ (all_4_14 = all_4_24) & ~ (all_4_15 = all_4_16) & ~ % 126.35/17.23 | (all_4_15 = all_4_17) & ~ (all_4_15 = all_4_18) & ~ (all_4_15 = % 126.35/17.23 | all_4_19) & ~ (all_4_15 = all_4_20) & ~ (all_4_16 = all_4_17) & ~ % 126.35/17.23 | (all_4_16 = all_4_18) & ~ (all_4_16 = all_4_19) & ~ (all_4_16 = % 126.35/17.23 | all_4_21) & ~ (all_4_17 = all_4_18) & ~ (all_4_17 = all_4_19) & ~ % 126.35/17.23 | (all_4_17 = all_4_22) & ~ (all_4_18 = all_4_19) & ~ (all_4_18 = % 126.35/17.23 | all_4_23) & ~ (all_4_19 = all_4_24) & ~ (all_4_20 = all_4_21) & ~ % 126.35/17.23 | (all_4_20 = all_4_22) & ~ (all_4_20 = all_4_23) & ~ (all_4_20 = % 126.35/17.23 | all_4_24) & ~ (all_4_21 = all_4_22) & ~ (all_4_21 = all_4_23) & ~ % 126.35/17.23 | (all_4_21 = all_4_24) & ~ (all_4_22 = all_4_23) & ~ (all_4_22 = % 126.35/17.23 | all_4_24) & ~ (all_4_23 = all_4_24) & op(e4, e4) = all_4_0 & op(e4, % 126.35/17.23 | e3) = all_4_5 & op(e4, e2) = all_4_10 & op(e4, e1) = all_4_15 & % 126.35/17.23 | op(e4, e0) = all_4_20 & op(e3, e4) = all_4_1 & op(e3, e3) = all_4_6 & % 126.35/17.23 | op(e3, e2) = all_4_11 & op(e3, e1) = all_4_16 & op(e3, e0) = all_4_21 % 126.35/17.23 | & op(e2, e4) = all_4_2 & op(e2, e3) = all_4_7 & op(e2, e2) = all_4_12 % 126.35/17.23 | & op(e2, e1) = all_4_17 & op(e2, e0) = all_4_22 & op(e1, e4) = all_4_3 % 126.35/17.23 | & op(e1, e3) = all_4_8 & op(e1, e2) = all_4_13 & op(e1, e1) = all_4_18 % 126.35/17.23 | & op(e1, e0) = all_4_23 & op(e0, e4) = all_4_4 & op(e0, e3) = all_4_9 % 126.35/17.23 | & op(e0, e2) = all_4_14 & op(e0, e1) = all_4_19 & op(e0, e0) = % 126.35/17.23 | all_4_24 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & $i(all_4_3) & % 126.35/17.23 | $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & $i(all_4_7) & $i(all_4_8) & % 126.35/17.23 | $i(all_4_9) & $i(all_4_10) & $i(all_4_11) & $i(all_4_12) & % 126.35/17.23 | $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & $i(all_4_16) & % 126.35/17.23 | $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & $i(all_4_20) & % 126.35/17.23 | $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & $i(all_4_24) % 126.35/17.23 | % 126.35/17.23 | ALPHA: (26) implies: % 126.35/17.23 | (27) ~ (all_4_23 = all_4_24) % 126.35/17.23 | (28) ~ (all_4_22 = all_4_24) % 126.35/17.23 | (29) ~ (all_4_22 = all_4_23) % 126.35/17.23 | (30) ~ (all_4_21 = all_4_24) % 126.35/17.23 | (31) ~ (all_4_21 = all_4_23) % 126.35/17.23 | (32) ~ (all_4_21 = all_4_22) % 126.35/17.23 | (33) ~ (all_4_20 = all_4_24) % 126.35/17.23 | (34) ~ (all_4_20 = all_4_23) % 126.35/17.23 | (35) ~ (all_4_20 = all_4_22) % 126.35/17.23 | (36) ~ (all_4_20 = all_4_21) % 126.35/17.23 | (37) ~ (all_4_19 = all_4_24) % 126.35/17.23 | (38) ~ (all_4_18 = all_4_19) % 126.35/17.23 | (39) ~ (all_4_17 = all_4_22) % 126.35/17.23 | (40) ~ (all_4_17 = all_4_19) % 126.35/17.23 | (41) ~ (all_4_17 = all_4_18) % 126.35/17.23 | (42) ~ (all_4_16 = all_4_21) % 126.35/17.23 | (43) ~ (all_4_16 = all_4_19) % 126.35/17.24 | (44) ~ (all_4_16 = all_4_18) % 126.35/17.24 | (45) ~ (all_4_16 = all_4_17) % 126.35/17.24 | (46) ~ (all_4_15 = all_4_20) % 126.35/17.24 | (47) ~ (all_4_15 = all_4_19) % 126.35/17.24 | (48) ~ (all_4_15 = all_4_18) % 126.35/17.24 | (49) ~ (all_4_15 = all_4_17) % 126.35/17.24 | (50) ~ (all_4_15 = all_4_16) % 126.35/17.24 | (51) ~ (all_4_14 = all_4_24) % 126.35/17.24 | (52) ~ (all_4_14 = all_4_19) % 126.35/17.24 | (53) ~ (all_4_13 = all_4_23) % 126.35/17.24 | (54) ~ (all_4_13 = all_4_18) % 126.35/17.24 | (55) ~ (all_4_13 = all_4_14) % 126.35/17.24 | (56) ~ (all_4_12 = all_4_22) % 126.35/17.24 | (57) ~ (all_4_12 = all_4_17) % 126.35/17.24 | (58) ~ (all_4_12 = all_4_14) % 126.35/17.24 | (59) ~ (all_4_12 = all_4_13) % 126.35/17.24 | (60) ~ (all_4_11 = all_4_21) % 126.35/17.24 | (61) ~ (all_4_11 = all_4_16) % 126.35/17.24 | (62) ~ (all_4_11 = all_4_14) % 126.35/17.24 | (63) ~ (all_4_11 = all_4_13) % 126.35/17.24 | (64) ~ (all_4_11 = all_4_12) % 126.35/17.24 | (65) ~ (all_4_10 = all_4_20) % 126.35/17.24 | (66) ~ (all_4_10 = all_4_15) % 126.35/17.24 | (67) ~ (all_4_10 = all_4_14) % 126.35/17.24 | (68) ~ (all_4_10 = all_4_13) % 126.35/17.24 | (69) ~ (all_4_10 = all_4_12) % 126.35/17.24 | (70) ~ (all_4_10 = all_4_11) % 126.35/17.24 | (71) ~ (all_4_9 = all_4_24) % 126.35/17.24 | (72) ~ (all_4_9 = all_4_19) % 126.35/17.24 | (73) ~ (all_4_9 = all_4_14) % 126.35/17.24 | (74) ~ (all_4_8 = all_4_18) % 126.35/17.24 | (75) ~ (all_4_8 = all_4_13) % 126.35/17.24 | (76) ~ (all_4_8 = all_4_9) % 126.35/17.24 | (77) ~ (all_4_7 = all_4_22) % 126.35/17.24 | (78) ~ (all_4_7 = all_4_17) % 126.35/17.24 | (79) ~ (all_4_7 = all_4_12) % 126.35/17.24 | (80) ~ (all_4_7 = all_4_9) % 126.35/17.24 | (81) ~ (all_4_6 = all_4_21) % 126.35/17.24 | (82) ~ (all_4_6 = all_4_16) % 126.35/17.24 | (83) ~ (all_4_6 = all_4_11) % 126.35/17.24 | (84) ~ (all_4_6 = all_4_9) % 126.35/17.24 | (85) ~ (all_4_6 = all_4_7) % 126.35/17.24 | (86) ~ (all_4_5 = all_4_20) % 126.35/17.24 | (87) ~ (all_4_5 = all_4_15) % 126.35/17.24 | (88) ~ (all_4_5 = all_4_10) % 126.35/17.24 | (89) ~ (all_4_5 = all_4_9) % 126.35/17.24 | (90) ~ (all_4_5 = all_4_7) % 126.35/17.24 | (91) ~ (all_4_4 = all_4_24) % 126.35/17.24 | (92) ~ (all_4_4 = all_4_19) % 126.35/17.24 | (93) ~ (all_4_4 = all_4_14) % 126.35/17.24 | (94) ~ (all_4_4 = all_4_9) % 126.35/17.24 | (95) ~ (all_4_3 = all_4_18) % 126.35/17.24 | (96) ~ (all_4_3 = all_4_13) % 126.35/17.24 | (97) ~ (all_4_3 = all_4_8) % 126.35/17.24 | (98) ~ (all_4_3 = all_4_4) % 126.35/17.24 | (99) ~ (all_4_2 = all_4_22) % 126.35/17.24 | (100) ~ (all_4_2 = all_4_17) % 126.35/17.24 | (101) ~ (all_4_2 = all_4_12) % 126.35/17.24 | (102) ~ (all_4_2 = all_4_7) % 126.35/17.24 | (103) ~ (all_4_2 = all_4_4) % 126.35/17.24 | (104) ~ (all_4_2 = all_4_3) % 126.35/17.24 | (105) ~ (all_4_1 = all_4_16) % 126.35/17.24 | (106) ~ (all_4_1 = all_4_11) % 126.35/17.24 | (107) ~ (all_4_1 = all_4_4) % 126.35/17.24 | (108) ~ (all_4_1 = all_4_3) % 126.35/17.24 | (109) ~ (all_4_1 = all_4_2) % 126.35/17.24 | (110) ~ (all_4_0 = all_4_20) % 126.35/17.24 | (111) ~ (all_4_0 = all_4_10) % 126.35/17.24 | (112) ~ (all_4_0 = all_4_5) % 126.35/17.24 | (113) ~ (all_4_0 = all_4_4) % 126.35/17.24 | (114) ~ (all_4_0 = all_4_3) % 126.35/17.24 | (115) ~ (all_4_0 = all_4_2) % 126.35/17.24 | (116) ~ (all_4_0 = all_4_1) % 126.35/17.24 | (117) op(e0, e0) = all_4_24 % 126.35/17.24 | (118) op(e0, e1) = all_4_19 % 126.35/17.24 | (119) op(e0, e2) = all_4_14 % 126.35/17.24 | (120) op(e0, e3) = all_4_9 % 126.35/17.24 | (121) op(e0, e4) = all_4_4 % 126.35/17.24 | (122) op(e1, e0) = all_4_23 % 126.35/17.24 | (123) op(e1, e1) = all_4_18 % 126.35/17.24 | (124) op(e1, e2) = all_4_13 % 126.35/17.24 | (125) op(e1, e3) = all_4_8 % 126.35/17.24 | (126) op(e1, e4) = all_4_3 % 126.35/17.24 | (127) op(e2, e0) = all_4_22 % 126.35/17.24 | (128) op(e2, e1) = all_4_17 % 126.35/17.24 | (129) op(e2, e2) = all_4_12 % 126.35/17.24 | (130) op(e2, e3) = all_4_7 % 126.35/17.24 | (131) op(e2, e4) = all_4_2 % 126.35/17.24 | (132) op(e3, e0) = all_4_21 % 126.35/17.24 | (133) op(e3, e1) = all_4_16 % 126.35/17.24 | (134) op(e3, e2) = all_4_11 % 126.35/17.24 | (135) op(e3, e3) = all_4_6 % 126.35/17.24 | (136) op(e3, e4) = all_4_1 % 126.35/17.24 | (137) op(e4, e0) = all_4_20 % 126.35/17.24 | (138) op(e4, e1) = all_4_15 % 126.35/17.24 | (139) op(e4, e2) = all_4_10 % 126.35/17.24 | (140) op(e4, e3) = all_4_5 % 126.35/17.24 | (141) op(e4, e4) = all_4_0 % 126.35/17.24 | % 126.35/17.24 | DELTA: instantiating (1) with fresh symbols all_6_0, all_6_1, all_6_2, % 126.35/17.24 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 126.35/17.24 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16, % 126.35/17.24 | all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23, % 126.35/17.24 | all_6_24 gives: % 126.35/17.25 | (142) op(e4, e4) = all_6_0 & op(e4, e3) = all_6_1 & op(e4, e2) = all_6_2 & % 126.35/17.25 | op(e4, e1) = all_6_3 & op(e4, e0) = all_6_4 & op(e3, e4) = all_6_5 & % 126.35/17.25 | op(e3, e3) = all_6_6 & op(e3, e2) = all_6_7 & op(e3, e1) = all_6_8 & % 126.35/17.25 | op(e3, e0) = all_6_9 & op(e2, e4) = all_6_10 & op(e2, e3) = all_6_11 % 126.35/17.25 | & op(e2, e2) = all_6_12 & op(e2, e1) = all_6_13 & op(e2, e0) = % 126.35/17.25 | all_6_14 & op(e1, e4) = all_6_15 & op(e1, e3) = all_6_16 & op(e1, e2) % 126.35/17.25 | = all_6_17 & op(e1, e1) = all_6_18 & op(e1, e0) = all_6_19 & op(e0, % 126.35/17.25 | e4) = all_6_20 & op(e0, e3) = all_6_21 & op(e0, e2) = all_6_22 & % 126.35/17.25 | op(e0, e1) = all_6_23 & op(e0, e0) = all_6_24 & $i(all_6_0) & % 126.35/17.25 | $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4) & $i(all_6_5) & % 126.35/17.25 | $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & $i(all_6_9) & $i(all_6_10) % 126.35/17.25 | & $i(all_6_11) & $i(all_6_12) & $i(all_6_13) & $i(all_6_14) & % 126.35/17.25 | $i(all_6_15) & $i(all_6_16) & $i(all_6_17) & $i(all_6_18) & % 126.35/17.25 | $i(all_6_19) & $i(all_6_20) & $i(all_6_21) & $i(all_6_22) & % 126.35/17.25 | $i(all_6_23) & $i(all_6_24) & (all_6_0 = e4 | all_6_0 = e3 | all_6_0 % 126.35/17.25 | = e2 | all_6_0 = e1 | all_6_0 = e0) & (all_6_1 = e4 | all_6_1 = e3 % 126.35/17.25 | | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = e0) & (all_6_2 = e4 | % 126.35/17.25 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0) & % 126.35/17.25 | (all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 % 126.35/17.25 | = e0) & (all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 % 126.35/17.25 | | all_6_4 = e0) & (all_6_5 = e4 | all_6_5 = e3 | all_6_5 = e2 | % 126.35/17.25 | all_6_5 = e1 | all_6_5 = e0) & (all_6_6 = e4 | all_6_6 = e3 | % 126.35/17.25 | all_6_6 = e2 | all_6_6 = e1 | all_6_6 = e0) & (all_6_7 = e4 | % 126.35/17.25 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0) & % 126.35/17.25 | (all_6_8 = e4 | all_6_8 = e3 | all_6_8 = e2 | all_6_8 = e1 | all_6_8 % 126.35/17.25 | = e0) & (all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 % 126.35/17.25 | | all_6_9 = e0) & (all_6_10 = e4 | all_6_10 = e3 | all_6_10 = e2 | % 126.35/17.25 | all_6_10 = e1 | all_6_10 = e0) & (all_6_11 = e4 | all_6_11 = e3 | % 126.35/17.25 | all_6_11 = e2 | all_6_11 = e1 | all_6_11 = e0) & (all_6_12 = e4 | % 126.35/17.25 | all_6_12 = e3 | all_6_12 = e2 | all_6_12 = e1 | all_6_12 = e0) & % 126.35/17.25 | (all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 126.35/17.25 | all_6_13 = e0) & (all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | % 126.35/17.25 | all_6_14 = e1 | all_6_14 = e0) & (all_6_15 = e4 | all_6_15 = e3 | % 126.35/17.25 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 = e0) & (all_6_16 = e4 | % 126.35/17.25 | all_6_16 = e3 | all_6_16 = e2 | all_6_16 = e1 | all_6_16 = e0) & % 126.35/17.25 | (all_6_17 = e4 | all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | % 126.35/17.25 | all_6_17 = e0) & (all_6_18 = e4 | all_6_18 = e3 | all_6_18 = e2 | % 126.35/17.25 | all_6_18 = e1 | all_6_18 = e0) & (all_6_19 = e4 | all_6_19 = e3 | % 126.35/17.25 | all_6_19 = e2 | all_6_19 = e1 | all_6_19 = e0) & (all_6_20 = e4 | % 126.35/17.25 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 = e0) & % 126.35/17.25 | (all_6_21 = e4 | all_6_21 = e3 | all_6_21 = e2 | all_6_21 = e1 | % 126.35/17.25 | all_6_21 = e0) & (all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | % 126.35/17.25 | all_6_22 = e1 | all_6_22 = e0) & (all_6_23 = e4 | all_6_23 = e3 | % 126.35/17.25 | all_6_23 = e2 | all_6_23 = e1 | all_6_23 = e0) & (all_6_24 = e4 | % 126.35/17.25 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | all_6_24 = e0) % 126.35/17.25 | % 126.35/17.25 | ALPHA: (142) implies: % 126.35/17.25 | (143) op(e0, e0) = all_6_24 % 126.35/17.25 | (144) op(e0, e1) = all_6_23 % 126.35/17.25 | (145) op(e0, e2) = all_6_22 % 126.35/17.25 | (146) op(e0, e3) = all_6_21 % 126.35/17.25 | (147) op(e0, e4) = all_6_20 % 126.35/17.25 | (148) op(e1, e0) = all_6_19 % 126.35/17.25 | (149) op(e1, e1) = all_6_18 % 126.35/17.25 | (150) op(e1, e2) = all_6_17 % 126.35/17.25 | (151) op(e1, e3) = all_6_16 % 126.35/17.25 | (152) op(e1, e4) = all_6_15 % 126.35/17.25 | (153) op(e2, e0) = all_6_14 % 126.35/17.25 | (154) op(e2, e1) = all_6_13 % 126.35/17.25 | (155) op(e2, e2) = all_6_12 % 126.35/17.25 | (156) op(e2, e3) = all_6_11 % 126.35/17.25 | (157) op(e2, e4) = all_6_10 % 126.35/17.25 | (158) op(e3, e0) = all_6_9 % 126.35/17.25 | (159) op(e3, e1) = all_6_8 % 126.35/17.25 | (160) op(e3, e2) = all_6_7 % 126.35/17.25 | (161) op(e3, e3) = all_6_6 % 126.35/17.25 | (162) op(e3, e4) = all_6_5 % 126.35/17.25 | (163) op(e4, e0) = all_6_4 % 126.35/17.25 | (164) op(e4, e1) = all_6_3 % 126.35/17.25 | (165) op(e4, e2) = all_6_2 % 126.35/17.25 | (166) op(e4, e3) = all_6_1 % 126.35/17.25 | (167) op(e4, e4) = all_6_0 % 126.35/17.25 | (168) all_6_24 = e4 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 126.35/17.25 | all_6_24 = e0 % 126.35/17.25 | (169) all_6_22 = e4 | all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 126.35/17.25 | all_6_22 = e0 % 126.35/17.25 | (170) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 126.35/17.25 | all_6_20 = e0 % 126.35/17.25 | (171) all_6_18 = e4 | all_6_18 = e3 | all_6_18 = e2 | all_6_18 = e1 | % 126.35/17.25 | all_6_18 = e0 % 126.35/17.25 | (172) all_6_17 = e4 | all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | % 126.35/17.25 | all_6_17 = e0 % 126.35/17.25 | (173) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 126.35/17.25 | all_6_15 = e0 % 126.35/17.25 | (174) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 126.35/17.25 | all_6_14 = e0 % 126.35/17.25 | (175) all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 126.35/17.25 | all_6_13 = e0 % 126.35/17.25 | (176) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 126.35/17.25 | all_6_11 = e0 % 126.35/17.25 | (177) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 | all_6_9 = % 126.35/17.25 | e0 % 126.35/17.25 | (178) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = % 126.35/17.25 | e0 % 126.35/17.25 | (179) all_6_4 = e4 | all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | all_6_4 = % 126.35/17.25 | e0 % 126.35/17.25 | (180) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 = % 126.35/17.25 | e0 % 126.35/17.25 | (181) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = % 126.35/17.25 | e0 % 126.35/17.25 | (182) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = % 126.35/17.25 | e0 % 126.35/17.25 | % 126.35/17.25 | DELTA: instantiating (25) with fresh symbols all_8_0, all_8_1, all_8_2, % 126.35/17.25 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 126.35/17.25 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16, % 126.35/17.25 | all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23, % 126.35/17.25 | all_8_24, all_8_25, all_8_26, all_8_27, all_8_28, all_8_29, all_8_30, % 126.35/17.25 | all_8_31, all_8_32, all_8_33, all_8_34, all_8_35, all_8_36, all_8_37, % 126.35/17.25 | all_8_38, all_8_39, all_8_40, all_8_41, all_8_42, all_8_43, all_8_44, % 126.35/17.25 | all_8_45, all_8_46, all_8_47, all_8_48, all_8_49, all_8_50, all_8_51, % 126.35/17.25 | all_8_52, all_8_53, all_8_54, all_8_55, all_8_56, all_8_57, all_8_58, % 126.35/17.25 | all_8_59, all_8_60, all_8_61, all_8_62, all_8_63, all_8_64, all_8_65, % 126.35/17.25 | all_8_66, all_8_67, all_8_68, all_8_69, all_8_70, all_8_71, all_8_72, % 126.35/17.25 | all_8_73, all_8_74, all_8_75, all_8_76, all_8_77, all_8_78, all_8_79, % 126.35/17.25 | all_8_80, all_8_81, all_8_82, all_8_83, all_8_84, all_8_85, all_8_86, % 126.35/17.25 | all_8_87, all_8_88, all_8_89, all_8_90, all_8_91, all_8_92, all_8_93, % 126.35/17.25 | all_8_94, all_8_95, all_8_96, all_8_97, all_8_98, all_8_99 gives: % 126.35/17.26 | (183) ((all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 126.35/17.26 | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 126.35/17.26 | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 126.35/17.26 | $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 % 126.35/17.26 | = all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 126.35/17.26 | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) % 126.35/17.26 | & $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 126.35/17.26 | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & % 126.35/17.26 | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = % 126.35/17.26 | all_8_48 & $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | (all_8_7 % 126.35/17.26 | = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 126.35/17.26 | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = % 126.35/17.26 | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) & % 126.35/17.26 | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 % 126.35/17.26 | = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 126.35/17.26 | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 126.35/17.26 | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ % 126.35/17.26 | (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = % 126.35/17.26 | all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & op(e2, % 126.35/17.26 | e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 126.35/17.26 | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 126.35/17.26 | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) % 126.35/17.26 | = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) % 126.35/17.26 | & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 126.35/17.26 | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 126.35/17.26 | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 126.35/17.26 | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 126.35/17.26 | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 126.35/17.26 | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 126.35/17.26 | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 126.35/17.26 | & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ % 126.35/17.26 | (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) % 126.35/17.26 | = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 126.35/17.26 | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ % 126.35/17.26 | (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = % 126.35/17.26 | all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & op(e1, % 126.35/17.26 | e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | % 126.35/17.26 | (all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 126.35/17.26 | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) % 126.35/17.26 | = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) % 126.35/17.26 | & $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ % 126.35/17.26 | (all_8_48 = all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, e1) % 126.35/17.26 | = all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 126.35/17.26 | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ % 126.35/17.26 | (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = % 126.35/17.26 | e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, % 126.35/17.26 | e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | % 126.35/17.26 | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & % 126.35/17.26 | op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) % 126.35/17.26 | = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) % 126.35/17.26 | & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ % 126.35/17.26 | (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & % 126.35/17.26 | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = % 126.35/17.26 | all_8_87 & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 126.35/17.26 | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 126.35/17.26 | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) % 126.35/17.26 | = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) % 126.35/17.26 | & $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ % 126.35/17.26 | (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) % 126.35/17.26 | = all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 126.35/17.26 | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ % 126.35/17.26 | (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) = % 126.35/17.26 | e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & op(e0, % 126.35/17.26 | e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | % 126.35/17.26 | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 126.35/17.26 | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & op(e1, e0) % 126.35/17.26 | = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & $i(all_8_87) % 126.35/17.26 | & $i(all_8_99))) & ((all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 126.35/17.26 | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & op(e3, e4) = % 126.35/17.26 | all_8_42 & $i(all_8_41) & $i(all_8_42)) | (all_8_43 = e2 & ~ % 126.35/17.26 | (all_8_44 = e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) = % 126.35/17.26 | all_8_44 & op(e2, e4) = all_8_45 & $i(all_8_44) & $i(all_8_45)) | % 126.35/17.26 | (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, all_8_48) = e1 & % 126.35/17.26 | op(e1, all_8_48) = all_8_47 & op(e1, e4) = all_8_48 & % 126.35/17.26 | $i(all_8_47) & $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 126.35/17.26 | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) = all_8_50 & % 126.35/17.26 | op(e0, e4) = all_8_51 & $i(all_8_50) & $i(all_8_51))) & % 126.35/17.26 | ((all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, all_8_54) = all_8_53 & % 126.35/17.26 | op(e4, e3) = all_8_54 & op(e3, all_8_54) = e4 & $i(all_8_53) & % 126.35/17.26 | $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 126.35/17.26 | all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & op(e2, e3) = % 126.35/17.26 | all_8_57 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e1 & ~ % 126.35/17.26 | (all_8_59 = e3) & op(e3, all_8_60) = e1 & op(e1, all_8_60) = % 126.35/17.26 | all_8_59 & op(e1, e3) = all_8_60 & $i(all_8_59) & $i(all_8_60)) | % 126.35/17.26 | (all_8_61 = e0 & ~ (all_8_62 = e3) & op(e3, all_8_63) = e0 & % 126.35/17.26 | op(e0, all_8_63) = all_8_62 & op(e0, e3) = all_8_63 & % 126.35/17.26 | $i(all_8_62) & $i(all_8_63))) & ((all_8_64 = e4 & ~ (all_8_65 = % 126.35/17.26 | e2) & op(e4, all_8_66) = all_8_65 & op(e4, e2) = all_8_66 & % 126.35/17.26 | op(e2, all_8_66) = e4 & $i(all_8_65) & $i(all_8_66)) | (all_8_67 % 126.35/17.26 | = e3 & ~ (all_8_68 = e2) & op(e3, all_8_69) = all_8_68 & op(e3, % 126.35/17.26 | e2) = all_8_69 & op(e2, all_8_69) = e3 & $i(all_8_68) & % 126.35/17.26 | $i(all_8_69)) | (all_8_70 = e1 & ~ (all_8_71 = e2) & op(e2, % 126.35/17.26 | all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & op(e1, e2) = % 126.35/17.26 | all_8_72 & $i(all_8_71) & $i(all_8_72)) | (all_8_73 = e0 & ~ % 126.35/17.26 | (all_8_74 = e2) & op(e2, all_8_75) = e0 & op(e0, all_8_75) = % 126.35/17.26 | all_8_74 & op(e0, e2) = all_8_75 & $i(all_8_74) & $i(all_8_75))) % 126.35/17.26 | & ((all_8_76 = e4 & ~ (all_8_77 = e1) & op(e4, all_8_78) = all_8_77 % 126.35/17.26 | & op(e4, e1) = all_8_78 & op(e1, all_8_78) = e4 & $i(all_8_77) & % 126.35/17.26 | $i(all_8_78)) | (all_8_79 = e3 & ~ (all_8_80 = e1) & op(e3, % 126.35/17.26 | all_8_81) = all_8_80 & op(e3, e1) = all_8_81 & op(e1, all_8_81) % 126.35/17.26 | = e3 & $i(all_8_80) & $i(all_8_81)) | (all_8_82 = e2 & ~ % 126.35/17.26 | (all_8_83 = e1) & op(e2, all_8_84) = all_8_83 & op(e2, e1) = % 126.35/17.26 | all_8_84 & op(e1, all_8_84) = e2 & $i(all_8_83) & $i(all_8_84)) | % 126.35/17.26 | (all_8_85 = e0 & ~ (all_8_86 = e1) & op(e1, all_8_87) = e0 & % 126.35/17.26 | op(e0, all_8_87) = all_8_86 & op(e0, e1) = all_8_87 & % 126.35/17.26 | $i(all_8_86) & $i(all_8_87))) & ((all_8_88 = e4 & ~ (all_8_89 = % 126.35/17.26 | e0) & op(e4, all_8_90) = all_8_89 & op(e4, e0) = all_8_90 & % 126.35/17.26 | op(e0, all_8_90) = e4 & $i(all_8_89) & $i(all_8_90)) | (all_8_91 % 126.35/17.26 | = e3 & ~ (all_8_92 = e0) & op(e3, all_8_93) = all_8_92 & op(e3, % 126.35/17.26 | e0) = all_8_93 & op(e0, all_8_93) = e3 & $i(all_8_92) & % 126.35/17.26 | $i(all_8_93)) | (all_8_94 = e2 & ~ (all_8_95 = e0) & op(e2, % 126.35/17.26 | all_8_96) = all_8_95 & op(e2, e0) = all_8_96 & op(e0, all_8_96) % 126.35/17.26 | = e2 & $i(all_8_95) & $i(all_8_96)) | (all_8_97 = e1 & ~ % 126.35/17.26 | (all_8_98 = e0) & op(e1, all_8_99) = all_8_98 & op(e1, e0) = % 126.35/17.27 | all_8_99 & op(e0, all_8_99) = e1 & $i(all_8_98) & $i(all_8_99))) % 126.35/17.27 | % 126.35/17.27 | ALPHA: (183) implies: % 126.35/17.27 | (184) (all_8_88 = e4 & ~ (all_8_89 = e0) & op(e4, all_8_90) = all_8_89 & % 126.35/17.27 | op(e4, e0) = all_8_90 & op(e0, all_8_90) = e4 & $i(all_8_89) & % 126.35/17.27 | $i(all_8_90)) | (all_8_91 = e3 & ~ (all_8_92 = e0) & op(e3, % 126.35/17.27 | all_8_93) = all_8_92 & op(e3, e0) = all_8_93 & op(e0, all_8_93) = % 126.35/17.27 | e3 & $i(all_8_92) & $i(all_8_93)) | (all_8_94 = e2 & ~ (all_8_95 = % 126.35/17.27 | e0) & op(e2, all_8_96) = all_8_95 & op(e2, e0) = all_8_96 & % 126.35/17.27 | op(e0, all_8_96) = e2 & $i(all_8_95) & $i(all_8_96)) | (all_8_97 = % 126.35/17.27 | e1 & ~ (all_8_98 = e0) & op(e1, all_8_99) = all_8_98 & op(e1, e0) % 126.35/17.27 | = all_8_99 & op(e0, all_8_99) = e1 & $i(all_8_98) & $i(all_8_99)) % 126.35/17.27 | (185) (all_8_76 = e4 & ~ (all_8_77 = e1) & op(e4, all_8_78) = all_8_77 & % 126.35/17.27 | op(e4, e1) = all_8_78 & op(e1, all_8_78) = e4 & $i(all_8_77) & % 126.35/17.27 | $i(all_8_78)) | (all_8_79 = e3 & ~ (all_8_80 = e1) & op(e3, % 126.35/17.27 | all_8_81) = all_8_80 & op(e3, e1) = all_8_81 & op(e1, all_8_81) = % 126.35/17.27 | e3 & $i(all_8_80) & $i(all_8_81)) | (all_8_82 = e2 & ~ (all_8_83 = % 126.35/17.27 | e1) & op(e2, all_8_84) = all_8_83 & op(e2, e1) = all_8_84 & % 126.35/17.27 | op(e1, all_8_84) = e2 & $i(all_8_83) & $i(all_8_84)) | (all_8_85 = % 126.35/17.27 | e0 & ~ (all_8_86 = e1) & op(e1, all_8_87) = e0 & op(e0, all_8_87) % 126.35/17.27 | = all_8_86 & op(e0, e1) = all_8_87 & $i(all_8_86) & $i(all_8_87)) % 126.35/17.27 | (186) (all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, all_8_66) = all_8_65 & % 126.35/17.27 | op(e4, e2) = all_8_66 & op(e2, all_8_66) = e4 & $i(all_8_65) & % 126.35/17.27 | $i(all_8_66)) | (all_8_67 = e3 & ~ (all_8_68 = e2) & op(e3, % 126.35/17.27 | all_8_69) = all_8_68 & op(e3, e2) = all_8_69 & op(e2, all_8_69) = % 126.35/17.27 | e3 & $i(all_8_68) & $i(all_8_69)) | (all_8_70 = e1 & ~ (all_8_71 = % 126.35/17.27 | e2) & op(e2, all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & % 126.35/17.27 | op(e1, e2) = all_8_72 & $i(all_8_71) & $i(all_8_72)) | (all_8_73 = % 126.35/17.27 | e0 & ~ (all_8_74 = e2) & op(e2, all_8_75) = e0 & op(e0, all_8_75) % 126.35/17.27 | = all_8_74 & op(e0, e2) = all_8_75 & $i(all_8_74) & $i(all_8_75)) % 126.35/17.27 | (187) (all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, all_8_54) = all_8_53 & % 126.35/17.27 | op(e4, e3) = all_8_54 & op(e3, all_8_54) = e4 & $i(all_8_53) & % 126.35/17.27 | $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 126.35/17.27 | all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & op(e2, e3) = % 126.35/17.27 | all_8_57 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e1 & ~ % 126.35/17.27 | (all_8_59 = e3) & op(e3, all_8_60) = e1 & op(e1, all_8_60) = % 126.35/17.27 | all_8_59 & op(e1, e3) = all_8_60 & $i(all_8_59) & $i(all_8_60)) | % 126.35/17.27 | (all_8_61 = e0 & ~ (all_8_62 = e3) & op(e3, all_8_63) = e0 & op(e0, % 126.35/17.27 | all_8_63) = all_8_62 & op(e0, e3) = all_8_63 & $i(all_8_62) & % 126.35/17.27 | $i(all_8_63)) % 126.35/17.27 | (188) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, all_8_42) = e3 & op(e3, % 126.35/17.27 | all_8_42) = all_8_41 & op(e3, e4) = all_8_42 & $i(all_8_41) & % 126.35/17.27 | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 126.35/17.27 | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & op(e2, e4) = % 126.35/17.27 | all_8_45 & $i(all_8_44) & $i(all_8_45)) | (all_8_46 = e1 & ~ % 126.35/17.27 | (all_8_47 = e4) & op(e4, all_8_48) = e1 & op(e1, all_8_48) = % 126.35/17.27 | all_8_47 & op(e1, e4) = all_8_48 & $i(all_8_47) & $i(all_8_48)) | % 126.35/17.27 | (all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, all_8_51) = e0 & op(e0, % 126.35/17.27 | all_8_51) = all_8_50 & op(e0, e4) = all_8_51 & $i(all_8_50) & % 126.35/17.27 | $i(all_8_51)) % 126.35/17.28 | (189) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 126.35/17.28 | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 126.35/17.28 | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 126.35/17.28 | $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 126.35/17.28 | all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 126.35/17.28 | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 126.35/17.28 | $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & % 126.35/17.28 | ~ (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, % 126.35/17.28 | e1) = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 126.35/17.28 | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ % 126.35/17.28 | (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = % 126.35/17.28 | all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, % 126.35/17.28 | e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 126.35/17.28 | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 126.35/17.28 | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) = % 126.35/17.28 | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) & % 126.35/17.28 | $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 126.35/17.28 | = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 % 126.35/17.28 | & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & % 126.35/17.28 | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) % 126.35/17.28 | & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = all_8_12 & % 126.35/17.28 | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 126.35/17.28 | all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 % 126.35/17.28 | = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, % 126.35/17.28 | e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 126.35/17.28 | op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) % 126.35/17.28 | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 126.35/17.28 | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 126.35/17.28 | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 126.35/17.28 | $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 126.35/17.28 | = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 % 126.35/17.28 | & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 126.35/17.28 | $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) % 126.35/17.28 | & ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & % 126.35/17.28 | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = % 126.35/17.28 | all_8_72 & $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 % 126.35/17.28 | = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, % 126.35/17.28 | e2) = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 126.35/17.28 | op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) % 126.35/17.28 | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 126.35/17.28 | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 126.35/17.28 | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & % 126.35/17.28 | $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 126.35/17.28 | = all_8_81) & op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 % 126.35/17.28 | & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & % 126.35/17.28 | $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) % 126.35/17.28 | & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, % 126.35/17.28 | e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 126.35/17.28 | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ % 126.35/17.28 | (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = % 126.35/17.28 | all_8_30 & op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & op(e0, % 126.35/17.28 | e1) = all_8_87 & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 126.35/17.28 | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 126.35/17.28 | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 126.35/17.28 | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & % 126.35/17.28 | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 126.35/17.28 | = all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 % 126.35/17.28 | & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 126.35/17.28 | $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = e2) % 126.35/17.28 | & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, % 126.35/17.28 | e0) = all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 126.35/17.28 | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 & ~ % 126.35/17.28 | (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 % 126.35/17.28 | & op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) % 126.35/17.28 | = all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 126.35/17.28 | % 126.35/17.28 | DELTA: instantiating (13) with fresh symbols all_9_0, all_9_1, all_9_2, % 126.35/17.28 | all_9_3, all_9_4, all_9_5, all_9_6, all_9_7, all_9_8, all_9_9, % 126.35/17.28 | all_9_10, all_9_11, all_9_12, all_9_13, all_9_14, all_9_15, all_9_16, % 126.35/17.28 | all_9_17, all_9_18, all_9_19, all_9_20, all_9_21, all_9_22, all_9_23, % 126.35/17.28 | all_9_24 gives: % 126.35/17.29 | (190) ((all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 126.35/17.29 | | (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = % 126.35/17.29 | e4) | (all_9_16 = e4 & op(e4, e0) = e4)) & ((all_9_0 = e4 & % 126.35/17.29 | op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_6 = % 126.35/17.29 | e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 126.35/17.29 | (all_9_20 = e4 & op(e0, e4) = e4)) & ((all_9_0 = e3 & op(e4, e4) = % 126.35/17.29 | e3) | (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_4 = e3 & op(e4, % 126.35/17.29 | e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & % 126.35/17.29 | op(e4, e0) = e3)) & ((all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 % 126.35/17.29 | = e3 & op(e3, e4) = e3) | (all_9_6 = e3 & op(e2, e4) = e3) | % 126.35/17.29 | (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_20 = e3 & op(e0, e4) = % 126.35/17.29 | e3)) & ((all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, % 126.35/17.29 | e3) = e2) | (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 126.35/17.29 | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2)) & ((all_9_0 % 126.35/17.29 | = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 126.35/17.29 | (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = % 126.35/17.29 | e2) | (all_9_20 = e2 & op(e0, e4) = e2)) & ((all_9_0 = e1 & % 126.35/17.29 | op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | (all_9_4 = % 126.35/17.29 | e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 126.35/17.29 | (all_9_16 = e1 & op(e4, e0) = e1)) & ((all_9_0 = e1 & op(e4, e4) = % 126.35/17.29 | e1) | (all_9_2 = e1 & op(e3, e4) = e1) | (all_9_6 = e1 & op(e2, % 126.35/17.29 | e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 % 126.35/17.29 | & op(e0, e4) = e1)) & ((all_9_0 = e0 & op(e4, e4) = e0) | % 126.35/17.29 | (all_9_1 = e0 & op(e4, e3) = e0) | (all_9_4 = e0 & op(e4, e2) = e0) % 126.35/17.29 | | (all_9_9 = e0 & op(e4, e1) = e0) | (all_9_16 = e0 & op(e4, e0) = % 126.35/17.29 | e0)) & ((all_9_0 = e0 & op(e4, e4) = e0) | (all_9_2 = e0 & op(e3, % 126.35/17.29 | e4) = e0) | (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_12 = e0 & % 126.35/17.29 | op(e1, e4) = e0) | (all_9_20 = e0 & op(e0, e4) = e0)) & ((all_9_1 % 126.35/17.29 | = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 126.35/17.29 | (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = % 126.35/17.29 | e4) | (all_9_21 = e4 & op(e0, e3) = e4)) & ((all_9_1 = e3 & % 126.35/17.29 | op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | (all_9_7 = % 126.35/17.29 | e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 126.35/17.29 | (all_9_21 = e3 & op(e0, e3) = e3)) & ((all_9_1 = e2 & op(e4, e3) = % 126.35/17.29 | e2) | (all_9_3 = e2 & op(e3, e3) = e2) | (all_9_7 = e2 & op(e2, % 126.35/17.29 | e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | (all_9_21 = e2 % 126.35/17.29 | & op(e0, e3) = e2)) & ((all_9_1 = e1 & op(e4, e3) = e1) | % 126.35/17.29 | (all_9_3 = e1 & op(e3, e3) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) % 126.35/17.29 | | (all_9_13 = e1 & op(e1, e3) = e1) | (all_9_21 = e1 & op(e0, e3) = % 126.35/17.29 | e1)) & ((all_9_1 = e0 & op(e4, e3) = e0) | (all_9_3 = e0 & op(e3, % 126.35/17.29 | e3) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | (all_9_13 = e0 & % 126.35/17.29 | op(e1, e3) = e0) | (all_9_21 = e0 & op(e0, e3) = e0)) & ((all_9_2 % 126.35/17.29 | = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 126.35/17.29 | (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = % 126.35/17.29 | e4) | (all_9_17 = e4 & op(e3, e0) = e4)) & ((all_9_2 = e3 & % 126.35/17.29 | op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | (all_9_5 = % 126.35/17.29 | e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 126.35/17.29 | (all_9_17 = e3 & op(e3, e0) = e3)) & ((all_9_2 = e2 & op(e3, e4) = % 126.35/17.29 | e2) | (all_9_3 = e2 & op(e3, e3) = e2) | (all_9_5 = e2 & op(e3, % 126.35/17.29 | e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 126.35/17.29 | & op(e3, e0) = e2)) & ((all_9_2 = e1 & op(e3, e4) = e1) | % 126.35/17.29 | (all_9_3 = e1 & op(e3, e3) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) % 126.35/17.29 | | (all_9_10 = e1 & op(e3, e1) = e1) | (all_9_17 = e1 & op(e3, e0) = % 126.35/17.29 | e1)) & ((all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & op(e3, % 126.35/17.29 | e3) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 & % 126.35/17.29 | op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) = e0)) & ((all_9_4 % 126.35/17.29 | = e4 & op(e4, e2) = e4) | (all_9_5 = e4 & op(e3, e2) = e4) | % 126.35/17.29 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_14 = e4 & op(e1, e2) = % 126.35/17.29 | e4) | (all_9_22 = e4 & op(e0, e2) = e4)) & ((all_9_4 = e3 & % 126.35/17.29 | op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_8 = % 126.35/17.29 | e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 126.35/17.29 | (all_9_22 = e3 & op(e0, e2) = e3)) & ((all_9_4 = e2 & op(e4, e2) = % 126.35/17.29 | e2) | (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_8 = e2 & op(e2, % 126.35/17.29 | e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 126.35/17.29 | & op(e0, e2) = e2)) & ((all_9_4 = e1 & op(e4, e2) = e1) | % 126.35/17.29 | (all_9_5 = e1 & op(e3, e2) = e1) | (all_9_8 = e1 & op(e2, e2) = e1) % 126.35/17.29 | | (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_22 = e1 & op(e0, e2) = % 126.35/17.29 | e1)) & ((all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, % 126.35/17.29 | e2) = e0) | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & % 126.35/17.29 | op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) = e0)) & ((all_9_6 % 126.35/17.29 | = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) | % 126.35/17.29 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = % 126.35/17.29 | e4) | (all_9_18 = e4 & op(e2, e0) = e4)) & ((all_9_6 = e3 & % 126.35/17.29 | op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_8 = % 126.35/17.29 | e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) | % 126.35/17.29 | (all_9_18 = e3 & op(e2, e0) = e3)) & ((all_9_6 = e2 & op(e2, e4) = % 126.35/17.29 | e2) | (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_8 = e2 & op(e2, % 126.35/17.29 | e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 126.35/17.29 | & op(e2, e0) = e2)) & ((all_9_6 = e1 & op(e2, e4) = e1) | % 126.35/17.29 | (all_9_7 = e1 & op(e2, e3) = e1) | (all_9_8 = e1 & op(e2, e2) = e1) % 126.35/17.29 | | (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_18 = e1 & op(e2, e0) = % 126.35/17.29 | e1)) & ((all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, % 126.35/17.29 | e3) = e0) | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & % 126.35/17.29 | op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) = e0)) & ((all_9_9 % 126.35/17.29 | = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 126.35/17.29 | (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = % 126.35/17.29 | e4) | (all_9_23 = e4 & op(e0, e1) = e4)) & ((all_9_9 = e3 & % 126.35/17.29 | op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_11 % 126.35/17.29 | = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 126.35/17.29 | (all_9_23 = e3 & op(e0, e1) = e3)) & ((all_9_9 = e2 & op(e4, e1) = % 126.35/17.29 | e2) | (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_11 = e2 & op(e2, % 126.35/17.29 | e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 % 126.35/17.29 | & op(e0, e1) = e2)) & ((all_9_9 = e1 & op(e4, e1) = e1) | % 126.35/17.29 | (all_9_10 = e1 & op(e3, e1) = e1) | (all_9_11 = e1 & op(e2, e1) = % 126.35/17.29 | e1) | (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, % 126.35/17.29 | e1) = e1)) & ((all_9_9 = e0 & op(e4, e1) = e0) | (all_9_10 = e0 % 126.35/17.29 | & op(e3, e1) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 126.35/17.29 | (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_23 = e0 & op(e0, e1) = % 126.35/17.29 | e0)) & ((all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & % 126.35/17.29 | op(e1, e3) = e4) | (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 % 126.35/17.29 | = e4 & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) = e4)) & % 126.35/17.29 | ((all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 & op(e1, e3) = % 126.35/17.29 | e3) | (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 & op(e1, % 126.35/17.29 | e1) = e3) | (all_9_19 = e3 & op(e1, e0) = e3)) & ((all_9_12 = % 126.35/17.29 | e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 126.35/17.29 | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 126.35/17.29 | e2) | (all_9_19 = e2 & op(e1, e0) = e2)) & ((all_9_12 = e1 & % 126.35/17.29 | op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | (all_9_14 % 126.35/17.29 | = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 126.35/17.29 | (all_9_19 = e1 & op(e1, e0) = e1)) & ((all_9_12 = e0 & op(e1, e4) = % 126.35/17.29 | e0) | (all_9_13 = e0 & op(e1, e3) = e0) | (all_9_14 = e0 & op(e1, % 126.35/17.29 | e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 126.35/17.29 | & op(e1, e0) = e0)) & ((all_9_16 = e4 & op(e4, e0) = e4) | % 126.35/17.29 | (all_9_17 = e4 & op(e3, e0) = e4) | (all_9_18 = e4 & op(e2, e0) = % 126.35/17.29 | e4) | (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, % 126.35/17.29 | e0) = e4)) & ((all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = % 126.35/17.29 | e3 & op(e3, e0) = e3) | (all_9_18 = e3 & op(e2, e0) = e3) | % 126.35/17.29 | (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = % 126.35/17.29 | e3)) & ((all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & % 126.35/17.29 | op(e3, e0) = e2) | (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 % 126.35/17.29 | = e2 & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) = e2)) & % 126.35/17.29 | ((all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = % 126.35/17.29 | e1) | (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, % 126.35/17.29 | e0) = e1) | (all_9_24 = e1 & op(e0, e0) = e1)) & ((all_9_20 = % 126.35/17.29 | e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 126.35/17.29 | (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = % 126.35/17.29 | e4) | (all_9_24 = e4 & op(e0, e0) = e4)) & ((all_9_20 = e3 & % 126.35/17.29 | op(e0, e4) = e3) | (all_9_21 = e3 & op(e0, e3) = e3) | (all_9_22 % 126.35/17.29 | = e3 & op(e0, e2) = e3) | (all_9_23 = e3 & op(e0, e1) = e3) | % 126.35/17.29 | (all_9_24 = e3 & op(e0, e0) = e3)) & ((all_9_20 = e2 & op(e0, e4) = % 126.35/17.29 | e2) | (all_9_21 = e2 & op(e0, e3) = e2) | (all_9_22 = e2 & op(e0, % 126.35/17.29 | e2) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) | (all_9_24 = e2 % 126.35/17.29 | & op(e0, e0) = e2)) & ((all_9_20 = e1 & op(e0, e4) = e1) | % 126.35/17.29 | (all_9_21 = e1 & op(e0, e3) = e1) | (all_9_22 = e1 & op(e0, e2) = % 126.35/17.29 | e1) | (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, % 126.35/17.29 | e0) = e1)) & ((all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = % 126.35/17.29 | e0 & op(e4, e0) = e0) | (all_9_17 = e0 & op(e3, e0) = e0) | % 126.35/17.29 | (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 126.35/17.29 | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 126.35/17.29 | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = e0) | % 126.35/17.29 | (all_9_23 = e0 & op(e0, e1) = e0)))) % 126.35/17.29 | % 126.35/17.29 | ALPHA: (190) implies: % 126.67/17.29 | (191) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = % 126.67/17.29 | e0) | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 126.67/17.29 | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & % 126.67/17.29 | ((all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = % 126.67/17.29 | e0) | (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 126.67/17.29 | op(e0, e1) = e0))) % 126.67/17.29 | (192) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) % 126.67/17.29 | | (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = % 126.67/17.29 | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 126.67/17.29 | (193) (all_9_20 = e2 & op(e0, e4) = e2) | (all_9_21 = e2 & op(e0, e3) = e2) % 126.67/17.29 | | (all_9_22 = e2 & op(e0, e2) = e2) | (all_9_23 = e2 & op(e0, e1) = % 126.67/17.29 | e2) | (all_9_24 = e2 & op(e0, e0) = e2) % 126.67/17.30 | (194) (all_9_20 = e3 & op(e0, e4) = e3) | (all_9_21 = e3 & op(e0, e3) = e3) % 126.67/17.30 | | (all_9_22 = e3 & op(e0, e2) = e3) | (all_9_23 = e3 & op(e0, e1) = % 126.67/17.30 | e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 126.67/17.30 | (195) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) % 126.67/17.30 | | (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = % 126.67/17.30 | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 126.67/17.30 | (196) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) % 126.67/17.30 | | (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = % 126.67/17.30 | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 126.67/17.30 | (197) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) % 126.67/17.30 | | (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = % 126.67/17.30 | e2) | (all_9_24 = e2 & op(e0, e0) = e2) % 126.67/17.30 | (198) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 126.67/17.30 | | (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = % 126.67/17.30 | e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 126.67/17.30 | (199) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) % 126.67/17.30 | | (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = % 126.67/17.30 | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 126.67/17.30 | (200) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) % 126.67/17.30 | | (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = % 126.67/17.30 | e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 126.67/17.30 | (201) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 126.67/17.30 | | (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = % 126.67/17.30 | e1) | (all_9_19 = e1 & op(e1, e0) = e1) % 126.67/17.30 | (202) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 126.67/17.30 | | (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 126.67/17.30 | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 126.67/17.30 | (203) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) % 126.67/17.30 | | (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 & op(e1, e1) = % 126.67/17.30 | e3) | (all_9_19 = e3 & op(e1, e0) = e3) % 126.67/17.30 | (204) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) % 126.67/17.30 | | (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = % 126.67/17.30 | e4) | (all_9_19 = e4 & op(e1, e0) = e4) % 126.67/17.30 | (205) (all_9_9 = e0 & op(e4, e1) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) % 126.67/17.30 | | (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_15 = e0 & op(e1, e1) = % 126.67/17.30 | e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 126.67/17.30 | (206) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) % 126.67/17.30 | | (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = % 126.67/17.30 | e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 126.67/17.30 | (207) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) % 126.67/17.30 | | (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = % 126.67/17.30 | e2) | (all_9_23 = e2 & op(e0, e1) = e2) % 126.67/17.30 | (208) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 126.67/17.30 | | (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = % 126.67/17.30 | e3) | (all_9_23 = e3 & op(e0, e1) = e3) % 126.67/17.30 | (209) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 126.67/17.30 | | (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = % 126.67/17.30 | e4) | (all_9_23 = e4 & op(e0, e1) = e4) % 126.67/17.30 | (210) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 126.67/17.30 | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) % 126.67/17.30 | | (all_9_18 = e0 & op(e2, e0) = e0) % 126.67/17.30 | (211) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 126.67/17.30 | (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) % 126.67/17.30 | | (all_9_18 = e1 & op(e2, e0) = e1) % 126.67/17.30 | (212) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) | % 126.67/17.30 | (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) % 126.67/17.30 | | (all_9_18 = e2 & op(e2, e0) = e2) % 126.67/17.30 | (213) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) | % 126.67/17.30 | (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) % 126.67/17.30 | | (all_9_18 = e3 & op(e2, e0) = e3) % 126.67/17.30 | (214) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) | % 126.67/17.30 | (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & op(e2, e1) = e4) % 126.67/17.30 | | (all_9_18 = e4 & op(e2, e0) = e4) % 126.67/17.30 | (215) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | % 126.67/17.30 | (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) % 126.67/17.30 | | (all_9_22 = e0 & op(e0, e2) = e0) % 126.67/17.31 | (216) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) | % 126.67/17.31 | (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) % 126.67/17.31 | | (all_9_22 = e1 & op(e0, e2) = e1) % 126.67/17.31 | (217) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 126.67/17.31 | (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 126.67/17.31 | | (all_9_22 = e2 & op(e0, e2) = e2) % 126.67/17.31 | (218) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 126.67/17.31 | (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) % 126.67/17.31 | | (all_9_22 = e3 & op(e0, e2) = e3) % 126.67/17.31 | (219) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & op(e3, e3) = e0) | % 126.67/17.31 | (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) % 126.67/17.31 | | (all_9_17 = e0 & op(e3, e0) = e0) % 126.67/17.31 | (220) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 126.67/17.31 | (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) % 126.67/17.31 | | (all_9_17 = e2 & op(e3, e0) = e2) % 126.67/17.31 | (221) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 126.67/17.31 | (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 126.67/17.31 | | (all_9_17 = e3 & op(e3, e0) = e3) % 126.67/17.31 | (222) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 126.67/17.31 | (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 126.67/17.31 | | (all_9_17 = e4 & op(e3, e0) = e4) % 126.67/17.31 | (223) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 126.67/17.31 | (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 126.67/17.31 | | (all_9_21 = e2 & op(e0, e3) = e2) % 126.67/17.31 | (224) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 126.67/17.31 | (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) % 126.67/17.31 | | (all_9_21 = e3 & op(e0, e3) = e3) % 126.67/17.31 | (225) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 126.67/17.31 | (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) % 126.67/17.31 | | (all_9_21 = e4 & op(e0, e3) = e4) % 126.67/17.31 | (226) (all_9_0 = e0 & op(e4, e4) = e0) | (all_9_2 = e0 & op(e3, e4) = e0) | % 126.67/17.31 | (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_12 = e0 & op(e1, e4) = e0) % 126.67/17.31 | | (all_9_20 = e0 & op(e0, e4) = e0) % 126.67/17.31 | (227) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 126.67/17.31 | (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) % 126.67/17.31 | | (all_9_20 = e1 & op(e0, e4) = e1) % 126.67/17.31 | (228) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 126.67/17.31 | (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 126.67/17.31 | (all_9_16 = e1 & op(e4, e0) = e1) % 126.67/17.31 | (229) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 126.67/17.31 | (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) % 126.67/17.31 | | (all_9_20 = e2 & op(e0, e4) = e2) % 126.67/17.31 | (230) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 126.67/17.31 | (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 126.67/17.31 | (all_9_16 = e2 & op(e4, e0) = e2) % 126.67/17.31 | (231) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 126.67/17.31 | (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) % 126.67/17.31 | | (all_9_20 = e3 & op(e0, e4) = e3) % 126.67/17.31 | (232) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 126.67/17.31 | (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 126.67/17.31 | (all_9_16 = e3 & op(e4, e0) = e3) % 126.67/17.31 | (233) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 126.67/17.31 | (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 126.67/17.31 | | (all_9_20 = e4 & op(e0, e4) = e4) % 126.67/17.31 | (234) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 126.67/17.31 | (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 126.67/17.31 | (all_9_16 = e4 & op(e4, e0) = e4) % 126.67/17.31 | % 126.67/17.31 | GROUND_INST: instantiating (function-axioms) with all_4_24, all_6_24, e0, e0, % 126.67/17.31 | simplifying with (117), (143) gives: % 126.67/17.31 | (235) all_6_24 = all_4_24 % 126.67/17.31 | % 126.67/17.31 | GROUND_INST: instantiating (function-axioms) with all_4_19, all_6_23, e1, e0, % 126.67/17.31 | simplifying with (118), (144) gives: % 126.67/17.31 | (236) all_6_23 = all_4_19 % 126.67/17.31 | % 126.67/17.31 | GROUND_INST: instantiating (function-axioms) with all_4_14, all_6_22, e2, e0, % 126.67/17.31 | simplifying with (119), (145) gives: % 126.67/17.31 | (237) all_6_22 = all_4_14 % 126.67/17.31 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_9, all_6_21, e3, e0, % 126.67/17.32 | simplifying with (120), (146) gives: % 126.67/17.32 | (238) all_6_21 = all_4_9 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_4, all_6_20, e4, e0, % 126.67/17.32 | simplifying with (121), (147) gives: % 126.67/17.32 | (239) all_6_20 = all_4_4 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_4, e0, e4, e0, % 126.67/17.32 | simplifying with (121) gives: % 126.67/17.32 | (240) all_4_4 = e0 | ~ (op(e0, e4) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_21, e0, e3, e0, % 126.67/17.32 | simplifying with (146) gives: % 126.67/17.32 | (241) all_6_21 = e0 | ~ (op(e0, e3) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_9, e0, e3, e0, % 126.67/17.32 | simplifying with (120) gives: % 126.67/17.32 | (242) all_4_9 = e0 | ~ (op(e0, e3) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_14, e0, e2, e0, % 126.67/17.32 | simplifying with (119) gives: % 126.67/17.32 | (243) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_23, e0, e1, e0, % 126.67/17.32 | simplifying with (144) gives: % 126.67/17.32 | (244) all_6_23 = e0 | ~ (op(e0, e1) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_19, e0, e1, e0, % 126.67/17.32 | simplifying with (118) gives: % 126.67/17.32 | (245) all_4_19 = e0 | ~ (op(e0, e1) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_24, e0, e0, e0, % 126.67/17.32 | simplifying with (143) gives: % 126.67/17.32 | (246) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_24, e0, e0, e0, % 126.67/17.32 | simplifying with (117) gives: % 126.67/17.32 | (247) all_4_24 = e0 | ~ (op(e0, e0) = e0) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_23, all_6_19, e0, e1, % 126.67/17.32 | simplifying with (122), (148) gives: % 126.67/17.32 | (248) all_6_19 = all_4_23 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_18, all_6_18, e1, e1, % 126.67/17.32 | simplifying with (123), (149) gives: % 126.67/17.32 | (249) all_6_18 = all_4_18 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_13, all_6_17, e2, e1, % 126.67/17.32 | simplifying with (124), (150) gives: % 126.67/17.32 | (250) all_6_17 = all_4_13 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_8, all_6_16, e3, e1, % 126.67/17.32 | simplifying with (125), (151) gives: % 126.67/17.32 | (251) all_6_16 = all_4_8 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_3, all_6_15, e4, e1, % 126.67/17.32 | simplifying with (126), (152) gives: % 126.67/17.32 | (252) all_6_15 = all_4_3 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_3, e1, e4, e1, % 126.67/17.32 | simplifying with (126) gives: % 126.67/17.32 | (253) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_16, e1, e3, e1, % 126.67/17.32 | simplifying with (151) gives: % 126.67/17.32 | (254) all_6_16 = e1 | ~ (op(e1, e3) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_17, e1, e2, e1, % 126.67/17.32 | simplifying with (150) gives: % 126.67/17.32 | (255) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_18, e1, e1, e1, % 126.67/17.32 | simplifying with (149) gives: % 126.67/17.32 | (256) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_19, e1, e0, e1, % 126.67/17.32 | simplifying with (148) gives: % 126.67/17.32 | (257) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_23, e1, e0, e1, % 126.67/17.32 | simplifying with (122) gives: % 126.67/17.32 | (258) all_4_23 = e1 | ~ (op(e1, e0) = e1) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_22, all_6_14, e0, e2, % 126.67/17.32 | simplifying with (127), (153) gives: % 126.67/17.32 | (259) all_6_14 = all_4_22 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_17, all_6_13, e1, e2, % 126.67/17.32 | simplifying with (128), (154) gives: % 126.67/17.32 | (260) all_6_13 = all_4_17 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_12, all_6_12, e2, e2, % 126.67/17.32 | simplifying with (129), (155) gives: % 126.67/17.32 | (261) all_6_12 = all_4_12 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with e4, all_6_12, e2, e2, % 126.67/17.32 | simplifying with (21), (155) gives: % 126.67/17.32 | (262) all_6_12 = e4 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_7, all_6_11, e3, e2, % 126.67/17.32 | simplifying with (130), (156) gives: % 126.67/17.32 | (263) all_6_11 = all_4_7 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_6_10, e4, e2, % 126.67/17.32 | simplifying with (131), (157) gives: % 126.67/17.32 | (264) all_6_10 = all_4_2 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with e3, all_6_10, e4, e2, % 126.67/17.32 | simplifying with (22), (157) gives: % 126.67/17.32 | (265) all_6_10 = e3 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_10, e2, e4, e2, % 126.67/17.32 | simplifying with (157) gives: % 126.67/17.32 | (266) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_11, e2, e3, e2, % 126.67/17.32 | simplifying with (156) gives: % 126.67/17.32 | (267) all_6_11 = e2 | ~ (op(e2, e3) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_7, e2, e3, e2, % 126.67/17.32 | simplifying with (130) gives: % 126.67/17.32 | (268) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with e4, e2, e2, e2, simplifying % 126.67/17.32 | with (21) gives: % 126.67/17.32 | (269) e4 = e2 | ~ (op(e2, e2) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_6_13, e2, e1, e2, % 126.67/17.32 | simplifying with (154) gives: % 126.67/17.32 | (270) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_17, e2, e1, e2, % 126.67/17.32 | simplifying with (128) gives: % 126.67/17.32 | (271) all_4_17 = e2 | ~ (op(e2, e1) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_22, e2, e0, e2, % 126.67/17.32 | simplifying with (127) gives: % 126.67/17.32 | (272) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_21, all_6_9, e0, e3, % 126.67/17.32 | simplifying with (132), (158) gives: % 126.67/17.32 | (273) all_6_9 = all_4_21 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_16, all_6_8, e1, e3, % 126.67/17.32 | simplifying with (133), (159) gives: % 126.67/17.32 | (274) all_6_8 = all_4_16 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_11, all_6_7, e2, e3, % 126.67/17.32 | simplifying with (134), (160) gives: % 126.67/17.32 | (275) all_6_7 = all_4_11 % 126.67/17.32 | % 126.67/17.32 | GROUND_INST: instantiating (function-axioms) with all_4_6, all_6_6, e3, e3, % 126.67/17.32 | simplifying with (135), (161) gives: % 126.67/17.33 | (276) all_6_6 = all_4_6 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_6_5, e4, e3, % 126.67/17.33 | simplifying with (136), (162) gives: % 126.67/17.33 | (277) all_6_5 = all_4_1 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with e1, all_6_5, e4, e3, % 126.67/17.33 | simplifying with (23), (162) gives: % 126.67/17.33 | (278) all_6_5 = e1 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_5, e3, e4, e3, % 126.67/17.33 | simplifying with (162) gives: % 126.67/17.33 | (279) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with e1, e3, e4, e3, simplifying % 126.67/17.33 | with (23) gives: % 126.67/17.33 | (280) e3 = e1 | ~ (op(e3, e4) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_6, e3, e3, e3, % 126.67/17.33 | simplifying with (135) gives: % 126.67/17.33 | (281) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_7, e3, e2, e3, % 126.67/17.33 | simplifying with (160) gives: % 126.67/17.33 | (282) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_8, e3, e1, e3, % 126.67/17.33 | simplifying with (159) gives: % 126.67/17.33 | (283) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_16, e3, e1, e3, % 126.67/17.33 | simplifying with (133) gives: % 126.67/17.33 | (284) all_4_16 = e3 | ~ (op(e3, e1) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_9, e3, e0, e3, % 126.67/17.33 | simplifying with (158) gives: % 126.67/17.33 | (285) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_21, e3, e0, e3, % 126.67/17.33 | simplifying with (132) gives: % 126.67/17.33 | (286) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_20, all_6_4, e0, e4, % 126.67/17.33 | simplifying with (137), (163) gives: % 126.67/17.33 | (287) all_6_4 = all_4_20 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_15, all_6_3, e1, e4, % 126.67/17.33 | simplifying with (138), (164) gives: % 126.67/17.33 | (288) all_6_3 = all_4_15 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_10, all_6_2, e2, e4, % 126.67/17.33 | simplifying with (139), (165) gives: % 126.67/17.33 | (289) all_6_2 = all_4_10 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_5, all_6_1, e3, e4, % 126.67/17.33 | simplifying with (140), (166) gives: % 126.67/17.33 | (290) all_6_1 = all_4_5 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_6_0, e4, e4, % 126.67/17.33 | simplifying with (141), (167) gives: % 126.67/17.33 | (291) all_6_0 = all_4_0 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with e0, all_6_0, e4, e4, % 126.67/17.33 | simplifying with (24), (167) gives: % 126.67/17.33 | (292) all_6_0 = e0 % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_0, e4, e4, e4, % 126.67/17.33 | simplifying with (141) gives: % 126.67/17.33 | (293) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_1, e4, e3, e4, % 126.67/17.33 | simplifying with (166) gives: % 126.67/17.33 | (294) all_6_1 = e4 | ~ (op(e4, e3) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_5, e4, e3, e4, % 126.67/17.33 | simplifying with (140) gives: % 126.67/17.33 | (295) all_4_5 = e4 | ~ (op(e4, e3) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_2, e4, e2, e4, % 126.67/17.33 | simplifying with (165) gives: % 126.67/17.33 | (296) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_10, e4, e2, e4, % 126.67/17.33 | simplifying with (139) gives: % 126.67/17.33 | (297) all_4_10 = e4 | ~ (op(e4, e2) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_3, e4, e1, e4, % 126.67/17.33 | simplifying with (164) gives: % 126.67/17.33 | (298) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_15, e4, e1, e4, % 126.67/17.33 | simplifying with (138) gives: % 126.67/17.33 | (299) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_4, e4, e0, e4, % 126.67/17.33 | simplifying with (163) gives: % 126.67/17.33 | (300) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_20, e4, e0, e4, % 126.67/17.33 | simplifying with (137) gives: % 126.67/17.33 | (301) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_4, e0, e0, e4, % 126.67/17.33 | simplifying with (163) gives: % 126.67/17.33 | (302) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_21, e0, e0, e3, % 126.67/17.33 | simplifying with (132) gives: % 126.67/17.33 | (303) all_4_21 = e0 | ~ (op(e3, e0) = e0) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_14, e0, e0, e2, % 126.67/17.33 | simplifying with (153) gives: % 126.67/17.33 | (304) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_19, e0, e0, e1, % 126.67/17.33 | simplifying with (148) gives: % 126.67/17.33 | (305) all_6_19 = e0 | ~ (op(e1, e0) = e0) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_23, e0, e0, e1, % 126.67/17.33 | simplifying with (122) gives: % 126.67/17.33 | (306) all_4_23 = e0 | ~ (op(e1, e0) = e0) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_3, e1, e1, e4, % 126.67/17.33 | simplifying with (164) gives: % 126.67/17.33 | (307) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_8, e1, e1, e3, % 126.67/17.33 | simplifying with (159) gives: % 126.67/17.33 | (308) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_13, e1, e1, e2, % 126.67/17.33 | simplifying with (154) gives: % 126.67/17.33 | (309) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_23, e1, e1, e0, % 126.67/17.33 | simplifying with (144) gives: % 126.67/17.33 | (310) all_6_23 = e1 | ~ (op(e0, e1) = e1) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_2, e2, e2, e4, % 126.67/17.33 | simplifying with (165) gives: % 126.67/17.33 | (311) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_10, e2, e2, e4, % 126.67/17.33 | simplifying with (139) gives: % 126.67/17.33 | (312) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_7, e2, e2, e3, % 126.67/17.33 | simplifying with (160) gives: % 126.67/17.33 | (313) all_6_7 = e2 | ~ (op(e3, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_11, e2, e2, e3, % 126.67/17.33 | simplifying with (134) gives: % 126.67/17.33 | (314) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_17, e2, e2, e1, % 126.67/17.33 | simplifying with (150) gives: % 126.67/17.33 | (315) all_6_17 = e2 | ~ (op(e1, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_13, e2, e2, e1, % 126.67/17.33 | simplifying with (124) gives: % 126.67/17.33 | (316) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_6_22, e2, e2, e0, % 126.67/17.33 | simplifying with (145) gives: % 126.67/17.33 | (317) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 126.67/17.33 | % 126.67/17.33 | GROUND_INST: instantiating (function-axioms) with all_4_14, e2, e2, e0, % 126.67/17.33 | simplifying with (119) gives: % 126.67/17.33 | (318) all_4_14 = e2 | ~ (op(e0, e2) = e2) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_1, e3, e3, e4, % 126.67/17.34 | simplifying with (166) gives: % 126.67/17.34 | (319) all_6_1 = e3 | ~ (op(e4, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_4_5, e3, e3, e4, % 126.67/17.34 | simplifying with (140) gives: % 126.67/17.34 | (320) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_11, e3, e3, e2, % 126.67/17.34 | simplifying with (156) gives: % 126.67/17.34 | (321) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_4_7, e3, e3, e2, % 126.67/17.34 | simplifying with (130) gives: % 126.67/17.34 | (322) all_4_7 = e3 | ~ (op(e2, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_16, e3, e3, e1, % 126.67/17.34 | simplifying with (151) gives: % 126.67/17.34 | (323) all_6_16 = e3 | ~ (op(e1, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_21, e3, e3, e0, % 126.67/17.34 | simplifying with (146) gives: % 126.67/17.34 | (324) all_6_21 = e3 | ~ (op(e0, e3) = e3) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_5, e4, e4, e3, % 126.67/17.34 | simplifying with (162) gives: % 126.67/17.34 | (325) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_4_1, e4, e4, e3, % 126.67/17.34 | simplifying with (136) gives: % 126.67/17.34 | (326) all_4_1 = e4 | ~ (op(e3, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with e1, e4, e4, e3, simplifying % 126.67/17.34 | with (23) gives: % 126.67/17.34 | (327) e4 = e1 | ~ (op(e3, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, e4, e2, % 126.67/17.34 | simplifying with (131) gives: % 126.67/17.34 | (328) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with e3, e4, e4, e2, simplifying % 126.67/17.34 | with (22) gives: % 126.67/17.34 | (329) e4 = e3 | ~ (op(e2, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_15, e4, e4, e1, % 126.67/17.34 | simplifying with (152) gives: % 126.67/17.34 | (330) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_4_3, e4, e4, e1, % 126.67/17.34 | simplifying with (126) gives: % 126.67/17.34 | (331) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | GROUND_INST: instantiating (function-axioms) with all_6_20, e4, e4, e0, % 126.67/17.34 | simplifying with (147) gives: % 126.67/17.34 | (332) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 126.67/17.34 | % 126.67/17.34 | COMBINE_EQS: (291), (292) imply: % 126.67/17.34 | (333) all_4_0 = e0 % 126.67/17.34 | % 126.67/17.34 | SIMP: (333) implies: % 126.67/17.34 | (334) all_4_0 = e0 % 126.67/17.34 | % 126.67/17.34 | COMBINE_EQS: (277), (278) imply: % 126.67/17.34 | (335) all_4_1 = e1 % 126.67/17.34 | % 126.67/17.34 | SIMP: (335) implies: % 126.67/17.34 | (336) all_4_1 = e1 % 126.67/17.34 | % 126.67/17.34 | COMBINE_EQS: (264), (265) imply: % 126.67/17.34 | (337) all_4_2 = e3 % 126.67/17.34 | % 126.67/17.34 | SIMP: (337) implies: % 126.67/17.34 | (338) all_4_2 = e3 % 126.67/17.34 | % 126.67/17.34 | COMBINE_EQS: (261), (262) imply: % 126.67/17.34 | (339) all_4_12 = e4 % 126.67/17.34 | % 126.67/17.34 | SIMP: (339) implies: % 126.67/17.34 | (340) all_4_12 = e4 % 126.67/17.34 | % 126.67/17.34 | REDUCE: (116), (334), (336) imply: % 126.67/17.34 | (341) ~ (e1 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (341) implies: % 126.67/17.34 | (342) ~ (e1 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (115), (334), (338) imply: % 126.67/17.34 | (343) ~ (e3 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (343) implies: % 126.67/17.34 | (344) ~ (e3 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (114), (334) imply: % 126.67/17.34 | (345) ~ (all_4_3 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (345) implies: % 126.67/17.34 | (346) ~ (all_4_3 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (113), (334) imply: % 126.67/17.34 | (347) ~ (all_4_4 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (347) implies: % 126.67/17.34 | (348) ~ (all_4_4 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (112), (334) imply: % 126.67/17.34 | (349) ~ (all_4_5 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (349) implies: % 126.67/17.34 | (350) ~ (all_4_5 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (111), (334) imply: % 126.67/17.34 | (351) ~ (all_4_10 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (351) implies: % 126.67/17.34 | (352) ~ (all_4_10 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (110), (334) imply: % 126.67/17.34 | (353) ~ (all_4_20 = e0) % 126.67/17.34 | % 126.67/17.34 | SIMP: (353) implies: % 126.67/17.34 | (354) ~ (all_4_20 = e0) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (109), (336), (338) imply: % 126.67/17.34 | (355) ~ (e3 = e1) % 126.67/17.34 | % 126.67/17.34 | SIMP: (355) implies: % 126.67/17.34 | (356) ~ (e3 = e1) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (108), (336) imply: % 126.67/17.34 | (357) ~ (all_4_3 = e1) % 126.67/17.34 | % 126.67/17.34 | SIMP: (357) implies: % 126.67/17.34 | (358) ~ (all_4_3 = e1) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (107), (336) imply: % 126.67/17.34 | (359) ~ (all_4_4 = e1) % 126.67/17.34 | % 126.67/17.34 | SIMP: (359) implies: % 126.67/17.34 | (360) ~ (all_4_4 = e1) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (106), (336) imply: % 126.67/17.34 | (361) ~ (all_4_11 = e1) % 126.67/17.34 | % 126.67/17.34 | SIMP: (361) implies: % 126.67/17.34 | (362) ~ (all_4_11 = e1) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (105), (336) imply: % 126.67/17.34 | (363) ~ (all_4_16 = e1) % 126.67/17.34 | % 126.67/17.34 | SIMP: (363) implies: % 126.67/17.34 | (364) ~ (all_4_16 = e1) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (104), (338) imply: % 126.67/17.34 | (365) ~ (all_4_3 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (365) implies: % 126.67/17.34 | (366) ~ (all_4_3 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (103), (338) imply: % 126.67/17.34 | (367) ~ (all_4_4 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (367) implies: % 126.67/17.34 | (368) ~ (all_4_4 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (102), (338) imply: % 126.67/17.34 | (369) ~ (all_4_7 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (369) implies: % 126.67/17.34 | (370) ~ (all_4_7 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (101), (338), (340) imply: % 126.67/17.34 | (371) ~ (e4 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (371) implies: % 126.67/17.34 | (372) ~ (e4 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (100), (338) imply: % 126.67/17.34 | (373) ~ (all_4_17 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (373) implies: % 126.67/17.34 | (374) ~ (all_4_17 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (99), (338) imply: % 126.67/17.34 | (375) ~ (all_4_22 = e3) % 126.67/17.34 | % 126.67/17.34 | SIMP: (375) implies: % 126.67/17.34 | (376) ~ (all_4_22 = e3) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (79), (340) imply: % 126.67/17.34 | (377) ~ (all_4_7 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (69), (340) imply: % 126.67/17.34 | (378) ~ (all_4_10 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (64), (340) imply: % 126.67/17.34 | (379) ~ (all_4_11 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (59), (340) imply: % 126.67/17.34 | (380) ~ (all_4_13 = e4) % 126.67/17.34 | % 126.67/17.34 | SIMP: (380) implies: % 126.67/17.34 | (381) ~ (all_4_13 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (58), (340) imply: % 126.67/17.34 | (382) ~ (all_4_14 = e4) % 126.67/17.34 | % 126.67/17.34 | SIMP: (382) implies: % 126.67/17.34 | (383) ~ (all_4_14 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (57), (340) imply: % 126.67/17.34 | (384) ~ (all_4_17 = e4) % 126.67/17.34 | % 126.67/17.34 | SIMP: (384) implies: % 126.67/17.34 | (385) ~ (all_4_17 = e4) % 126.67/17.34 | % 126.67/17.34 | REDUCE: (56), (340) imply: % 126.67/17.34 | (386) ~ (all_4_22 = e4) % 126.67/17.34 | % 126.67/17.34 | SIMP: (386) implies: % 126.67/17.34 | (387) ~ (all_4_22 = e4) % 126.67/17.34 | % 126.67/17.34 | BETA: splitting (226) gives: % 126.67/17.34 | % 126.67/17.35 | Case 1: % 126.67/17.35 | | % 126.67/17.35 | | (388) (all_9_0 = e0 & op(e4, e4) = e0) | (all_9_2 = e0 & op(e3, e4) = e0) % 126.67/17.35 | | % 126.67/17.35 | | BETA: splitting (388) gives: % 126.67/17.35 | | % 126.67/17.35 | | Case 1: % 126.67/17.35 | | | % 126.67/17.35 | | | (389) all_9_0 = e0 & op(e4, e4) = e0 % 126.67/17.35 | | | % 126.67/17.35 | | | ALPHA: (389) implies: % 126.67/17.35 | | | (390) all_9_0 = e0 % 126.67/17.35 | | | % 126.67/17.35 | | | BETA: splitting (227) gives: % 126.67/17.35 | | | % 126.67/17.35 | | | Case 1: % 126.67/17.35 | | | | % 126.67/17.35 | | | | (391) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = % 126.67/17.35 | | | | e1) % 126.67/17.35 | | | | % 126.67/17.35 | | | | BETA: splitting (391) gives: % 126.67/17.35 | | | | % 126.67/17.35 | | | | Case 1: % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | (392) all_9_0 = e1 & op(e4, e4) = e1 % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | ALPHA: (392) implies: % 126.67/17.35 | | | | | (393) op(e4, e4) = e1 % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | REF_CLOSE: (24), (342), (393), (function-axioms) are inconsistent by % 126.67/17.35 | | | | | sub-proof #321. % 126.67/17.35 | | | | | % 126.67/17.35 | | | | Case 2: % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | (394) all_9_2 = e1 & op(e3, e4) = e1 % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | ALPHA: (394) implies: % 126.67/17.35 | | | | | (395) all_9_2 = e1 % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | BETA: splitting (213) gives: % 126.67/17.35 | | | | | % 126.67/17.35 | | | | | Case 1: % 126.67/17.35 | | | | | | % 126.67/17.35 | | | | | | (396) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, % 126.67/17.35 | | | | | | e3) = e3) % 126.67/17.35 | | | | | | % 126.67/17.35 | | | | | | BETA: splitting (396) gives: % 126.67/17.35 | | | | | | % 126.67/17.35 | | | | | | Case 1: % 126.67/17.35 | | | | | | | % 126.67/17.35 | | | | | | | (397) all_9_6 = e3 & op(e2, e4) = e3 % 126.67/17.35 | | | | | | | % 126.67/17.35 | | | | | | | ALPHA: (397) implies: % 126.67/17.35 | | | | | | | (398) all_9_6 = e3 % 126.67/17.35 | | | | | | | % 126.67/17.35 | | | | | | | BETA: splitting (214) gives: % 126.67/17.35 | | | | | | | % 126.67/17.35 | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | | (399) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & % 126.67/17.35 | | | | | | | | op(e2, e3) = e4) % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | | REF_CLOSE: (130), (329), (372), (377), (399), (function-axioms) % 126.67/17.35 | | | | | | | | are inconsistent by sub-proof #318. % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | Case 2: % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | | (400) (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 & % 126.67/17.35 | | | | | | | | op(e2, e1) = e4) | (all_9_18 = e4 & op(e2, e0) = e4) % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | | BETA: splitting (400) gives: % 126.67/17.35 | | | | | | | | % 126.67/17.35 | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | % 126.67/17.35 | | | | | | | | | (401) all_9_8 = e4 & op(e2, e2) = e4 % 126.67/17.35 | | | | | | | | | % 126.67/17.35 | | | | | | | | | ALPHA: (401) implies: % 126.67/17.35 | | | | | | | | | (402) all_9_8 = e4 % 126.67/17.35 | | | | | | | | | % 126.67/17.35 | | | | | | | | | BETA: splitting (332) gives: % 126.67/17.35 | | | | | | | | | % 126.67/17.35 | | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | (403) ~ (op(e0, e4) = e4) % 126.67/17.35 | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | PRED_UNIFY: (11), (403) imply: % 126.67/17.35 | | | | | | | | | | (404) ~ (unit = e0) % 126.67/17.35 | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | BETA: splitting (233) gives: % 126.67/17.35 | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | (405) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 126.67/17.35 | | | | | | | | | | | op(e3, e4) = e4) % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | REF_CLOSE: (18), (19), (278), (293), (325), (334), (405) are % 126.67/17.35 | | | | | | | | | | | inconsistent by sub-proof #315. % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | Case 2: % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | (406) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 % 126.67/17.35 | | | | | | | | | | | & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) % 126.67/17.35 | | | | | | | | | | | = e4) % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | BETA: splitting (406) gives: % 126.67/17.35 | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | (407) all_9_6 = e4 & op(e2, e4) = e4 % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | ALPHA: (407) implies: % 126.67/17.35 | | | | | | | | | | | | (408) op(e2, e4) = e4 % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | REF_CLOSE: (329), (372), (408) are inconsistent by sub-proof % 126.67/17.35 | | | | | | | | | | | | #320. % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | Case 2: % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | (409) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 126.67/17.35 | | | | | | | | | | | | & op(e0, e4) = e4) % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | BETA: splitting (409) gives: % 126.67/17.35 | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | (410) all_9_12 = e4 & op(e1, e4) = e4 % 126.67/17.35 | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | ALPHA: (410) implies: % 126.67/17.35 | | | | | | | | | | | | | (411) all_9_12 = e4 % 126.67/17.35 | | | | | | | | | | | | | (412) op(e1, e4) = e4 % 126.67/17.35 | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | BETA: splitting (330) gives: % 126.67/17.35 | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | Case 1: % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | (413) ~ (op(e1, e4) = e4) % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | PRED_UNIFY: (412), (413) imply: % 126.67/17.35 | | | | | | | | | | | | | | (414) $false % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | Case 2: % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | (415) all_6_15 = e4 % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | COMBINE_EQS: (252), (415) imply: % 126.67/17.35 | | | | | | | | | | | | | | (416) all_4_3 = e4 % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | SIMP: (416) implies: % 126.67/17.35 | | | | | | | | | | | | | | (417) all_4_3 = e4 % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | REDUCE: (98), (417) imply: % 126.67/17.35 | | | | | | | | | | | | | | (418) ~ (all_4_4 = e4) % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | SIMP: (418) implies: % 126.67/17.35 | | | | | | | | | | | | | | (419) ~ (all_4_4 = e4) % 126.67/17.35 | | | | | | | | | | | | | | % 126.67/17.35 | | | | | | | | | | | | | | REDUCE: (97), (417) imply: % 126.67/17.36 | | | | | | | | | | | | | | (420) ~ (all_4_8 = e4) % 126.67/17.36 | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | SIMP: (420) implies: % 126.67/17.36 | | | | | | | | | | | | | | (421) ~ (all_4_8 = e4) % 126.67/17.36 | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | BETA: splitting (229) gives: % 126.67/17.36 | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | (422) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & % 126.67/17.36 | | | | | | | | | | | | | | | op(e3, e4) = e2) % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (23), (390), (422), (function-axioms) % 126.67/17.36 | | | | | | | | | | | | | | | are inconsistent by sub-proof #312. % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | (423) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 126.67/17.36 | | | | | | | | | | | | | | | = e2) % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 126.67/17.36 | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | (424) all_9_6 = e2 & op(e2, e4) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (265), (266), (424) are inconsistent by % 126.67/17.36 | | | | | | | | | | | | | | | | sub-proof #311. % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | (425) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | & op(e0, e4) = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | BETA: splitting (425) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | (426) all_9_12 = e2 & op(e1, e4) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | ALPHA: (426) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | (427) all_9_12 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (411), (427) are inconsistent by sub-proof % 126.67/17.36 | | | | | | | | | | | | | | | | | #310. % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | (428) all_9_20 = e2 & op(e0, e4) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | ALPHA: (428) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | (429) all_9_20 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | (430) all_6_20 = e4 % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (239), (419), (430) are inconsistent by sub-proof % 126.67/17.36 | | | | | | | | | | | | | | | | | | #309. % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | (431) ~ (all_6_20 = e4) % 126.67/17.36 | | | | | | | | | | | | | | | | | | (432) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 126.67/17.36 | | | | | | | | | | | | | | | | | | all_6_20 = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (433) all_6_20 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (433) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (434) all_4_4 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | SIMP: (434) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (435) all_4_4 = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (94), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (436) ~ (all_4_9 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | SIMP: (436) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (437) ~ (all_4_9 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (93), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (438) ~ (all_4_14 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | SIMP: (438) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (439) ~ (all_4_14 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (92), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (440) ~ (all_4_19 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | SIMP: (440) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (441) ~ (all_4_19 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (91), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (442) ~ (all_4_24 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | SIMP: (442) implies: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (443) ~ (all_4_24 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (419), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (444) ~ (e4 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (445) ~ (e3 = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (435) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | (446) op(e0, e4) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | (447) ~ (op(e0, e3) = e3) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | (448) ~ (op(e4, e3) = e3) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (10), (448) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | (449) ~ (unit = e4) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (140), (448) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | (450) ~ (all_4_5 = e3) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | (451) ~ (op(e2, e4) = e4) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (11), (451) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | (452) ~ (unit = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | (453) ~ (op(e4, e3) = e4) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (453) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | (454) ~ (unit = e3) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | (455) unit = e4 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (455) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | (456) $false % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (456) is inconsistent. % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | (457) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | (458) unit = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (452), (458) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | (459) $false % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (459) is inconsistent. % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | (460) unit = e3 | unit = e1 | unit = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (461) unit = e3 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (454), (461) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (462) $false % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (462) is inconsistent. % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (463) unit = e1 | unit = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) unit = e1 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) op(e1, e2) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) op(e1, e0) = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) op(e4, e1) = e4 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) op(e3, e1) = e3 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) op(e2, e1) = e2 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) op(e1, e1) = e1 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (464) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) op(e0, e1) = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (op(e1, e0) = e0) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (466), (472) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) $false % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent. % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_4_23 = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (474) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_6_19 = e0 % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (474) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) ~ (all_4_22 = e0) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) ~ (op(e1, e2) = e2) % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (465), (477) imply: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) $false % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_4_13 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (479) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_6_17 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (479) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) ~ (all_4_10 = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (479) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) ~ (all_4_11 = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) ~ (op(e3, e1) = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (468), (483) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) $false % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (484) is inconsistent. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_4_16 = e3 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) ~ (all_4_6 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) ~ (all_4_11 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) ~ (all_4_15 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_4_18 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (489) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_4_18 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) ~ (all_4_19 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (491) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) ~ (all_4_19 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (485) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) ~ (all_4_21 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (493) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) ~ (all_4_21 = e3) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) ~ (op(e1, e1) = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (470), (495) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) $false % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (496) is inconsistent. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_6_18 = e1 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (497) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_4_18 = e1 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (498) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_4_18 = e1 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (499) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) ~ (all_4_8 = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (499) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) ~ (all_4_15 = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (499) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) ~ (all_4_17 = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (499) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) ~ (all_4_19 = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (503) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) ~ (all_4_19 = e1) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) ~ (op(e4, e1) = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (467), (505) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) $false % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_6_3 = e4 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (507) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_4_15 = e4 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (508) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (all_4_5 = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (508) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) ~ (all_4_19 = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (510) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_4_19 = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (508) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) ~ (all_4_20 = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (512) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) ~ (all_4_20 = e4) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) ~ (op(e2, e1) = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (469), (514) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) $false % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_6_13 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (516) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_4_17 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (517) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) ~ (all_4_7 = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (517) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_4_22 = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) ~ (all_4_22 = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) ~ (op(e0, e1) = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (471), (521) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) $false % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (522) is inconsistent. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_6_23 = e0 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (523) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_4_19 = e0 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (524) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_4_19 = e0 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (525) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_4_9 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (525) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) ~ (all_4_14 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (525) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) ~ (all_4_24 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (528) implies: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) ~ (all_4_24 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (511), (525) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) ~ (e4 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (441), (525) imply: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) ~ (e2 = e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (265), (266), (268), (518), (532) are % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_9_8 = e2 & op(e2, e2) = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (269), (534) are inconsistent by sub-proof % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_9_11 = e2 & op(e2, e1) = e2 % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 126.67/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_9_11 = e2 % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_44 & op(e2, e4) = all_8_45 & % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44) & $i(all_8_45)) % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (23), (233), (278), (293), % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (334), (372), (411), (429), (467), % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539), (function-axioms) are inconsistent by % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #301. % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.03/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_44) & % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (540) implies: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) op(e2, e4) = all_8_45 % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) op(e4, all_8_45) = e2 % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (293), (334), (453), (543) are inconsistent % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #299. % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (544) gives: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_9_4 = e4 & op(e4, e2) = e4 % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (545) implies: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) op(e4, e2) = e4 % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (296), (378), (546) are inconsistent by % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #298. % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.03/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (547) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_9_9 = e4 & op(e4, e1) = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_9_9 = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_6_7 = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (550) imply: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_4_11 = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (551) imply: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) $false % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (552) is inconsistent. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) ~ (all_6_7 = e4) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_6_14 = e4 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (387), (555) are inconsistent by sub-proof % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) ~ (all_6_14 = e4) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (558) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_9_1 = e3 & op(e4, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (448), (559) are inconsistent by sub-proof #296. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_9_3 = e3 & op(e3, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) op(e3, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (486), (561) are inconsistent by sub-proof % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #295. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e3) | (all_9_21 = e3 & op(e0, e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_9_7 = e3 & op(e2, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) op(e2, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (321), (370), (564) are inconsistent by % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) (all_9_13 = e3 & op(e1, e3) = e3) | (all_9_21 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_9_13 = e3 & op(e1, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_9_13 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) op(e1, e3) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (356), (395), (486), (569) are inconsistent % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #293. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (570) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_9_5 = e3 & op(e3, e2) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) op(e3, e2) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (282), (487), (572) are inconsistent by % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (573) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_9_10 = e3 & op(e3, e1) = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (574) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_9_10 = e3 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_9_4 = e0 & op(e4, e2) = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_9_4 = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (227), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (239), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (265), (266), (278), (289), (293), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311), (325), (329), (330), (331), (332), (334), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (411), (429), % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (481), (549), (578), (function-axioms) are % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #258. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_9_5 = e0 & op(e3, e2) = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (579) implies: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_9_5 = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_6_14 = e2 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (520), (581) are inconsistent by sub-proof % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #257. % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) ~ (all_6_14 = e2) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_9_6 = e0 & op(e2, e4) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (398), (585) are inconsistent by sub-proof % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #256. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_9_7 = e0 & op(e2, e3) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (586) implies: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_9_7 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_6_14 = e3 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (376), (588) are inconsistent by sub-proof % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #255. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) ~ (all_6_14 = e3) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_6_14 = e1 | all_6_14 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_6_7 = e2 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (591) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_4_11 = e2 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (482), (592) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) $false % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (593) is inconsistent. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) ~ (all_6_7 = e2) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_6_7 = e3 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (596) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_4_11 = e3 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (487), (597) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) $false % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (598) is inconsistent. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) ~ (all_6_7 = e3) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_6_7 = e1 | all_6_7 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_6_7 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (601) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_4_11 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (602) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) $false % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (603) is inconsistent. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_6_7 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (604) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_4_11 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (605) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) ~ (all_4_14 = e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (605) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) op(e3, e2) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (608) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_9_12 = e0 & op(e1, e4) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (411), (609) are inconsistent by sub-proof % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #254. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_9_13 = e0 & op(e1, e3) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (610) implies: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_9_13 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (611) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) e3 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (612) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) $false % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (613) is inconsistent. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (614) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) all_9_14 = e0 & op(e1, e2) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (615) implies: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_9_14 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (201), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (217), (227), (229), (231), (233), (237), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (251), (252), (253), (254), (257), (265), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (269), (278), (289), (293), (311), (314), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (411), (429), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (475), (481), (500), (567), (605), (616), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #242. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (617) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_9_15 = e0 & op(e1, e1) = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (618) implies: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_9_15 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e1) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (253), (254), (358), (500), (620) are % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (621) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_9_14 = e1 & op(e1, e2) = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (255), (265), (266), (278), (293), (325), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (429), (480), (622), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_9_15 = e1 & op(e1, e1) = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_9_15 = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (619), (625) imply: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) e1 = e0 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (626), (function-axioms) are % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #264. % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_9_19 = e1 & op(e1, e0) = e1 % 127.04/17.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (257), (265), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (293), (329), (330), (331), (332), (334), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (395), (475), (627), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_9_19 = e0 & op(e1, e0) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (628) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_9_19 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (590) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_6_14 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (630) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_4_22 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (631) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_4_22 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (632) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) ~ (all_4_7 = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (632) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) ~ (all_4_20 = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (632) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) ~ (e4 = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (520), (632) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (e2 = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (632) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) op(e2, e0) = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (253), (254), (358), (500), (638) are % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (639) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_9_14 = e1 & op(e1, e2) = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (255), (265), (266), (278), (293), (325), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (429), (480), (640), % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_9_15 = e1 & op(e1, e1) = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_9_15 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_9_24 = e0 & op(e0, e0) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) op(e0, e0) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (246), (529), (645) are inconsistent by % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #240. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (648) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_9_20 = e0 & op(e0, e4) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (429), (649) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #239. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_9_21 = e0 & op(e0, e3) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) op(e0, e3) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) ~ (op(e0, e3) = e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (651), (652) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) $false % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (653) is inconsistent. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) all_4_9 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (526), (654) imply: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) $false % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (655) is inconsistent. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_9_22 = e0 & op(e0, e2) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (527), (657) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_9_23 = e0 & op(e0, e1) = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (658) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_9_23 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e2) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (411), (567), (660) are inconsistent % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #252. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_9_14 = e2 & op(e1, e2) = e2 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (662) implies: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_9_14 = e2 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_6_11 = e4 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (377), (664) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) ~ (all_6_11 = e4) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (666) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_6_11 = e2 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (518), (667) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_6_11 = e3 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (370), (669) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #235. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) ~ (all_6_11 = e3) % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_6_11 = e1 | all_6_11 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (671) gives: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_6_11 = e1 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (633), (672) are inconsistent by sub-proof % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #234. % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_6_11 = e0 % 127.04/17.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (673) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_4_7 = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (674) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_4_7 = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (675) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) op(e2, e3) = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_45, % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (22), (541) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_8_45 = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (451), (541) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) ~ (all_8_45 = e4) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e2, % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_4_5 = e2 | ~ (op(e4, e3) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_20, e2, % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (137) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_4_20 = e2 | ~ (op(e4, e0) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (677) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) op(e4, e3) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) ~ (op(e2, e3) = e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) ~ (op(e4, e3) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (681), (683) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) $false % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (684) is inconsistent. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_4_5 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (685) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) ~ (all_4_10 = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (685) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) ~ (all_4_20 = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (687) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) ~ (all_4_20 = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_9_0 = e2 & op(e4, e4) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (690) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_9_0 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (390), (691) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) e2 = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (692) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) e2 = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (663), (693) imply: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_9_14 = e0 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (643), (694), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_9_1 = e2 & op(e4, e3) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) all_9_1 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_9_2 = e2 & op(e3, e4) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) op(e3, e4) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (699), (function-axioms) are % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #313. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_9_3 = e2 & op(e3, e3) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (700) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_9_3 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_9_16 = e2 & op(e4, e0) = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (703) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_9_16 = e2 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (278), (325), (701), (705) are % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_9_5 = e4 & op(e3, e2) = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (580), (707) are inconsistent by sub-proof % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #231. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (708) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_9_10 = e4 & op(e3, e1) = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (575), (709) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #230. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) all_9_17 = e4 & op(e3, e0) = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (710) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) all_9_17 = e4 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (712) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_9_0 = e3 & op(e4, e4) = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (390), (713) are inconsistent by sub-proof % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_9_1 = e3 & op(e4, e3) = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (448), (714) are inconsistent by sub-proof #296. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_9_4 = e3 & op(e4, e2) = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_9_4 = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (273), (285), (494), (704), (718) are % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_9_18 = e3 & op(e2, e0) = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) op(e2, e0) = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (376), (721), (function-axioms) are % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_9_19 = e3 & op(e1, e0) = e3 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (227), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (239), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (265), (266), (278), (289), (293), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311), (325), (329), (330), (331), (332), (334), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (411), (429), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (481), (549), (629), (717), (723), % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #225. % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_9_24 = e3 & op(e0, e0) = e3 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_9_24 = e3 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e1) % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_9_0 = e1 & op(e4, e4) = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (727) implies: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) op(e4, e4) = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (342), (728), (function-axioms) are % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_9_1 = e1 & op(e4, e3) = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (729) implies: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_9_1 = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (696), (730) imply: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) e2 = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (731) imply: % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_9_16 = e1 % 127.04/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (199), (202), (211), (217), (227), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (237), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (269), (272), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273), (278), (285), (289), (293), (311), (314), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (390), (395), (398), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (411), (429), (439), (448), (481), (494), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520), (537), (549), (567), (587), (605), (629), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643), (663), (732), (function-axioms) are % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_9_4 = e1 & op(e4, e2) = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (734) implies: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_9_4 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (717), (735) imply: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) e3 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (736) implies: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) e3 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (725), (737) imply: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) all_9_24 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (199), (202), (211), (217), (227), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (231), (233), (237), (239), (252), (253), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (269), (272), (273), (278), (285), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (311), (314), (317), (325), (329), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330), (331), (332), (334), (342), (344), (346), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348), (356), (358), (360), (366), (368), (372), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376), (390), (395), (398), (402), (411), (429), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (481), (494), (520), (537), (567), (587), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (629), (643), (663), (738), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #205. % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e1) % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_9_9 = e1 & op(e4, e1) = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_9_9 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (741) imply: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) e4 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (742) implies: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) e4 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (711), (743) imply: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_9_17 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (228), (229), (230), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (239), (252), (253), (265), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (273), (278), (285), (289), (293), (311), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (376), (390), (395), (398), (402), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (448), (481), (494), (537), (549), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (629), (704), (717), (744), % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #204. % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_9_16 = e1 & op(e4, e0) = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (745) implies: % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_9_16 = e1 % 127.21/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (199), (202), (211), (217), (227), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (237), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (269), (272), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273), (278), (285), (289), (293), (311), (314), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (390), (395), (398), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (411), (429), (439), (448), (481), (494), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520), (537), (549), (567), (587), (605), (629), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643), (663), (746), (function-axioms) are % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_9_9 = e3 & op(e4, e1) = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (748) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_9_9 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (749) imply: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) e4 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (750) are % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #217. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_9_16 = e3 & op(e4, e0) = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_9_16 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (704), (752) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #229. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_9_17 = e2 & op(e3, e0) = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_9_17 = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (222), (233), (278), (293), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (334), (372), (411), (429), (575), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580), (701), (754) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #203. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (755) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_9_18 = e2 & op(e2, e0) = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (756) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) op(e2, e0) = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (520), (757) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #214. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_9_19 = e2 & op(e1, e0) = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (629), (643), (663), (759), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #209. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_9_24 = e2 & op(e0, e0) = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (760) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_9_24 = e2 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_9_1 = e4 & op(e4, e3) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (453), (763) are inconsistent by sub-proof #300. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_9_3 = e4 & op(e3, e3) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (701), (764) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #233. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_9_7 = e4 & op(e2, e3) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_9_7 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (587), (767) imply: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) e4 = e0 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (768) imply: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) $false % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (769) is inconsistent. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) (all_9_13 = e4 & op(e1, e3) = e4) | (all_9_21 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (770) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_9_13 = e4 & op(e1, e3) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (771) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_9_13 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (772) imply: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) e4 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (773) imply: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_9_12 = e3 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (429), (774) are inconsistent % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #303. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_9_21 = e4 & op(e0, e3) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (775) implies: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_9_21 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (278), (325), (701), (777) are % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #232. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_9_5 = e4 & op(e3, e2) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (580), (779) are inconsistent by sub-proof % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #231. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_9_10 = e4 & op(e3, e1) = e4 % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (575), (781) % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #230. % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_9_17 = e4 & op(e3, e0) = e4 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (782) implies: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_9_17 = e4 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) (all_9_20 = e3 & op(e0, e4) = e3) | (all_9_21 = e3 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e3) % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (447), (784), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #200. % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) (all_9_22 = e3 & op(e0, e2) = e3) | (all_9_23 = e3 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) | (all_9_24 = e3 & op(e0, e0) % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_9_22 = e3 & op(e0, e2) = e3 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (786) implies: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_9_22 = e3 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e1) % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_9_20 = e1 & op(e0, e4) = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_9_20 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (790), (function-axioms) are % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_9_21 = e1 & op(e0, e3) = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_9_21 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (776), (792) imply: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) e4 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (793) implies: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) e4 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (794) imply: % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_9_17 = e1 % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (229), (231), (233), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (273), (278), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285), (293), (325), (329), (330), (331), (332), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (342), (344), (346), (348), (356), (358), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360), (366), (368), (372), (376), (390), (395), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (411), (429), (494), (537), (587), % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629), (761), (795), (function-axioms) are % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 127.21/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, e0) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_9_22 = e1 & op(e0, e2) = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_9_22 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (787), (798) imply: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) e3 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (799) implies: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) e3 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (800) imply: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) $false % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (801) is inconsistent. % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (802) gives: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_9_23 = e1 & op(e0, e1) = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (659), (803), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198. % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_9_24 = e1 & op(e0, e0) = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (804) implies: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) all_9_24 = e1 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (199), (202), (211), (217), (227), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (231), (233), (237), (239), (252), (253), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (269), (272), (273), (278), (285), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (311), (314), (317), (325), (329), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330), (331), (332), (334), (342), (344), (346), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348), (356), (358), (360), (366), (368), (372), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376), (390), (395), (398), (402), (411), (429), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (481), (494), (520), (537), (567), (587), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (629), (643), (663), (805), % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #205. % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) (all_9_23 = e3 & op(e0, e1) = e3) | (all_9_24 = e3 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_9_23 = e3 & op(e0, e1) = e3 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (659), (807) are inconsistent by sub-proof % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #197. % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_9_24 = e3 & op(e0, e0) = e3 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (761), (808) are inconsistent by sub-proof % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #212. % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (809) gives: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_9_5 = e2 & op(e3, e2) = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (810) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_9_5 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (580), (811) imply: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) e2 = e0 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (812) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) e2 = e0 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (663), (813) imply: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_9_14 = e0 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (643), (814), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (815) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_9_10 = e2 & op(e3, e1) = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_9_10 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (575), (817) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #196. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_9_17 = e2 & op(e3, e0) = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (818) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_9_17 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) op(e3, e0) = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_9_16 = e4 & op(e4, e0) = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (300), (513), (822) are inconsistent by % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #195. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_9_17 = e4 & op(e3, e0) = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (819), (823) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #224. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, e0) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_9_18 = e4 & op(e2, e0) = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_9_18 = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (211), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (229), (231), (233), (239), (252), (253), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (278), (293), (325), (329), (330), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (332), (334), (342), (344), (346), (348), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (390), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (402), (429), (537), (587), (826), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #221. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (827) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_9_19 = e4 & op(e1, e0) = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (629), (828) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #220. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_9_24 = e4 & op(e0, e0) = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (829) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_9_24 = e4 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_9_16 = e3 & op(e4, e0) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_9_16 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) (all_9_20 = e3 & op(e0, e4) = e3) | (all_9_21 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e3) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (447), (834), % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #200. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) (all_9_22 = e3 & op(e0, e2) = e3) | (all_9_23 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) | (all_9_24 = e3 & op(e0, e0) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (835) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_9_22 = e3 & op(e0, e2) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (836) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) all_9_22 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) op(e0, e2) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e1) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (839) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_9_0 = e1 & op(e4, e4) = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (840) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) op(e4, e4) = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (342), (841), (function-axioms) are % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_9_1 = e1 & op(e4, e3) = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (842) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_9_1 = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (696), (843) imply: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) e2 = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (844) imply: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_9_17 = e1 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (846) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_9_16 = e2 & op(e4, e0) = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_9_16 = e2 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (849) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_9_0 = e3 & op(e4, e4) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (390), (850) are inconsistent by sub-proof % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_9_1 = e3 & op(e4, e3) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (448), (851) are inconsistent by sub-proof #296. % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (852) gives: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_9_4 = e3 & op(e4, e2) = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (853) implies: % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) all_9_4 = e3 % 127.31/17.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (228), (229), (230), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (239), (252), (253), (265), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (273), (278), (285), (289), (293), (311), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (376), (390), (395), (398), (402), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (448), (481), (494), (537), (549), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (629), (845), (848), (854), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #204. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (855) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_9_9 = e3 & op(e4, e1) = e3 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (549), (856) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #289. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (833), (848) are inconsistent by sub-proof % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #229. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (845) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) e2 = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (844) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_9_20 = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (858), (function-axioms) are % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_9_18 = e2 & op(e2, e0) = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (860) implies: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) op(e2, e0) = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (520), (861) are inconsistent by sub-proof % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #214. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (862) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) all_9_19 = e2 & op(e1, e0) = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (629), (643), (663), (863), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #213. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_9_24 = e2 & op(e0, e0) = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (864) implies: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_9_24 = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (229), (231), (233), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (273), (278), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285), (293), (325), (329), (330), (331), (332), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (342), (344), (346), (348), (356), (358), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360), (366), (368), (372), (376), (390), (395), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (411), (429), (494), (537), (587), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629), (845), (865), (function-axioms) are % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (866) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_9_4 = e1 & op(e4, e2) = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (867) implies: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) op(e4, e2) = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e1) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_9_20 = e1 & op(e0, e4) = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) all_9_20 = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (871), (function-axioms) are % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_9_21 = e1 & op(e0, e3) = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (872) implies: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) op(e0, e3) = e1 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_6_4 = e4 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (874) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_4_20 = e4 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (513), (875) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) $false % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (876) is inconsistent. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) ~ (all_6_4 = e4) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_6_4 = e3 | all_6_4 = e2 | all_6_4 = e1 | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_4 = e0 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (878) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_6_4 = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (879) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_4_20 = e2 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (688), (880) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) $false % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (881) is inconsistent. % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) ~ (all_6_4 = e2) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_6_4 = e3 | all_6_4 = e1 | all_6_4 = e0 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (883) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_6_4 = e3 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (884) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_4_20 = e3 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (885) imply: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) op(e4, e0) = e3 % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) (all_8_88 = e4 & ~ (all_8_89 = e0) & op(e4, % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) = all_8_89 & op(e4, e0) = all_8_90 & % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_90) = e4 & $i(all_8_89) & % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_91 = e3 & ~ (all_8_92 = % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, all_8_93) = all_8_92 & op(e3, e0) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93 & op(e0, all_8_93) = e3 & % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_92) & $i(all_8_93)) % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (887) gives: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_8_88 = e4 & ~ (all_8_89 = e0) & op(e4, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) = all_8_89 & op(e4, e0) = all_8_90 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_90) = e4 & $i(all_8_89) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (888) implies: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) op(e0, all_8_90) = e4 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) op(e4, e0) = all_8_90 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_10 & op(all_8_69, e2) = e3 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_81, e3) = all_8_12 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e2 & op(all_8_45, e2) = all_8_16 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_57, e3) = e2 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_57) & $i(all_8_69)) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (891) gives: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (892) gives: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (893) gives: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_54) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (894) implies: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) op(e4, e3) = all_8_54 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (312), (314), (317), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (327), (329), (330), (331), (332), (334), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (378), (390), (395), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (403), (411), (412), (429), (439), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (447), (448), (453), (465), (466), (467), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (469), (471), (481), (494), (520), (537), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (567), (568), (587), (605), (607), (629), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682), (819), (820), (830), (833), (838), (868), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873), (886), (889), (890), (895), % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170. % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) & op(all_8_66, e4) = all_8_2 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_2) & $i(all_8_45) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_66) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (896) implies: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) ~ (all_8_45 = all_8_66) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) op(e4, e2) = all_8_66 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) op(all_8_66, e2) = e4 % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (677), (897) imply: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) ~ (all_8_66 = e3) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (900) implies: % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) ~ (all_8_66 = e3) % 127.31/17.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (18), (20), (22), (23), (24), (98), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (126), (170), (173), (197), (199), (202), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (217), (227), (229), (231), (233), (237), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (269), (272), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (296), (311), (312), (314), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (358), (360), (366), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (378), (390), (395), (398), (402), (403), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (439), (481), (520), (537), (567), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (605), (629), (643), (663), (830), (833), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868), (873), (886), (889), (890), (898), (899), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901), (function-axioms) are inconsistent by % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169. % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (902) gives: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_78) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (903) implies: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) ~ (all_8_48 = all_8_78) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) op(e1, e4) = all_8_48 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) op(e4, e1) = all_8_78 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (412), (467), (904), (905), (906), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189. % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (907) gives: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_90) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (908) implies: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ (all_8_51 = all_8_90) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) op(e0, e4) = all_8_51 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (18), (19), (22), (23), (24), (98), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (126), (170), (173), (197), (199), (202), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (217), (227), (229), (231), (233), (237), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (269), (272), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (330), (331), (332), (334), (342), (344), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346), (348), (356), (358), (360), (366), (368), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (398), (402), (403), (411), (429), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (446), (481), (520), (537), (567), (587), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (629), (643), (663), (830), (833), (873), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886), (889), (890), (909), (910), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #168. % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_8 & op(e4, e3) = all_8_54 & op(e3, % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (911) implies: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) op(e4, e3) = all_8_54 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (312), (314), (317), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (327), (329), (330), (331), (332), (334), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (378), (390), (395), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (403), (411), (412), (429), (439), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (447), (448), (453), (465), (466), (467), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (469), (471), (481), (494), (520), (537), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (567), (568), (587), (605), (607), (629), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682), (819), (820), (830), (833), (838), (868), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873), (886), (889), (890), (912), % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170. % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_14 & op(all_8_93, e0) = e3 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (913) gives: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (314), (317), (325), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (330), (331), (332), (334), (342), (344), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346), (348), (356), (358), (360), (366), (368), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (376), (378), (390), (395), (398), (402), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (411), (412), (429), (439), (446), (447), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (453), (465), (466), (467), (468), (469), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471), (481), (494), (520), (537), (549), (567), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568), (587), (605), (607), (629), (637), (643), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663), (675), (676), (677), (681), (682), (819), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820), (830), (833), (838), (868), (873), (886), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889), (890), (914), (function-axioms) are % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174. % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_16) & $i(all_8_45) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e2 & op(all_8_57, e2) = all_8_18 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (916) implies: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) op(e0, e3) = all_8_63 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (312), (314), (317), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (327), (329), (330), (331), (332), (334), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (378), (390), (395), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (403), (411), (412), (429), (439), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (447), (448), (453), (465), (466), (467), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (469), (471), (481), (494), (520), (537), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (567), (568), (587), (605), (607), (629), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682), (819), (820), (830), (833), (838), (868), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873), (886), (889), (890), (917), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #164. % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (314), (317), (325), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (330), (331), (332), (334), (342), (344), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346), (348), (356), (358), (360), (366), (368), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (376), (378), (390), (395), (398), (402), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (411), (412), (429), (439), (446), (447), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (453), (465), (466), (467), (468), (469), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471), (481), (494), (520), (537), (549), (567), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568), (587), (605), (607), (629), (637), (643), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663), (675), (676), (677), (681), (682), (819), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820), (830), (833), (838), (868), (873), (886), % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889), (890), (918), (function-axioms) are % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_30 & op(all_8_99, e0) = e1 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_34) & $i(all_8_63) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(all_8_75, e0) = all_8_36 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_87) & $i(all_8_99)) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (919) gives: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (18), (19), (20), (22), (23), (24), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (197), (199), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (211), (217), (227), (229), (231), (233), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (269), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272), (278), (289), (293), (311), (314), (317), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (358), (360), (366), (368), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (398), (402), (403), (411), (412), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429), (439), (465), (467), (468), (469), (481), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520), (537), (567), (568), (587), (605), (629), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (830), (833), (838), (873), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886), (889), (890), (920), (function-axioms) are % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165. % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & op(all_8_63, e0) = all_8_34 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (921) gives: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (922) gives: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (923) implies: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) ~ (all_8_87 = all_8_99) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) op(e0, e1) = all_8_87 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) op(e1, e0) = all_8_99 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (471), (924), (925), (926), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #177. % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) ~ (all_8_51 = all_8_90) % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) op(e0, e4) = all_8_51 % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (18), (19), (22), (23), (24), (98), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (126), (170), (173), (197), (199), (202), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (217), (227), (229), (231), (233), (237), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (252), (253), (265), (266), (269), (272), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (330), (331), (332), (334), (342), (344), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346), (348), (356), (358), (360), (366), (368), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (398), (402), (403), (411), (429), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (446), (481), (520), (537), (567), (587), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (629), (643), (663), (830), (833), (873), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886), (889), (890), (928), (929), % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #168. % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_36) & $i(all_8_75) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(all_8_87, e0) = all_8_38 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (930) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (931) implies: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) op(e0, e3) = all_8_63 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (197), (198), (199), (202), (211), (217), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (229), (230), (231), (232), (233), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (268), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (273), (278), (279), (285), (286), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (311), (312), (314), (317), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (327), (329), (330), (331), (332), (334), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (376), (378), (390), (395), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (402), (403), (411), (412), (429), (439), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (447), (448), (453), (465), (466), (467), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (469), (471), (481), (494), (520), (537), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549), (567), (568), (587), (605), (607), (629), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682), (819), (820), (830), (833), (838), (868), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873), (886), (889), (890), (932), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #164. % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (933) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) & $i(all_8_96) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (934) implies: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_8_75 = all_8_96) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) op(e0, e2) = all_8_75 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) op(e2, e0) = all_8_96 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (18), (19), (20), (22), (23), (24), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (197), (199), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (211), (217), (227), (229), (231), (233), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (252), (253), (265), (266), (269), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272), (278), (289), (293), (311), (314), (317), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (358), (360), (366), (368), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (398), (402), (403), (411), (429), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (481), (520), (537), (567), (587), (605), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629), (637), (643), (663), (830), (833), (838), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873), (886), (889), (890), (935), (936), (937), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #166. % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (938) implies: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) ~ (all_8_87 = all_8_99) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) op(e0, e1) = all_8_87 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) op(e1, e0) = all_8_99 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (471), (939), (940), (941), % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #177. % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) all_8_91 = e3 & ~ (all_8_92 = e0) & op(e3, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93) = all_8_92 & op(e3, e0) = all_8_93 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_93) = e3 & $i(all_8_92) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) ~ (all_8_92 = e0) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) op(e3, e0) = all_8_93 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) op(e3, all_8_93) = all_8_92 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_93, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (820), (944) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_8_93 = e2 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_92, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (607) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_8_92 = e0 | ~ (op(e3, e2) = all_8_92) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (945), (946) imply: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) op(e3, e2) = all_8_92 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (947) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) ~ (op(e3, e2) = all_8_92) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (948), (949) imply: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) $false % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (950) is inconsistent. % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_8_92 = e0 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (943), (951) imply: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) $false % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (952) is inconsistent. % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) (all_8_94 = e2 & ~ (all_8_95 = e0) & op(e2, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96) = all_8_95 & op(e2, e0) = all_8_96 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_96) = e2 & $i(all_8_95) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_97 = e1 & ~ (all_8_98 = % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, all_8_99) = all_8_98 & op(e1, e0) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99 & op(e0, all_8_99) = e1 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_98) & $i(all_8_99)) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (953) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_8_94 = e2 & ~ (all_8_95 = e0) & op(e2, % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96) = all_8_95 & op(e2, e0) = all_8_96 & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_96) = e2 & $i(all_8_95) & % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (954) implies: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) op(e0, all_8_96) = e2 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) op(e2, e0) = all_8_96 % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) ~ (op(e2, e0) = e2) % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_10 & op(all_8_69, e2) = e3 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_81, e3) = all_8_12 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e2 & op(all_8_45, e2) = all_8_16 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_57, e3) = e2 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_57) & $i(all_8_69)) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (958) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (960) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_54) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (961) implies: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) op(e3, e4) = all_8_42 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) op(e4, e3) = all_8_54 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) ~ (op(e3, e4) = e4) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (471) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) e2 = e0 | ~ (op(e0, e1) = e2) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_96, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (637), (956) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) all_8_96 = e1 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_42, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e3, simplifying with (23), (962) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_8_42 = e1 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_54, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (681), (963) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_8_54 = e2 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (453), (963) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) ~ (all_8_54 = e4) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (448), (963) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) ~ (all_8_54 = e3) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (956), (957) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) ~ (all_8_96 = e2) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (962), (964) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) ~ (all_8_42 = e4) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (643), (663), (955), (965), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966), (function-axioms) are inconsistent by % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) op(e3, e4) = e4 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (278), (325), (973) are inconsistent by % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) & op(all_8_66, e4) = all_8_2 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_2) & $i(all_8_45) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_66) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) op(e4, e2) = all_8_66 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) op(all_8_66, e2) = e4 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) ~ (op(e4, e2) = e4) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (471) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) e2 = e0 | ~ (op(e0, e1) = e2) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_96, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (637), (956) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_8_96 = e1 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_66, % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e4, simplifying with (868), (975) gives: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_8_66 = e1 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (956), (957) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) ~ (all_8_96 = e2) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (976), (977) imply: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) ~ (all_8_66 = e4) % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (18), (20), (23), (202), (217), (229), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (265), (266), (269), (278), (289), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (311), (314), (317), (325), (329), (334), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (390), (411), (429), (439), (481), (567), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (643), (663), (955), (978), (979), (980), % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981), (982), (function-axioms) are inconsistent % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #162. % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) op(e4, e2) = e4 % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (296), (378), (983) are inconsistent by % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #298. % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_78) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (985) implies: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) ~ (all_8_48 = all_8_78) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) op(e1, e4) = all_8_48 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) op(e4, e1) = all_8_78 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (412), (467), (986), (987), (988), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189. % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (989) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_90) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (990) implies: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) ~ (all_8_51 = all_8_90) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) op(e0, e4) = all_8_51 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) op(e4, e0) = all_8_90 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (19), (20), (23), (202), (217), (229), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (265), (266), (269), (278), (289), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (300), (311), (314), (317), (325), (329), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (403), (411), (429), (439), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (471), (481), (567), (605), (637), (643), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663), (884), (886), (955), (956), (957), (991), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992), (993), (function-axioms) are inconsistent % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #160. % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_8 & op(e4, e3) = all_8_54 & op(e3, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) op(e3, e4) = all_8_42 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) op(e4, e3) = all_8_54 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) op(all_8_42, e4) = e3 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) ~ (op(e3, e4) = e4) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_42, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e3, simplifying with (23), (995) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_8_42 = e1 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_54, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (681), (996) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_8_54 = e2 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (453), (996) imply: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_8_54 = e4) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, e3, e4, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (412) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) e4 = e3 | ~ (op(e1, e4) = e3) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (995), (998) imply: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) ~ (all_8_42 = e4) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (997), (999) imply: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) op(e1, e4) = e3 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1002) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) ~ (op(e1, e4) = e3) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1004), (1005) imply: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) $false % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1006) is inconsistent. % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) e4 = e3 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (1007) imply: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_9_12 = e3 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (429), (1008) are % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #303. % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) op(e3, e4) = e4 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (278), (325), (1009) are inconsistent by % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_14 & op(all_8_93, e0) = e3 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1011) gives: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69) % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1012) implies: % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) op(e2, e3) = all_8_57 % 127.31/17.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (127), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (202), (217), (229), (233), (237), (265), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (268), (269), (273), (278), (285), (286), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (297), (301), (311), (314), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (334), (372), (376), (378), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (403), (411), (412), (429), (439), (446), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (453), (465), (466), (467), (468), (469), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471), (481), (494), (567), (568), (605), (607), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820), (868), (885), (886), (955), (956), (957), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013), (function-axioms) are inconsistent by % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #155. % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_81, e3) = all_8_12 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1014) implies: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) ~ (all_8_60 = all_8_81) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) op(e1, e3) = all_8_60 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) op(e3, e1) = all_8_81 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (568), (1015), (1016), (1017), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #184. % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_16) & $i(all_8_45) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e2 & op(all_8_57, e2) = all_8_18 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1018) gives: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (273), (285), (376), (494), (820), (1019), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #183. % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1020) gives: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) & $i(all_8_66) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1021) implies: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) op(all_8_45, e4) = e2 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (677), (1022) imply: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) op(e3, e4) = e2 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (1023), (function-axioms) are % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #313. % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_57, e3) = e2 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1024) implies: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) op(e2, e3) = all_8_57 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (127), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (202), (217), (229), (233), (237), (265), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (268), (269), (273), (278), (285), (286), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (297), (301), (311), (314), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (334), (372), (376), (378), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (403), (411), (412), (429), (439), (446), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (453), (465), (466), (467), (468), (469), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471), (481), (494), (567), (568), (605), (607), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637), (643), (663), (675), (676), (677), (681), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820), (868), (885), (886), (955), (956), (957), % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025), (function-axioms) are inconsistent by % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #155. % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_30 & op(all_8_99, e0) = e1 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_34) & $i(all_8_63) & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(all_8_75, e0) = all_8_36 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_87) & $i(all_8_99)) % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1026) gives: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1027) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1028) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1029) implies: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) ~ (all_8_72 = all_8_84) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) op(e1, e2) = all_8_72 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) op(e2, e1) = all_8_84 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (465), (469), (1030), (1031), (1032), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #181. % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_96, e2) = all_8_22 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_75 & $i(all_8_22) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) & $i(all_8_96) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1033) implies: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) op(all_8_96, e0) = e2 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (471) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) e2 = e0 | ~ (op(e0, e1) = e2) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_96, % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (637), (956) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_8_96 = e1 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (957), (1034) imply: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) ~ (all_8_96 = e2) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (643), (663), (955), (1035), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036), (function-axioms) are inconsistent by % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_78) & op(all_8_48, e4) = e1 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_60, e3) = e1 & op(all_8_60, e1) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_26) & $i(all_8_60) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1 & op(all_8_72, e1) = all_8_28 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (412), (465), (467), (468), (469), (568), (1038), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #178. % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & op(all_8_63, e0) = all_8_34 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1039) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1040) gives: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1041) implies: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) ~ (all_8_87 = all_8_99) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) op(e0, e1) = all_8_87 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) op(e1, e0) = all_8_99 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (471), (1042), (1043), (1044), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #177. % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1045) implies: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) ~ (all_8_51 = all_8_90) % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) op(e0, e4) = all_8_51 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) op(e4, e0) = all_8_90 % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (19), (20), (23), (202), (217), (229), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (265), (266), (269), (278), (289), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (300), (311), (314), (317), (325), (329), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (403), (411), (429), (439), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (471), (481), (567), (605), (637), (643), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663), (884), (886), (955), (956), (957), (1046), % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047), (1048), (function-axioms) are inconsistent % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #160. % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_36) & $i(all_8_75) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(all_8_87, e0) = all_8_38 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1050) implies: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) op(e3, e0) = all_8_93 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) ~ (op(e3, e0) = e3) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (471) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) e2 = e0 | ~ (op(e0, e1) = e2) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_96, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (637), (956) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_8_96 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_93, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (820), (1051) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) all_8_93 = e2 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (956), (957) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ (all_8_96 = e2) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1051), (1052) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) ~ (all_8_93 = e3) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (19), (20), (23), (202), (217), (229), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (265), (266), (269), (278), (289), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (311), (314), (317), (325), (329), (334), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (390), (411), (429), (439), (481), (567), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605), (643), (663), (955), (1053), (1054), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055), (1056), (1057), (function-axioms) are % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #156. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) op(e3, e0) = e3 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (273), (285), (494), (1058) are inconsistent by % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #228. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1059) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) & $i(all_8_96) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (471) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) e2 = e0 | ~ (op(e0, e1) = e2) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_96, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (637), (956) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_8_96 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (956), (957) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) ~ (all_8_96 = e2) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (202), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (229), (233), (237), (265), (266), (269), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (289), (293), (311), (314), (317), (325), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (411), (429), (439), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481), (567), (605), (643), (663), (955), (1061), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062), (function-axioms) are inconsistent by % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1064) implies: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) ~ (all_8_87 = all_8_99) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) op(e0, e1) = all_8_87 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) op(e1, e0) = all_8_99 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (471), (1065), (1066), (1067), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #177. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) op(e2, e0) = e2 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (520), (1068) are inconsistent by sub-proof % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #214. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_8_97 = e1 & ~ (all_8_98 = e0) & op(e1, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99) = all_8_98 & op(e1, e0) = all_8_99 & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_8_99) = e1 & $i(all_8_98) & % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1069) implies: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) ~ (all_8_98 = e0) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) op(e1, e0) = all_8_99 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) op(e1, all_8_99) = all_8_98 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_99, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (466), (1071) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_8_99 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_98, % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (466) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_8_98 = e0 | ~ (op(e1, e0) = all_8_98) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1072), (1073) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) op(e1, e0) = all_8_98 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1074) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) ~ (op(e1, e0) = all_8_98) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1075), (1076) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) $false % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1077) is inconsistent. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_8_98 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1070), (1078) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) $false % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1079) is inconsistent. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) op(e3, e0) = e3 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (273), (285), (494), (1080) are inconsistent by % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #228. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) all_6_4 = e1 | all_6_4 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1081) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_6_4 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1082) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_4_20 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (634), (1083) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) $false % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1084) is inconsistent. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) all_6_4 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1085) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_4_20 = e0 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (1086) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) $false % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1087) is inconsistent. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, e0) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1088) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_9_22 = e1 & op(e0, e2) = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1089) implies: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_9_22 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (837), (1090) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) e3 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1091) implies: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) e3 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (833), (1092) imply: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) all_9_16 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (228), (229), (230), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (239), (252), (253), (265), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (273), (278), (285), (289), (293), (311), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (376), (390), (395), (398), (402), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (448), (481), (494), (537), (549), % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (629), (819), (1093), (function-axioms) are % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215. % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_9_23 = e1 & op(e0, e1) = e1 % 127.73/17.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (659), (1095), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_9_24 = e1 & op(e0, e0) = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1096) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) all_9_24 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (197), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (202), (211), (217), (227), (229), (231), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (239), (252), (253), (265), (266), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (278), (289), (293), (311), (314), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (398), (402), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (439), (481), (520), (537), (567), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (605), (629), (643), (663), (833), (1097), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #207. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e1) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1098) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_9_9 = e1 & op(e4, e1) = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1099) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_9_9 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (1100) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) e4 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (830), (1101) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_9_24 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (197), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (202), (211), (217), (227), (229), (231), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (239), (252), (253), (265), (266), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (272), (278), (289), (293), (311), (314), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (398), (402), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (439), (481), (520), (537), (567), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (605), (629), (643), (663), (833), (1102), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #207. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_9_16 = e1 & op(e4, e0) = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_9_16 = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (127), (170), (173), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (199), (211), (227), (228), (229), (230), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (239), (252), (253), (265), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (273), (278), (285), (289), (293), (311), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (330), (331), (332), (334), (342), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (376), (390), (395), (398), (402), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411), (429), (448), (481), (494), (537), (549), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587), (629), (819), (1104), (function-axioms) are % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_9_23 = e3 & op(e0, e1) = e3) | (all_9_24 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_9_23 = e3 & op(e0, e1) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (659), (1106) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #197. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_9_24 = e3 & op(e0, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1107) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_9_24 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (830), (1108) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) e4 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (1109) are % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #217. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_9_17 = e3 & op(e3, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1110) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) op(e3, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (273), (285), (494), (1111) are inconsistent by % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #228. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1112) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_9_18 = e3 & op(e2, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1113) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) op(e2, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (376), (1114), (function-axioms) are % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1115) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_9_19 = e3 & op(e1, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (629), (1116) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #206. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_9_24 = e3 & op(e0, e0) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_9_24 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (830), (1118) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) e4 = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (411), (429), (1119) are % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #217. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (289), (311), (481), (549), (680), (688), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) are inconsistent by sub-proof #153. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) op(e2, e3) = e3 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (321), (370), (1121) are inconsistent by % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (429), (629), (643), (1122), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #249. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_9_19 = e1 & op(e1, e0) = e1 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (257), (265), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (293), (329), (330), (331), (332), (334), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (395), (475), (1123), % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_6_14 = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (476), (1124) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1125) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_9_8 = e0 & op(e2, e2) = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (402), (1126) are inconsistent by sub-proof % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1127) gives: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_9_11 = e0 & op(e2, e1) = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1128) implies: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_9_11 = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (1129) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) e2 = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (1130) imply: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) $false % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1131) is inconsistent. % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_9_18 = e0 & op(e2, e0) = e0 % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) op(e2, e0) = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (304), (476), (1133) are inconsistent by % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1134) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) all_9_8 = e0 & op(e2, e2) = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (402), (1135) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1136) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_9_14 = e0 & op(e1, e2) = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1137) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_9_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) all_6_7 = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1139) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_4_11 = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (482), (1140) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) $false % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1141) is inconsistent. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) ~ (all_6_7 = e2) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1143) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_6_7 = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1144) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_4_11 = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (487), (1145) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) $false % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1146) is inconsistent. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) ~ (all_6_7 = e3) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_6_7 = e1 | all_6_7 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1148) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_6_7 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1149) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_4_11 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1150) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) $false % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1151) is inconsistent. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) all_6_7 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1152) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_4_11 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (201), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (217), (227), (229), (231), (233), (237), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (251), (252), (253), (254), (257), (265), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (269), (278), (289), (293), (311), (314), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (325), (329), (330), (331), (332), (334), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366), (368), (372), (390), (395), (411), (429), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439), (475), (481), (500), (567), (1138), (1153), % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #242. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_9_22 = e0 & op(e0, e2) = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (527), (1154) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_9_17 = e3 & op(e3, e0) = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1155) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) op(e3, e0) = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (273), (285), (494), (1156) are inconsistent by % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #228. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) all_9_21 = e3 & op(e0, e3) = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (447), (1157) are inconsistent by sub-proof #201. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) all_9_16 = e4 & op(e4, e0) = e4 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (300), (513), (1158) are inconsistent by % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #195. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_50 & op(e0, e4) = all_8_51 & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_50) & $i(all_8_51)) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1160) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) op(e1, e4) = all_8_48 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) op(e4, all_8_48) = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) all_6_14 = e4 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (387), (1163) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1164) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) all_6_14 = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (520), (1165) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #257. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1166) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) all_6_14 = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (376), (1167) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #255. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_6_14 = e1 | all_6_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1168) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_6_14 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1169) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) all_4_22 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1170) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) all_4_22 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (1171) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) ~ (all_4_7 = e1) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_6_11 = e4 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (377), (1173) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1174) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_6_11 = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (518), (1175) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1176) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) all_6_11 = e3 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (370), (1177) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #235. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_6_11 = e1 | all_6_11 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1178) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_6_11 = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1172), (1179) are inconsistent by % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #234. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) all_6_11 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (1180) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_4_7 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1181) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_4_7 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_48, % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e1, simplifying with (412), (1161) gives: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) all_8_48 = e4 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1162), (1183) imply: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) op(e4, e4) = e1 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (342), (1184), (function-axioms) are % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_6_14 = e0 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (476), (1185) are inconsistent by sub-proof % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51) = e0 & op(e0, all_8_51) = all_8_50 & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_50) & % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (352), (446), (1186), (function-axioms) are % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149. % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_9_18 = e2 & op(e2, e0) = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1187) implies: % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) op(e2, e0) = e2 % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (272), (520), (1188) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #214. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) unit = e0 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (404), (1189) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) $false % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1190) is inconsistent. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1191) all_6_1 = e4 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1191) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1192) all_4_5 = e4 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1192) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1193) op(e4, e3) = e4 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1194) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | = all_8_44 & op(e2, e4) = all_8_45 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44) & $i(all_8_45)) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1194) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1195) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1195) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1196) op(e3, e4) = all_8_42 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1197) op(e4, all_8_42) = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) ~ (op(e3, e4) = e4) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (18), (20), (23), (233), (278), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (325), (329), (334), (372), (404), (411), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (429), (449), (452), (1196), (1197), (1198), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | #148. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) op(e3, e4) = e4 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (278), (325), (1199) are inconsistent by % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_44) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1201) op(e2, e4) = all_8_45 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1202) op(e4, all_8_45) = e2 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (22), (1193), (1201), (1202), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1203) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | = all_8_50 & op(e0, e4) = all_8_51 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_50) & $i(all_8_51)) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (139), (342), (352), (412), (446), (1203), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | #146. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | (1204) op(e2, e4) = e4 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (329), (372), (1204) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | #320. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | (1205) all_6_1 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1205) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | (1206) all_4_5 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (1206) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | (1207) ~ (all_4_15 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | SIMP: (1207) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | (1208) ~ (all_4_15 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1206) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | (1209) op(e4, e3) = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | (1210) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | = all_8_44 & op(e2, e4) = all_8_45 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44) & $i(all_8_45)) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1211) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1211) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1212) op(e3, e4) = all_8_42 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1213) op(e4, all_8_42) = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_42, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | e4, e3, simplifying with (23), (1212) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1214) all_8_42 = e1 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_15, e3, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (138) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1215) all_4_15 = e3 | ~ (op(e4, e1) = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1213), (1214) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1216) op(e4, e1) = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1215) gives: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1217) ~ (op(e4, e1) = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1216), (1217) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1218) $false % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1218) is inconsistent. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1219) all_4_15 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1208), (1219) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1220) $false % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1220) is inconsistent. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1221) all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_44) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1221) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1222) op(e2, e4) = all_8_45 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1223) op(e4, all_8_45) = e2 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (328), (329), (372), (1209), (1222), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1223), (function-axioms) are inconsistent by % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #145. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | (1224) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | = all_8_50 & op(e0, e4) = all_8_51 & % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_50) & $i(all_8_51)) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (139), (342), (352), (412), (446), (1224), % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | #146. % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | End of split % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | Case 2: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1225) all_6_21 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (1225) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1226) all_4_9 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | SIMP: (1226) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1227) all_4_9 = e3 % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (1227) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1228) ~ (all_4_5 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (1227) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1229) ~ (all_4_6 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (1227) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1230) ~ (all_4_8 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (1227) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1231) ~ (all_4_14 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | SIMP: (1231) implies: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1232) ~ (all_4_14 = e3) % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (1227) imply: % 127.73/17.59 | | | | | | | | | | | | | | | | | | | | (1233) ~ (all_4_19 = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | SIMP: (1233) implies: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | (1234) ~ (all_4_19 = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (1227) imply: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | (1235) ~ (all_4_24 = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | SIMP: (1235) implies: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | (1236) ~ (all_4_24 = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | (1237) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (320), (1228), (1229), (1237) are % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143. % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | (1238) (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e3) | (all_9_21 = e3 & op(e0, e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1238) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | (1239) all_9_7 = e3 & op(e2, e3) = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1239) implies: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | (1240) op(e2, e3) = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (321), (370), (1240) are inconsistent by % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | (1241) (all_9_13 = e3 & op(e1, e3) = e3) | (all_9_21 = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1241) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1242) all_9_13 = e3 & op(e1, e3) = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (323), (1230), (1242) are inconsistent by % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #142. % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1243) all_9_21 = e3 & op(e0, e3) = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1243) implies: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | (1244) all_9_21 = e3 % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1245) ~ (op(e2, e4) = e4) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (11), (1245) imply: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | (1246) ~ (unit = e2) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1247) ~ (op(e4, e3) = e4) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (1247) imply: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1248) ~ (unit = e3) % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) (all_9_1 = e4 & op(e4, e3) = e4) | (all_9_3 = e4 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1249) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) all_9_1 = e4 & op(e4, e3) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1247), (1250) are inconsistent by sub-proof #300. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_9_3 = e4 & op(e3, e3) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1251) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) all_9_3 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) op(e3, e3) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_6, e4, % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (135), (1253) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) all_4_6 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (1254) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) ~ (all_4_7 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (1254) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) ~ (all_4_11 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) ~ (op(e3, e2) = e2) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (134), (1257) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) ~ (all_4_11 = e2) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) ~ (op(e0, e1) = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2), (1259) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) ~ (unit = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) unit = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (1261) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) op(e1, e4) = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (253), (358), (1262) are inconsistent by sub-proof % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #268. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (404), (1246), (1248), (1260), (1263) are % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) all_4_19 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) ~ (all_4_14 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) ~ (all_4_15 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) ~ (all_4_16 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) ~ (all_4_17 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) ~ (all_4_24 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1269) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) ~ (all_4_24 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (441), (1264) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) ~ (e2 = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) all_6_22 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (1272) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_4_14 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1273) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) all_4_14 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (1274) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) $false % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1275) is inconsistent. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_6_22 = e3 | all_6_22 = e2 | all_6_22 = e1 | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_22 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1276) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) all_6_22 = e2 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (237), (439), (1277) are inconsistent by sub-proof % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) ~ (all_6_22 = e2) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) all_6_22 = e3 | all_6_22 = e1 | all_6_22 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1279) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) all_6_22 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (1280) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) all_4_14 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1281) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_4_14 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1232), (1282) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) $false % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1283) is inconsistent. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) ~ (all_6_22 = e3) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) all_6_22 = e1 | all_6_22 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1285) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) all_6_22 = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (1286) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) all_4_14 = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1287) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) all_4_14 = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (1288) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) ~ (all_4_10 = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (1288) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) ~ (all_4_13 = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (1288) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) ~ (all_4_24 = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1291) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) ~ (all_4_24 = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1288) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) ~ (e2 = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) all_6_24 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (235), (1294) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) all_4_24 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (1295) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) ~ (all_4_20 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (1295) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) ~ (all_4_21 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (293), (334), (1247), (1298) are % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #299. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1299) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_9_4 = e4 & op(e4, e2) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1300) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) op(e4, e2) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (296), (378), (1301) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #298. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1302) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) all_9_9 = e4 & op(e4, e1) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1303) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) all_9_9 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) op(e4, e1) = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e1) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1306) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) all_9_4 = e1 & op(e4, e2) = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1307) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) all_9_4 = e1 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) ~ (op(e4, e1) = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1305), (1309) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) $false % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1310) is inconsistent. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) all_6_3 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1311) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) all_4_15 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1312) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_4_15 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (1313) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) ~ (all_4_16 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1314) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) ~ (all_4_16 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (1313) imply: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) ~ (all_4_20 = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (320), (344), (390), (1228), (1317) are % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1318) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) all_9_4 = e3 & op(e4, e2) = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1319) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_9_4 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (356), (1308), (1320) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #138. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1321) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_9_9 = e3 & op(e4, e1) = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1322) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) all_9_9 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (234), (278), (287), % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (300), (325), (329), (334), % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (378), (411), (429), (1247), (1296), (1323) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) all_9_16 = e3 & op(e4, e0) = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1324) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) all_9_16 = e3 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1326) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) all_9_0 = e2 & op(e4, e4) = e2 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (390), (1327) are inconsistent by sub-proof % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_9_1 = e2 & op(e4, e3) = e2 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1328) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) all_9_1 = e2 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) all_9_24 = e0 & op(e0, e0) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1330) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) op(e0, e0) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (246), (1270), (1331) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #240. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1332) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1333) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1335) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) all_9_20 = e0 & op(e0, e4) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (429), (1336) are inconsistent by sub-proof % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #239. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) all_9_21 = e0 & op(e0, e3) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (1244), (1337) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1338) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_9_22 = e0 & op(e0, e2) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (1265), (1339) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_9_23 = e0 & op(e0, e1) = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1340) implies: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_9_23 = e0 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (234), (278), (287), % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (300), (325), (329), (334), % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (378), (403), (411), (429), (1244), (1247), % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296), (1304), (1342) are inconsistent by % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #134. % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1343) gives: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) all_9_22 = e4 & op(e0, e2) = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1344) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) all_9_22 = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1346) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) all_9_16 = e4 & op(e4, e0) = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (300), (1296), (1347) are inconsistent by % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #195. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) all_9_17 = e4 & op(e3, e0) = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1348) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) all_9_17 = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (23), (1252), (1350), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #133. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1351) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) all_9_5 = e2 & op(e3, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1257), (1352) are inconsistent by sub-proof #132. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) all_9_10 = e2 & op(e3, e1) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) all_9_10 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (356), (395), (1229), (1356) are % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1357) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_9_5 = e3 & op(e3, e2) = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1358) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) all_9_5 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) op(e3, e2) = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) ~ (op(e3, e2) = e3) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1360), (1361) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1362) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) all_6_7 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1363) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_4_11 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (1252), (1365), (function-axioms) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #131. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1366) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) all_9_5 = e0 & op(e3, e2) = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1367) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_9_5 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1359), (1368) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) e3 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1363), (1369) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) all_6_7 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) ~ (op(e3, e2) = e3) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1360), (1371) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1372) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1363), (1370) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) e3 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (1369) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1374) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) (all_9_10 = e0 & op(e3, e1) = e0) | (all_9_17 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_9_10 = e0 & op(e3, e1) = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1376) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_9_10 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1355), (1377) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1378) e2 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (1378) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1379) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1379) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_9_17 = e0 & op(e3, e0) = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1380) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1381) op(e3, e0) = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (31), (248), (253), (303), (305), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358), (404), (1246), (1248), (1381) are % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1382) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1382) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_9_10 = e3 & op(e3, e1) = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1383) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_9_10 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1355), (1384) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #196. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1385) all_9_17 = e3 & op(e3, e0) = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1385) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386) all_9_17 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (1386) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387) e4 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1304), (1387) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1388) all_9_9 = e3 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (234), (278), (287), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (300), (325), (329), (334), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (378), (411), (429), (1247), (1296), (1388) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_9_17 = e2 & op(e3, e0) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1389) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) all_9_17 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (1390) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) e4 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (1391) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1392) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1393) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) all_9_18 = e4 & op(e2, e0) = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1394) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_9_18 = e4 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e1) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (356), (372), (390), (1244), (1396), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #128. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1397) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) all_9_22 = e1 & op(e0, e2) = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1398) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) all_9_22 = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (21), (23), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (70), (181), (217), (218), (229), (233), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (250), (265), (266), (269), (275), (278), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282), (289), (293), (315), (317), (325), (329), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (352), (372), (378), (390), (429), (439), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257), (1289), (1308), (1399), (function-axioms) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #122. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1400) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) all_9_23 = e1 & op(e0, e1) = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (1341), (1401), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) all_9_24 = e1 & op(e0, e0) = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1402) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) all_9_24 = e1 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) all_9_4 = e2 & op(e4, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (429), (1308), (1405), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #127. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) all_9_5 = e2 & op(e3, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1257), (1406) are inconsistent by sub-proof #132. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1407) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) all_9_8 = e2 & op(e2, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (269), (1408) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1409) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) all_9_14 = e2 & op(e1, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1410) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) all_9_14 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) op(e1, e2) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) ~ (op(e1, e2) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1412), (1413) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) $false % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1414) is inconsistent. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) all_6_17 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (1415) imply: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) all_4_13 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1416) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) all_4_13 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1418) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) all_9_16 = e2 & op(e4, e0) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1325), (1419) are inconsistent by sub-proof % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) all_9_17 = e2 & op(e3, e0) = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1420) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) all_9_17 = e2 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (1252), (1422), (function-axioms) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #131. % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1423) gives: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) all_9_5 = e0 & op(e3, e2) = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1424) implies: % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) all_9_5 = e0 % 127.97/17.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1426) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) all_9_6 = e0 & op(e2, e4) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (398), (1427) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #256. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_9_7 = e0 & op(e2, e3) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1428) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) all_9_7 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (356), (395), (1229), (1430) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) all_9_5 = e3 & op(e3, e2) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (1425), (1432) are inconsistent by % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #121. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1433) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_9_10 = e3 & op(e3, e1) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1434) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_9_10 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1436) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) all_9_6 = e2 & op(e2, e4) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (265), (266), (1437) are inconsistent by % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #311. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) all_9_7 = e2 & op(e2, e3) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_9_7 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (1439) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) e2 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1440) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) e2 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (1441) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) $false % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1442) is inconsistent. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1443) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_9_8 = e2 & op(e2, e2) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (269), (1444) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1445) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_9_11 = e2 & op(e2, e1) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1446) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_9_11 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (211), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (229), (231), (233), (239), (252), (253), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (278), (293), (325), (329), (330), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (332), (334), (342), (344), (346), (348), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (390), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (402), (429), (1395), (1429), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447), (function-axioms) are inconsistent by % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #221. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) all_9_18 = e2 & op(e2, e0) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (222), (233), (278), (293), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (334), (372), (411), (429), (1252), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395), (1421), (1425), (1435), (1448) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) all_9_17 = e3 & op(e3, e0) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1421), (1449) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #119. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_9_8 = e0 & op(e2, e2) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (402), (1451) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1452) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) all_9_11 = e0 & op(e2, e1) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1453) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_9_11 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (356), (395), (1229), (1455) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1456) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_9_5 = e3 & op(e3, e2) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (1425), (1457) are inconsistent by % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #121. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1458) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_9_10 = e3 & op(e3, e1) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1459) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_9_10 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) op(e3, e1) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) ~ (op(e3, e1) = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1461), (1462) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) $false % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1463) is inconsistent. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) all_6_8 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1464) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_4_16 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1465) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) all_4_16 = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (1466) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) ~ (all_4_11 = e3) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1468) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_9_6 = e2 & op(e2, e4) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (265), (266), (1469) are inconsistent by % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #311. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_9_7 = e2 & op(e2, e3) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1470) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_9_7 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e1) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_9_6 = e1 & op(e2, e4) = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_9_6 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (356), (398), (1474) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_9_7 = e1 & op(e2, e3) = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1475) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_9_7 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1471), (1476) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) e2 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1477) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) all_9_20 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (1478), (function-axioms) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) | (all_9_18 = e1 & op(e2, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1479) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) all_9_8 = e1 & op(e2, e2) = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1480) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_9_8 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (1481) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) e4 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1482) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) e4 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (1483) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_9_22 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (218), (275), (282), (356), (372), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308), (1411), (1467), (1484), (function-axioms) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #124. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_18 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e1) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) all_9_11 = e1 & op(e2, e1) = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (1454), (1486), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #118. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) all_9_18 = e1 & op(e2, e0) = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1487) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_9_18 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1395), (1488) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) e4 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1489) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) e4 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (1490) imply: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_9_22 = e1 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (218), (275), (282), (356), (372), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308), (1411), (1467), (1491), (function-axioms) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #124. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1492) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_9_8 = e2 & op(e2, e2) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (269), (1493) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1494) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_9_11 = e2 & op(e2, e1) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1454), (1495) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #117. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) all_9_18 = e2 & op(e2, e0) = e2 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (222), (233), (278), (293), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (334), (372), (411), (429), (1252), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395), (1421), (1425), (1460), (1496) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) all_9_17 = e3 & op(e3, e0) = e3 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1421), (1497) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #119. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_9_18 = e0 & op(e2, e0) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (29), (248), (253), (259), (304), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (358), (404), (1246), (1248), (1498) are % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #116. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) (all_9_10 = e0 & op(e3, e1) = e0) | (all_9_17 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1499) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_9_10 = e0 & op(e3, e1) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1500) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_9_10 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1502) gives: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_9_4 = e0 & op(e4, e2) = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1503) implies: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) all_9_4 = e0 % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (170), (173), (227), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (231), (233), (239), (252), (253), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (278), (293), (325), (329), (330), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (332), (334), (342), (344), (346), (348), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (390), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (429), (1304), (1325), (1329), (1504), % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_9_5 = e0 & op(e3, e2) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1505) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_9_5 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (221), (281), (344), (356), (395), (1229), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421), (1501), (1506) are inconsistent by % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (243), (402), (1265), (1411), (1507) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #113. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_9_17 = e0 & op(e3, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1508) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) op(e3, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (31), (248), (253), (303), (305), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358), (404), (1246), (1248), (1509) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1510) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_9_18 = e2 & op(e2, e0) = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1511) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) all_9_18 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1395), (1512) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) e4 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (1513) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1514) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1515) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_9_19 = e2 & op(e1, e0) = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1516) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) all_9_19 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e3) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1518) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) all_9_12 = e3 & op(e1, e4) = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1519) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) all_9_12 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (429), (1520) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #303. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_9_13 = e3 & op(e1, e3) = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (251), (323), (1230), (1521) are inconsistent by % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #142. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_19 = e3 & op(e1, e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1522) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_9_14 = e3 & op(e1, e2) = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1411), (1523) are inconsistent by sub-proof % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #125. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_19 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1524) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) all_9_15 = e3 & op(e1, e1) = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1525) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) all_9_15 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e1) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1527) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_9_12 = e1 & op(e1, e4) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1528) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) op(e1, e4) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (253), (358), (1529) are inconsistent by sub-proof % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #268. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_9_13 = e1 & op(e1, e3) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1530) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_9_13 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1532) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_9_12 = e0 & op(e1, e4) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (411), (1533) are inconsistent by sub-proof % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #254. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_9_13 = e0 & op(e1, e3) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1534) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_9_13 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1531), (1535) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) e1 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (1536) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) all_9_2 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (1537), (function-axioms) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1538) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) all_9_14 = e0 & op(e1, e2) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1411), (1539) are inconsistent by sub-proof % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1540) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) all_9_15 = e0 & op(e1, e1) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1541) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) all_9_15 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1526), (1542) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) e3 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (1543) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1544) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) all_9_19 = e0 & op(e1, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1545) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_9_19 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1517), (1546) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) e2 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (1547) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1548) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1549) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_9_14 = e1 & op(e1, e2) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (255), (265), (266), (278), (293), (325), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (390), (429), (1415), (1550), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1551) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_9_15 = e1 & op(e1, e1) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1552) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_9_15 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1526), (1553) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) e3 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (1554) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1555) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_9_19 = e1 & op(e1, e0) = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1556) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_9_19 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1517), (1557) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) e2 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1558) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_9_20 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (1559), (function-axioms) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_9_19 = e3 & op(e1, e0) = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1560) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_9_19 = e3 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1517), (1561) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) e3 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1562) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) e3 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (1563) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1564) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) all_9_24 = e2 & op(e0, e0) = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1565) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_9_24 = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1403), (1566) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) e2 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1567) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) e2 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1568) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) all_9_20 = e1 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (1569), (function-axioms) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_9_22 = e2 & op(e0, e2) = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1570) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) op(e0, e2) = e2 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (237), (317), (439), (1571) are inconsistent by % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #246. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1572) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) all_9_19 = e4 & op(e1, e0) = e4 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1573) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) all_9_19 = e4 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1575) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) all_9_16 = e0 & op(e4, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (302), (354), (1576) are inconsistent by % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #112. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_9_17 = e0 & op(e3, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1577) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) op(e3, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (31), (248), (253), (303), (305), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358), (404), (1246), (1248), (1578) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1579) gives: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_9_18 = e0 & op(e2, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (29), (248), (253), (259), (304), % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (358), (404), (1246), (1248), (1580) are % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #116. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) all_9_19 = e0 & op(e1, e0) = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1581) implies: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) all_9_19 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1574), (1582) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) e4 = e0 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (1583) imply: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) $false % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1584) is inconsistent. % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_9_24 = e4 & op(e0, e0) = e4 % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1585) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_9_24 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (21), (22), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (68), (70), (98), (121), (126), (170), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (181), (192), (217), (218), (227), (229), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (239), (250), (252), (253), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (269), (275), (278), (282), (289), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (315), (317), (325), (329), (330), (331), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (334), (342), (344), (346), (348), (352), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (378), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (429), (439), (1244), (1257), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289), (1308), (1341), (1586), (function-axioms) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #111. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1587) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) all_9_23 = e4 & op(e0, e1) = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (128), (170), (173), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (205), (206), (207), (208), (220), (221), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (229), (231), (233), (234), (235), (239), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (246), (252), (253), (265), (266), (274), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (281), (287), (289), (293), (296), (300), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308), (325), (329), (330), (331), (332), (334), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (366), (368), (372), (374), (378), (390), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (411), (429), (1229), (1244), (1247), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252), (1257), (1265), (1270), (1296), (1304), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588), (function-axioms) are inconsistent by % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #102. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_9_24 = e4 & op(e0, e0) = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1589) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) all_9_24 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (21), (22), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (68), (70), (98), (121), (126), (170), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (181), (192), (217), (218), (227), (229), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (239), (250), (252), (253), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (269), (275), (278), (282), (289), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (315), (317), (325), (329), (330), (331), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (334), (342), (344), (346), (348), (352), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (378), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (429), (439), (1244), (1257), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289), (1308), (1341), (1590), (function-axioms) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #111. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1591) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_9_4 = e2 & op(e4, e2) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (429), (1308), (1592), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #127. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1593) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1593) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) all_9_9 = e2 & op(e4, e1) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (1304), (1594) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_9_16 = e2 & op(e4, e0) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1325), (1595) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) all_9_5 = e1 & op(e3, e2) = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1596) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_9_5 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1598) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) all_9_2 = e0 & op(e3, e4) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1599) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) all_9_2 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (1600), (function-axioms) are % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_9_3 = e0 & op(e3, e3) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1601) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) all_9_3 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1252), (1602) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) e4 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1603) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) e4 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (1604) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) $false % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1605) is inconsistent. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1606) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) all_9_5 = e0 & op(e3, e2) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1607) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) all_9_5 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (121), (126), (170), (173), (227), (229), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (239), (252), (253), (265), (266), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (329), (330), (331), (332), (334), (342), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (346), (348), (356), (358), (360), (366), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (372), (395), (1597), (1608), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #101. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) (all_9_10 = e0 & op(e3, e1) = e0) | (all_9_17 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1609) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_9_10 = e0 & op(e3, e1) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1610) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_9_10 = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (23), (1252), (1612), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #133. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1613) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) all_9_5 = e2 & op(e3, e2) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1257), (1614) are inconsistent by sub-proof #132. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1615) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_9_10 = e2 & op(e3, e1) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1611), (1616) are inconsistent by sub-proof % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #110. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_9_17 = e2 & op(e3, e0) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1617) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_9_17 = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (356), (395), (1229), (1619) are % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #293. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1620) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_9_5 = e3 & op(e3, e2) = e3 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1621) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_9_5 = e3 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1597), (1622) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) e3 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1623) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) e3 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (1624) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) $false % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1625) is inconsistent. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (344), (1611), (1618), (1626) are % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #108. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_9_17 = e0 & op(e3, e0) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1627) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) op(e3, e0) = e0 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (31), (248), (253), (303), (305), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358), (404), (1246), (1248), (1628) are % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #129. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) | (all_9_22 = e1 & op(e0, e2) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1629) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) all_9_8 = e1 & op(e2, e2) = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1630) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) all_9_8 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (1631) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) e4 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (1632) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) $false % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1633) is inconsistent. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_22 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e1) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1634) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_9_14 = e1 & op(e1, e2) = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (255), (1290), (1635) are inconsistent by % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #99. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) all_9_22 = e1 & op(e0, e2) = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1636) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_9_22 = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) op(e0, e2) = e1 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) ~ (op(e4, e1) = e4) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1305), (1639) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) $false % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1640) is inconsistent. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) all_6_3 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1641) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_4_15 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1642) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_4_15 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (1643) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) ~ (all_4_5 = e4) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (1643) imply: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) ~ (all_4_20 = e4) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_44 & op(e2, e4) = all_8_45 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44) & $i(all_8_45)) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1646) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (23), (233), (278), (293), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (329), (334), (372), (411), (429), (1305), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647), (function-axioms) are inconsistent by % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #301. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_44) & % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1648) implies: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) op(e2, e4) = all_8_45 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) op(e4, all_8_45) = e2 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (234), (278), (287), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (300), (325), (329), (334), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (378), (403), (411), (429), (1244), (1247), % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296), (1304), (1651) are inconsistent by % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #134. % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1652) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_9_22 = e4 & op(e0, e2) = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1653) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_9_22 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1637), (1654) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) e4 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1655) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) e4 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (1656) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) $false % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1657) is inconsistent. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e4) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1658) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) all_9_23 = e4 & op(e0, e1) = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (23), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (98), (121), (126), (128), (170), (173), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (205), (206), (207), (208), (220), (221), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (229), (231), (233), (234), (235), (239), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (246), (252), (253), (265), (266), (274), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (281), (287), (289), (293), (296), (300), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308), (325), (329), (330), (331), (332), (334), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (344), (346), (348), (356), (358), (360), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (366), (368), (372), (374), (378), (390), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (411), (429), (1229), (1244), (1247), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252), (1257), (1265), (1270), (1296), (1304), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659), (function-axioms) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #102. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) all_9_24 = e4 & op(e0, e0) = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1660) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1661) all_9_24 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1662) all_9_24 = e0 & op(e0, e0) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1662) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663) op(e0, e0) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (246), (1270), (1663) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #240. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1664) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1664) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1665) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1665) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1666) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e0) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1666) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1667) all_9_20 = e0 & op(e0, e4) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (429), (1667) are inconsistent by sub-proof % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #239. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1668) all_9_21 = e0 & op(e0, e3) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (1244), (1668) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1669) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e0) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1669) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670) all_9_22 = e0 & op(e0, e2) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (1265), (1670) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1671) all_9_23 = e0 & op(e0, e1) = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1671) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1672) all_9_23 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_45, % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (22), (1649) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673) all_8_45 = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1245), (1649) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674) ~ (all_8_45 = e4) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_5, e2, % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (140) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1675) all_4_5 = e2 | ~ (op(e4, e3) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_20, e2, % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (137) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1676) all_4_20 = e2 | ~ (op(e4, e0) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1650), (1673) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1677) op(e4, e3) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1675) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1678) ~ (op(e4, e3) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1677), (1678) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1679) $false % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1679) is inconsistent. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1680) all_4_5 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (1680) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1681) ~ (all_4_10 = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1681) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1682) ~ (all_4_10 = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (1680) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683) ~ (all_4_20 = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1683) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1684) ~ (all_4_20 = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1685) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e1) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1685) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1686) all_9_0 = e1 & op(e4, e4) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1686) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1687) op(e4, e4) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (342), (1687), (function-axioms) are % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1688) all_9_1 = e1 & op(e4, e3) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1688) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1689) all_9_1 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1690) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1690) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1691) all_9_0 = e2 & op(e4, e4) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (390), (1691) are inconsistent by sub-proof % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1692) all_9_1 = e2 & op(e4, e3) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1692) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693) all_9_1 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1689), (1693) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1694) e2 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1694) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1695) e2 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1695) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1696) all_9_20 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (265), (266), (278), (293), (325), (329), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (372), (390), (1696), (function-axioms) are % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1697) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (289), (311), (1304), (1676), (1682), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1684), (1697) are inconsistent by sub-proof #153. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1698) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1698) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1699) all_9_4 = e1 & op(e4, e2) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1699) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1700) all_9_4 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (21), (22), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (68), (70), (98), (121), (126), (170), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (181), (192), (217), (218), (227), (229), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (239), (250), (252), (253), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (266), (269), (275), (278), (282), (289), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (315), (317), (325), (329), (330), (331), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (334), (342), (344), (346), (348), (352), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356), (358), (360), (366), (368), (372), (378), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (395), (429), (439), (1244), (1257), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289), (1661), (1672), (1700), (function-axioms) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #111. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1701) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e1) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1701) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1702) all_9_9 = e1 & op(e4, e1) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (1304), (1702) are inconsistent by sub-proof % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1703) all_9_16 = e1 & op(e4, e0) = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1704) all_9_16 = e1 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1705) all_6_2 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1705) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706) all_4_10 = e4 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1706) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1707) $false % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1707) is inconsistent. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1708) ~ (all_6_2 = e4) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1709) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1709) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1710) all_6_2 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1710) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1711) all_4_10 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1682), (1711) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1712) $false % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1712) is inconsistent. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) ~ (all_6_2 = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1714) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) all_6_2 = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1715) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) all_4_10 = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (1716) imply: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) ~ (all_4_11 = e3) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1717) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) ~ (all_4_11 = e3) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1719) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1720) all_9_0 = e3 & op(e4, e4) = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (390), (1720) are inconsistent by sub-proof % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1721) all_9_1 = e3 & op(e4, e3) = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722) op(e4, e3) = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (328), (329), (372), (1649), (1650), % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722), (function-axioms) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #145. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1723) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1723) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1724) all_9_4 = e3 & op(e4, e2) = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1724) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1725) all_9_4 = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1726) op(e4, e2) = e3 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1727) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1727) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1728) all_9_4 = e2 & op(e4, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1728) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1729) op(e4, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (311), (1682), (1729) are inconsistent by % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #261. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1730) all_9_5 = e2 & op(e3, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1257), (1730) are inconsistent by sub-proof #132. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1731) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1732) all_9_8 = e2 & op(e2, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (269), (1732) are inconsistent by sub-proof % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1733) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1734) all_9_14 = e2 & op(e1, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1734) implies: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) all_9_14 = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) op(e1, e2) = e2 % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) (all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) = all_8_65 & op(e4, e2) = all_8_66 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_66) = e4 & $i(all_8_65) & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_67 = e3 & ~ (all_8_68 = % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, all_8_69) = all_8_68 & op(e3, e2) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69 & op(e2, all_8_69) = e3 & % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_68) & $i(all_8_69)) % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1737) gives: % 127.97/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) = all_8_65 & op(e4, e2) = all_8_66 & % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_66) = e4 & $i(all_8_65) & % 127.97/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1738) implies: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) op(e2, all_8_66) = e4 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) op(e4, e2) = all_8_66 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) all_6_7 = e4 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1741) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) all_4_11 = e4 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (1742) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) $false % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1743) is inconsistent. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1744) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) all_6_7 = e2 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1745) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746) all_4_11 = e2 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1746) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) $false % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1747) is inconsistent. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1748) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_6_7 = e3 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1749) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_4_11 = e3 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1718), (1750) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) $false % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1751) is inconsistent. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) all_6_7 = e1 | all_6_7 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1752) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_6_7 = e1 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1753) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1754) all_4_11 = e1 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1754) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755) $false % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1755) is inconsistent. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_66, % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e4, simplifying with (1726), (1740) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1756) all_8_66 = e3 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1739), (1756) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1757) op(e2, e3) = e4 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (377), (1757), (function-axioms) are % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1758) all_8_67 = e3 & ~ (all_8_68 = e2) & op(e3, % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69) = all_8_68 & op(e3, e2) = all_8_69 & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_69) = e3 & $i(all_8_68) & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1758) implies: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1759) op(e2, all_8_69) = e3 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760) op(e3, e2) = all_8_69 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1761) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1761) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) all_9_4 = e0 & op(e4, e2) = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1762) implies: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) all_9_4 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1725), (1763) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) e3 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (1764) imply: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) $false % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1765) is inconsistent. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) all_9_5 = e0 & op(e3, e2) = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1766) implies: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) op(e3, e2) = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (177), (273), (376), (1297), (1759), % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760), (1767), (function-axioms) are inconsistent % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #98. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (243), (402), (1265), (1735), (1768) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #113. % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) (all_8_70 = e1 & ~ (all_8_71 = e2) & op(e2, % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_71) & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72)) | (all_8_73 = e0 & ~ (all_8_74 = % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, all_8_75) = e0 & op(e0, all_8_75) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_74 & op(e0, e2) = all_8_75 & % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_74) & $i(all_8_75)) % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1769) gives: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.24/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) all_8_70 = e1 & ~ (all_8_71 = e2) & op(e2, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_71) & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1770) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) ~ (all_8_71 = e2) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) op(e1, e2) = all_8_72 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) op(e1, all_8_72) = all_8_71 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) all_6_7 = e4 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1774) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) all_4_11 = e4 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (1775) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1776) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1777) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) all_6_7 = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1778) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) all_4_11 = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1779) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1780) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1781) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) all_6_7 = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1782) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1783) all_4_11 = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1718), (1783) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1784) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1784) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1785) all_6_7 = e1 | all_6_7 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1785) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1786) all_6_7 = e1 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1786) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1787) all_4_11 = e1 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1787) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1788) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_72, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (1736), (1772) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) all_8_72 = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_71, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (1736) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) all_8_71 = e2 | ~ (op(e1, e2) = all_8_71) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1773), (1789) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) op(e1, e2) = all_8_71 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1790) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) ~ (op(e1, e2) = all_8_71) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1791), (1792) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1793) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) all_8_71 = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1771), (1794) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1795) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) all_8_73 = e0 & ~ (all_8_74 = e2) & op(e2, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75) = e0 & op(e0, all_8_75) = all_8_74 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_75 & $i(all_8_74) & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1796) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) op(e0, e2) = all_8_75 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) op(e2, all_8_75) = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_8_75, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (1638), (1797) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) all_8_75 = e1 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_17, e0, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (128) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) all_4_17 = e0 | ~ (op(e2, e1) = e0) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1798), (1799) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) op(e2, e1) = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1800) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) ~ (op(e2, e1) = e0) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1801), (1802) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1803) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) all_4_17 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1268), (1804) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) $false % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1805) is inconsistent. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) op(e0, e2) = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (237), (317), (439), (1806) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #246. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) all_9_22 = e2 & op(e0, e2) = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1807) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) op(e0, e2) = e2 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (237), (317), (439), (1808) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #246. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1809) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) all_9_9 = e3 & op(e4, e1) = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1810) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1811) all_9_9 = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (234), (278), (287), % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289), (293), (296), (300), (325), (329), (334), % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (378), (411), (429), (1247), (1296), (1811) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) all_9_16 = e3 & op(e4, e0) = e3 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (356), (1704), (1812) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #219. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) all_6_2 = e1 | all_6_2 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (352), (1289), (1813) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #123. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1814) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_50 & op(e0, e4) = all_8_51 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_50) & $i(all_8_51)) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1814) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1815) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1816) op(e1, e4) = all_8_48 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) op(e4, all_8_48) = e1 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) all_9_24 = e0 & op(e0, e0) = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) op(e0, e0) = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (246), (1270), (1819) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #240. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_8_48, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e1, simplifying with (412), (1816) gives: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) all_8_48 = e4 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1817), (1820) imply: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) op(e4, e4) = e1 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (342), (1821), (function-axioms) are % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51) = e0 & op(e0, all_8_51) = all_8_50 & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_50) & % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (352), (446), (1822), (function-axioms) are % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_9_16 = e4 & op(e4, e0) = e4 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (300), (1296), (1823) are inconsistent by % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #195. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_24 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (235), (443), (1236), (1270), (1292), (1824) are % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #97. % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) all_6_22 = e0 % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (1825) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) all_4_14 = e0 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1826) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_4_14 = e0 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1265), (1827) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) $false % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1828) is inconsistent. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) all_6_7 = e2 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1829) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) all_4_11 = e2 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1830) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) ~ (all_4_13 = e2) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1831) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) ~ (all_4_13 = e2) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (12), (18), (293), (316), (334), (404), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246), (1248), (1832) are inconsistent by % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #95. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) (all_9_7 = e4 & op(e2, e3) = e4) | (all_9_13 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) | (all_9_21 = e4 & op(e0, e3) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1833) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_9_7 = e4 & op(e2, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1834) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) op(e2, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_7, e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (130), (1835) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) all_4_7 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (1836) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) $false % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1837) is inconsistent. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) (all_9_13 = e4 & op(e1, e3) = e4) | (all_9_21 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e4) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1838) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) all_9_13 = e4 & op(e1, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1839) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) op(e1, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_8, e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (125), (1840) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) all_4_8 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (1841) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) $false % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1842) is inconsistent. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_9_21 = e4 & op(e0, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1843) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) all_9_21 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1244), (1844) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) e4 = e3 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (1845) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) all_9_12 = e3 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (20), (233), (278), (293), (325), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (334), (372), (429), (1846) are % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #303. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_6_1 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1847) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | (1848) all_4_5 = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1848) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | (1849) op(e4, e3) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) (all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42)) | (all_8_43 = e2 & ~ (all_8_44 = % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_45) = e2 & op(e2, all_8_45) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_44 & op(e2, e4) = all_8_45 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_44) & $i(all_8_45)) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1850) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42) = e3 & op(e3, all_8_42) = all_8_41 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_41) & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1851) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) op(e3, e4) = all_8_42 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) op(e4, all_8_42) = e3 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) ~ (op(e3, e4) = e4) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) ~ (op(e3, e4) = e3) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5), (1855) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) ~ (unit = e4) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (18), (20), (23), (233), (278), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293), (325), (329), (334), (372), (404), (411), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429), (1246), (1852), (1853), (1854), (1856), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) e3 = e1 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (1857) imply: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) $false % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1858) is inconsistent. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) op(e3, e4) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (278), (325), (1859) are inconsistent by % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) all_8_43 = e2 & ~ (all_8_44 = e4) & op(e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45) = e2 & op(e2, all_8_45) = all_8_44 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_44) & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1860) implies: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) op(e2, e4) = all_8_45 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) op(e4, all_8_45) = e2 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (22), (1849), (1861), (1862), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_48) = e1 & op(e1, all_8_48) = all_8_47 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_47) & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & op(e4, all_8_51) = e0 & op(e0, all_8_51) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_50 & op(e0, e4) = all_8_51 & % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_50) & $i(all_8_51)) % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (139), (342), (352), (412), (446), (1863), % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #146. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | (1864) op(e2, e4) = e4 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (329), (372), (1864) are inconsistent by sub-proof % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | #320. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | (1865) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 128.26/17.67 | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (239), (348), (360), (368), (1865) are % 128.26/17.67 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #269. % 128.26/17.67 | | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | (1866) all_9_20 = e4 & op(e0, e4) = e4 % 128.26/17.67 | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | | REF_CLOSE: (403), (1866) are inconsistent by sub-proof #135. % 128.26/17.67 | | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | (1867) all_6_20 = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | COMBINE_EQS: (239), (1867) imply: % 128.26/17.67 | | | | | | | | | | (1868) all_4_4 = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (98), (1868) imply: % 128.26/17.67 | | | | | | | | | | (1869) ~ (all_4_3 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (94), (1868) imply: % 128.26/17.67 | | | | | | | | | | (1870) ~ (all_4_9 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | SIMP: (1870) implies: % 128.26/17.67 | | | | | | | | | | (1871) ~ (all_4_9 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (92), (1868) imply: % 128.26/17.67 | | | | | | | | | | (1872) ~ (all_4_19 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | SIMP: (1872) implies: % 128.26/17.67 | | | | | | | | | | (1873) ~ (all_4_19 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (91), (1868) imply: % 128.26/17.67 | | | | | | | | | | (1874) ~ (all_4_24 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | SIMP: (1874) implies: % 128.26/17.67 | | | | | | | | | | (1875) ~ (all_4_24 = e4) % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 128.26/17.67 | | | | | | | | | | (11), (12), (15), (16), (17), (18), (19), (20), % 128.26/17.67 | | | | | | | | | | (21), (22), (23), (24), (27), (28), (29), (30), % 128.26/17.67 | | | | | | | | | | (32), (35), (36), (37), (38), (39), (40), (41), % 128.26/17.67 | | | | | | | | | | (42), (43), (46), (47), (48), (49), (51), (52), % 128.26/17.67 | | | | | | | | | | (53), (54), (55), (60), (62), (63), (65), (66), % 128.26/17.67 | | | | | | | | | | (67), (68), (70), (71), (72), (74), (75), (76), % 128.26/17.67 | | | | | | | | | | (77), (78), (80), (81), (84), (86), (87), (88), % 128.26/17.67 | | | | | | | | | | (89), (90), (95), (96), (98), (117), (118), (119), % 128.26/17.67 | | | | | | | | | | (120), (121), (122), (123), (125), (126), (127), % 128.26/17.67 | | | | | | | | | | (128), (130), (132), (139), (140), (168), (170), % 128.26/17.67 | | | | | | | | | | (171), (172), (173), (174), (175), (176), (177), % 128.26/17.67 | | | | | | | | | | (178), (180), (181), (182), (185), (186), (187), % 128.26/17.67 | | | | | | | | | | (189), (191), (193), (195), (196), (197), (198), % 128.26/17.67 | | | | | | | | | | (200), (203), (204), (206), (207), (208), (209), % 128.26/17.67 | | | | | | | | | | (210), (211), (212), (215), (216), (217), (218), % 128.26/17.67 | | | | | | | | | | (219), (220), (221), (222), (223), (224), (227), % 128.26/17.67 | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234), % 128.26/17.67 | | | | | | | | | | (235), (236), (238), (239), (240), (241), (243), % 128.26/17.67 | | | | | | | | | | (246), (247), (249), (250), (251), (252), (253), % 128.26/17.67 | | | | | | | | | | (255), (256), (258), (259), (260), (263), (265), % 128.26/17.67 | | | | | | | | | | (266), (267), (268), (269), (270), (271), (272), % 128.26/17.67 | | | | | | | | | | (273), (274), (275), (278), (281), (282), (283), % 128.26/17.67 | | | | | | | | | | (285), (287), (288), (289), (290), (293), (295), % 128.26/17.67 | | | | | | | | | | (296), (298), (299), (301), (302), (303), (304), % 128.26/17.67 | | | | | | | | | | (306), (307), (308), (309), (310), (311), (312), % 128.26/17.67 | | | | | | | | | | (314), (316), (318), (320), (321), (322), (323), % 128.26/17.67 | | | | | | | | | | (324), (325), (328), (329), (330), (331), (332), % 128.26/17.67 | | | | | | | | | | (334), (344), (346), (348), (350), (354), (358), % 128.26/17.67 | | | | | | | | | | (360), (362), (366), (368), (372), (374), (376), % 128.26/17.67 | | | | | | | | | | (377), (379), (381), (383), (385), (387), (390), % 128.26/17.67 | | | | | | | | | | (395), (398), (402), (1868), (1869), (1871), % 128.26/17.67 | | | | | | | | | | (1873), (1875), (function-axioms) are inconsistent % 128.26/17.67 | | | | | | | | | | by sub-proof #3. % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | % 128.26/17.67 | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | % 128.26/17.67 | | | | | | | | | (1876) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_18 = e4 & % 128.26/17.67 | | | | | | | | | op(e2, e0) = e4) % 128.26/17.67 | | | | | | | | | % 128.26/17.67 | | | | | | | | | BETA: splitting (1876) gives: % 128.26/17.67 | | | | | | | | | % 128.26/17.67 | | | | | | | | | Case 1: % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | (1877) all_9_11 = e4 & op(e2, e1) = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | ALPHA: (1877) implies: % 128.26/17.67 | | | | | | | | | | (1878) op(e2, e1) = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_17, e4, % 128.26/17.67 | | | | | | | | | | e1, e2, simplifying with (128), (1878) gives: % 128.26/17.67 | | | | | | | | | | (1879) all_4_17 = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (385), (1879) imply: % 128.26/17.67 | | | | | | | | | | (1880) $false % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | CLOSE: (1880) is inconsistent. % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | Case 2: % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | (1881) all_9_18 = e4 & op(e2, e0) = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | ALPHA: (1881) implies: % 128.26/17.67 | | | | | | | | | | (1882) op(e2, e0) = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_22, e4, % 128.26/17.67 | | | | | | | | | | e0, e2, simplifying with (127), (1882) gives: % 128.26/17.67 | | | | | | | | | | (1883) all_4_22 = e4 % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | REDUCE: (387), (1883) imply: % 128.26/17.67 | | | | | | | | | | (1884) $false % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | | CLOSE: (1884) is inconsistent. % 128.26/17.67 | | | | | | | | | | % 128.26/17.67 | | | | | | | | | End of split % 128.26/17.67 | | | | | | | | | % 128.26/17.67 | | | | | | | | End of split % 128.26/17.67 | | | | | | | | % 128.26/17.67 | | | | | | | End of split % 128.26/17.67 | | | | | | | % 128.26/17.67 | | | | | | Case 2: % 128.26/17.67 | | | | | | | % 128.26/17.67 | | | | | | | (1885) all_9_7 = e3 & op(e2, e3) = e3 % 128.26/17.67 | | | | | | | % 128.26/17.67 | | | | | | | ALPHA: (1885) implies: % 128.26/17.67 | | | | | | | (1886) op(e2, e3) = e3 % 128.26/17.67 | | | | | | | % 128.26/17.67 | | | | | | | REF_CLOSE: (263), (321), (370), (1886) are inconsistent by % 128.26/17.67 | | | | | | | sub-proof #294. % 128.26/17.67 | | | | | | | % 128.26/17.67 | | | | | | End of split % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | Case 2: % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | | (1887) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, % 128.26/17.67 | | | | | | e1) = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | | REF_CLOSE: (21), (127), (128), (372), (374), (376), (1887), % 128.26/17.67 | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | End of split % 128.26/17.67 | | | | | % 128.26/17.67 | | | | End of split % 128.26/17.67 | | | | % 128.26/17.67 | | | Case 2: % 128.26/17.67 | | | | % 128.26/17.67 | | | | (1888) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) % 128.26/17.67 | | | | = e1) | (all_9_20 = e1 & op(e0, e4) = e1) % 128.26/17.67 | | | | % 128.26/17.67 | | | | BETA: splitting (1888) gives: % 128.26/17.67 | | | | % 128.26/17.67 | | | | Case 1: % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | (1889) all_9_6 = e1 & op(e2, e4) = e1 % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | ALPHA: (1889) implies: % 128.26/17.67 | | | | | (1890) all_9_6 = e1 % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | REF_CLOSE: (21), (127), (128), (213), (263), (321), (356), (370), % 128.26/17.67 | | | | | (372), (374), (376), (1890), (function-axioms) are % 128.26/17.67 | | | | | inconsistent by sub-proof #1. % 128.26/17.67 | | | | | % 128.26/17.67 | | | | Case 2: % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | (1891) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 & op(e0, % 128.26/17.67 | | | | | e4) = e1) % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | BETA: splitting (1891) gives: % 128.26/17.67 | | | | | % 128.26/17.67 | | | | | Case 1: % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | | (1892) all_9_12 = e1 & op(e1, e4) = e1 % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | | ALPHA: (1892) implies: % 128.26/17.67 | | | | | | (1893) op(e1, e4) = e1 % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | | REF_CLOSE: (253), (358), (1893) are inconsistent by sub-proof #268. % 128.26/17.67 | | | | | | % 128.26/17.67 | | | | | Case 2: % 128.26/17.67 | | | | | | % 128.26/17.68 | | | | | | (1894) all_9_20 = e1 & op(e0, e4) = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | ALPHA: (1894) implies: % 128.26/17.68 | | | | | | (1895) all_9_20 = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (23), (229), (233), % 128.26/17.68 | | | | | | (265), (266), (278), (293), (325), (329), (334), (372), % 128.26/17.68 | | | | | | (390), (1895), (function-axioms) are inconsistent by % 128.26/17.68 | | | | | | sub-proof #283. % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | End of split % 128.26/17.68 | | | | | % 128.26/17.68 | | | | End of split % 128.26/17.68 | | | | % 128.26/17.68 | | | End of split % 128.26/17.68 | | | % 128.26/17.68 | | Case 2: % 128.26/17.68 | | | % 128.26/17.68 | | | (1896) all_9_2 = e0 & op(e3, e4) = e0 % 128.26/17.68 | | | % 128.26/17.68 | | | ALPHA: (1896) implies: % 128.26/17.68 | | | (1897) all_9_2 = e0 % 128.26/17.68 | | | % 128.26/17.68 | | | REF_CLOSE: (15), (16), (17), (18), (19), (20), (22), (24), (98), (121), % 128.26/17.68 | | | (126), (170), (173), (227), (229), (231), (233), (239), (252), % 128.26/17.68 | | | (253), (265), (266), (293), (329), (330), (331), (332), (334), % 128.26/17.68 | | | (342), (344), (346), (348), (356), (358), (360), (366), (368), % 128.26/17.68 | | | (372), (1897), (function-axioms) are inconsistent by sub-proof % 128.26/17.68 | | | #265. % 128.26/17.68 | | | % 128.26/17.68 | | End of split % 128.26/17.68 | | % 128.26/17.68 | Case 2: % 128.26/17.68 | | % 128.26/17.68 | | (1898) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_12 = e0 & op(e1, e4) = % 128.26/17.68 | | e0) | (all_9_20 = e0 & op(e0, e4) = e0) % 128.26/17.68 | | % 128.26/17.68 | | BETA: splitting (1898) gives: % 128.26/17.68 | | % 128.26/17.68 | | Case 1: % 128.26/17.68 | | | % 128.26/17.68 | | | (1899) all_9_6 = e0 & op(e2, e4) = e0 % 128.26/17.68 | | | % 128.26/17.68 | | | ALPHA: (1899) implies: % 128.26/17.68 | | | (1900) all_9_6 = e0 % 128.26/17.68 | | | % 128.26/17.68 | | | BETA: splitting (213) gives: % 128.26/17.68 | | | % 128.26/17.68 | | | Case 1: % 128.26/17.68 | | | | % 128.26/17.68 | | | | (1901) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) % 128.26/17.68 | | | | = e3) % 128.26/17.68 | | | | % 128.26/17.68 | | | | BETA: splitting (1901) gives: % 128.26/17.68 | | | | % 128.26/17.68 | | | | Case 1: % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | (1902) all_9_6 = e3 & op(e2, e4) = e3 % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | ALPHA: (1902) implies: % 128.26/17.68 | | | | | (1903) all_9_6 = e3 % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | REF_CLOSE: (344), (1900), (1903) are inconsistent by sub-proof #14. % 128.26/17.68 | | | | | % 128.26/17.68 | | | | Case 2: % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | (1904) all_9_7 = e3 & op(e2, e3) = e3 % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | ALPHA: (1904) implies: % 128.26/17.68 | | | | | (1905) op(e2, e3) = e3 % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | REF_CLOSE: (263), (321), (370), (1905) are inconsistent by sub-proof % 128.26/17.68 | | | | | #294. % 128.26/17.68 | | | | | % 128.26/17.68 | | | | End of split % 128.26/17.68 | | | | % 128.26/17.68 | | | Case 2: % 128.26/17.68 | | | | % 128.26/17.68 | | | | (1906) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) % 128.26/17.68 | | | | = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.68 | | | | % 128.26/17.68 | | | | REF_CLOSE: (21), (127), (128), (372), (374), (376), (1906), % 128.26/17.68 | | | | (function-axioms) are inconsistent by sub-proof #2. % 128.26/17.68 | | | | % 128.26/17.68 | | | End of split % 128.26/17.68 | | | % 128.26/17.68 | | Case 2: % 128.26/17.68 | | | % 128.26/17.68 | | | (1907) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_20 = e0 & op(e0, e4) % 128.26/17.68 | | | = e0) % 128.26/17.68 | | | % 128.26/17.68 | | | BETA: splitting (1907) gives: % 128.26/17.68 | | | % 128.26/17.68 | | | Case 1: % 128.26/17.68 | | | | % 128.26/17.68 | | | | (1908) all_9_12 = e0 & op(e1, e4) = e0 % 128.26/17.68 | | | | % 128.26/17.68 | | | | ALPHA: (1908) implies: % 128.26/17.68 | | | | (1909) all_9_12 = e0 % 128.26/17.68 | | | | % 128.26/17.68 | | | | BETA: splitting (227) gives: % 128.26/17.68 | | | | % 128.26/17.68 | | | | Case 1: % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | (1910) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, % 128.26/17.68 | | | | | e4) = e1) % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | BETA: splitting (1910) gives: % 128.26/17.68 | | | | | % 128.26/17.68 | | | | | Case 1: % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | (1911) all_9_0 = e1 & op(e4, e4) = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | ALPHA: (1911) implies: % 128.26/17.68 | | | | | | (1912) op(e4, e4) = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | REF_CLOSE: (24), (342), (1912), (function-axioms) are inconsistent % 128.26/17.68 | | | | | | by sub-proof #321. % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | Case 2: % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | (1913) all_9_2 = e1 & op(e3, e4) = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | ALPHA: (1913) implies: % 128.26/17.68 | | | | | | (1914) all_9_2 = e1 % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | BETA: splitting (213) gives: % 128.26/17.68 | | | | | | % 128.26/17.68 | | | | | | Case 1: % 128.26/17.68 | | | | | | | % 128.26/17.68 | | | | | | | (1915) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & % 128.26/17.68 | | | | | | | op(e2, e3) = e3) % 128.26/17.68 | | | | | | | % 128.26/17.68 | | | | | | | BETA: splitting (1915) gives: % 128.26/17.68 | | | | | | | % 128.26/17.68 | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | % 128.26/17.68 | | | | | | | | (1916) all_9_6 = e3 & op(e2, e4) = e3 % 128.26/17.68 | | | | | | | | % 128.26/17.68 | | | | | | | | ALPHA: (1916) implies: % 128.26/17.68 | | | | | | | | (1917) all_9_6 = e3 % 128.26/17.68 | | | | | | | | % 128.26/17.68 | | | | | | | | BETA: splitting (229) gives: % 128.26/17.68 | | | | | | | | % 128.26/17.68 | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | (1918) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & % 128.26/17.68 | | | | | | | | | op(e3, e4) = e2) % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | BETA: splitting (1918) gives: % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | (1919) all_9_0 = e2 & op(e4, e4) = e2 % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | ALPHA: (1919) implies: % 128.26/17.68 | | | | | | | | | | (1920) all_9_0 = e2 % 128.26/17.68 | | | | | | | | | | (1921) op(e4, e4) = e2 % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | BETA: splitting (214) gives: % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | (1922) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & % 128.26/17.68 | | | | | | | | | | | op(e2, e3) = e4) % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | REF_CLOSE: (130), (329), (372), (377), (1922), % 128.26/17.68 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.26/17.68 | | | | | | | | | | | #318. % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | (1923) (all_9_8 = e4 & op(e2, e2) = e4) | (all_9_11 = e4 % 128.26/17.68 | | | | | | | | | | | & op(e2, e1) = e4) | (all_9_18 = e4 & op(e2, e0) % 128.26/17.68 | | | | | | | | | | | = e4) % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | BETA: splitting (1923) gives: % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | (1924) all_9_8 = e4 & op(e2, e2) = e4 % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | ALPHA: (1924) implies: % 128.26/17.68 | | | | | | | | | | | | (1925) all_9_8 = e4 % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | BETA: splitting (233) gives: % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | (1926) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 128.26/17.68 | | | | | | | | | | | | | op(e3, e4) = e4) % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | REF_CLOSE: (18), (19), (278), (293), (325), (334), (1926) are % 128.26/17.68 | | | | | | | | | | | | | inconsistent by sub-proof #315. % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | (1927) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 % 128.26/17.68 | | | | | | | | | | | | | & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) % 128.26/17.68 | | | | | | | | | | | | | = e4) % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | BETA: splitting (1927) gives: % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | (1928) all_9_6 = e4 & op(e2, e4) = e4 % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | ALPHA: (1928) implies: % 128.26/17.68 | | | | | | | | | | | | | | (1929) op(e2, e4) = e4 % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | REF_CLOSE: (329), (372), (1929) are inconsistent by sub-proof % 128.26/17.68 | | | | | | | | | | | | | | #320. % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | (1930) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 128.26/17.68 | | | | | | | | | | | | | | & op(e0, e4) = e4) % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | BETA: splitting (1930) gives: % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | (1931) all_9_12 = e4 & op(e1, e4) = e4 % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | ALPHA: (1931) implies: % 128.26/17.68 | | | | | | | | | | | | | | | (1932) all_9_12 = e4 % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | COMBINE_EQS: (1909), (1932) imply: % 128.26/17.68 | | | | | | | | | | | | | | | (1933) e4 = e0 % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | REDUCE: (18), (1933) imply: % 128.26/17.68 | | | | | | | | | | | | | | | (1934) $false % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | CLOSE: (1934) is inconsistent. % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | (1935) all_9_20 = e4 & op(e0, e4) = e4 % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | ALPHA: (1935) implies: % 128.26/17.68 | | | | | | | | | | | | | | | (1936) op(e0, e4) = e4 % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | (1937) ~ (op(e0, e4) = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | PRED_UNIFY: (1936), (1937) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1938) $false % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | CLOSE: (1938) is inconsistent. % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | (1939) all_6_20 = e4 % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (1939) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1940) all_4_4 = e4 % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | SIMP: (1940) implies: % 128.26/17.68 | | | | | | | | | | | | | | | | (1941) all_4_4 = e4 % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | REDUCE: (98), (1941) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1942) ~ (all_4_3 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | REDUCE: (94), (1941) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1943) ~ (all_4_9 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | SIMP: (1943) implies: % 128.26/17.68 | | | | | | | | | | | | | | | | (1944) ~ (all_4_9 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | REDUCE: (92), (1941) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1945) ~ (all_4_19 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | SIMP: (1945) implies: % 128.26/17.68 | | | | | | | | | | | | | | | | (1946) ~ (all_4_19 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | REDUCE: (91), (1941) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | (1947) ~ (all_4_24 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | SIMP: (1947) implies: % 128.26/17.68 | | | | | | | | | | | | | | | | (1948) ~ (all_4_24 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | (1949) all_6_15 = e4 % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (1942), (1949) are inconsistent by % 128.26/17.68 | | | | | | | | | | | | | | | | | sub-proof #278. % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | (1950) ~ (all_6_15 = e4) % 128.26/17.68 | | | | | | | | | | | | | | | | | (1951) all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 128.26/17.68 | | | | | | | | | | | | | | | | | all_6_15 = e0 % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | BETA: splitting (1951) gives: % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1952) all_6_15 = e2 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (1952) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1953) all_4_3 = e2 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | SIMP: (1953) implies: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1954) all_4_3 = e2 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | REDUCE: (1942), (1954) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1955) ~ (e4 = e2) % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | REDUCE: (366), (1954) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1956) ~ (e3 = e2) % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e4, % 128.26/17.68 | | | | | | | | | | | | | | | | | | e4, simplifying with (24), (1921) gives: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1957) e2 = e0 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1920), (1957) imply: % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1958) all_9_0 = e0 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (11), (12), (15), (16), (17), (18), (19), (20), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (21), (22), (23), (24), (27), (28), (29), (30), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (32), (35), (36), (37), (38), (39), (40), (41), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (42), (43), (46), (47), (48), (49), (51), (52), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (53), (54), (55), (60), (62), (63), (65), (66), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (67), (68), (70), (71), (72), (74), (75), (76), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (77), (78), (80), (81), (84), (86), (87), (88), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (89), (90), (95), (96), (98), (117), (118), (119), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (125), (126), (127), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (128), (130), (132), (139), (140), (168), (170), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (171), (172), (173), (174), (175), (176), (177), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (178), (180), (181), (182), (185), (186), (187), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (189), (191), (193), (195), (196), (197), (198), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (200), (203), (204), (206), (207), (208), (209), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (210), (211), (212), (215), (216), (217), (218), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (219), (220), (221), (222), (223), (224), (227), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (235), (236), (238), (239), (240), (241), (243), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (246), (247), (249), (250), (251), (252), (253), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (255), (256), (258), (259), (260), (263), (265), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (266), (267), (268), (269), (270), (271), (272), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (273), (274), (275), (278), (281), (282), (283), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (285), (287), (288), (289), (290), (293), (295), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (296), (298), (299), (301), (302), (303), (304), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (306), (307), (308), (309), (310), (311), (312), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (314), (316), (318), (320), (321), (322), (323), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (324), (325), (328), (329), (330), (331), (332), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (334), (344), (346), (348), (350), (354), (358), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (360), (362), (366), (368), (372), (374), (376), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (377), (379), (381), (383), (385), (387), (1914), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1917), (1925), (1941), (1942), (1944), (1946), % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1948), (1958), (function-axioms) are inconsistent % 128.26/17.68 | | | | | | | | | | | | | | | | | | by sub-proof #3. % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | (1959) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (252), (346), (358), (366), (1959) are % 128.26/17.68 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #276. % 128.26/17.68 | | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | (1960) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_18 = e4 % 128.26/17.68 | | | | | | | | | | | | & op(e2, e0) = e4) % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | BETA: splitting (1960) gives: % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | (1961) all_9_11 = e4 & op(e2, e1) = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | ALPHA: (1961) implies: % 128.26/17.68 | | | | | | | | | | | | | (1962) op(e2, e1) = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_17, e4, % 128.26/17.68 | | | | | | | | | | | | | e1, e2, simplifying with (128), (1962) gives: % 128.26/17.68 | | | | | | | | | | | | | (1963) all_4_17 = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | REDUCE: (385), (1963) imply: % 128.26/17.68 | | | | | | | | | | | | | (1964) $false % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | CLOSE: (1964) is inconsistent. % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | (1965) all_9_18 = e4 & op(e2, e0) = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | ALPHA: (1965) implies: % 128.26/17.68 | | | | | | | | | | | | | (1966) op(e2, e0) = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_22, e4, % 128.26/17.68 | | | | | | | | | | | | | e0, e2, simplifying with (127), (1966) gives: % 128.26/17.68 | | | | | | | | | | | | | (1967) all_4_22 = e4 % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | REDUCE: (387), (1967) imply: % 128.26/17.68 | | | | | | | | | | | | | (1968) $false % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | | CLOSE: (1968) is inconsistent. % 128.26/17.68 | | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | (1969) all_9_2 = e2 & op(e3, e4) = e2 % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | ALPHA: (1969) implies: % 128.26/17.68 | | | | | | | | | | (1970) op(e3, e4) = e2 % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | REF_CLOSE: (16), (23), (1970), (function-axioms) are % 128.26/17.68 | | | | | | | | | | inconsistent by sub-proof #313. % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | End of split % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | Case 2: % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | (1971) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 128.26/17.68 | | | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = % 128.26/17.68 | | | | | | | | | e2) % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | BETA: splitting (1971) gives: % 128.26/17.68 | | | | | | | | | % 128.26/17.68 | | | | | | | | | Case 1: % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | (1972) all_9_6 = e2 & op(e2, e4) = e2 % 128.26/17.68 | | | | | | | | | | % 128.26/17.68 | | | | | | | | | | REF_CLOSE: (17), (265), (266), (1972) are inconsistent by % 128.26/17.68 | | | | | | | | | | sub-proof #311. % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | (1973) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 128.26/17.69 | | | | | | | | | | & op(e0, e4) = e2) % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | BETA: splitting (1973) gives: % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | (1974) all_9_12 = e2 & op(e1, e4) = e2 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | ALPHA: (1974) implies: % 128.26/17.69 | | | | | | | | | | | (1975) all_9_12 = e2 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | COMBINE_EQS: (1909), (1975) imply: % 128.26/17.69 | | | | | | | | | | | (1976) e2 = e0 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | REDUCE: (15), (1976) imply: % 128.26/17.69 | | | | | | | | | | | (1977) $false % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | CLOSE: (1977) is inconsistent. % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | (1978) all_9_20 = e2 & op(e0, e4) = e2 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | ALPHA: (1978) implies: % 128.26/17.69 | | | | | | | | | | | (1979) all_9_20 = e2 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | BETA: splitting (233) gives: % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | (1980) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 128.26/17.69 | | | | | | | | | | | | op(e3, e4) = e4) % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | REF_CLOSE: (18), (19), (278), (293), (325), (334), (1980) are % 128.26/17.69 | | | | | | | | | | | | inconsistent by sub-proof #315. % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | (1981) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 % 128.26/17.69 | | | | | | | | | | | | & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) % 128.26/17.69 | | | | | | | | | | | | = e4) % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | BETA: splitting (1981) gives: % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | (1982) all_9_6 = e4 & op(e2, e4) = e4 % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | ALPHA: (1982) implies: % 128.26/17.69 | | | | | | | | | | | | | (1983) op(e2, e4) = e4 % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | REF_CLOSE: (329), (372), (1983) are inconsistent by sub-proof % 128.26/17.69 | | | | | | | | | | | | | #320. % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | (1984) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 128.26/17.69 | | | | | | | | | | | | | & op(e0, e4) = e4) % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | BETA: splitting (1984) gives: % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | (1985) all_9_12 = e4 & op(e1, e4) = e4 % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | ALPHA: (1985) implies: % 128.26/17.69 | | | | | | | | | | | | | | (1986) all_9_12 = e4 % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | COMBINE_EQS: (1909), (1986) imply: % 128.26/17.69 | | | | | | | | | | | | | | (1987) e4 = e0 % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | SIMP: (1987) implies: % 128.26/17.69 | | | | | | | | | | | | | | (1988) e4 = e0 % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | REDUCE: (18), (1988) imply: % 128.26/17.69 | | | | | | | | | | | | | | (1989) $false % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | CLOSE: (1989) is inconsistent. % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | (1990) all_9_20 = e4 & op(e0, e4) = e4 % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | | REF_CLOSE: (20), (1979), (1990) are inconsistent by sub-proof % 128.26/17.69 | | | | | | | | | | | | | | #304. % 128.26/17.69 | | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | End of split % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | (1991) all_9_7 = e3 & op(e2, e3) = e3 % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | ALPHA: (1991) implies: % 128.26/17.69 | | | | | | | | (1992) op(e2, e3) = e3 % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | REF_CLOSE: (263), (321), (370), (1992) are inconsistent by % 128.26/17.69 | | | | | | | | sub-proof #294. % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | End of split % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | Case 2: % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | (1993) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & % 128.26/17.69 | | | | | | | op(e2, e1) = e3) | (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | REF_CLOSE: (21), (127), (128), (372), (374), (376), (1993), % 128.26/17.69 | | | | | | | (function-axioms) are inconsistent by sub-proof #2. % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | End of split % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | End of split % 128.26/17.69 | | | | | % 128.26/17.69 | | | | Case 2: % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | (1994) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, % 128.26/17.69 | | | | | e4) = e1) | (all_9_20 = e1 & op(e0, e4) = e1) % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | BETA: splitting (1994) gives: % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | Case 1: % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | (1995) all_9_6 = e1 & op(e2, e4) = e1 % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | ALPHA: (1995) implies: % 128.26/17.69 | | | | | | (1996) all_9_6 = e1 % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | REF_CLOSE: (21), (127), (128), (213), (263), (321), (356), (370), % 128.26/17.69 | | | | | | (372), (374), (376), (1996), (function-axioms) are % 128.26/17.69 | | | | | | inconsistent by sub-proof #1. % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | Case 2: % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | (1997) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 & % 128.26/17.69 | | | | | | op(e0, e4) = e1) % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | BETA: splitting (1997) gives: % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | | Case 1: % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | (1998) all_9_12 = e1 & op(e1, e4) = e1 % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | ALPHA: (1998) implies: % 128.26/17.69 | | | | | | | (1999) op(e1, e4) = e1 % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | REF_CLOSE: (253), (358), (1999) are inconsistent by sub-proof % 128.26/17.69 | | | | | | | #268. % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | Case 2: % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | (2000) all_9_20 = e1 & op(e0, e4) = e1 % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | ALPHA: (2000) implies: % 128.26/17.69 | | | | | | | (2001) all_9_20 = e1 % 128.26/17.69 | | | | | | | (2002) op(e0, e4) = e1 % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | BETA: splitting (229) gives: % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | (2003) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & % 128.26/17.69 | | | | | | | | op(e3, e4) = e2) % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | BETA: splitting (2003) gives: % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | (2004) all_9_0 = e2 & op(e4, e4) = e2 % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | ALPHA: (2004) implies: % 128.26/17.69 | | | | | | | | | (2005) op(e4, e4) = e2 % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | BETA: splitting (233) gives: % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | (2006) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 128.26/17.69 | | | | | | | | | | op(e3, e4) = e4) % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | REF_CLOSE: (18), (19), (278), (293), (325), (334), (2006) are % 128.26/17.69 | | | | | | | | | | inconsistent by sub-proof #315. % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | (2007) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 % 128.26/17.69 | | | | | | | | | | & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) % 128.26/17.69 | | | | | | | | | | = e4) % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | BETA: splitting (2007) gives: % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | Case 1: % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | (2008) all_9_6 = e4 & op(e2, e4) = e4 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | ALPHA: (2008) implies: % 128.26/17.69 | | | | | | | | | | | (2009) op(e2, e4) = e4 % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | REF_CLOSE: (329), (372), (2009) are inconsistent by sub-proof % 128.26/17.69 | | | | | | | | | | | #320. % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | (2010) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 128.26/17.69 | | | | | | | | | | | & op(e0, e4) = e4) % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | | REF_CLOSE: (19), (24), (98), (121), (170), (239), (252), % 128.26/17.69 | | | | | | | | | | | (330), (342), (348), (360), (368), (2001), (2002), % 128.26/17.69 | | | | | | | | | | | (2005), (2010), (function-axioms) are inconsistent % 128.26/17.69 | | | | | | | | | | | by sub-proof #266. % 128.26/17.69 | | | | | | | | | | | % 128.26/17.69 | | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | | % 128.26/17.69 | | | | | | | | | End of split % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | (2011) all_9_2 = e2 & op(e3, e4) = e2 % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | ALPHA: (2011) implies: % 128.26/17.69 | | | | | | | | | (2012) op(e3, e4) = e2 % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | | REF_CLOSE: (16), (23), (2012), (function-axioms) are % 128.26/17.69 | | | | | | | | | inconsistent by sub-proof #313. % 128.26/17.69 | | | | | | | | | % 128.26/17.69 | | | | | | | | End of split % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | Case 2: % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | (2013) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 128.26/17.69 | | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | | REF_CLOSE: (16), (17), (18), (19), (20), (233), (265), (266), % 128.26/17.69 | | | | | | | | (278), (293), (325), (329), (334), (372), (2001), % 128.26/17.69 | | | | | | | | (2013) are inconsistent by sub-proof #284. % 128.26/17.69 | | | | | | | | % 128.26/17.69 | | | | | | | End of split % 128.26/17.69 | | | | | | | % 128.26/17.69 | | | | | | End of split % 128.26/17.69 | | | | | | % 128.26/17.69 | | | | | End of split % 128.26/17.69 | | | | | % 128.26/17.69 | | | | End of split % 128.26/17.69 | | | | % 128.26/17.69 | | | Case 2: % 128.26/17.69 | | | | % 128.26/17.69 | | | | (2014) all_9_20 = e0 & op(e0, e4) = e0 % 128.26/17.69 | | | | % 128.26/17.69 | | | | ALPHA: (2014) implies: % 128.26/17.69 | | | | (2015) op(e0, e4) = e0 % 128.26/17.69 | | | | % 128.26/17.69 | | | | BETA: splitting (240) gives: % 128.26/17.69 | | | | % 128.26/17.69 | | | | Case 1: % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | (2016) ~ (op(e0, e4) = e0) % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | PRED_UNIFY: (2015), (2016) imply: % 128.26/17.69 | | | | | (2017) $false % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | CLOSE: (2017) is inconsistent. % 128.26/17.69 | | | | | % 128.26/17.69 | | | | Case 2: % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | (2018) all_4_4 = e0 % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | REDUCE: (348), (2018) imply: % 128.26/17.69 | | | | | (2019) $false % 128.26/17.69 | | | | | % 128.26/17.69 | | | | | CLOSE: (2019) is inconsistent. % 128.26/17.69 | | | | | % 128.26/17.69 | | | | End of split % 128.26/17.69 | | | | % 128.26/17.69 | | | End of split % 128.26/17.69 | | | % 128.26/17.69 | | End of split % 128.26/17.69 | | % 128.26/17.69 | End of split % 128.26/17.69 | % 128.26/17.69 End of proof % 128.26/17.69 % 128.26/17.69 Sub-proof #1 shows that the following formulas are inconsistent: % 128.26/17.69 ---------------------------------------------------------------- % 128.26/17.69 (1) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) | % 128.26/17.69 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) | % 128.26/17.69 (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.69 (2) all_9_6 = e1 % 128.26/17.69 (3) ~ (all_4_7 = e3) % 128.26/17.69 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 128.26/17.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 128.26/17.69 (5) ~ (all_4_17 = e3) % 128.26/17.69 (6) ~ (all_4_22 = e3) % 128.26/17.69 (7) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 128.26/17.69 (8) ~ (e3 = e1) % 128.26/17.69 (9) op(e2, e0) = all_4_22 % 128.26/17.69 (10) op(e2, e2) = e4 % 128.26/17.69 (11) ~ (e4 = e3) % 128.26/17.69 (12) all_6_11 = all_4_7 % 128.26/17.69 (13) op(e2, e1) = all_4_17 % 128.26/17.69 % 128.26/17.69 Begin of proof % 128.26/17.69 | % 128.26/17.69 | BETA: splitting (1) gives: % 128.26/17.69 | % 128.26/17.69 | Case 1: % 128.26/17.69 | | % 128.26/17.69 | | (14) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_7 = e3 & op(e2, e3) = e3) % 128.26/17.69 | | % 128.26/17.69 | | BETA: splitting (14) gives: % 128.26/17.69 | | % 128.26/17.69 | | Case 1: % 128.26/17.69 | | | % 128.26/17.69 | | | (15) all_9_6 = e3 & op(e2, e4) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | ALPHA: (15) implies: % 128.26/17.69 | | | (16) all_9_6 = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #282. % 128.26/17.69 | | | % 128.26/17.69 | | Case 2: % 128.26/17.69 | | | % 128.26/17.69 | | | (17) all_9_7 = e3 & op(e2, e3) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | ALPHA: (17) implies: % 128.26/17.69 | | | (18) op(e2, e3) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | REF_CLOSE: (3), (7), (12), (18) are inconsistent by sub-proof #294. % 128.26/17.69 | | | % 128.26/17.69 | | End of split % 128.26/17.69 | | % 128.26/17.69 | Case 2: % 128.26/17.69 | | % 128.26/17.69 | | (19) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) % 128.26/17.69 | | | (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.69 | | % 128.26/17.69 | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (13), (19) are inconsistent by % 128.26/17.69 | | sub-proof #2. % 128.26/17.69 | | % 128.26/17.69 | End of split % 128.26/17.69 | % 128.26/17.69 End of proof % 128.26/17.69 % 128.26/17.69 Sub-proof #2 shows that the following formulas are inconsistent: % 128.26/17.69 ---------------------------------------------------------------- % 128.26/17.69 (1) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_11 = e3 & op(e2, e1) = e3) | % 128.26/17.69 (all_9_18 = e3 & op(e2, e0) = e3) % 128.26/17.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 128.26/17.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 128.26/17.69 (3) ~ (all_4_17 = e3) % 128.26/17.69 (4) ~ (all_4_22 = e3) % 128.26/17.69 (5) op(e2, e0) = all_4_22 % 128.26/17.69 (6) op(e2, e2) = e4 % 128.26/17.69 (7) ~ (e4 = e3) % 128.26/17.69 (8) op(e2, e1) = all_4_17 % 128.26/17.69 % 128.26/17.69 Begin of proof % 128.26/17.69 | % 128.26/17.69 | BETA: splitting (1) gives: % 128.26/17.69 | % 128.26/17.69 | Case 1: % 128.26/17.69 | | % 128.26/17.69 | | (9) all_9_8 = e3 & op(e2, e2) = e3 % 128.26/17.69 | | % 128.26/17.69 | | REF_CLOSE: (2), (6), (7), (9) are inconsistent by sub-proof #126. % 128.26/17.69 | | % 128.26/17.69 | Case 2: % 128.26/17.69 | | % 128.26/17.69 | | (10) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_18 = e3 & op(e2, e0) = % 128.26/17.69 | | e3) % 128.26/17.69 | | % 128.26/17.69 | | BETA: splitting (10) gives: % 128.26/17.69 | | % 128.26/17.69 | | Case 1: % 128.26/17.69 | | | % 128.26/17.69 | | | (11) all_9_11 = e3 & op(e2, e1) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | ALPHA: (11) implies: % 128.26/17.69 | | | (12) op(e2, e1) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | REF_CLOSE: (2), (3), (8), (12) are inconsistent by sub-proof #103. % 128.26/17.69 | | | % 128.26/17.69 | | Case 2: % 128.26/17.69 | | | % 128.26/17.69 | | | (13) all_9_18 = e3 & op(e2, e0) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | ALPHA: (13) implies: % 128.26/17.69 | | | (14) op(e2, e0) = e3 % 128.26/17.69 | | | % 128.26/17.69 | | | REF_CLOSE: (2), (4), (5), (14) are inconsistent by sub-proof #226. % 128.26/17.69 | | | % 128.26/17.69 | | End of split % 128.26/17.69 | | % 128.26/17.69 | End of split % 128.26/17.69 | % 128.26/17.69 End of proof % 128.26/17.69 % 128.26/17.69 Sub-proof #3 shows that the following formulas are inconsistent: % 128.26/17.69 ---------------------------------------------------------------- % 128.26/17.69 (1) all_9_8 = e4 % 128.26/17.69 (2) ~ (all_4_19 = all_4_24) % 128.26/17.69 (3) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 128.26/17.69 (4) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) | % 128.26/17.69 (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) | % 128.26/17.69 (all_9_24 = e4 & op(e0, e0) = e4) % 128.26/17.69 (5) all_6_16 = all_4_8 % 128.26/17.69 (6) op(e2, e3) = all_4_7 % 128.26/17.69 (7) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 128.26/17.69 (8) all_6_9 = all_4_21 % 128.26/17.69 (9) all_4_5 = e4 | ~ (op(e4, e3) = e4) % 128.26/17.69 (10) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 128.26/17.69 (11) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 128.26/17.69 (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 128.26/17.69 (all_9_21 = e3 & op(e0, e3) = e3) % 128.26/17.69 (12) op(e1, unit) = e1 % 128.26/17.69 (13) ~ (all_4_13 = all_4_23) % 128.26/17.69 (14) all_6_3 = e1 | ~ (op(e4, e1) = e1) % 128.26/17.69 (15) op(e4, unit) = e4 % 128.26/17.69 (16) all_6_5 = e1 % 128.26/17.69 (17) ~ (e4 = e0) % 128.26/17.69 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 128.26/17.69 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 128.26/17.69 (all_9_16 = e4 & op(e4, e0) = e4) % 128.26/17.69 (19) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 128.26/17.70 (20) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 128.26/17.70 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 128.26/17.70 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 128.26/17.70 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 128.26/17.70 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 128.26/17.70 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 128.26/17.70 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 128.26/17.70 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 128.26/17.70 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 128.26/17.70 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 128.26/17.70 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 128.26/17.70 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 128.26/17.70 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 128.26/17.70 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 128.26/17.70 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 128.26/17.70 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 128.26/17.70 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 128.26/17.70 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 128.26/17.70 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 128.26/17.70 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 128.26/17.70 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 128.26/17.70 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 128.26/17.70 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 128.26/17.70 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 128.26/17.70 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 128.26/17.70 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 128.26/17.70 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 128.26/17.70 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 128.26/17.70 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 128.26/17.70 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 128.26/17.70 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 128.26/17.70 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 128.26/17.70 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 128.26/17.70 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 128.26/17.70 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 128.26/17.70 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 128.26/17.70 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 128.26/17.70 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 128.26/17.70 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 128.26/17.70 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 128.26/17.70 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 128.26/17.70 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 128.26/17.70 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 128.26/17.70 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 128.26/17.70 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 128.26/17.70 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 128.26/17.70 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 128.26/17.70 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 128.26/17.70 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 128.26/17.70 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 128.26/17.70 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 128.26/17.70 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 128.26/17.70 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 128.26/17.70 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 128.26/17.70 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 128.26/17.70 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 128.26/17.70 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 128.26/17.70 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 128.26/17.70 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 128.26/17.70 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 128.26/17.70 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 128.26/17.70 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 128.26/17.70 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 128.26/17.70 $i(all_8_87) & $i(all_8_99)) % 128.26/17.70 (21) all_4_24 = e0 | ~ (op(e0, e0) = e0) % 128.26/17.70 (22) all_6_10 = e3 % 128.26/17.70 (23) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 128.26/17.70 (24) ~ (all_4_3 = all_4_4) % 128.26/17.70 (25) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 128.26/17.70 (26) op(unit, e4) = e4 % 128.26/17.70 (27) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 128.26/17.70 (28) ~ (e4 = e2) % 128.26/17.70 (29) ~ (all_4_14 = all_4_24) % 128.26/17.70 (30) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 128.26/17.70 (31) ~ (all_4_5 = all_4_7) % 128.26/17.70 (32) all_6_17 = e4 | all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | all_6_17 % 128.26/17.70 = e0 % 128.26/17.70 (33) all_6_17 = all_4_13 % 128.26/17.70 (34) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 128.26/17.70 (35) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 128.26/17.70 (36) ~ (all_4_6 = all_4_9) % 128.26/17.70 (37) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 128.26/17.70 (38) ~ (all_4_10 = all_4_11) % 128.26/17.70 (39) e4 = e3 | ~ (op(e2, e4) = e4) % 128.26/17.70 (40) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 128.26/17.70 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 128.26/17.70 (all_9_16 = e2 & op(e4, e0) = e2) % 128.26/17.70 (41) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 128.26/17.70 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 128.26/17.70 (all_9_18 = e0 & op(e2, e0) = e0) % 128.26/17.70 (42) all_6_3 = e4 | all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | all_6_3 = e0 % 128.26/17.70 (43) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 128.26/17.70 (44) ~ (all_4_20 = all_4_22) % 128.26/17.70 (45) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 128.26/17.70 (46) ~ (all_4_11 = all_4_13) % 128.26/17.70 (47) all_4_17 = e2 | ~ (op(e2, e1) = e2) % 128.26/17.70 (48) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 128.26/17.70 (49) all_4_14 = e2 | ~ (op(e0, e2) = e2) % 128.26/17.70 (50) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 128.26/17.70 (51) ~ (all_4_7 = e4) % 128.26/17.70 (52) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 128.26/17.70 (53) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) | % 128.26/17.70 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) | % 128.26/17.70 (all_9_22 = e1 & op(e0, e2) = e1) % 128.26/17.70 (54) ~ (all_4_10 = all_4_13) % 128.26/17.70 (55) op(e4, e2) = all_4_10 % 128.26/17.70 (56) ~ (all_4_14 = e4) % 128.26/17.70 (57) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 128.26/17.70 (58) ~ (all_4_6 = all_4_21) % 128.26/17.70 (59) all_4_4 = e0 | ~ (op(e0, e4) = e0) % 128.26/17.70 (60) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 128.26/17.70 (61) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 128.26/17.70 (62) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 128.26/17.70 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 128.26/17.70 (all_9_23 = e1 & op(e0, e1) = e1) % 128.26/17.70 (63) op(e1, e0) = all_4_23 % 128.26/17.70 (64) ~ (all_4_3 = e3) % 128.26/17.70 (65) all_6_20 = all_4_4 % 128.26/17.70 (66) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 & op(e1, e3) = e3) | % 128.26/17.70 (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 128.26/17.70 (all_9_19 = e3 & op(e1, e0) = e3) % 128.26/17.70 (67) e4 = e2 | ~ (op(e2, e2) = e2) % 128.26/17.70 (68) ~ (all_4_17 = e4) % 128.26/17.70 (69) ~ (e3 = e0) % 128.26/17.70 (70) ~ (all_4_17 = all_4_19) % 128.26/17.70 (71) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 128.26/17.70 (72) op(e0, unit) = e0 % 128.26/17.70 (73) ~ (all_4_23 = all_4_24) % 128.26/17.70 (74) ~ (all_4_11 = all_4_14) % 128.26/17.70 (75) ~ (all_4_13 = e4) % 128.26/17.70 (76) op(e0, e0) = all_4_24 % 128.26/17.70 (77) all_6_8 = all_4_16 % 128.26/17.70 (78) ~ (all_4_9 = all_4_24) % 128.26/17.70 (79) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 128.26/17.70 = e0 % 128.26/17.70 (80) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 128.26/17.70 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 128.26/17.70 (all_9_17 = e2 & op(e3, e0) = e2) % 128.26/17.70 (81) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 128.26/17.70 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 128.26/17.70 (all_9_18 = e1 & op(e2, e0) = e1) % 128.26/17.70 (82) ~ (all_4_21 = all_4_24) % 128.26/17.70 (83) ~ (all_4_14 = all_4_19) % 128.26/17.70 (84) ~ (all_4_5 = all_4_9) % 128.26/17.70 (85) op(e2, unit) = e2 % 128.26/17.70 (86) ~ (e2 = e0) % 128.26/17.70 (87) ~ (all_4_22 = all_4_23) % 128.26/17.70 (88) all_9_0 = e0 % 128.26/17.70 (89) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 128.26/17.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 128.26/17.70 (90) ~ (all_4_4 = e3) % 128.26/17.70 (91) ~ (all_4_17 = e3) % 128.26/17.70 (92) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & op(e3, e3) = e0) | % 128.26/17.70 (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) | % 128.26/17.70 (all_9_17 = e0 & op(e3, e0) = e0) % 128.26/17.70 (93) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 128.26/17.70 (94) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 128.26/17.70 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 128.26/17.70 (all_9_24 = e2 & op(e0, e0) = e2) % 128.26/17.70 (95) ~ (all_4_11 = e1) % 128.26/17.70 (96) all_6_7 = e4 | all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | all_6_7 = e0 % 128.26/17.70 (97) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 128.26/17.70 (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 128.26/17.70 (all_9_17 = e4 & op(e3, e0) = e4) % 128.26/17.70 (98) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 128.26/17.70 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 128.26/17.70 (all_9_22 = e3 & op(e0, e2) = e3) % 128.26/17.70 (99) all_4_4 = e4 % 128.26/17.70 (100) ~ (all_4_22 = e3) % 128.26/17.70 (101) ~ (all_4_10 = all_4_15) % 128.26/17.70 (102) ~ (all_4_19 = e4) % 128.26/17.70 (103) op(unit, e0) = e0 % 128.46/17.70 (104) (all_8_76 = e4 & ~ (all_8_77 = e1) & op(e4, all_8_78) = all_8_77 & % 128.46/17.70 op(e4, e1) = all_8_78 & op(e1, all_8_78) = e4 & $i(all_8_77) & % 128.46/17.70 $i(all_8_78)) | (all_8_79 = e3 & ~ (all_8_80 = e1) & op(e3, % 128.46/17.70 all_8_81) = all_8_80 & op(e3, e1) = all_8_81 & op(e1, all_8_81) = % 128.46/17.70 e3 & $i(all_8_80) & $i(all_8_81)) | (all_8_82 = e2 & ~ (all_8_83 = % 128.46/17.70 e1) & op(e2, all_8_84) = all_8_83 & op(e2, e1) = all_8_84 & op(e1, % 128.46/17.70 all_8_84) = e2 & $i(all_8_83) & $i(all_8_84)) | (all_8_85 = e0 & ~ % 128.46/17.70 (all_8_86 = e1) & op(e1, all_8_87) = e0 & op(e0, all_8_87) = all_8_86 % 128.46/17.70 & op(e0, e1) = all_8_87 & $i(all_8_86) & $i(all_8_87)) % 128.46/17.70 (105) all_6_11 = e2 | ~ (op(e2, e3) = e2) % 128.46/17.70 (106) all_6_18 = e4 | all_6_18 = e3 | all_6_18 = e2 | all_6_18 = e1 | % 128.46/17.70 all_6_18 = e0 % 128.46/17.70 (107) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 128.46/17.70 (108) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 128.46/17.70 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 128.46/17.70 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 128.46/17.70 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 % 128.46/17.70 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 128.46/17.70 (109) ~ (all_4_16 = all_4_21) % 128.46/17.70 (110) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 128.46/17.70 (111) all_9_6 = e3 % 128.46/17.70 (112) ~ (all_4_22 = all_4_24) % 128.46/17.70 (113) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 128.46/17.70 (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 128.46/17.70 (all_9_21 = e2 & op(e0, e3) = e2) % 128.46/17.70 (114) all_6_7 = all_4_11 % 128.46/17.70 (115) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 128.46/17.70 (116) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = % 128.46/17.70 e0 % 128.46/17.70 (117) all_6_21 = all_4_9 % 128.46/17.70 (118) ~ (all_4_22 = e4) % 128.46/17.70 (119) op(e3, e0) = all_4_21 % 128.46/17.70 (120) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 128.46/17.70 (121) ~ (all_4_5 = all_4_15) % 128.46/17.70 (122) ~ (all_4_16 = all_4_19) % 128.46/17.70 (123) op(e0, e2) = all_4_14 % 128.46/17.70 (124) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 128.46/17.70 (125) all_6_24 = all_4_24 % 128.46/17.70 (126) ~ (all_4_9 = all_4_19) % 128.46/17.70 (127) all_6_13 = e4 | all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 128.46/17.70 all_6_13 = e0 % 128.46/17.70 (128) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 128.46/17.70 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 128.46/17.70 (all_9_20 = e3 & op(e0, e4) = e3) % 128.46/17.70 (129) ~ (all_4_13 = all_4_18) % 128.46/17.70 (130) ~ (all_4_15 = all_4_20) % 128.46/17.70 (131) all_6_23 = all_4_19 % 128.46/17.70 (132) ~ (e3 = e2) % 128.46/17.70 (133) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 128.46/17.70 (134) all_6_14 = all_4_22 % 128.46/17.70 (135) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 128.46/17.70 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 128.46/17.70 (all_9_17 = e3 & op(e3, e0) = e3) % 128.46/17.70 (136) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 128.46/17.70 (137) ~ (all_4_20 = all_4_21) % 128.46/17.70 (138) ~ (all_4_8 = all_4_13) % 128.46/17.70 (139) ~ (all_4_5 = all_4_10) % 128.46/17.70 (140) all_6_23 = e1 | ~ (op(e0, e1) = e1) % 128.46/17.70 (141) all_6_13 = all_4_17 % 128.46/17.70 (142) all_4_23 = e1 | ~ (op(e1, e0) = e1) % 128.46/17.70 (143) op(e0, e4) = all_4_4 % 128.46/17.70 (144) ~ (all_4_11 = all_4_21) % 128.46/17.70 (145) (all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, all_8_54) = all_8_53 & % 128.46/17.70 op(e4, e3) = all_8_54 & op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.46/17.70 $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 128.46/17.70 all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & op(e2, e3) = % 128.46/17.70 all_8_57 & $i(all_8_56) & $i(all_8_57)) | (all_8_58 = e1 & ~ % 128.46/17.70 (all_8_59 = e3) & op(e3, all_8_60) = e1 & op(e1, all_8_60) = all_8_59 % 128.46/17.70 & op(e1, e3) = all_8_60 & $i(all_8_59) & $i(all_8_60)) | (all_8_61 = % 128.46/17.70 e0 & ~ (all_8_62 = e3) & op(e3, all_8_63) = e0 & op(e0, all_8_63) = % 128.46/17.70 all_8_62 & op(e0, e3) = all_8_63 & $i(all_8_62) & $i(all_8_63)) % 128.46/17.70 (146) ~ (e4 = e1) % 128.46/17.70 (147) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 | all_6_9 = % 128.46/17.70 e0 % 128.46/17.70 (148) ~ (all_4_3 = e0) % 128.46/17.70 (149) op(e1, e1) = all_4_18 % 128.46/17.70 (150) ~ (all_4_13 = all_4_14) % 128.46/17.70 (151) op(unit, e3) = e3 % 128.46/17.70 (152) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 128.46/17.70 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 128.46/17.70 (all_9_22 = e2 & op(e0, e2) = e2) % 128.46/17.70 (153) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 128.46/17.70 (154) ~ (all_4_15 = all_4_19) % 128.46/17.70 (155) op(e3, unit) = e3 % 128.46/17.70 (156) op(e3, e4) = e1 % 128.46/17.70 (157) op(e0, e3) = all_4_9 % 128.46/17.70 (158) ~ (all_4_7 = all_4_9) % 128.46/17.70 (159) ~ (all_4_20 = e0) % 128.46/17.70 (160) ~ (all_4_10 = all_4_20) % 128.46/17.70 (161) all_6_1 = e4 | all_6_1 = e3 | all_6_1 = e2 | all_6_1 = e1 | all_6_1 = % 128.46/17.70 e0 % 128.46/17.70 (162) (all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, all_8_66) = all_8_65 & % 128.46/17.70 op(e4, e2) = all_8_66 & op(e2, all_8_66) = e4 & $i(all_8_65) & % 128.46/17.70 $i(all_8_66)) | (all_8_67 = e3 & ~ (all_8_68 = e2) & op(e3, % 128.46/17.70 all_8_69) = all_8_68 & op(e3, e2) = all_8_69 & op(e2, all_8_69) = % 128.46/17.70 e3 & $i(all_8_68) & $i(all_8_69)) | (all_8_70 = e1 & ~ (all_8_71 = % 128.46/17.70 e2) & op(e2, all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & op(e1, % 128.46/17.70 e2) = all_8_72 & $i(all_8_71) & $i(all_8_72)) | (all_8_73 = e0 & ~ % 128.46/17.70 (all_8_74 = e2) & op(e2, all_8_75) = e0 & op(e0, all_8_75) = all_8_74 % 128.46/17.70 & op(e0, e2) = all_8_75 & $i(all_8_74) & $i(all_8_75)) % 128.46/17.70 (163) all_6_24 = e4 | all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 128.46/17.70 all_6_24 = e0 % 128.46/17.70 (164) op(e1, e4) = all_4_3 % 128.46/17.70 (165) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 128.46/17.70 (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 128.46/17.70 (all_9_19 = e4 & op(e1, e0) = e4) % 128.46/17.70 (166) ~ (all_4_8 = all_4_9) % 128.46/17.70 (167) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) | % 128.46/17.70 (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = e1) | % 128.46/17.70 (all_9_24 = e1 & op(e0, e0) = e1) % 128.46/17.70 (168) all_6_18 = all_4_18 % 128.46/17.70 (169) ~ (all_4_3 = all_4_18) % 128.46/17.70 (170) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 128.46/17.70 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 128.46/17.70 (all_9_20 = e2 & op(e0, e4) = e2) % 128.46/17.70 (171) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 128.46/17.70 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 128.46/17.70 (all_9_16 = e3 & op(e4, e0) = e3) % 128.46/17.70 (172) op(e2, e0) = all_4_22 % 128.46/17.70 (173) op(e0, e1) = all_4_19 % 128.46/17.70 (174) op(e1, e3) = all_4_8 % 128.46/17.70 (175) ~ (all_4_3 = e4) % 128.46/17.71 (176) op(e2, e2) = e4 % 128.46/17.71 (177) ~ (all_4_10 = all_4_14) % 128.46/17.71 (178) ~ (e4 = e3) % 128.46/17.71 (179) ~ (all_4_15 = all_4_17) % 128.46/17.71 (180) ~ (all_4_9 = e4) % 128.46/17.71 (181) all_6_14 = e4 | all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 128.46/17.71 all_6_14 = e0 % 128.46/17.71 (182) ~ (all_4_8 = all_4_18) % 128.46/17.71 (183) all_6_4 = all_4_20 % 128.46/17.71 (184) ~ (all_4_4 = e0) % 128.46/17.71 (185) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 128.46/17.71 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 128.46/17.71 (all_9_16 = e1 & op(e4, e0) = e1) % 128.46/17.71 (186) ~ (all_4_17 = all_4_22) % 128.46/17.71 (187) ~ (all_4_3 = e1) % 128.46/17.71 (188) all_4_15 = e4 | ~ (op(e4, e1) = e4) % 128.46/17.71 (189) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) | % 128.46/17.71 (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 128.46/17.71 (all_9_19 = e0 & op(e1, e0) = e0) % 128.46/17.71 (190) op(unit, e2) = e2 % 128.46/17.71 (191) op(unit, e1) = e1 % 128.46/17.71 (192) ~ (all_4_5 = all_4_20) % 128.46/17.71 (193) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 128.46/17.71 (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 128.46/17.71 (all_9_23 = e3 & op(e0, e1) = e3) % 128.46/17.71 (194) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 128.46/17.71 (195) all_6_1 = all_4_5 % 128.46/17.71 (196) (all_9_20 = e2 & op(e0, e4) = e2) | (all_9_21 = e2 & op(e0, e3) = e2) | % 128.46/17.71 (all_9_22 = e2 & op(e0, e2) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) | % 128.46/17.71 (all_9_24 = e2 & op(e0, e0) = e2) % 128.46/17.71 (197) ~ (all_4_15 = all_4_18) % 128.46/17.71 (198) ~ (all_4_11 = e4) % 128.46/17.71 (199) op(e4, e3) = all_4_5 % 128.46/17.71 (200) all_6_11 = all_4_7 % 128.46/17.71 (201) all_6_2 = all_4_10 % 128.46/17.71 (202) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 128.46/17.71 (203) all_6_11 = e4 | all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 128.46/17.71 all_6_11 = e0 % 128.46/17.71 (204) all_6_21 = e0 | ~ (op(e0, e3) = e0) % 128.46/17.71 (205) ~ (all_4_21 = all_4_22) % 128.46/17.71 (206) ~ (all_4_24 = e4) % 128.46/17.71 (207) op(e2, e4) = e3 % 128.46/17.71 (208) ~ (all_4_17 = all_4_18) % 128.46/17.71 (209) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 128.46/17.71 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 128.46/17.71 (all_9_20 = e4 & op(e0, e4) = e4) % 128.46/17.71 (210) all_4_23 = e0 | ~ (op(e1, e0) = e0) % 128.46/17.71 (211) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 128.46/17.71 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 128.46/17.71 (all_9_23 = e4 & op(e0, e1) = e4) % 128.46/17.71 (212) op(e2, e1) = all_4_17 % 128.46/17.71 (213) ~ (all_4_5 = e0) % 128.46/17.71 (214) all_6_16 = e3 | ~ (op(e1, e3) = e3) % 128.46/17.71 (215) all_9_2 = e1 % 128.46/17.71 (216) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 128.46/17.71 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 128.46/17.71 (all_9_20 = e1 & op(e0, e4) = e1) % 128.46/17.71 (217) ~ (all_4_7 = all_4_17) % 128.46/17.71 (218) all_6_3 = all_4_15 % 128.46/17.71 (219) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 128.46/17.71 all_6_15 = e0 % 128.46/17.71 (220) all_4_21 = e0 | ~ (op(e3, e0) = e0) % 128.46/17.71 (221) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 128.46/17.71 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 128.46/17.71 (all_9_24 = e3 & op(e0, e0) = e3) % 128.46/17.71 (222) all_4_7 = e3 | ~ (op(e2, e3) = e3) % 128.46/17.71 (223) ~ (all_4_4 = e1) % 128.46/17.71 (224) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 128.46/17.71 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 128.46/17.71 (all_9_23 = e2 & op(e0, e1) = e2) % 128.46/17.71 (225) all_4_0 = e0 % 128.46/17.71 (226) ~ (all_4_18 = all_4_19) % 128.46/17.71 (227) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & op(e3, e2) = e0) | % 128.46/17.71 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) | % 128.46/17.71 (all_9_22 = e0 & op(e0, e2) = e0) % 128.46/17.71 (228) ~ (e2 = e1) % 128.46/17.71 (229) all_6_15 = all_4_3 % 128.46/17.71 (230) all_6_21 = e3 | ~ (op(e0, e3) = e3) % 128.46/17.71 (231) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 128.46/17.71 (232) op(e4, e4) = e0 % 128.46/17.71 (233) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) | % 128.46/17.71 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 & op(e2, e1) = e2) | % 128.46/17.71 (all_9_18 = e2 & op(e2, e0) = e2) % 128.46/17.71 (234) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 128.46/17.71 (235) ~ (all_4_3 = all_4_13) % 128.46/17.71 (236) ~ (all_4_7 = all_4_22) % 128.46/17.71 % 128.46/17.71 Begin of proof % 128.46/17.71 | % 128.46/17.71 | BETA: splitting (170) gives: % 128.46/17.71 | % 128.46/17.71 | Case 1: % 128.46/17.71 | | % 128.46/17.71 | | (237) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) % 128.46/17.71 | | % 128.46/17.71 | | REF_CLOSE: (86), (88), (89), (156), (228), (237) are inconsistent by % 128.46/17.71 | | sub-proof #312. % 128.46/17.71 | | % 128.46/17.71 | Case 2: % 128.46/17.71 | | % 128.46/17.71 | | (238) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = % 128.46/17.71 | | e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 128.46/17.71 | | % 128.46/17.71 | | BETA: splitting (238) gives: % 128.46/17.71 | | % 128.46/17.71 | | Case 1: % 128.46/17.71 | | | % 128.46/17.71 | | | (239) all_9_6 = e2 & op(e2, e4) = e2 % 128.46/17.71 | | | % 128.46/17.71 | | | REF_CLOSE: (19), (22), (132), (239) are inconsistent by sub-proof #311. % 128.46/17.71 | | | % 128.46/17.71 | | Case 2: % 128.46/17.71 | | | % 128.46/17.71 | | | (240) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = % 128.46/17.71 | | | e2) % 128.46/17.71 | | | % 128.46/17.71 | | | BETA: splitting (240) gives: % 128.46/17.71 | | | % 128.46/17.71 | | | Case 1: % 128.46/17.71 | | | | % 128.46/17.71 | | | | (241) all_9_12 = e2 & op(e1, e4) = e2 % 128.46/17.71 | | | | % 128.46/17.71 | | | | ALPHA: (241) implies: % 128.46/17.71 | | | | (242) all_9_12 = e2 % 128.46/17.71 | | | | % 128.46/17.71 | | | | BETA: splitting (219) gives: % 128.46/17.71 | | | | % 128.46/17.71 | | | | Case 1: % 128.46/17.71 | | | | | % 128.46/17.71 | | | | | (243) all_6_15 = e4 % 128.46/17.71 | | | | | % 128.46/17.71 | | | | | REF_CLOSE: (175), (229), (243) are inconsistent by sub-proof #278. % 128.46/17.71 | | | | | % 128.46/17.71 | | | | Case 2: % 128.46/17.71 | | | | | % 128.46/17.71 | | | | | (244) ~ (all_6_15 = e4) % 128.46/17.71 | | | | | (245) all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 = e0 % 128.46/17.71 | | | | | % 128.46/17.71 | | | | | BETA: splitting (4) gives: % 128.46/17.71 | | | | | % 128.46/17.71 | | | | | Case 1: % 128.46/17.71 | | | | | | % 128.46/17.71 | | | | | | (246) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, % 128.46/17.71 | | | | | | e3) = e4) % 128.46/17.71 | | | | | | % 128.46/17.71 | | | | | | BETA: splitting (246) gives: % 128.46/17.71 | | | | | | % 128.46/17.71 | | | | | | Case 1: % 128.46/17.71 | | | | | | | % 128.46/17.71 | | | | | | | (247) all_9_20 = e4 & op(e0, e4) = e4 % 128.46/17.71 | | | | | | | % 128.46/17.71 | | | | | | | ALPHA: (247) implies: % 128.46/17.71 | | | | | | | (248) all_9_20 = e4 % 128.46/17.71 | | | | | | | % 128.46/17.71 | | | | | | | BETA: splitting (245) gives: % 128.46/17.71 | | | | | | | % 128.46/17.71 | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | (249) all_6_15 = e2 % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | COMBINE_EQS: (229), (249) imply: % 128.46/17.71 | | | | | | | | (250) all_4_3 = e2 % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | SIMP: (250) implies: % 128.46/17.71 | | | | | | | | (251) all_4_3 = e2 % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | REDUCE: (235), (251) imply: % 128.46/17.71 | | | | | | | | (252) ~ (all_4_13 = e2) % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | SIMP: (252) implies: % 128.46/17.71 | | | | | | | | (253) ~ (all_4_13 = e2) % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | REDUCE: (169), (251) imply: % 128.46/17.71 | | | | | | | | (254) ~ (all_4_18 = e2) % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | SIMP: (254) implies: % 128.46/17.71 | | | | | | | | (255) ~ (all_4_18 = e2) % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | REDUCE: (164), (251) imply: % 128.46/17.71 | | | | | | | | (256) op(e1, e4) = e2 % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | BETA: splitting (45) gives: % 128.46/17.71 | | | | | | | | % 128.46/17.71 | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | % 128.46/17.71 | | | | | | | | | (257) ~ (op(e1, e4) = e4) % 128.46/17.71 | | | | | | | | | % 128.46/17.71 | | | | | | | | | PRED_UNIFY: (26), (257) imply: % 128.46/17.71 | | | | | | | | | (258) ~ (unit = e1) % 128.46/17.71 | | | | | | | | | % 128.46/17.71 | | | | | | | | | BETA: splitting (230) gives: % 128.46/17.71 | | | | | | | | | % 128.46/17.71 | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | (259) ~ (op(e0, e3) = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | PRED_UNIFY: (151), (259) imply: % 128.46/17.71 | | | | | | | | | | (260) ~ (unit = e0) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | BETA: splitting (23) gives: % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | (261) ~ (op(e3, e4) = e4) % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | PRED_UNIFY: (26), (261) imply: % 128.46/17.71 | | | | | | | | | | | (262) ~ (unit = e3) % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | BETA: splitting (39) gives: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | (263) ~ (op(e2, e4) = e4) % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | PRED_UNIFY: (26), (263) imply: % 128.46/17.71 | | | | | | | | | | | | (264) ~ (unit = e2) % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | REF_CLOSE: (17), (26), (27), (50), (124), (190), (225), % 128.46/17.71 | | | | | | | | | | | | (253), (260), (262), (264) are inconsistent by % 128.46/17.71 | | | | | | | | | | | | sub-proof #95. % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | (265) op(e2, e4) = e4 % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | REF_CLOSE: (39), (178), (265) are inconsistent by sub-proof % 128.46/17.71 | | | | | | | | | | | | #320. % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | End of split % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | (266) op(e3, e4) = e4 % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | REF_CLOSE: (16), (23), (146), (266) are inconsistent by % 128.46/17.71 | | | | | | | | | | | sub-proof #316. % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | End of split % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | (267) all_6_21 = e3 % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | COMBINE_EQS: (117), (267) imply: % 128.46/17.71 | | | | | | | | | | (268) all_4_9 = e3 % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | SIMP: (268) implies: % 128.46/17.71 | | | | | | | | | | (269) all_4_9 = e3 % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (84), (269) imply: % 128.46/17.71 | | | | | | | | | | (270) ~ (all_4_5 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (36), (269) imply: % 128.46/17.71 | | | | | | | | | | (271) ~ (all_4_6 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (158), (269) imply: % 128.46/17.71 | | | | | | | | | | (272) ~ (all_4_7 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (166), (269) imply: % 128.46/17.71 | | | | | | | | | | (273) ~ (all_4_8 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (126), (269) imply: % 128.46/17.71 | | | | | | | | | | (274) ~ (all_4_19 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | SIMP: (274) implies: % 128.46/17.71 | | | | | | | | | | (275) ~ (all_4_19 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (78), (269) imply: % 128.46/17.71 | | | | | | | | | | (276) ~ (all_4_24 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | SIMP: (276) implies: % 128.46/17.71 | | | | | | | | | | (277) ~ (all_4_24 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | REDUCE: (180), (269) imply: % 128.46/17.71 | | | | | | | | | | (278) ~ (e4 = e3) % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | BETA: splitting (11) gives: % 128.46/17.71 | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | (279) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & % 128.46/17.71 | | | | | | | | | | | op(e3, e3) = e3) % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | REF_CLOSE: (52), (194), (270), (271), (279) are inconsistent % 128.46/17.71 | | | | | | | | | | | by sub-proof #143. % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | (280) (all_9_7 = e3 & op(e2, e3) = e3) | (all_9_13 = e3 % 128.46/17.71 | | | | | | | | | | | & op(e1, e3) = e3) | (all_9_21 = e3 & op(e0, e3) % 128.46/17.71 | | | | | | | | | | | = e3) % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | BETA: splitting (280) gives: % 128.46/17.71 | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | (281) all_9_7 = e3 & op(e2, e3) = e3 % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | ALPHA: (281) implies: % 128.46/17.71 | | | | | | | | | | | | (282) op(e2, e3) = e3 % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (282) are inconsistent by % 128.46/17.71 | | | | | | | | | | | | sub-proof #294. % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | (283) (all_9_13 = e3 & op(e1, e3) = e3) | (all_9_21 = e3 % 128.46/17.71 | | | | | | | | | | | | & op(e0, e3) = e3) % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | BETA: splitting (283) gives: % 128.46/17.71 | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | (284) all_9_13 = e3 & op(e1, e3) = e3 % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | REF_CLOSE: (5), (214), (273), (284) are inconsistent by % 128.46/17.71 | | | | | | | | | | | | | sub-proof #142. % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | (285) all_9_21 = e3 & op(e0, e3) = e3 % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | ALPHA: (285) implies: % 128.46/17.71 | | | | | | | | | | | | | (286) all_9_21 = e3 % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | BETA: splitting (153) gives: % 128.46/17.71 | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | (287) ~ (op(e2, e4) = e4) % 128.46/17.71 | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | PRED_UNIFY: (26), (287) imply: % 128.46/17.71 | | | | | | | | | | | | | | (288) ~ (unit = e2) % 128.46/17.71 | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | BETA: splitting (59) gives: % 128.46/17.71 | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | (289) ~ (op(e0, e4) = e0) % 128.46/17.71 | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | PRED_UNIFY: (72), (289) imply: % 128.46/17.71 | | | | | | | | | | | | | | | (290) ~ (unit = e4) % 128.46/17.71 | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 128.46/17.71 | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | (291) ~ (op(e4, e1) = e1) % 128.46/17.71 | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | (292) ~ (op(e1, e0) = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | BETA: splitting (30) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | (293) ~ (op(e2, e0) = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (172), (293) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | (294) ~ (all_4_22 = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | (295) ~ (op(e3, e0) = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (103), (295) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | (296) ~ (unit = e3) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (119), (295) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | (297) ~ (all_4_21 = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | (298) unit = e4 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (290), (298) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | (299) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | (300) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | (301) unit = e2 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (288), (301) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | (302) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | (303) unit = e3 | unit = e1 | unit = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | (304) unit = e3 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (296), (304) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | (305) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | (306) unit = e1 | unit = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | (307) all_9_24 = e0 & op(e0, e0) = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | (308) all_9_24 = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | (309) op(e0, e0) = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | (310) ~ (op(e0, e0) = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (309), (310) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | (311) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (311) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | (312) all_4_24 = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (312) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_4_14 = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (312) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_4_19 = e0) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (315) unit = e1 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (315) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (316) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (316) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (317) unit = e0 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (318) op(e0, e4) = e4 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (319) op(e0, e3) = e3 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (320) op(e0, e2) = e2 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (321) op(e0, e1) = e1 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (322) op(e4, e0) = e4 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (323) op(e3, e0) = e3 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (324) op(e2, e0) = e2 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (317) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | (325) op(e1, e0) = e1 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (op(e4, e0) = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (322), (326) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_4_20 = e4 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (328) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_4_5 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (328) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_4_10 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (328) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_4_15 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (328) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (332) ~ (all_4_21 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_4_21 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (328) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_4_22 = e4) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (op(e1, e0) = e1) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (325), (335) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) $false % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent. % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_4_23 = e1 % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (337) imply: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (all_4_13 = e1) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (op(e3, e0) = e3) % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (323), (339) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_6_9 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (341) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_4_21 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (342) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_4_11 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (342) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_4_16 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (342) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_4_22 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (op(e0, e2) = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (320), (346) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_4_14 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (348) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_4_10 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (348) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_4_11 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (348) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_4_19 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (351) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_4_19 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_6_7 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (353) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_4_11 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (354) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) ~ (all_6_7 = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_6_7 = e3 | all_6_7 = e2 | all_6_7 = e1 | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_7 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (357) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_6_7 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (358) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_4_11 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (359) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_6_7 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_6_7 = e3 | all_6_7 = e1 | all_6_7 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (op(e2, e0) = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (324), (363) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (364) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_4_22 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (365) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) ~ (all_4_7 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (365) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_4_17 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (365) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (e4 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (365) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (e3 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_6_7 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (370) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_4_11 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (371) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_6_7 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_6_7 = e1 | all_6_7 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_6_7 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (375) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_4_11 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (376) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_6_7 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (378) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_4_11 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (379) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_4_10 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (379) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) ~ (all_4_13 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (381) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) ~ (all_4_13 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (379) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) ~ (e4 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (379) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) ~ (e2 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_9_0 = e4 & op(e4, e4) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) op(e4, e4) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (27), (225), (387) are inconsistent by % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #317. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_9_1 = e4 & op(e4, e3) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) op(e4, e3) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (329), (389) are inconsistent by sub-proof % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_9_4 = e4 & op(e4, e2) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) op(e4, e2) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (201), (330), (392) are inconsistent by % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #298. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_9_9 = e4 & op(e4, e1) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (394) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) op(e4, e1) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (218), (331), (395) are inconsistent by % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_9_16 = e4 & op(e4, e0) = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (396) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_9_16 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) ~ (op(e0, e1) = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (321), (398) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_6_23 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (400) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_4_19 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_4_19 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) ~ (all_4_16 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_4_17 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (226), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) ~ (all_4_18 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ~ (e4 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ~ (e3 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (407) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) ~ (e3 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) ~ (e2 = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (402) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (e1 = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_6_17 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (411) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_4_13 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (412) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_4_13 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (413) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_6_17 = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_6_17 = e3 | all_6_17 = e2 | all_6_17 = e1 | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_17 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_6_17 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (417) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_4_13 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (418) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_4_13 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (419) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (420) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) ~ (all_6_17 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_6_17 = e3 | all_6_17 = e1 | all_6_17 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) (all_9_20 = e2 & op(e0, e4) = e2) | (all_9_21 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_9_20 = e2 & op(e0, e4) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_9_20 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (425) are % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #90. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_9_21 = e2 & op(e0, e3) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (426) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_9_21 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (427) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) e3 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (428) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) (all_9_22 = e2 & op(e0, e2) = e2) | (all_9_23 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e2) | (all_9_24 = e2 & op(e0, e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_9_22 = e2 & op(e0, e2) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_9_22 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e1) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_9_6 = e1 & op(e2, e4) = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (408), (434) are inconsistent by sub-proof % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #223. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_9_7 = e1 & op(e2, e3) = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_9_7 = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) op(e2, e3) = e1 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (422) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_6_17 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (438) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_4_13 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (439) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_4_13 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (440) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_4_10 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (440) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ~ (all_4_18 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (442) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_4_18 = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_9_16 = e3 & op(e4, e0) = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_9_16 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (446) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) e4 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (447) are inconsistent % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #89. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_9_17 = e3 & op(e3, e0) = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_9_17 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_9_16 = e2 & op(e4, e0) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (248), (397), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) are inconsistent by sub-proof #88. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_9_17 = e2 & op(e3, e0) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (452) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_9_17 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (453) are % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_9_18 = e2 & op(e2, e0) = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (455) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_9_18 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_9_4 = e0 & op(e4, e2) = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_9_4 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (52), (60), (64), (65), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (71), (77), (79), (86), (88), (89), (90), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (128), (132), (135), (143), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (148), (164), (170), (171), (175), (178), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (185), (187), (194), (201), (202), (207), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (215), (216), (219), (223), (225), (228), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (270), (271), (291), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (449), % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) are inconsistent by sub-proof #79. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_9_5 = e0 & op(e3, e2) = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_9_5 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) op(e3, e2) = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_6_2 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (463) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_4_10 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (464) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) ~ (all_6_2 = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_2 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_6_2 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (468) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_4_10 = e2 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (469) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (470) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) ~ (all_6_2 = e2) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_6_13 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (473) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_4_17 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (474) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_4_17 = e4 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (475) imply: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) $false % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (476) is inconsistent. % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) ~ (all_6_13 = e4) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_6_13 = e3 | all_6_13 = e2 | all_6_13 = e1 | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_13 = e0 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_9_9 = e3 & op(e4, e1) = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_9_9 = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) op(e4, e1) = e3 % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 128.46/17.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (24), (27), (28), (39), (45), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (69), (71), (79), (86), (89), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (111), (128), (132), (143), (146), (148), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (170), (178), (184), (187), (202), (207), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (215), (216), (219), (223), (225), (228), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (408), (410), (436), (483) are % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #78. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_9_8 = e0 & op(e2, e2) = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (485) are inconsistent by sub-proof % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_9_11 = e0 & op(e2, e1) = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_9_11 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) op(e2, e1) = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_9_9 = e2 & op(e4, e1) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (449), (481), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) are inconsistent by sub-proof #77. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_9_10 = e2 & op(e3, e1) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_9_10 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) op(e3, e1) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_13 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e3) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_9_12 = e3 & op(e1, e4) = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_9_12 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (88), (89), (156), (228), (498) are % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #312. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_9_6 = e2 & op(e2, e4) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (132), (499) are inconsistent by % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #311. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (497) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) e3 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (500) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (501) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_9_20 = e2 & op(e0, e4) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_9_20 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (497), (503) are inconsistent by % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #303. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_9_13 = e3 & op(e1, e3) = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (214), (273), (504) are inconsistent by % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #142. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_15 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_19 = e3 & op(e1, e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_9_14 = e3 & op(e1, e2) = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (506) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_9_14 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) op(e1, e2) = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (509) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_9_2 = e4 & op(e3, e4) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (510) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) op(e3, e4) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (146), (511) are inconsistent by % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_9_3 = e4 & op(e3, e3) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (512) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_9_3 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) op(e3, e3) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_6_13 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (367), (515) are inconsistent by sub-proof % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #76. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_6_13 = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_6_13 = e3 | all_6_13 = e1 | all_6_13 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (517) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_6_13 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (518) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_4_17 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_4_17 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (520) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) ~ (all_6_13 = e3) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_6_13 = e1 | all_6_13 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_6_2 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (524) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_4_10 = e3 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (441), (525) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (526) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) ~ (all_6_2 = e3) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_6_2 = e1 | all_6_2 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_6_2 = e1 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (529) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_4_10 = e1 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (530) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) ~ (all_4_5 = e1) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (530) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) ~ (all_4_15 = e1) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (532) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) ~ (all_4_15 = e1) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (530) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) op(e4, e2) = e1 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_6_1 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (535) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_4_5 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (536) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_4_5 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (537) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (538) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) ~ (all_6_1 = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_6_1 = e3 | all_6_1 = e2 | all_6_1 = e1 | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_1 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) (all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) = all_8_65 & op(e4, e2) = all_8_66 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_66) = e4 & $i(all_8_65) & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_67 = e3 & ~ (all_8_68 = % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, all_8_69) = all_8_68 & op(e3, e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69 & op(e2, all_8_69) = e3 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_68) & $i(all_8_69)) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (541) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_8_64 = e4 & ~ (all_8_65 = e2) & op(e4, % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) = all_8_65 & op(e4, e2) = all_8_66 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_66) = e4 & $i(all_8_65) & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) op(e2, all_8_66) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) op(e4, e2) = all_8_66 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_9_1 = e2 & op(e4, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_9_1 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (548) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_9_12 = e0 & op(e1, e4) = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (242), (549) are inconsistent by sub-proof % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #75. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_9_13 = e0 & op(e1, e3) = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_9_13 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (552) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_9_12 = e4 & op(e1, e4) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (553) are inconsistent by sub-proof #74. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_9_13 = e4 & op(e1, e3) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_9_13 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (555) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) e4 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (556) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (557) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (558) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_9_14 = e4 & op(e1, e2) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (559) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_9_14 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (50), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (67), (77), (86), (89), (98), (107), (110), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (132), (135), (146), (152), (176), (178), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (201), (209), (215), (225), (228), (232), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (248), (253), (271), (291), (343), (344), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349), (397), (408), (410), (432), (449), (461), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547), (560) are inconsistent by sub-proof #69. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_9_15 = e4 & op(e1, e1) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_9_15 = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, e4, e1, e2, % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (489) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) e4 = e0 | ~ (op(e2, e1) = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (287), (543) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) ~ (all_8_66 = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_66, e2, e4, % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (534), (544) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_8_66 = e1 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (543), (566) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) op(e2, e1) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) ~ (op(e2, e1) = e4) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (567), (568) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) $false % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (569) is inconsistent. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) e4 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (563), (570) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_9_15 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (178), (209), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (218), (225), (229), (248), (331), (488), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (571) are inconsistent by sub-proof #64. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) op(e2, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (366), (572) are inconsistent by sub-proof % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_9_19 = e4 & op(e1, e0) = e4 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (449), (456), (461), (573) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #60. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (40), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (52), (69), (77), (86), (88), (89), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (102), (107), (110), (114), (132), (135), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (173), (175), (176), (178), (185), (201), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (215), (218), (225), (228), (229), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (271), (291), (292), (331), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (432), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (481), (488), (493), (574) are inconsistent % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_9_3 = e2 & op(e3, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (575) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_9_3 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (576) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) e4 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (577) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) e4 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (578) imply: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_9_20 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (579) are % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #90. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e2) | (all_9_21 = e2 & op(e0, e3) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_9_7 = e2 & op(e2, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (581) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) op(e2, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (366), (582) are inconsistent by sub-proof % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308. % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_9_13 = e2 & op(e1, e3) = e2) | (all_9_21 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = e2) % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_9_13 = e2 & op(e1, e3) = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (584) implies: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_9_13 = e2 % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_9_12 = e0 & op(e1, e4) = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (242), (587) are inconsistent by sub-proof % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #75. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_9_13 = e0 & op(e1, e3) = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (588) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_9_13 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (585), (589) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) e2 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (590) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) e2 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (591) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) $false % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (592) is inconsistent. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_9_14 = e0 & op(e1, e2) = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_9_14 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (507), (595) are inconsistent by sub-proof % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #57. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (178), (209), % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (218), (225), (229), (248), (292), (331), % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488), (493), (596) are inconsistent by sub-proof % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #54. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_9_21 = e2 & op(e0, e3) = e2 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) all_9_21 = e2 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (598) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) e3 = e2 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (449), (599) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #82. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_8_67 = e3 & ~ (all_8_68 = e2) & op(e3, % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69) = all_8_68 & op(e3, e2) = all_8_69 & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, all_8_69) = e3 & $i(all_8_68) & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (600) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) op(e2, all_8_69) = e3 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) op(e3, e2) = all_8_69 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (89), (100), (147), (172), (333), (462), % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601), (602) are inconsistent by sub-proof #98. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_8_70 = e1 & ~ (all_8_71 = e2) & op(e2, % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_71) & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72)) | (all_8_73 = e0 & ~ (all_8_74 = % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, all_8_75) = e0 & op(e0, all_8_75) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_74 & op(e0, e2) = all_8_75 & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_74) & $i(all_8_75)) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_8_70 = e1 & ~ (all_8_71 = e2) & op(e2, % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72) = e1 & op(e1, all_8_72) = all_8_71 & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_71) & % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (604) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) op(e1, e2) = all_8_72 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) op(e1, all_8_72) = all_8_71 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) op(e2, all_8_72) = e1 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_6_13 = e1 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (404), (608) are inconsistent by sub-proof % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #52. % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_6_13 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (609) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_4_17 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (610) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_4_17 = e0 % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (611) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) ~ (all_4_7 = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (611) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) ~ (all_4_15 = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (611) imply: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) ~ (all_4_18 = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (614) implies: % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) ~ (all_4_18 = e0) % 128.46/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (611) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) ~ (e3 = e0) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (404), (611) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) ~ (e1 = e0) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (175), (178), (209), (218), (225), (229), % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (331), (493), (618) are inconsistent by % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #67. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (619) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_9_11 = e4 & op(e2, e1) = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (488), (620) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #66. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (621) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_9_15 = e4 & op(e1, e1) = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_9_15 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_6_11 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (200), (624) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) ~ (all_6_11 = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_6_11 = e3 | all_6_11 = e2 | all_6_11 = e1 | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_11 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_6_11 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (366), (627) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_6_11 = e3 | all_6_11 = e1 | all_6_11 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e0) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_9_12 = e0 & op(e1, e4) = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (242), (630) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #75. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_9_13 = e0 & op(e1, e3) = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) op(e1, e3) = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_6_18 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (633) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_4_18 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (634) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_4_18 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (635) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_4_8 = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (635) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) op(e1, e1) = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (540) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) all_6_1 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (638) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_4_5 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (639) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_4_5 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (640) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) ~ (all_4_7 = e2) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (640) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) ~ (all_4_15 = e2) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (642) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) ~ (all_4_15 = e2) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (640) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) op(e4, e3) = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_6_3 = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (218), (331), (645) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #93. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) ~ (all_6_3 = e4) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_6_3 = e3 | all_6_3 = e2 | all_6_3 = e1 | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_3 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_6_3 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (648) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_4_15 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (649) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_4_15 = e2 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (643), (650) imply: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) $false % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (651) is inconsistent. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_6_11 = e3 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (272), (653) are inconsistent by sub-proof % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #235. % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (all_6_11 = e3) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_6_11 = e1 | all_6_11 = e0 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_10 & op(all_8_69, e2) = e3 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_81, e3) = all_8_12 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e2 & op(all_8_45, e2) = all_8_16 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_57, e3) = e2 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_57) & $i(all_8_69)) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (657) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_54, e4) = all_8_0 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_54, e3) = e4 & op(e4, e3) = all_8_54 & % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_54) % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (659) implies: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) op(e4, e3) = all_8_54 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) op(all_8_54, e3) = e4 % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (655) gives: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_54, e3, e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (644), (660) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_8_54 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (661), (662) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) op(e2, e3) = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (89), (663) are inconsistent by % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #319. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_6_11 = e0 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (664) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_4_7 = e0 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (665) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_4_7 = e0 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (612), (666) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (667) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66) & op(all_8_66, e4) = all_8_2 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e4) = all_8_45 & $i(all_8_2) & $i(all_8_45) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_66) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (668) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) ~ (all_8_2 = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) op(e4, e2) = all_8_66 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) op(all_8_66, e4) = all_8_2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_66, e2, e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (534), (670) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_8_66 = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_2, e4, e1, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (256) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_8_2 = e2 | ~ (op(e1, e4) = all_8_2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (671), (672) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) op(e1, e4) = all_8_2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (673) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) ~ (op(e1, e4) = all_8_2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (674), (675) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (676) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_8_2 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (669), (677) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (678) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) & op(all_8_78, e4) = all_8_4 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_78) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (680) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) op(e1, e4) = all_8_48 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) op(e4, e1) = all_8_78 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) op(all_8_78, e1) = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) (all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_57) = e2 & op(e2, all_8_57) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_56 & op(e2, e3) = all_8_57 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_56) & $i(all_8_57)) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (89), (462), (644), (685) are inconsistent % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #51. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_56) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) op(e2, e3) = all_8_57 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) ~ (op(e2, e3) = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) ~ (op(e4, e1) = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) (all_8_76 = e4 & ~ (all_8_77 = e1) & op(e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) = all_8_77 & op(e4, e1) = all_8_78 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_8_78) = e4 & $i(all_8_77) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_78)) | (all_8_79 = e3 & ~ (all_8_80 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e3, all_8_81) = all_8_80 & op(e3, e1) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81 & op(e1, all_8_81) = e3 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_80) & $i(all_8_81)) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_8_76 = e4 & ~ (all_8_77 = e1) & op(e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78) = all_8_77 & op(e4, e1) = all_8_78 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_8_78) = e4 & $i(all_8_77) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_78) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (691) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) op(e1, all_8_78) = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_78, e1, e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (482), (682) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_8_78 = e3 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (692), (693) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) op(e1, e3) = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_4_8, e4, e3, e1, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (174), (694) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_4_8 = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (636), (695) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (696) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) op(e2, e3) = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (366), (697) are inconsistent by sub-proof % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_8_79 = e3 & ~ (all_8_80 = e1) & op(e3, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81) = all_8_80 & op(e3, e1) = all_8_81 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_8_81) = e3 & $i(all_8_80) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) op(e3, e1) = all_8_81 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) ~ (op(e3, e1) = e3) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_48, e4, e1, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (256), (681) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_8_48 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (257), (681) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) ~ (all_8_48 = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_57, e3, e2, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (437), (687) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_8_57 = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_81, e1, e3, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (494), (699) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_8_81 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_78, e1, e4, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (482), (682) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_8_78 = e3 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (291), (682) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ (all_8_78 = e1) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_8_81, e4, e1, e3, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (699) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_8_81 = e4 | ~ (op(e3, e1) = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (687), (688) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) ~ (all_8_57 = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (699), (700) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) ~ (all_8_81 = e3) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (683), (689) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) ~ (all_8_78 = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (683), (705) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) op(e3, e1) = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (707) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) ~ (op(e3, e1) = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (711), (712) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (713) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_8_81 = e4 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (704), (714) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) e4 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (715) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) e4 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (623), (716) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_9_15 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (50), (52), (60), (64), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (98), (107), (110), (114), (128), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (143), (146), (148), (152), (164), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (170), (175), (176), (178), (184), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (189), (201), (202), (207), (209), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (257), (271), (291), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292), (308), (343), (344), (349), (397), (408), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (432), (449), (456), (461), (481), (717) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #46. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) op(e3, e1) = e3 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (77), (344), (718) are inconsistent by % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) (all_8_82 = e2 & ~ (all_8_83 = e1) & op(e2, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_84) = all_8_83 & op(e2, e1) = all_8_84 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_8_84) = e2 & $i(all_8_83) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) | (all_8_85 = e0 & ~ (all_8_86 = % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, all_8_87) = e0 & op(e0, all_8_87) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_86 & op(e0, e1) = all_8_87 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_86) & $i(all_8_87)) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_8_82 = e2 & ~ (all_8_83 = e1) & op(e2, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_84) = all_8_83 & op(e2, e1) = all_8_84 & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_8_84) = e2 & $i(all_8_83) & % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) op(e1, all_8_84) = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) op(e2, e1) = all_8_84 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) ~ (op(e2, e1) = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_48, e4, e1, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (256), (681) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_8_48 = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (257), (681) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) ~ (all_8_48 = e4) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, e2, e0, e1, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (325) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) e2 = e1 | ~ (op(e1, e0) = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_84, e1, e2, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (489), (722) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_8_84 = e0 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_57, e3, e2, % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (437), (687) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_8_57 = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (722), (723) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) ~ (all_8_84 = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (687), (688) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) ~ (all_8_57 = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (721), (727) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) op(e1, e0) = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) ~ (op(e1, e0) = e2) % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (731), (732) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) $false % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (733) is inconsistent. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) e2 = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (432), (734) imply: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_9_22 = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (50), (67), (86), (107), (152), (201), % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (253), (349), (461), (735) are inconsistent % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #73. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) op(e2, e1) = e1 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (141), (404), (736) are inconsistent by % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) op(e2, e1) = e2 % 128.65/17.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (737) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) all_8_85 = e0 & ~ (all_8_86 = e1) & op(e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87) = e0 & op(e0, all_8_87) = all_8_86 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_86) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (738) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) op(e0, e1) = all_8_87 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) op(e1, all_8_87) = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_87, e1, e0, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (321), (739) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_8_87 = e1 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_72, e2, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (508), (605) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_8_72 = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_71, e3, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (632) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_8_71 = e0 | ~ (op(e1, e3) = all_8_71) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e4, all_8_71, e1, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (637) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_8_71 = e4 | ~ (op(e1, e1) = all_8_71) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (742) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) op(e1, e3) = all_8_71 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (740), (741) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) op(e1, e1) = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (743) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) ~ (op(e1, e3) = all_8_71) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (745), (747) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) $false % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (748) is inconsistent. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_8_71 = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) ~ (op(e1, e1) = all_8_71) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (749), (750) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) ~ (op(e1, e1) = e0) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (746), (751) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) $false % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (752) is inconsistent. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_8_71 = e4 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (749), (753) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) e4 = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (623), (754) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_9_15 = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (178), (209), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (218), (225), (229), (248), (331), (488), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (755) are inconsistent by sub-proof #64. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) op(e4, e1) = e4 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (218), (331), (756) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) op(e2, e3) = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (366), (757) are inconsistent by sub-proof % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) (all_8_58 = e1 & ~ (all_8_59 = e3) & op(e3, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60) = e1 & op(e1, all_8_60) = all_8_59 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_59) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (all_8_61 = e0 & ~ (all_8_62 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_63) = e0 & op(e0, all_8_63) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_62 & op(e0, e3) = all_8_63 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_62) & $i(all_8_63)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (209), (211), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (225), (229), (248), (319), (323), (331), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (488), (493), (514), (533), (613), (623), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632), (652), (758) are inconsistent by sub-proof % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #42. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_90) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (760) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) ~ (all_8_51 = all_8_90) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) op(e0, e4) = all_8_51 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) op(e4, e0) = all_8_90 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (318), (322), (761), (762), (763) are % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #41. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_8 & op(e4, e3) = all_8_54 & op(e3, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) op(e3, e4) = all_8_42 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) op(e4, e3) = all_8_54 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) op(all_8_42, e4) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) ~ (op(e4, e3) = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) ~ (op(e2, e1) = e1) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_72, e2, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (508), (605) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_8_72 = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_42, e4, e3, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (156), (765) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_8_42 = e1 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_54, e3, e4, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (644), (766) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_8_54 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, e3, e4, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (256) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) e3 = e2 | ~ (op(e1, e4) = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (607), (769) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) ~ (all_8_72 = e1) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (766), (768) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) ~ (all_8_54 = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (767), (771) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) op(e1, e4) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) ~ (op(e1, e4) = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (776), (777) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) $false % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (778) is inconsistent. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) e3 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (779) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_9_17 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (780) are % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) op(e2, e1) = e1 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (141), (404), (781) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) op(e4, e3) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (270), (782) are inconsistent by sub-proof % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_8_14 & op(all_8_93, e0) = e3 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_69, e3) = all_8_10 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_10) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (785) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) op(e3, e2) = all_8_69 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) op(all_8_69, e2) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (op(e2, e1) = e1) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_72, e2, e1, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (508), (605) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_8_72 = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_69, e2, e3, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (462), (786) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_8_69 = e0 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, e3, e2, e0, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (320) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) e3 = e2 | ~ (op(e0, e2) = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (607), (788) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) ~ (all_8_72 = e1) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (787), (790) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) op(e0, e2) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) ~ (op(e0, e2) = e3) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (793), (794) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) $false % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (795) is inconsistent. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) e3 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (796) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_9_17 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (797) are % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) op(e2, e1) = e1 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (141), (404), (798) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_81, e3) = all_8_12 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (799) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) op(e3, e1) = all_8_81 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) op(all_8_81, e1) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_81, e1, e3, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (494), (800) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_8_81 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (801), (802) imply: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) op(e2, e1) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (91), (212), (803) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) op(e2, e3) = e3 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (804) are inconsistent by % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_45 & $i(all_8_16) & $i(all_8_45) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e2 & op(all_8_57, e2) = all_8_18 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_93, e3) = all_8_14 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_8_63 & $i(all_8_14) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (806) implies: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) ~ (all_8_63 = all_8_93) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) op(e0, e3) = all_8_63 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) op(e3, e0) = all_8_93 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (319), (323), (807), (808), (809) are % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40. % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57 & $i(all_8_18) & $i(all_8_57) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_69)) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_66) & op(all_8_45, e4) = e2 & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_45) & $i(all_8_66) % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) op(e2, e4) = all_8_45 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) op(e4, e2) = all_8_66 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) op(all_8_45, e4) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) ~ (op(e4, e2) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_45, e4, e2, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (207), (812) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_8_45 = e3 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_66, e2, e4, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (534), (813) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_8_66 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (813), (815) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) ~ (all_8_66 = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (814), (816) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) op(e3, e4) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (156), (228), (819) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) op(e2, e3) = e3 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (820) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) op(e4, e2) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (201), (349), (821) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #261. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_69) & op(all_8_57, e3) = e2 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) & $i(all_8_69) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (822) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) op(e2, e3) = all_8_57 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) op(e3, e2) = all_8_69 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) op(all_8_57, e3) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) ~ (op(e3, e2) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_57, e3, e2, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (437), (823) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_8_57 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_69, e2, e3, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (462), (824) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_8_69 = e0 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, e2, e3, e1, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (632) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) e2 = e0 | ~ (op(e1, e3) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (824), (826) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) ~ (all_8_69 = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (825), (827) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) op(e1, e3) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (829) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (op(e1, e3) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (831), (832) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) $false % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (833) is inconsistent. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) e2 = e0 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (834) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) $false % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (835) is inconsistent. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) op(e3, e1) = e3 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (77), (344), (836) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) op(e3, e2) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (86), (379), (837) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #39. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_8_30 & op(all_8_99, e0) = e1 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_63 & $i(all_8_34) & $i(all_8_63) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(all_8_75, e0) = all_8_36 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_87) & $i(all_8_99)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (838) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = e1 & op(all_8_48, e1) = all_8_24 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (839) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_84, e2) = all_8_20 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_84, e1) = e2 & op(e2, e1) = all_8_84 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_72 & $i(all_8_20) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (841) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) op(e2, e1) = all_8_84 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) op(all_8_84, e1) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) ~ (op(e2, e1) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) (all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_57) = e2 & op(e2, all_8_57) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_56 & op(e2, e3) = all_8_57 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_56) & $i(all_8_57)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (845) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (89), (462), (644), (846) are inconsistent % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #51. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_56) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) op(e2, e3) = all_8_57 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) ~ (op(e2, e3) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_84, e1, e2, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (489), (842) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_8_84 = e0 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_57, e3, e2, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (437), (848) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_8_57 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, e2, e1, e0, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (321) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) e2 = e1 | ~ (op(e0, e1) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (843), (844) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) ~ (all_8_84 = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (848), (849) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) ~ (all_8_57 = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (843), (850) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) op(e0, e1) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (852) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) ~ (op(e0, e1) = e2) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (855), (856) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) $false % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (857) is inconsistent. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) e2 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (432), (858) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) all_9_22 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (50), (67), (86), (107), (152), (201), % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (253), (349), (461), (859) are inconsistent % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #73. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) op(e2, e3) = e3 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (860) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) op(e2, e3) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (366), (861) are inconsistent by sub-proof % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #308. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) (all_8_58 = e1 & ~ (all_8_59 = e3) & op(e3, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60) = e1 & op(e1, all_8_60) = all_8_59 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_59) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (all_8_61 = e0 & ~ (all_8_62 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_63) = e0 & op(e0, all_8_63) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_62 & op(e0, e3) = all_8_63 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_62) & $i(all_8_63)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (209), (211), % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (225), (229), (248), (319), (323), (331), % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (488), (493), (514), (533), (613), (623), % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632), (652), (862) are inconsistent by sub-proof % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #42. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) op(e2, e1) = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (863) are inconsistent by % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_96, e2) = all_8_22 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_75 & $i(all_8_22) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) & $i(all_8_96) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (864) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) ~ (all_8_75 = all_8_96) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) op(e0, e2) = all_8_75 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) op(e2, e0) = all_8_96 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (320), (324), (865), (866), (867) are % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #38. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_78) & op(all_8_48, e4) = e1 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_60, e3) = e1 & op(all_8_60, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60 & $i(all_8_26) & $i(all_8_60) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1 & op(all_8_72, e1) = all_8_28 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (868) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_78) & op(all_8_48, e4) = e1 & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_48) & $i(all_8_78) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (869) implies: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) op(e1, e4) = all_8_48 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) op(e4, e1) = all_8_78 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) op(all_8_48, e4) = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_48, e4, e1, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (256), (870) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_8_48 = e2 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, e1, e4, e2, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (207) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) e3 = e1 | ~ (op(e2, e4) = e1) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_78, e1, e4, % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (482), (871) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_8_78 = e3 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (291), (871) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) ~ (all_8_78 = e1) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (872), (873) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) op(e2, e4) = e1 % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (874) gives: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) ~ (op(e2, e4) = e1) % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (877), (878) imply: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) $false % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (879) is inconsistent. % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) e3 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (408), (880) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (881) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) op(e2, e3) = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (882) are inconsistent by % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_84)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (883) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_81) & op(all_8_60, e3) = e1 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60) & $i(all_8_81) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (884) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) op(e1, e3) = all_8_60 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) op(all_8_60, e3) = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) (all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54)) | (all_8_55 = e2 & ~ (all_8_56 = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_57) = e2 & op(e2, all_8_57) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_56 & op(e2, e3) = all_8_57 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_56) & $i(all_8_57)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (887) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_54) = all_8_53 & op(e4, e3) = all_8_54 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, all_8_54) = e4 & $i(all_8_53) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_54) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (89), (462), (644), (888) are inconsistent % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #51. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_8_55 = e2 & ~ (all_8_56 = e3) & op(e3, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_57) = e2 & op(e2, all_8_57) = all_8_56 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_8_57 & $i(all_8_56) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_57) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) op(e2, e3) = all_8_57 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) ~ (op(e2, e3) = e3) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e0, all_8_60, e3, e1, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (632), (885) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_8_60 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e1, all_8_57, e3, e2, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (437), (890) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_8_57 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, e1, e3, e0, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (319) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) e3 = e1 | ~ (op(e0, e3) = e1) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (890), (891) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_8_57 = e3) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (886), (892) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) op(e0, e3) = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (894) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) ~ (op(e0, e3) = e1) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (896), (897) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (898) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) e3 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (408), (899) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (900) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) op(e2, e3) = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (200), (272), (901) are inconsistent by % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #294. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) (all_8_58 = e1 & ~ (all_8_59 = e3) & op(e3, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_60) = e1 & op(e1, all_8_60) = all_8_59 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_60 & $i(all_8_59) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_60)) | (all_8_61 = e0 & ~ (all_8_62 = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, all_8_63) = e0 & op(e0, all_8_63) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_62 & op(e0, e3) = all_8_63 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_62) & $i(all_8_63)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (209), (211), % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (225), (229), (248), (319), (323), (331), % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (488), (493), (514), (533), (613), (623), % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632), (652), (902) are inconsistent by sub-proof % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #42. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_84) & op(all_8_72, e2) = e1 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_72, e1) = all_8_28 & op(e2, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_72) & $i(all_8_84) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (903) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) ~ (all_8_28 = e2) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) op(all_8_72, e1) = all_8_28 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (652) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e3, all_8_72, e2, e1, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (508), (605) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_8_72 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_28, e1, e3, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (494) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_8_28 = e2 | ~ (op(e3, e1) = all_8_28) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (905), (906) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) op(e3, e1) = all_8_28 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (907) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ (op(e3, e1) = all_8_28) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (908), (909) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (910) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_8_28 = e2 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (904), (911) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (912) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_6_3 = e1 | all_6_3 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (218), (533), (613), (913) are inconsistent by % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & op(all_8_63, e0) = all_8_34 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (914) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_51 & $i(all_8_32) & $i(all_8_51) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_90)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_99, e1) = all_8_30 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_8_87 & $i(all_8_30) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (916) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_8_87 = all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) op(e0, e1) = all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) op(e1, e0) = all_8_99 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (321), (325), (917), (918), (919) are % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #37. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_90) & op(all_8_51, e4) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_51) & $i(all_8_90) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (920) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) ~ (all_8_51 = all_8_90) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) op(e0, e4) = all_8_51 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) op(e4, e0) = all_8_90 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (318), (322), (921), (922), (923) are % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #41. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75 & $i(all_8_36) & $i(all_8_75) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0 & op(all_8_87, e0) = all_8_38 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (924) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_93) & op(all_8_63, e3) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_63) & $i(all_8_93) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (925) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) ~ (all_8_63 = all_8_93) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) op(e0, e3) = all_8_63 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) op(e3, e0) = all_8_93 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (319), (323), (926), (927), (928) are % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_99)) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (929) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_96) & op(all_8_75, e2) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) & $i(all_8_96) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (930) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) ~ (all_8_75 = all_8_96) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) op(e0, e2) = all_8_75 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) op(e2, e0) = all_8_96 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (320), (324), (931), (932), (933) are % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #38. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_8_99) & op(all_8_87, e1) = e0 & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_87) & $i(all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (934) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_8_87 = all_8_99) % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) op(e0, e1) = all_8_87 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) op(e1, e0) = all_8_99 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (321), (325), (935), (936), (937) are % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #37. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_6_1 = e3 | all_6_1 = e1 | all_6_1 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_6_1 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (939) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_4_5 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (940) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_4_5 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (941) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (942) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_6_1 = e1 | all_6_1 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (943) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_6_1 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (944) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_4_5 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (945) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_4_5 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (531), (946) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (947) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_6_1 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (948) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_4_5 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (949) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_4_5 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (950) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (951) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_6_18 = e3 | all_6_18 = e2 | all_6_18 = e1 | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_6_18 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (952) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_6_18 = e2 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (953) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_4_18 = e2 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (954) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_4_18 = e2 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (955) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (956) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_6_18 = e3 | all_6_18 = e1 | all_6_18 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (957) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_6_18 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (958) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_4_18 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (959) implies: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_4_18 = e3 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (960) imply: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) $false % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (961) is inconsistent. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_6_18 = e1 | all_6_18 = e0 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (962) gives: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_6_18 = e1 % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (405), (963) are inconsistent by sub-proof % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #36. % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_6_18 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (964) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_4_18 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (965) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) all_4_18 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (615), (966) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) $false % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (967) is inconsistent. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (40), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (52), (69), (77), (86), (88), (89), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (102), (107), (110), (114), (132), (135), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (173), (175), (176), (178), (185), (201), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (215), (218), (225), (228), (229), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (271), (291), (292), (331), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (432), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (481), (488), (493), (968) are inconsistent % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_9_23 = e4 & op(e0, e1) = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (102), (173), (969) are inconsistent by % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_8_73 = e0 & ~ (all_8_74 = e2) & op(e2, % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_75) = e0 & op(e0, all_8_75) = all_8_74 & % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_8_75 & $i(all_8_74) & % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_75) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) ~ (all_8_74 = e2) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) op(e0, e2) = all_8_75 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) op(e0, all_8_75) = all_8_74 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_75, e2, e0, % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (320), (972) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_8_75 = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_8_74, e2, e0, % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (320) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_8_74 = e2 | ~ (op(e0, e2) = all_8_74) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (973), (974) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) op(e0, e2) = all_8_74 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (975) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) ~ (op(e0, e2) = all_8_74) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (976), (977) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) $false % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (978) is inconsistent. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_8_74 = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (971), (979) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) $false % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (980) is inconsistent. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_6_2 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (981) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_4_10 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (982) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) $false % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (983) is inconsistent. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) all_9_5 = e4 & op(e3, e2) = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (985) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_9_5 = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (986) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) e4 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (987) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) e4 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (988) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) $false % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (989) is inconsistent. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (990) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_9_10 = e4 & op(e3, e1) = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_9_10 = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (248), (493), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) are inconsistent by sub-proof #35. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_9_17 = e4 & op(e3, e0) = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (993) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_9_17 = e4 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (994) imply: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) e4 = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (995) are inconsistent % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #89. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_19 = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (996) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_9_15 = e3 & op(e1, e1) = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (997) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_9_15 = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (178), (209), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (218), (225), (229), (242), (248), (331), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488), (493), (998) are inconsistent by sub-proof % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_9_19 = e3 & op(e1, e0) = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (999) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_9_19 = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (449), (456), (461), (1000) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #32. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_9_11 = e2 & op(e2, e1) = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1002) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) op(e2, e1) = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (1003) are inconsistent by % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e2) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1004) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_9_15 = e2 & op(e1, e1) = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1005) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) all_9_15 = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (50), (52), (60), (64), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (98), (107), (110), (114), (128), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (143), (146), (148), (152), (164), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (170), (175), (176), (178), (184), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (189), (201), (202), (207), (209), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (257), (271), (291), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292), (308), (343), (344), (349), (397), (408), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (432), (449), (456), (461), (481), (1006) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #46. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_9_23 = e2 & op(e0, e1) = e2 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (228), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (291), (403), (404), (405), (1007) are % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #30. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_9_18 = e0 & op(e2, e0) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1008) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) op(e2, e0) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (134), (294), (1009) are inconsistent by % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) all_9_10 = e3 & op(e3, e1) = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1010) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) op(e3, e1) = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (77), (344), (1011) are inconsistent by % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (10), (16), (17), (19), (22), (23), (24), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (30), (33), (34), (39), (41), (45), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (50), (52), (53), (60), (61), (62), (64), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (91), (93), (102), (107), (110), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (128), (132), (133), (134), (135), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (146), (148), (152), (164), (168), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (171), (173), (175), (178), (184), (187), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (201), (202), (207), (209), (211), (212), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (219), (223), (224), (225), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (234), (242), (248), (253), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270), (271), (291), (294), (331), (338), (343), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (349), (367), (397), (403), (404), (405), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (436), (449), (461), (1012) are % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1013) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_9_8 = e0 & op(e2, e2) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1014) are inconsistent by sub-proof % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1015) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) all_9_14 = e0 & op(e1, e2) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1016) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) all_9_14 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1018) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) all_9_2 = e0 & op(e3, e4) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1019) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) all_9_2 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (24), (27), (28), (39), (45), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (69), (71), (79), (86), (89), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (128), (132), (143), (146), (148), (164), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (178), (184), (187), (202), (207), (209), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (219), (223), (225), (228), (229), (232), % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (1020) are inconsistent by sub-proof % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #265. % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_9_3 = e0 & op(e3, e3) = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1021) implies: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) all_9_3 = e0 % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (40), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (52), (69), (77), (86), (88), (89), (98), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (132), (135), (146), (175), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (178), (185), (201), (209), (215), (225), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (271), (291), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (432), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (1017), (1023) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1024) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) all_9_11 = e3 & op(e2, e1) = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1025) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) op(e2, e1) = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (91), (212), (1026) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1027) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) all_9_15 = e3 & op(e1, e1) = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1028) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_9_15 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (88), (194), (270), (1030) are inconsistent % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #139. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1031) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_9_4 = e3 & op(e4, e2) = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1032) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) all_9_4 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (52), (60), (64), (65), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (71), (77), (79), (86), (88), (89), (90), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (114), (128), (132), (135), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (164), (170), (171), (175), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (185), (187), (194), (201), (202), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (215), (216), (219), (223), (225), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (270), (271), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (343), (344), (349), (397), (408), (410), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436), (449), (1033), (1034) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1035) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_9_8 = e0 & op(e2, e2) = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1036) are inconsistent by sub-proof % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1037) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_9_11 = e0 & op(e2, e1) = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1038) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_9_11 = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (175), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (185), (201), (209), (215), (225), (228), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (257), (271), (286), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (343), (344), (349), (366), (397), (408), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (449), (1022), (1033), (1040) are % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1041) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_9_14 = e4 & op(e1, e2) = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1017), (1042) are inconsistent by sub-proof % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #19. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1043) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) all_9_15 = e4 & op(e1, e1) = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_9_15 = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1029), (1045) imply: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) e4 = e3 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (1046) are % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #89. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) all_9_19 = e4 & op(e1, e0) = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1047) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_9_19 = e4 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_9_0 = e2 & op(e4, e4) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (88), (1050) are inconsistent by sub-proof % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_9_1 = e2 & op(e4, e3) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1051) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_9_1 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1053) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_9_2 = e2 & op(e3, e4) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1054) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) op(e3, e4) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (156), (228), (1055) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_9_3 = e2 & op(e3, e3) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1056) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_9_3 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1022), (1057) imply: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) e2 = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1058) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) e2 = e0 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (1059) imply: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) $false % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1060) is inconsistent. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1061) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_9_5 = e2 & op(e3, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1062) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) op(e3, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (86), (379), (1063) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #39. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1064) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_9_10 = e2 & op(e3, e1) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1065) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_9_10 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (45), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (52), (77), (89), (98), (102), (110), (114), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (146), (173), (175), (176), (178), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (209), (211), (215), (218), (225), (228), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (271), (291), (331), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (397), (408), (410), (432), (449), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017), (1029), (1039), (1052), (1066) are % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #18. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_9_17 = e2 & op(e3, e0) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1067) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_9_17 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (1068) are % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1069) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_9_4 = e2 & op(e4, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) op(e4, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (201), (349), (1071) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #261. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1072) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_9_9 = e2 & op(e4, e1) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1073) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_9_9 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_9_2 = e2 & op(e3, e4) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) op(e3, e4) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (156), (228), (1077) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_9_3 = e2 & op(e3, e3) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (40), (45), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (86), (88), (89), (107), (146), (175), (178), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (201), (209), (225), (228), (229), (232), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (248), (291), (349), (397), (408), (410), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022), (1033), (1074), (1078) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1079) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_9_5 = e2 & op(e3, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1080) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) op(e3, e2) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (86), (379), (1081) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #39. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1082) gives: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_9_10 = e2 & op(e3, e1) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_9_10 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (48), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (146), (173), (175), (178), (209), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (218), (225), (229), (242), (248), (331), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029), (1039), (1084) are inconsistent by % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #33. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) all_9_17 = e2 & op(e3, e0) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1085) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_9_17 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (1086) are % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_9_16 = e2 & op(e4, e0) = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1087) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_9_16 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (1088) imply: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) e4 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1089) implies: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) e4 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1048), (1090) imply: % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_9_19 = e2 % 128.65/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (165), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (185), (201), (209), (215), (225), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (257), (271), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286), (291), (343), (344), (349), (366), (397), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (449), (1017), (1022), (1029), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033), (1091) are inconsistent by sub-proof #17. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_9_18 = e0 & op(e2, e0) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1092) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) op(e2, e0) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (134), (294), (1093) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (34), (39), (40), (41), (45), (48), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (60), (62), (64), (65), (69), (71), (77), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (86), (88), (89), (90), (93), (98), (102), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (114), (128), (132), (133), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (135), (141), (143), (146), (148), (164), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (173), (175), (176), (178), (184), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (201), (202), (207), (209), (211), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (219), (223), (224), (225), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (234), (242), (248), (271), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (294), (331), (343), (344), (349), (397), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (404), (405), (408), (410), (432), (436), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (1017), (1029), (1094) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #15. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_9_23 = e3 & op(e0, e1) = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1095) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_9_23 = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (234), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (403), (404), (405), (408), (1096) are % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (33), (34), (39), (40), (41), (45), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (50), (52), (53), (60), (61), (62), (64), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (91), (93), (98), (102), (107), (110), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (128), (132), (133), (134), (135), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (146), (148), (152), (164), (168), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (171), (173), (175), (176), (178), (184), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (193), (194), (201), (202), (207), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (212), (215), (216), (218), (219), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (223), (224), (225), (228), (229), (232), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (242), (248), (253), (270), (271), (291), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (297), (331), (338), (343), (344), (349), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (403), (404), (405), (408), (410), (432), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436), (449), (1017), (1097) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_9_22 = e0 & op(e0, e2) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (313), (1098) are inconsistent by sub-proof % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1099) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_9_19 = e2 & op(e1, e0) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_9_19 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1102) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_9_4 = e0 & op(e4, e2) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_9_4 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (52), (60), (64), (65), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (71), (77), (79), (86), (88), (89), (90), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (128), (132), (135), (143), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (148), (164), (170), (171), (175), (178), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (185), (187), (194), (201), (202), (207), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (215), (216), (219), (223), (225), (228), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (270), (271), (291), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (449), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) are inconsistent by sub-proof #79. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) all_9_5 = e0 & op(e3, e2) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1105) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_9_5 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1107) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_9_9 = e3 & op(e4, e1) = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1108) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_9_9 = e3 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (24), (27), (28), (39), (45), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (69), (71), (79), (86), (89), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (111), (128), (132), (143), (146), (148), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (170), (178), (184), (187), (202), (207), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (215), (216), (219), (223), (225), (228), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (408), (410), (436), (1110) are % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #78. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1111) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_9_8 = e0 & op(e2, e2) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1112) are inconsistent by sub-proof % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1113) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_9_11 = e0 & op(e2, e1) = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_9_11 = e0 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1116) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_9_9 = e2 & op(e4, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (449), (1109), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) are inconsistent by sub-proof #77. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_9_10 = e2 & op(e3, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1118) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_9_10 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (25), (132), (366), (1120) are % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1121) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_9_8 = e2 & op(e2, e2) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (67), (1122) are inconsistent by sub-proof % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1123) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_9_11 = e2 & op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1124) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (1125) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_9_18 = e2 & op(e2, e0) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1126) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_9_18 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (34), (39), (45), (50), (52), (60), (64), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (80), (86), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (97), (107), (110), (114), (128), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (143), (146), (148), (152), (156), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (170), (175), (178), (184), (187), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (202), (207), (209), (215), (216), (219), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (225), (228), (229), (232), (242), (248), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (271), (308), (343), (344), (349), (379), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (408), (410), (432), (449), (1101), (1106), % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119), (1127) are inconsistent by sub-proof #8. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1128) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_9_11 = e2 & op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1129) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (1130) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1131) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_9_15 = e2 & op(e1, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_9_15 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (25), (132), (366), (1134) are % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) all_9_8 = e2 & op(e2, e2) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (67), (1136) are inconsistent by sub-proof % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1137) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_9_11 = e2 & op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1138) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) op(e2, e1) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (1139) are inconsistent by % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_9_18 = e2 & op(e2, e0) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1140) implies: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_9_18 = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1142) gives: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) all_9_0 = e2 & op(e4, e4) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (88), (1143) are inconsistent by sub-proof % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #314. % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_9_1 = e2 & op(e4, e3) = e2 % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1144) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_9_1 = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1146) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_9_9 = e4 & op(e4, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1147) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) op(e4, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (218), (331), (1148) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_9_10 = e4 & op(e3, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1149) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_9_10 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) all_9_12 = e4 & op(e1, e4) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1152) are inconsistent by sub-proof #74. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_9_13 = e4 & op(e1, e3) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1153) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_9_13 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (50), (67), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (86), (89), (107), (110), (114), (146), (152), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (185), (201), (209), (225), (228), (232), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (248), (253), (291), (343), (349), (397), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (1106), (1145), (1155) are % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (34), (52), (69), (77), (86), (89), (110), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (132), (135), (176), (178), (189), (215), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (271), (292), (343), (344), (408), (432), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (1133), (1154), (1156) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #49. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1157) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) all_9_14 = e4 & op(e1, e2) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1158) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_9_14 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (50), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (67), (77), (86), (89), (98), (107), (110), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (132), (135), (146), (152), (176), (178), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (201), (209), (215), (225), (228), (232), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (248), (253), (271), (291), (343), (344), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349), (397), (408), (410), (432), (449), (1106), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145), (1159) are inconsistent by sub-proof #69. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1160) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_9_15 = e4 & op(e1, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1161) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) all_9_15 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1133), (1162) imply: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) e4 = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1150), (1163) imply: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) all_9_10 = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (34), (39), (45), (50), (52), (60), (64), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (80), (86), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (97), (107), (110), (114), (128), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (143), (146), (148), (152), (156), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (170), (175), (178), (184), (187), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (202), (207), (209), (215), (216), (219), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (225), (228), (229), (232), (242), (248), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (271), (308), (343), (344), (349), (379), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (408), (410), (432), (449), (1101), (1106), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141), (1164) are inconsistent by sub-proof #8. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) all_9_19 = e4 & op(e1, e0) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1165) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_9_19 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1101), (1166) imply: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) e4 = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1150), (1167) imply: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_9_10 = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (34), (39), (45), (50), (52), (60), (64), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (80), (86), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (97), (107), (110), (114), (128), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132), (135), (143), (146), (148), (152), (156), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (170), (175), (178), (184), (187), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (202), (207), (209), (215), (216), (219), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (225), (228), (229), (232), (242), (248), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (271), (308), (343), (344), (349), (379), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (408), (410), (432), (449), (1101), (1106), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141), (1168) are inconsistent by sub-proof #8. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1169) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) all_9_11 = e4 & op(e2, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1115), (1170) are inconsistent by sub-proof % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #66. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1171) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) all_9_15 = e4 & op(e1, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (248), (1133), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) are inconsistent by sub-proof #47. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_9_23 = e4 & op(e0, e1) = e4 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (102), (173), (1173) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (45), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (77), (107), (110), (114), (132), (135), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (175), (178), (201), (209), (215), (225), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (248), (271), (343), (344), (349), (397), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (449), (1109), (1174) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #48. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_9_23 = e2 & op(e0, e1) = e2 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (228), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (291), (403), (404), (405), (1175) are % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #30. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) all_9_18 = e0 & op(e2, e0) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1176) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) op(e2, e0) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (134), (294), (1177) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_9_10 = e3 & op(e3, e1) = e3 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1178) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) op(e3, e1) = e3 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (77), (344), (1179) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (10), (16), (17), (19), (22), (23), (24), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (30), (33), (34), (39), (41), (45), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (50), (52), (53), (60), (61), (62), (64), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (91), (93), (102), (107), (110), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (128), (132), (133), (134), (135), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (146), (148), (152), (164), (168), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (171), (173), (175), (178), (184), (187), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (201), (202), (207), (209), (211), (212), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (219), (223), (224), (225), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (234), (242), (248), (253), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270), (271), (291), (294), (331), (338), (343), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (349), (367), (397), (403), (404), (405), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (436), (449), (1106), (1180) are % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1181) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_9_8 = e0 & op(e2, e2) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1182) are inconsistent by sub-proof % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1183) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) all_9_14 = e0 & op(e1, e2) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1184) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_9_14 = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1186) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_9_2 = e0 & op(e3, e4) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1187) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_9_2 = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (24), (27), (28), (39), (45), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (69), (71), (79), (86), (89), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (128), (132), (143), (146), (148), (164), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (178), (184), (187), (202), (207), (209), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (219), (223), (225), (228), (229), (232), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (1188) are inconsistent by sub-proof % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #265. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_9_3 = e0 & op(e3, e3) = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1189) implies: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) all_9_3 = e0 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (40), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (52), (69), (77), (86), (88), (89), (98), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (132), (135), (146), (175), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (178), (185), (201), (209), (215), (225), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (271), (291), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (432), % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (1185), (1191) are inconsistent by % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1192) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_9_11 = e3 & op(e2, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1193) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) op(e2, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (91), (212), (1194) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1195) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_9_15 = e3 & op(e1, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1196) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_9_15 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (88), (194), (270), (1198) are inconsistent % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #139. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1199) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_9_4 = e3 & op(e4, e2) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) all_9_4 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (165), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (185), (201), (209), (215), (225), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (257), (271), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286), (291), (343), (344), (349), (366), (397), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (449), (1101), (1185), (1190), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197), (1201) are inconsistent by sub-proof #17. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (34), (39), (40), (41), (45), (48), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (60), (62), (64), (65), (69), (71), (77), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (86), (88), (89), (90), (93), (98), (102), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (114), (128), (132), (133), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (135), (141), (143), (146), (148), (164), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (173), (175), (176), (178), (184), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (201), (202), (207), (209), (211), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (219), (223), (224), (225), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (234), (242), (248), (271), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (294), (331), (343), (344), (349), (397), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (404), (405), (408), (410), (432), (436), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449), (1185), (1197), (1202) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #15. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) all_9_23 = e3 & op(e0, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1203) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) all_9_23 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (234), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (403), (404), (405), (408), (1204) are % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (19), (22), (23), (24), (27), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (33), (34), (39), (40), (41), (45), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (50), (52), (53), (60), (61), (62), (64), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (69), (71), (77), (79), (86), (88), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (91), (93), (98), (102), (107), (110), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (128), (132), (133), (134), (135), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (146), (148), (152), (164), (168), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (171), (173), (175), (176), (178), (184), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (193), (194), (201), (202), (207), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (212), (215), (216), (218), (219), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (223), (224), (225), (228), (229), (232), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (242), (248), (253), (270), (271), (291), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (297), (331), (338), (343), (344), (349), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (403), (404), (405), (408), (410), (432), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436), (449), (1185), (1205) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) all_9_22 = e0 & op(e0, e2) = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (313), (1206) are inconsistent by sub-proof % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_9_24 = e2 & op(e0, e0) = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (308), (1207) are inconsistent by sub-proof % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1208) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) all_9_18 = e3 & op(e2, e0) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1209) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) op(e2, e0) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (100), (172), (1210) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #226. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1211) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_9_19 = e3 & op(e1, e0) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1212) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_9_19 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1214) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_9_16 = e2 & op(e4, e0) = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (248), (397), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) are inconsistent by sub-proof #88. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_9_17 = e2 & op(e3, e0) = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1216) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) all_9_17 = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (52), (77), (110), (114), (132), (135), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (271), (343), (344), (408), (1217) are % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1218) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) all_9_18 = e2 & op(e2, e0) = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1219) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) all_9_18 = e2 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (215), (271), (408), (1221) are inconsistent % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #293. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1222) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) all_9_5 = e3 & op(e3, e2) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1223) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) op(e3, e2) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (114), (343), (1224) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1225) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) all_9_10 = e3 & op(e3, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1226) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) op(e3, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (77), (344), (1227) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) all_9_17 = e3 & op(e3, e0) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1228) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) all_9_17 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) (all_9_4 = e0 & op(e4, e2) = e0) | (all_9_5 = e0 & % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1230) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_9_4 = e0 & op(e4, e2) = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1231) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) all_9_4 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (52), (60), (64), (65), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (71), (77), (79), (86), (88), (89), (90), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (128), (132), (135), (143), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (148), (164), (170), (171), (175), (178), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (185), (187), (194), (201), (202), (207), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (215), (216), (219), (223), (225), (228), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (270), (271), (291), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (1229), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) are inconsistent by sub-proof #79. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) all_9_5 = e0 & op(e3, e2) = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1233) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_9_5 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (1213), (1220), (1229), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) are inconsistent by sub-proof #32. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1235) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) all_9_8 = e0 & op(e2, e2) = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1236) are inconsistent by sub-proof % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1237) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) all_9_14 = e0 & op(e1, e2) = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1238) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) all_9_14 = e0 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (34), (39), (40), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (52), (69), (77), (86), (88), (89), (98), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (114), (132), (135), (146), (175), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (178), (185), (201), (209), (215), (225), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (271), (291), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (397), (408), (410), (432), % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229), (1239), (1240) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1241) gives: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) all_9_11 = e3 & op(e2, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1242) implies: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) op(e2, e1) = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (91), (212), (1243) are inconsistent by % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #103. % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 % 128.65/17.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e3) % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1244) gives: % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) all_9_15 = e3 & op(e1, e1) = e3 % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1245) implies: % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) all_9_15 = e3 % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.65/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e3) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (88), (194), (270), (1247) are inconsistent % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #139. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1248) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) all_9_4 = e3 & op(e4, e2) = e3 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1249) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) all_9_4 = e3 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (39), (40), (45), (52), (60), (64), (65), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (71), (77), (79), (86), (88), (89), (90), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (114), (128), (132), (135), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (164), (170), (171), (175), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (185), (187), (194), (201), (202), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (215), (216), (219), (223), (225), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (242), (248), (270), (271), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (343), (344), (349), (397), (408), (410), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436), (1229), (1250), (1251) are inconsistent by % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1252) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) all_9_8 = e0 & op(e2, e2) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (1253) are inconsistent by sub-proof % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1254) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) all_9_11 = e0 & op(e2, e1) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1255) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) all_9_11 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1257) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) all_9_2 = e0 & op(e3, e4) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1258) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) all_9_2 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (24), (27), (28), (39), (45), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (69), (71), (79), (86), (89), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (128), (132), (143), (146), (148), (164), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (178), (184), (187), (202), (207), (209), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (219), (223), (225), (228), (229), (232), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (1259) are inconsistent by sub-proof % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #265. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) all_9_3 = e0 & op(e3, e3) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1260) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) all_9_3 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (175), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (185), (201), (209), (215), (225), (228), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (257), (271), (286), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (343), (344), (349), (366), (397), (408), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410), (1229), (1250), (1261), (1262) are % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (1213), (1239), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246), (1263) are inconsistent by sub-proof #6. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1264) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) all_9_5 = e0 & op(e3, e2) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1265) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) all_9_5 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (1213), (1220), (1229), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) are inconsistent by sub-proof #32. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) (all_9_10 = e0 & op(e3, e1) = e0) | (all_9_17 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1267) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) all_9_10 = e0 & op(e3, e1) = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1268) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) all_9_10 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e3) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1270) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_9_12 = e4 & op(e1, e4) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1271) are inconsistent by sub-proof #74. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) all_9_13 = e4 & op(e1, e3) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1272) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_9_13 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e3) = e2) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (86), (88), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (146), (178), (185), (209), (225), (228), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (291), (397), (408), (410), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250), (1274) are inconsistent by sub-proof #58. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1275) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_9_4 = e2 & op(e4, e2) = e2 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1276) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) op(e4, e2) = e2 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (201), (349), (1277) are inconsistent by % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #261. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e2) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1278) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) all_9_9 = e2 & op(e4, e1) = e2 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1279) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) all_9_9 = e2 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_9_2 = e4 & op(e3, e4) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1282) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) op(e3, e4) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (146), (1283) are inconsistent by % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) all_9_3 = e4 & op(e3, e3) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1284) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) all_9_3 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1286) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) all_9_9 = e4 & op(e4, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1287) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) op(e4, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (218), (331), (1288) are inconsistent by % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1289) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) all_9_10 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1269), (1290) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) e4 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1291) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) all_9_3 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (175), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (185), (201), (209), (215), (225), (228), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (271), (286), (291), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (366), (397), (408), (410), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229), (1250), (1273), (1280), (1292) are % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1293) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) all_9_11 = e4 & op(e2, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1294) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) all_9_11 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1256), (1295) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) e4 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1296) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_9_3 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (25), (27), (28), (34), (39), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (45), (52), (77), (86), (88), (89), (107), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (113), (114), (132), (135), (146), (175), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (185), (201), (209), (215), (225), (228), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (242), (248), (271), (286), (291), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (344), (349), (366), (397), (408), (410), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229), (1250), (1273), (1280), (1297) are % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (89), (102), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (173), (178), (209), (225), (242), (248), % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246), (1298) are inconsistent by sub-proof #34. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1299) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_9_5 = e4 & op(e3, e2) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1300) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) all_9_5 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = e4) % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1302) gives: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) all_9_9 = e4 & op(e4, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1303) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) op(e4, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (218), (331), (1304) are inconsistent by % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #92. % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1305) implies: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) all_9_10 = e4 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1269), (1306) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) e4 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1301), (1307) imply: % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) all_9_5 = e0 % 129.02/17.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (1213), (1220), (1229), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) are inconsistent by sub-proof #32. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1309) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) all_9_11 = e4 & op(e2, e1) = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1310) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) all_9_11 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1256), (1311) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) e4 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1301), (1312) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_9_5 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (19), (22), (23), (24), (27), (28), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (45), (50), (60), (64), (65), (67), (69), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (79), (86), (89), (90), (107), (128), (132), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (148), (152), (164), (167), (170), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (187), (201), (202), (207), (209), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (219), (223), (225), (228), (229), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (242), (248), (253), (308), (349), (397), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408), (410), (432), (1213), (1220), (1229), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) are inconsistent by sub-proof #32. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e4) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (89), (102), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (173), (178), (209), (225), (242), (248), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246), (1314) are inconsistent by sub-proof #12. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e4) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1315) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1269), (1316) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #13. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) all_9_17 = e4 & op(e3, e0) = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1317) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) all_9_17 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1229), (1318) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) e4 = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (1319) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #89. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_9_16 = e2 & op(e4, e0) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (178), (209), (225), (229), (248), (397), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) are inconsistent by sub-proof #88. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (1213), (1239), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246), (1321) are inconsistent by sub-proof #6. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_9_17 = e0 & op(e3, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (220), (297), (1322) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #11. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) all_9_18 = e0 & op(e2, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1323) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) op(e2, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (134), (294), (1324) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e4, e0) = e3) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1325) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) all_9_9 = e3 & op(e4, e1) = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1326) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) all_9_9 = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (19), (22), (23), (24), (27), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (28), (30), (34), (39), (40), (41), (45), (48), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (60), (62), (64), (65), (69), (71), (77), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (86), (88), (89), (90), (93), (98), (102), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (114), (128), (132), (133), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (135), (141), (143), (146), (148), (164), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (173), (175), (176), (178), (184), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (187), (201), (202), (207), (209), (211), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (219), (223), (224), (225), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (232), (234), (242), (248), (271), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (294), (331), (343), (344), (349), (397), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (404), (405), (408), (410), (432), (436), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229), (1239), (1246), (1327) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #16. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_9_16 = e3 & op(e4, e0) = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (146), (178), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (225), (242), (248), (397), (1328) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #80. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) all_9_23 = e3 & op(e0, e1) = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1329) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) all_9_23 = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (234), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291), (403), (404), (405), (408), (1330) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) all_9_22 = e0 & op(e0, e2) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (313), (1331) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1332) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) all_9_19 = e2 & op(e1, e0) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1333) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) all_9_19 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1213), (1334) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) e3 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1335) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) $false % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1336) is inconsistent. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) all_9_24 = e2 & op(e0, e0) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (308), (1337) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) all_9_24 = e3 & op(e0, e0) = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1338) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_9_24 = e3 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1339) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) e3 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1340) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) e3 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (1341) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) $false % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1342) is inconsistent. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_6_17 = e1 | all_6_17 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1343) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) all_6_17 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (338), (1344) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #100. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) all_6_17 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (1345) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) all_4_13 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1346) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) all_4_13 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (1347) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) $false % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1348) is inconsistent. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) | (all_9_18 = e1 & op(e2, e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1349) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) all_9_8 = e1 & op(e2, e2) = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (23), (27), (28), (39), (146), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (209), (225), (242), (248), (1350) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #29. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_18 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e1) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1351) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) all_9_11 = e1 & op(e2, e1) = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1352) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) op(e2, e1) = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (141), (404), (1353) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) all_9_18 = e1 & op(e2, e0) = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) all_9_18 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = e2) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (25), (132), (366), (1356) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_11 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) | (all_9_18 = e2 & op(e2, e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1357) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_9_8 = e2 & op(e2, e2) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (67), (1358) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #306. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_18 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = e2) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1359) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_9_11 = e2 & op(e2, e1) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1360) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) op(e2, e1) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (367), (1361) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #44. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) all_9_18 = e2 & op(e2, e0) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1362) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) all_9_18 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1355), (1363) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) e2 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1364) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) e2 = e1 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (228), (1365) imply: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) $false % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1366) is inconsistent. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) (all_9_23 = e2 & op(e0, e1) = e2) | (all_9_24 = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1367) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_9_23 = e2 & op(e0, e1) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (77), (93), (133), (141), (168), (228), % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (291), (403), (404), (405), (1368) are % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #30. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_9_24 = e2 & op(e0, e0) = e2 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (308), (1369) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | (1370) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_9_18 = e0 & % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_9_19 = e0 & op(e1, e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | = e0)) & ((all_9_20 = e0 & op(e0, e4) = e0) | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1370) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | (1371) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1371) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | (1372) (all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1372) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_9_16 = e0 & op(e4, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (183), (231), (1373) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #112. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1374) all_9_17 = e0 & op(e3, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (220), (297), (1374) are inconsistent by sub-proof % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | #11. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | (1375) (all_9_18 = e0 & op(e2, e0) = e0) | (all_9_19 = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e0) % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_9_18 = e0 & op(e2, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1376) implies: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1377) op(e2, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (134), (294), (1377) are inconsistent by % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1378) all_9_19 = e0 & op(e1, e0) = e0 % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (1378) are inconsistent by sub-proof #55. % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.85 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1379) all_4_21 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | REDUCE: (205), (1379) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1380) ~ (all_4_22 = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | REDUCE: (82), (1379) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1381) ~ (all_4_24 = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | SIMP: (1381) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1382) ~ (all_4_24 = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1383) ~ (op(e1, e0) = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (12), (1383) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1384) ~ (unit = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1385) unit = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (290), (1385) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1386) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1386) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1387) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (155), (258), (271), (288), (1384), (1387) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #5. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1388) all_4_23 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (1388) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1389) ~ (all_4_22 = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (1388) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1390) ~ (all_4_24 = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | SIMP: (1390) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1391) ~ (all_4_24 = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1392) all_6_14 = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (134), (1392) are inconsistent by sub-proof % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | #297. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1393) all_6_14 = e3 | all_6_14 = e2 | all_6_14 = e1 | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | all_6_14 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1393) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1394) all_6_14 = e2 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (1394) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1395) all_4_22 = e2 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1395) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1396) all_4_22 = e2 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (1396) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1397) ~ (all_4_24 = e2) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1397) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1398) ~ (all_4_24 = e2) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1399) all_6_24 = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (1399) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1400) all_4_24 = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1400) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1401) all_4_24 = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (1401) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1402) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1402) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1403) all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | all_6_24 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (277), (1382), (1391), (1398), (1403) are % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #97. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1404) all_6_14 = e3 | all_6_14 = e1 | all_6_14 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1405) all_6_14 = e3 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (134), (1405) are inconsistent by sub-proof % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | #255. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | (1406) all_6_14 = e1 | all_6_14 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1406) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | (1407) all_6_14 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (1407) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | (1408) all_4_22 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1408) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | (1409) all_4_22 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1389), (1409) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | (1410) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1410) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | (1411) all_6_14 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (294), (1411) are inconsistent by sub-proof % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | #152. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1412) all_6_14 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (1412) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1413) all_4_22 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | SIMP: (1413) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1414) all_4_22 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | REDUCE: (112), (1414) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1415) ~ (all_4_24 = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (43), (52), (57), (72), (124), (125), % 129.02/17.86 | | | | | | | | | | | | | | | | | | (155), (192), (258), (271), (288), (290), (1415) % 129.02/17.86 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #4. % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | (1416) all_4_23 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | REDUCE: (73), (1416) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | (1417) ~ (all_4_24 = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (43), (52), (57), (72), (124), (125), % 129.02/17.86 | | | | | | | | | | | | | | | | | (155), (192), (258), (271), (288), (290), (1417) % 129.02/17.86 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #4. % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | (1418) all_6_3 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (1418) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | (1419) all_4_15 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | SIMP: (1419) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | (1420) all_4_15 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | REDUCE: (154), (1420) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | (1421) ~ (all_4_19 = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | SIMP: (1421) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | (1422) ~ (all_4_19 = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | (1423) ~ (op(e0, e3) = e0) % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | PRED_UNIFY: (72), (1423) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | (1424) ~ (unit = e3) % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1425) unit = e4 % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | REDUCE: (290), (1425) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1426) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | CLOSE: (1426) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | (1427) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1428) unit = e2 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | REDUCE: (288), (1428) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1429) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | CLOSE: (1429) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | (1430) unit = e3 | unit = e1 | unit = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (1430) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1431) unit = e3 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | REDUCE: (1424), (1431) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1432) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | CLOSE: (1432) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | (1433) unit = e1 | unit = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1433) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1434) unit = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (1434) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1435) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1435) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1436) unit = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (1436) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | (1437) op(e0, e1) = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1438) ~ (op(e0, e1) = e1) % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1437), (1438) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1439) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1439) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1440) all_6_23 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (1440) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1441) all_4_19 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1441) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1442) all_4_19 = e1 % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1422), (1442) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | (1443) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1443) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | (1444) all_6_21 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (1444) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | (1445) e3 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | SIMP: (1445) implies: % 129.02/17.86 | | | | | | | | | | | | | | | | | (1446) e3 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | REDUCE: (69), (1446) imply: % 129.02/17.86 | | | | | | | | | | | | | | | | | (1447) $false % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | | CLOSE: (1447) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | (1448) all_4_4 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | COMBINE_EQS: (99), (1448) imply: % 129.02/17.86 | | | | | | | | | | | | | | | (1449) e4 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | SIMP: (1449) implies: % 129.02/17.86 | | | | | | | | | | | | | | | (1450) e4 = e0 % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | REDUCE: (17), (1450) imply: % 129.02/17.86 | | | | | | | | | | | | | | | (1451) $false % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | | CLOSE: (1451) is inconsistent. % 129.02/17.86 | | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | (1452) op(e2, e4) = e4 % 129.02/17.86 | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | | REF_CLOSE: (39), (178), (1452) are inconsistent by sub-proof % 129.02/17.86 | | | | | | | | | | | | | | #320. % 129.02/17.86 | | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | | % 129.02/17.86 | | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | | % 129.02/17.86 | | | | | | | | | End of split % 129.02/17.86 | | | | | | | | | % 129.02/17.86 | | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | | % 129.02/17.86 | | | | | | | | | (1453) op(e1, e4) = e4 % 129.02/17.86 | | | | | | | | | % 129.02/17.86 | | | | | | | | | REF_CLOSE: (45), (175), (229), (1453) are inconsistent by % 129.02/17.86 | | | | | | | | | sub-proof #91. % 129.02/17.86 | | | | | | | | | % 129.02/17.86 | | | | | | | | End of split % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | (1454) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | REF_CLOSE: (64), (148), (187), (229), (1454) are inconsistent by % 129.02/17.86 | | | | | | | | sub-proof #276. % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | End of split % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | Case 2: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | (1455) all_9_21 = e4 & op(e0, e3) = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | ALPHA: (1455) implies: % 129.02/17.86 | | | | | | | (1456) op(e0, e3) = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | GROUND_INST: instantiating (89) with all_4_9, e4, e3, e0, % 129.02/17.86 | | | | | | | simplifying with (157), (1456) gives: % 129.02/17.86 | | | | | | | (1457) all_4_9 = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | REDUCE: (180), (1457) imply: % 129.02/17.86 | | | | | | | (1458) $false % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | CLOSE: (1458) is inconsistent. % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | End of split % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | Case 2: % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | (1459) (all_9_22 = e4 & op(e0, e2) = e4) | (all_9_23 = e4 & % 129.02/17.86 | | | | | | op(e0, e1) = e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | BETA: splitting (1459) gives: % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | Case 1: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | (1460) all_9_22 = e4 & op(e0, e2) = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | ALPHA: (1460) implies: % 129.02/17.86 | | | | | | | (1461) op(e0, e2) = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | GROUND_INST: instantiating (89) with all_4_14, e4, e2, e0, % 129.02/17.86 | | | | | | | simplifying with (123), (1461) gives: % 129.02/17.86 | | | | | | | (1462) all_4_14 = e4 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | REDUCE: (56), (1462) imply: % 129.02/17.86 | | | | | | | (1463) $false % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | CLOSE: (1463) is inconsistent. % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | Case 2: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | (1464) (all_9_23 = e4 & op(e0, e1) = e4) | (all_9_24 = e4 & % 129.02/17.86 | | | | | | | op(e0, e0) = e4) % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | BETA: splitting (1464) gives: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | Case 1: % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | (1465) all_9_23 = e4 & op(e0, e1) = e4 % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | REF_CLOSE: (89), (102), (173), (1465) are inconsistent by % 129.02/17.86 | | | | | | | | sub-proof #65. % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | Case 2: % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | (1466) all_9_24 = e4 & op(e0, e0) = e4 % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | ALPHA: (1466) implies: % 129.02/17.86 | | | | | | | | (1467) op(e0, e0) = e4 % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | GROUND_INST: instantiating (89) with all_4_24, e4, e0, e0, % 129.02/17.86 | | | | | | | | simplifying with (76), (1467) gives: % 129.02/17.86 | | | | | | | | (1468) all_4_24 = e4 % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | REDUCE: (206), (1468) imply: % 129.02/17.86 | | | | | | | | (1469) $false % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | | CLOSE: (1469) is inconsistent. % 129.02/17.86 | | | | | | | | % 129.02/17.86 | | | | | | | End of split % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | End of split % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | End of split % 129.02/17.86 | | | | | % 129.02/17.86 | | | | End of split % 129.02/17.86 | | | | % 129.02/17.86 | | | Case 2: % 129.02/17.86 | | | | % 129.02/17.86 | | | | (1470) all_9_20 = e2 & op(e0, e4) = e2 % 129.02/17.86 | | | | % 129.02/17.86 | | | | ALPHA: (1470) implies: % 129.02/17.86 | | | | (1471) all_9_20 = e2 % 129.02/17.86 | | | | % 129.02/17.86 | | | | REF_CLOSE: (16), (17), (23), (27), (28), (39), (45), (146), (175), % 129.02/17.86 | | | | (178), (209), (225), (229), (1471) are inconsistent by % 129.02/17.86 | | | | sub-proof #90. % 129.02/17.86 | | | | % 129.02/17.86 | | | End of split % 129.02/17.86 | | | % 129.02/17.86 | | End of split % 129.02/17.86 | | % 129.02/17.86 | End of split % 129.02/17.86 | % 129.02/17.86 End of proof % 129.02/17.86 % 129.02/17.86 Sub-proof #4 shows that the following formulas are inconsistent: % 129.02/17.86 ---------------------------------------------------------------- % 129.02/17.86 (1) ~ (unit = e2) % 129.02/17.86 (2) all_4_5 = e4 | ~ (op(e4, e3) = e4) % 129.02/17.86 (3) op(e4, unit) = e4 % 129.02/17.86 (4) ~ (all_4_6 = e3) % 129.02/17.86 (5) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 129.02/17.86 (6) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.02/17.86 (7) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 129.02/17.86 (8) ~ (unit = e1) % 129.02/17.86 (9) op(e0, unit) = e0 % 129.02/17.86 (10) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 (11) all_6_24 = all_4_24 % 129.02/17.86 (12) op(e3, unit) = e3 % 129.02/17.86 (13) ~ (unit = e4) % 129.02/17.86 (14) ~ (all_4_24 = e0) % 129.02/17.86 (15) ~ (all_4_5 = all_4_20) % 129.02/17.86 % 129.02/17.86 Begin of proof % 129.02/17.86 | % 129.02/17.86 | SIMP: (14) implies: % 129.02/17.86 | (16) ~ (all_4_24 = e0) % 129.02/17.86 | % 129.02/17.86 | BETA: splitting (7) gives: % 129.02/17.86 | % 129.02/17.86 | Case 1: % 129.02/17.86 | | % 129.02/17.86 | | (17) ~ (op(e4, e0) = e4) % 129.02/17.86 | | % 129.02/17.86 | | PRED_UNIFY: (3), (17) imply: % 129.02/17.86 | | (18) ~ (unit = e0) % 129.02/17.86 | | % 129.02/17.86 | | BETA: splitting (10) gives: % 129.02/17.86 | | % 129.02/17.86 | | Case 1: % 129.02/17.86 | | | % 129.02/17.86 | | | (19) unit = e4 % 129.02/17.86 | | | % 129.02/17.86 | | | REDUCE: (13), (19) imply: % 129.02/17.86 | | | (20) $false % 129.02/17.86 | | | % 129.02/17.86 | | | CLOSE: (20) is inconsistent. % 129.02/17.86 | | | % 129.02/17.86 | | Case 2: % 129.02/17.86 | | | % 129.02/17.86 | | | (21) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 | | | % 129.02/17.86 | | | REF_CLOSE: (1), (4), (6), (8), (12), (18), (21) are inconsistent by % 129.02/17.86 | | | sub-proof #5. % 129.02/17.86 | | | % 129.02/17.86 | | End of split % 129.02/17.86 | | % 129.02/17.86 | Case 2: % 129.02/17.86 | | % 129.02/17.86 | | (22) all_4_20 = e4 % 129.02/17.86 | | % 129.02/17.86 | | REDUCE: (15), (22) imply: % 129.02/17.86 | | (23) ~ (all_4_5 = e4) % 129.02/17.86 | | % 129.02/17.86 | | BETA: splitting (2) gives: % 129.02/17.86 | | % 129.02/17.86 | | Case 1: % 129.02/17.86 | | | % 129.02/17.86 | | | (24) ~ (op(e4, e3) = e4) % 129.02/17.86 | | | % 129.02/17.86 | | | PRED_UNIFY: (3), (24) imply: % 129.02/17.86 | | | (25) ~ (unit = e3) % 129.02/17.86 | | | % 129.02/17.86 | | | BETA: splitting (10) gives: % 129.02/17.86 | | | % 129.02/17.86 | | | Case 1: % 129.02/17.86 | | | | % 129.02/17.86 | | | | (26) unit = e4 % 129.02/17.86 | | | | % 129.02/17.86 | | | | REDUCE: (13), (26) imply: % 129.02/17.86 | | | | (27) $false % 129.02/17.86 | | | | % 129.02/17.86 | | | | CLOSE: (27) is inconsistent. % 129.02/17.86 | | | | % 129.02/17.86 | | | Case 2: % 129.02/17.86 | | | | % 129.02/17.86 | | | | (28) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 | | | | % 129.02/17.86 | | | | BETA: splitting (28) gives: % 129.02/17.86 | | | | % 129.02/17.86 | | | | Case 1: % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | (29) unit = e2 % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | REDUCE: (1), (29) imply: % 129.02/17.86 | | | | | (30) $false % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | CLOSE: (30) is inconsistent. % 129.02/17.86 | | | | | % 129.02/17.86 | | | | Case 2: % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | (31) unit = e3 | unit = e1 | unit = e0 % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | BETA: splitting (31) gives: % 129.02/17.86 | | | | | % 129.02/17.86 | | | | | Case 1: % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | (32) unit = e3 % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | REDUCE: (25), (32) imply: % 129.02/17.86 | | | | | | (33) $false % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | CLOSE: (33) is inconsistent. % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | Case 2: % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | (34) unit = e1 | unit = e0 % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | BETA: splitting (34) gives: % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | | Case 1: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | (35) unit = e1 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | REDUCE: (8), (35) imply: % 129.02/17.86 | | | | | | | (36) $false % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | CLOSE: (36) is inconsistent. % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | Case 2: % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | (37) unit = e0 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | REDUCE: (9), (37) imply: % 129.02/17.86 | | | | | | | (38) op(e0, e0) = e0 % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | | REF_CLOSE: (5), (11), (16), (38) are inconsistent by sub-proof % 129.02/17.86 | | | | | | | #240. % 129.02/17.86 | | | | | | | % 129.02/17.86 | | | | | | End of split % 129.02/17.86 | | | | | | % 129.02/17.86 | | | | | End of split % 129.02/17.86 | | | | | % 129.02/17.86 | | | | End of split % 129.02/17.86 | | | | % 129.02/17.86 | | | End of split % 129.02/17.86 | | | % 129.02/17.86 | | Case 2: % 129.02/17.86 | | | % 129.02/17.86 | | | (39) op(e4, e3) = e4 % 129.02/17.86 | | | % 129.02/17.86 | | | REF_CLOSE: (2), (23), (39) are inconsistent by sub-proof #94. % 129.02/17.86 | | | % 129.02/17.86 | | End of split % 129.02/17.86 | | % 129.02/17.86 | End of split % 129.02/17.86 | % 129.02/17.86 End of proof % 129.02/17.86 % 129.02/17.86 Sub-proof #5 shows that the following formulas are inconsistent: % 129.02/17.86 ---------------------------------------------------------------- % 129.02/17.86 (1) ~ (unit = e2) % 129.02/17.86 (2) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.02/17.86 (3) ~ (all_4_6 = e3) % 129.02/17.86 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.02/17.86 (5) ~ (unit = e1) % 129.02/17.86 (6) op(e3, unit) = e3 % 129.02/17.86 (7) ~ (unit = e0) % 129.02/17.86 % 129.02/17.86 Begin of proof % 129.02/17.86 | % 129.02/17.86 | BETA: splitting (2) gives: % 129.02/17.86 | % 129.02/17.86 | Case 1: % 129.02/17.86 | | % 129.02/17.86 | | (8) unit = e2 % 129.02/17.86 | | % 129.02/17.86 | | REDUCE: (1), (8) imply: % 129.02/17.86 | | (9) $false % 129.02/17.87 | | % 129.02/17.87 | | CLOSE: (9) is inconsistent. % 129.02/17.87 | | % 129.02/17.87 | Case 2: % 129.02/17.87 | | % 129.02/17.87 | | (10) unit = e3 | unit = e1 | unit = e0 % 129.02/17.87 | | % 129.02/17.87 | | BETA: splitting (10) gives: % 129.02/17.87 | | % 129.02/17.87 | | Case 1: % 129.02/17.87 | | | % 129.02/17.87 | | | (11) unit = e3 % 129.02/17.87 | | | % 129.02/17.87 | | | REDUCE: (6), (11) imply: % 129.02/17.87 | | | (12) op(e3, e3) = e3 % 129.02/17.87 | | | % 129.02/17.87 | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #295. % 129.02/17.87 | | | % 129.02/17.87 | | Case 2: % 129.02/17.87 | | | % 129.02/17.87 | | | (13) unit = e1 | unit = e0 % 129.02/17.87 | | | % 129.02/17.87 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #141. % 129.02/17.87 | | | % 129.02/17.87 | | End of split % 129.02/17.87 | | % 129.02/17.87 | End of split % 129.02/17.87 | % 129.02/17.87 End of proof % 129.02/17.87 % 129.02/17.87 Sub-proof #6 shows that the following formulas are inconsistent: % 129.02/17.87 ---------------------------------------------------------------- % 129.02/17.87 (1) all_6_5 = e1 % 129.02/17.87 (2) ~ (e4 = e0) % 129.02/17.87 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.87 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.87 (5) ~ (e4 = e2) % 129.02/17.87 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.87 (7) all_9_12 = e2 % 129.02/17.87 (8) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.02/17.87 (all_9_19 = e4 & op(e1, e0) = e4) % 129.02/17.87 (9) ~ (e4 = e1) % 129.02/17.87 (10) all_9_15 = e3 % 129.02/17.87 (11) ~ (e4 = e3) % 129.02/17.87 (12) all_9_14 = e0 % 129.02/17.87 (13) all_9_19 = e3 % 129.02/17.87 (14) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.02/17.87 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.02/17.87 (all_9_20 = e4 & op(e0, e4) = e4) % 129.02/17.87 (15) all_4_0 = e0 % 129.02/17.87 (16) all_9_20 = e4 % 129.02/17.87 % 129.02/17.87 Begin of proof % 129.02/17.87 | % 129.02/17.87 | BETA: splitting (8) gives: % 129.02/17.87 | % 129.02/17.87 | Case 1: % 129.02/17.87 | | % 129.02/17.87 | | (17) all_9_14 = e4 & op(e1, e2) = e4 % 129.02/17.87 | | % 129.02/17.87 | | REF_CLOSE: (2), (12), (17) are inconsistent by sub-proof #19. % 129.02/17.87 | | % 129.02/17.87 | Case 2: % 129.02/17.87 | | % 129.02/17.87 | | (18) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) = % 129.02/17.87 | | e4) % 129.02/17.87 | | % 129.02/17.87 | | BETA: splitting (18) gives: % 129.02/17.87 | | % 129.02/17.87 | | Case 1: % 129.02/17.87 | | | % 129.02/17.87 | | | (19) all_9_15 = e4 & op(e1, e1) = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | ALPHA: (19) implies: % 129.02/17.87 | | | (20) all_9_15 = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | COMBINE_EQS: (10), (20) imply: % 129.02/17.87 | | | (21) e4 = e3 % 129.02/17.87 | | | % 129.02/17.87 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (14), (15), (16), % 129.02/17.87 | | | (21) are inconsistent by sub-proof #89. % 129.02/17.87 | | | % 129.02/17.87 | | Case 2: % 129.02/17.87 | | | % 129.02/17.87 | | | (22) all_9_19 = e4 & op(e1, e0) = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | ALPHA: (22) implies: % 129.02/17.87 | | | (23) all_9_19 = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | COMBINE_EQS: (13), (23) imply: % 129.02/17.87 | | | (24) e4 = e3 % 129.02/17.87 | | | % 129.02/17.87 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (14), (15), (16), % 129.02/17.87 | | | (24) are inconsistent by sub-proof #89. % 129.02/17.87 | | | % 129.02/17.87 | | End of split % 129.02/17.87 | | % 129.02/17.87 | End of split % 129.02/17.87 | % 129.02/17.87 End of proof % 129.02/17.87 % 129.02/17.87 Sub-proof #7 shows that the following formulas are inconsistent: % 129.02/17.87 ---------------------------------------------------------------- % 129.02/17.87 (1) all_9_24 = e2 & op(e0, e0) = e2 % 129.02/17.87 (2) all_9_24 = e0 % 129.02/17.87 (3) ~ (e2 = e0) % 129.02/17.87 % 129.02/17.87 Begin of proof % 129.02/17.87 | % 129.02/17.87 | ALPHA: (1) implies: % 129.02/17.87 | (4) all_9_24 = e2 % 129.02/17.87 | % 129.02/17.87 | COMBINE_EQS: (2), (4) imply: % 129.02/17.87 | (5) e2 = e0 % 129.02/17.87 | % 129.02/17.87 | SIMP: (5) implies: % 129.02/17.87 | (6) e2 = e0 % 129.02/17.87 | % 129.02/17.87 | REDUCE: (3), (6) imply: % 129.02/17.87 | (7) $false % 129.02/17.87 | % 129.02/17.87 | CLOSE: (7) is inconsistent. % 129.02/17.87 | % 129.02/17.87 End of proof % 129.02/17.87 % 129.02/17.87 Sub-proof #8 shows that the following formulas are inconsistent: % 129.02/17.87 ---------------------------------------------------------------- % 129.02/17.87 (1) ~ (all_4_16 = e3) % 129.02/17.87 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 129.02/17.87 (3) all_6_5 = e1 % 129.02/17.87 (4) ~ (e4 = e0) % 129.02/17.87 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.02/17.87 (6) all_6_10 = e3 % 129.02/17.87 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.87 (8) ~ (all_4_3 = all_4_4) % 129.02/17.87 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.87 (10) ~ (e4 = e2) % 129.02/17.87 (11) ~ (all_4_6 = e3) % 129.02/17.87 (12) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.02/17.87 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.87 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.87 (15) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.02/17.87 (16) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.02/17.87 (17) all_9_17 = e3 % 129.02/17.87 (18) ~ (all_4_13 = e2) % 129.02/17.87 (19) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.02/17.87 (20) all_9_24 = e0 % 129.02/17.87 (21) ~ (all_4_3 = e3) % 129.02/17.87 (22) all_6_20 = all_4_4 % 129.02/17.87 (23) e4 = e2 | ~ (op(e2, e2) = e2) % 129.02/17.87 (24) all_9_18 = e2 % 129.02/17.87 (25) ~ (e3 = e0) % 129.02/17.87 (26) ~ (all_4_11 = e3) % 129.02/17.87 (27) all_9_10 = e2 % 129.02/17.87 (28) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.87 (29) all_6_8 = all_4_16 % 129.02/17.87 (30) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.02/17.87 = e0 % 129.02/17.87 (31) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 129.02/17.87 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 129.02/17.87 (all_9_17 = e2 & op(e3, e0) = e2) % 129.02/17.87 (32) ~ (e2 = e0) % 129.02/17.87 (33) all_9_22 = e2 % 129.02/17.87 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.02/17.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.02/17.87 (35) ~ (all_4_4 = e3) % 129.02/17.87 (36) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 129.02/17.87 (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.02/17.87 (all_9_17 = e4 & op(e3, e0) = e4) % 129.02/17.87 (37) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.02/17.87 (38) all_9_12 = e2 % 129.02/17.87 (39) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.02/17.87 (40) ~ (e1 = e0) % 129.02/17.87 (41) all_6_7 = all_4_11 % 129.02/17.87 (42) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.02/17.87 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.02/17.87 (all_9_20 = e3 & op(e0, e4) = e3) % 129.02/17.87 (43) ~ (e3 = e2) % 129.02/17.87 (44) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.02/17.87 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.02/17.87 (all_9_17 = e3 & op(e3, e0) = e3) % 129.02/17.87 (45) op(e0, e4) = all_4_4 % 129.02/17.87 (46) ~ (e4 = e1) % 129.02/17.87 (47) ~ (all_4_3 = e0) % 129.02/17.87 (48) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.02/17.87 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.02/17.87 (all_9_22 = e2 & op(e0, e2) = e2) % 129.02/17.87 (49) all_9_5 = e0 % 129.02/17.87 (50) ~ (e3 = e1) % 129.02/17.87 (51) op(e3, e4) = e1 % 129.02/17.87 (52) op(e1, e4) = all_4_3 % 129.02/17.87 (53) all_4_11 = e0 % 129.02/17.87 (54) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) | % 129.02/17.87 (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = e1) | % 129.02/17.87 (all_9_24 = e1 & op(e0, e0) = e1) % 129.02/17.87 (55) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.02/17.87 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.02/17.87 (all_9_20 = e2 & op(e0, e4) = e2) % 129.02/17.87 (56) ~ (all_4_3 = e4) % 129.02/17.87 (57) ~ (e4 = e3) % 129.02/17.87 (58) ~ (all_4_4 = e0) % 129.02/17.87 (59) ~ (all_4_3 = e1) % 129.02/17.87 (60) all_9_19 = e2 % 129.02/17.87 (61) all_6_2 = all_4_10 % 129.02/17.87 (62) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.02/17.87 (63) op(e2, e4) = e3 % 129.02/17.87 (64) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.02/17.87 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.02/17.87 (all_9_20 = e4 & op(e0, e4) = e4) % 129.02/17.87 (65) all_9_2 = e1 % 129.02/17.87 (66) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.02/17.87 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.02/17.87 (all_9_20 = e1 & op(e0, e4) = e1) % 129.02/17.87 (67) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.02/17.87 = e0 % 129.02/17.87 (68) ~ (all_4_4 = e1) % 129.02/17.87 (69) ~ (all_4_10 = e2) % 129.02/17.87 (70) all_4_0 = e0 % 129.02/17.87 (71) all_9_20 = e4 % 129.02/17.87 (72) ~ (e2 = e1) % 129.02/17.87 (73) all_6_15 = all_4_3 % 129.02/17.87 (74) op(e4, e4) = e0 % 129.02/17.87 (75) all_9_16 = e4 % 129.02/17.87 % 129.02/17.87 Begin of proof % 129.02/17.87 | % 129.02/17.87 | BETA: splitting (36) gives: % 129.02/17.87 | % 129.02/17.87 | Case 1: % 129.02/17.87 | | % 129.02/17.87 | | (76) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) % 129.02/17.87 | | % 129.02/17.87 | | BETA: splitting (76) gives: % 129.02/17.87 | | % 129.02/17.87 | | Case 1: % 129.02/17.87 | | | % 129.02/17.87 | | | (77) all_9_2 = e4 & op(e3, e4) = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | ALPHA: (77) implies: % 129.02/17.87 | | | (78) op(e3, e4) = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | REF_CLOSE: (3), (7), (46), (78) are inconsistent by sub-proof #316. % 129.02/17.87 | | | % 129.02/17.87 | | Case 2: % 129.02/17.87 | | | % 129.02/17.87 | | | (79) all_9_3 = e4 & op(e3, e3) = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | ALPHA: (79) implies: % 129.02/17.87 | | | (80) all_9_3 = e4 % 129.02/17.87 | | | % 129.02/17.87 | | | BETA: splitting (54) gives: % 129.02/17.87 | | | % 129.02/17.87 | | | Case 1: % 129.02/17.87 | | | | % 129.02/17.87 | | | | (81) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) % 129.02/17.87 | | | | = e1) % 129.02/17.87 | | | | % 129.02/17.87 | | | | BETA: splitting (81) gives: % 129.02/17.87 | | | | % 129.02/17.87 | | | | Case 1: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | (82) all_9_16 = e1 & op(e4, e0) = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | ALPHA: (82) implies: % 129.02/17.87 | | | | | (83) all_9_16 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | COMBINE_EQS: (75), (83) imply: % 129.02/17.87 | | | | | (84) e4 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | COMBINE_EQS: (80), (84) imply: % 129.02/17.87 | | | | | (85) all_9_3 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | BETA: splitting (36) gives: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | Case 1: % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | BETA: splitting (76) gives: % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | Case 1: % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | (86) all_9_2 = e4 & op(e3, e4) = e4 % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | ALPHA: (86) implies: % 129.02/17.87 | | | | | | | (87) op(e3, e4) = e4 % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | REF_CLOSE: (3), (7), (46), (87) are inconsistent by sub-proof % 129.02/17.87 | | | | | | | #316. % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | Case 2: % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | COMBINE_EQS: (71), (84) imply: % 129.02/17.87 | | | | | | | (88) all_9_20 = e1 % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (38), (46), (57), (64), % 129.02/17.87 | | | | | | | (70), (88) are inconsistent by sub-proof #286. % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | End of split % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | Case 2: % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | (89) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, % 129.02/17.87 | | | | | | e1) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | BETA: splitting (89) gives: % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | Case 1: % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | (90) all_9_5 = e4 & op(e3, e2) = e4 % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | REF_CLOSE: (4), (49), (90) are inconsistent by sub-proof #231. % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | Case 2: % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | (91) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 & % 129.02/17.87 | | | | | | | op(e3, e0) = e4) % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | BETA: splitting (91) gives: % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | | Case 1: % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | (92) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | ALPHA: (92) implies: % 129.02/17.87 | | | | | | | | (93) all_9_10 = e4 % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | BETA: splitting (31) gives: % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | Case 1: % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | (94) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & % 129.02/17.87 | | | | | | | | | op(e3, e3) = e2) % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | BETA: splitting (94) gives: % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | Case 1: % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | (95) all_9_2 = e2 & op(e3, e4) = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | ALPHA: (95) implies: % 129.02/17.87 | | | | | | | | | | (96) op(e3, e4) = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | REF_CLOSE: (34), (51), (72), (96) are inconsistent by % 129.02/17.87 | | | | | | | | | | sub-proof #313. % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | Case 2: % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | (97) all_9_3 = e2 & op(e3, e3) = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | ALPHA: (97) implies: % 129.02/17.87 | | | | | | | | | | (98) all_9_3 = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | COMBINE_EQS: (85), (98) imply: % 129.02/17.87 | | | | | | | | | | (99) e2 = e1 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | COMBINE_EQS: (33), (99) imply: % 129.02/17.87 | | | | | | | | | | (100) all_9_22 = e1 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | REF_CLOSE: (10), (15), (18), (23), (32), (37), (48), (49), % 129.02/17.87 | | | | | | | | | | (61), (69), (72), (100) are inconsistent by % 129.02/17.87 | | | | | | | | | | sub-proof #73. % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | End of split % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | Case 2: % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | (101) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & % 129.02/17.87 | | | | | | | | | op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) = % 129.02/17.87 | | | | | | | | | e2) % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | BETA: splitting (101) gives: % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | | Case 1: % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | (102) all_9_5 = e2 & op(e3, e2) = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | ALPHA: (102) implies: % 129.02/17.87 | | | | | | | | | | (103) op(e3, e2) = e2 % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | REF_CLOSE: (2), (32), (53), (103) are inconsistent by % 129.02/17.87 | | | | | | | | | | sub-proof #39. % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | Case 2: % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | (104) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 % 129.02/17.87 | | | | | | | | | | & op(e3, e0) = e2) % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | BETA: splitting (104) gives: % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | Case 1: % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | | (105) all_9_10 = e2 & op(e3, e1) = e2 % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (14), (27), (46), % 129.02/17.87 | | | | | | | | | | | (56), (57), (64), (70), (71), (73), (93) are % 129.02/17.87 | | | | | | | | | | | inconsistent by sub-proof #35. % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | Case 2: % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | | (106) all_9_17 = e2 & op(e3, e0) = e2 % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | | ALPHA: (106) implies: % 129.02/17.87 | | | | | | | | | | | (107) all_9_17 = e2 % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | | REF_CLOSE: (1), (11), (12), (16), (26), (29), (39), (41), % 129.02/17.87 | | | | | | | | | | | (43), (44), (50), (65), (107) are inconsistent by % 129.02/17.87 | | | | | | | | | | | sub-proof #86. % 129.02/17.87 | | | | | | | | | | | % 129.02/17.87 | | | | | | | | | | End of split % 129.02/17.87 | | | | | | | | | | % 129.02/17.87 | | | | | | | | | End of split % 129.02/17.87 | | | | | | | | | % 129.02/17.87 | | | | | | | | End of split % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | Case 2: % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | (108) all_9_17 = e4 & op(e3, e0) = e4 % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (17), (38), (46), % 129.02/17.87 | | | | | | | | (57), (64), (70), (71), (108) are inconsistent by % 129.02/17.87 | | | | | | | | sub-proof #9. % 129.02/17.87 | | | | | | | | % 129.02/17.87 | | | | | | | End of split % 129.02/17.87 | | | | | | | % 129.02/17.87 | | | | | | End of split % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | End of split % 129.02/17.87 | | | | | % 129.02/17.87 | | | | Case 2: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | (109) all_9_17 = e1 & op(e3, e0) = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | ALPHA: (109) implies: % 129.02/17.87 | | | | | (110) all_9_17 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | COMBINE_EQS: (17), (110) imply: % 129.02/17.87 | | | | | (111) e3 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | SIMP: (111) implies: % 129.02/17.87 | | | | | (112) e3 = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | REDUCE: (50), (112) imply: % 129.02/17.87 | | | | | (113) $false % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | CLOSE: (113) is inconsistent. % 129.02/17.87 | | | | | % 129.02/17.87 | | | | End of split % 129.02/17.87 | | | | % 129.02/17.87 | | | Case 2: % 129.02/17.87 | | | | % 129.02/17.87 | | | | (114) (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) % 129.02/17.87 | | | | = e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 129.02/17.87 | | | | % 129.02/17.87 | | | | BETA: splitting (114) gives: % 129.02/17.87 | | | | % 129.02/17.87 | | | | Case 1: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | (115) all_9_18 = e1 & op(e2, e0) = e1 % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | REF_CLOSE: (10), (15), (18), (23), (24), (32), (33), (37), (48), (49), % 129.02/17.87 | | | | | (61), (69), (72), (115) are inconsistent by sub-proof #62. % 129.02/17.87 | | | | | % 129.02/17.87 | | | | Case 2: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | (116) (all_9_19 = e1 & op(e1, e0) = e1) | (all_9_24 = e1 & op(e0, % 129.02/17.87 | | | | | e0) = e1) % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | BETA: splitting (116) gives: % 129.02/17.87 | | | | | % 129.02/17.87 | | | | | Case 1: % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | (117) all_9_19 = e1 & op(e1, e0) = e1 % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | ALPHA: (117) implies: % 129.02/17.87 | | | | | | (118) all_9_19 = e1 % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | COMBINE_EQS: (60), (118) imply: % 129.02/17.87 | | | | | | (119) e2 = e1 % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | SIMP: (119) implies: % 129.02/17.87 | | | | | | (120) e2 = e1 % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | COMBINE_EQS: (33), (120) imply: % 129.02/17.87 | | | | | | (121) all_9_22 = e1 % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | | REF_CLOSE: (10), (15), (18), (23), (32), (37), (48), (49), (61), % 129.02/17.87 | | | | | | (69), (72), (121) are inconsistent by sub-proof #73. % 129.02/17.87 | | | | | | % 129.02/17.87 | | | | | Case 2: % 129.02/17.87 | | | | | | % 129.02/17.88 | | | | | | (122) all_9_24 = e1 & op(e0, e0) = e1 % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (13), (14), (19), (20), % 129.02/17.88 | | | | | | (21), (22), (25), (28), (30), (32), (34), (35), (40), % 129.02/17.88 | | | | | | (42), (43), (45), (46), (47), (50), (52), (55), (57), % 129.02/17.88 | | | | | | (58), (59), (62), (63), (64), (65), (66), (67), (68), % 129.02/17.88 | | | | | | (70), (72), (73), (74), (122) are inconsistent by % 129.02/17.88 | | | | | | sub-proof #61. % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | End of split % 129.02/17.88 | | | | | % 129.02/17.88 | | | | End of split % 129.02/17.88 | | | | % 129.02/17.88 | | | End of split % 129.02/17.88 | | | % 129.02/17.88 | | End of split % 129.02/17.88 | | % 129.02/17.88 | Case 2: % 129.02/17.88 | | % 129.02/17.88 | | (123) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = % 129.02/17.88 | | e4) | (all_9_17 = e4 & op(e3, e0) = e4) % 129.02/17.88 | | % 129.02/17.88 | | BETA: splitting (123) gives: % 129.02/17.88 | | % 129.02/17.88 | | Case 1: % 129.02/17.88 | | | % 129.02/17.88 | | | (124) all_9_5 = e4 & op(e3, e2) = e4 % 129.02/17.88 | | | % 129.02/17.88 | | | REF_CLOSE: (4), (49), (124) are inconsistent by sub-proof #231. % 129.02/17.88 | | | % 129.02/17.88 | | Case 2: % 129.02/17.88 | | | % 129.02/17.88 | | | (125) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) = % 129.02/17.88 | | | e4) % 129.02/17.88 | | | % 129.02/17.88 | | | BETA: splitting (125) gives: % 129.02/17.88 | | | % 129.02/17.88 | | | Case 1: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (126) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.88 | | | | % 129.02/17.88 | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (14), (27), (46), (56), (57), % 129.02/17.88 | | | | (64), (70), (71), (73), (126) are inconsistent by sub-proof % 129.02/17.88 | | | | #68. % 129.02/17.88 | | | | % 129.02/17.88 | | | Case 2: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (127) all_9_17 = e4 & op(e3, e0) = e4 % 129.02/17.88 | | | | % 129.02/17.88 | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (17), (38), (46), (57), (64), % 129.02/17.88 | | | | (70), (71), (127) are inconsistent by sub-proof #9. % 129.02/17.88 | | | | % 129.02/17.88 | | | End of split % 129.02/17.88 | | | % 129.02/17.88 | | End of split % 129.02/17.88 | | % 129.02/17.88 | End of split % 129.02/17.88 | % 129.02/17.88 End of proof % 129.02/17.88 % 129.02/17.88 Sub-proof #9 shows that the following formulas are inconsistent: % 129.02/17.88 ---------------------------------------------------------------- % 129.02/17.88 (1) all_6_5 = e1 % 129.02/17.88 (2) ~ (e4 = e0) % 129.02/17.88 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.88 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.88 (5) ~ (e4 = e2) % 129.02/17.88 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.88 (7) all_9_17 = e3 % 129.02/17.88 (8) all_9_12 = e2 % 129.02/17.88 (9) ~ (e4 = e1) % 129.02/17.88 (10) ~ (e4 = e3) % 129.02/17.88 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.02/17.88 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.02/17.88 (all_9_20 = e4 & op(e0, e4) = e4) % 129.02/17.88 (12) all_4_0 = e0 % 129.02/17.88 (13) all_9_17 = e4 & op(e3, e0) = e4 % 129.02/17.88 (14) all_9_20 = e4 % 129.02/17.88 % 129.02/17.88 Begin of proof % 129.02/17.88 | % 129.02/17.88 | ALPHA: (13) implies: % 129.02/17.88 | (15) all_9_17 = e4 % 129.02/17.88 | % 129.02/17.88 | COMBINE_EQS: (7), (15) imply: % 129.02/17.88 | (16) e4 = e3 % 129.02/17.88 | % 129.02/17.88 | COMBINE_EQS: (14), (16) imply: % 129.02/17.88 | (17) all_9_20 = e3 % 129.02/17.88 | % 129.02/17.88 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (17) are % 129.02/17.88 | inconsistent by sub-proof #202. % 129.02/17.88 | % 129.02/17.88 End of proof % 129.02/17.88 % 129.02/17.88 Sub-proof #10 shows that the following formulas are inconsistent: % 129.02/17.88 ---------------------------------------------------------------- % 129.02/17.88 (1) all_9_8 = e4 % 129.02/17.88 (2) ~ (op(e4, e1) = e1) % 129.02/17.88 (3) ~ (all_4_16 = e3) % 129.02/17.88 (4) all_6_5 = e1 % 129.02/17.88 (5) ~ (e4 = e0) % 129.02/17.88 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.02/17.88 (7) all_6_10 = e3 % 129.02/17.88 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.88 (9) ~ (all_4_3 = all_4_4) % 129.02/17.88 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.88 (11) ~ (e4 = e2) % 129.02/17.88 (12) (all_9_5 = e0 & op(e3, e2) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) | % 129.02/17.88 (all_9_17 = e0 & op(e3, e0) = e0) % 129.02/17.88 (13) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 129.02/17.88 (14) all_6_17 = all_4_13 % 129.02/17.88 (15) ~ (all_4_6 = e3) % 129.02/17.88 (16) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.02/17.88 (17) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.88 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.02/17.88 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.02/17.88 (all_9_16 = e2 & op(e4, e0) = e2) % 129.02/17.88 (19) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 129.02/17.88 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 129.02/17.88 (all_9_18 = e0 & op(e2, e0) = e0) % 129.02/17.88 (20) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.88 (21) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.02/17.88 (22) ~ (all_4_22 = e0) % 129.02/17.88 (23) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.02/17.88 (24) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.02/17.88 (25) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) | % 129.02/17.88 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) | % 129.02/17.88 (all_9_22 = e1 & op(e0, e2) = e1) % 129.02/17.88 (26) all_9_17 = e3 % 129.02/17.88 (27) ~ (all_4_13 = e2) % 129.02/17.88 (28) ~ (all_4_18 = e1) % 129.02/17.88 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.02/17.88 (30) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 129.02/17.88 (31) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.02/17.88 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.02/17.88 (all_9_23 = e1 & op(e0, e1) = e1) % 129.02/17.88 (32) ~ (all_4_3 = e3) % 129.02/17.88 (33) all_6_20 = all_4_4 % 129.02/17.88 (34) e4 = e2 | ~ (op(e2, e2) = e2) % 129.02/17.88 (35) ~ (all_4_13 = e1) % 129.02/17.88 (36) ~ (e3 = e0) % 129.02/17.88 (37) ~ (all_4_11 = e3) % 129.02/17.88 (38) ~ (all_4_5 = e3) % 129.02/17.88 (39) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.88 (40) ~ (all_4_17 = e1) % 129.02/17.88 (41) all_6_8 = all_4_16 % 129.02/17.88 (42) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.02/17.88 = e0 % 129.02/17.88 (43) ~ (e2 = e0) % 129.02/17.88 (44) all_9_22 = e2 % 129.02/17.88 (45) all_9_0 = e0 % 129.02/17.88 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.02/17.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.02/17.88 (47) ~ (all_4_4 = e3) % 129.02/17.88 (48) ~ (all_4_17 = e3) % 129.02/17.88 (49) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.02/17.88 (50) all_9_7 = e1 % 129.02/17.88 (51) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.02/17.88 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.02/17.88 (all_9_22 = e3 & op(e0, e2) = e3) % 129.02/17.88 (52) ~ (all_4_19 = e4) % 129.02/17.88 (53) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.02/17.88 (54) all_9_12 = e2 % 129.02/17.88 (55) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.02/17.88 (56) all_9_6 = e3 % 129.02/17.88 (57) ~ (e1 = e0) % 129.02/17.88 (58) all_6_7 = all_4_11 % 129.02/17.88 (59) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.02/17.88 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.02/17.88 (all_9_20 = e3 & op(e0, e4) = e3) % 129.02/17.88 (60) ~ (e3 = e2) % 129.02/17.88 (61) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.02/17.88 (62) all_6_14 = all_4_22 % 129.02/17.88 (63) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.02/17.88 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.02/17.88 (all_9_17 = e3 & op(e3, e0) = e3) % 129.02/17.88 (64) all_6_13 = all_4_17 % 129.02/17.88 (65) op(e0, e4) = all_4_4 % 129.02/17.88 (66) ~ (e4 = e1) % 129.02/17.88 (67) ~ (all_4_3 = e0) % 129.02/17.88 (68) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.02/17.88 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.02/17.88 (all_9_22 = e2 & op(e0, e2) = e2) % 129.02/17.88 (69) ~ (all_4_15 = e4) % 129.02/17.88 (70) ~ (e3 = e1) % 129.02/17.88 (71) op(e1, e4) = all_4_3 % 129.02/17.88 (72) all_6_18 = all_4_18 % 129.02/17.88 (73) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.02/17.88 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.02/17.88 (all_9_20 = e2 & op(e0, e4) = e2) % 129.02/17.88 (74) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 129.02/17.88 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 129.02/17.88 (all_9_16 = e3 & op(e4, e0) = e3) % 129.02/17.88 (75) ~ (all_4_21 = e0) % 129.02/17.88 (76) op(e0, e1) = all_4_19 % 129.02/17.88 (77) ~ (all_4_3 = e4) % 129.02/17.88 (78) op(e2, e2) = e4 % 129.02/17.88 (79) ~ (all_4_16 = e1) % 129.02/17.88 (80) ~ (e4 = e3) % 129.02/17.88 (81) all_9_14 = e0 % 129.02/17.88 (82) ~ (all_4_4 = e0) % 129.02/17.88 (83) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.02/17.88 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.02/17.88 (all_9_16 = e1 & op(e4, e0) = e1) % 129.02/17.88 (84) ~ (all_4_3 = e1) % 129.02/17.88 (85) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.02/17.88 (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 129.02/17.88 (all_9_23 = e3 & op(e0, e1) = e3) % 129.02/17.88 (86) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 129.02/17.88 (87) all_6_2 = all_4_10 % 129.02/17.88 (88) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.02/17.88 (89) op(e2, e4) = e3 % 129.02/17.88 (90) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.02/17.88 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.02/17.88 (all_9_20 = e4 & op(e0, e4) = e4) % 129.02/17.88 (91) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.02/17.88 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.02/17.88 (all_9_23 = e4 & op(e0, e1) = e4) % 129.02/17.88 (92) op(e2, e1) = all_4_17 % 129.02/17.88 (93) all_9_2 = e1 % 129.02/17.88 (94) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.02/17.88 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.02/17.88 (all_9_20 = e1 & op(e0, e4) = e1) % 129.02/17.88 (95) all_6_3 = all_4_15 % 129.02/17.88 (96) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.02/17.88 = e0 % 129.02/17.88 (97) all_4_21 = e0 | ~ (op(e3, e0) = e0) % 129.02/17.88 (98) ~ (all_4_4 = e1) % 129.02/17.88 (99) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 129.02/17.88 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 129.02/17.88 (all_9_23 = e2 & op(e0, e1) = e2) % 129.02/17.88 (100) ~ (all_4_10 = e2) % 129.02/17.88 (101) all_4_0 = e0 % 129.02/17.88 (102) all_9_20 = e4 % 129.02/17.88 (103) ~ (e2 = e1) % 129.02/17.88 (104) all_6_15 = all_4_3 % 129.02/17.88 (105) op(e4, e4) = e0 % 129.02/17.88 (106) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.02/17.88 (107) all_9_16 = e4 % 129.02/17.88 % 129.02/17.88 Begin of proof % 129.02/17.88 | % 129.02/17.88 | BETA: splitting (12) gives: % 129.02/17.88 | % 129.02/17.88 | Case 1: % 129.02/17.88 | | % 129.02/17.88 | | (108) all_9_5 = e0 & op(e3, e2) = e0 % 129.02/17.88 | | % 129.02/17.88 | | ALPHA: (108) implies: % 129.02/17.88 | | (109) all_9_5 = e0 % 129.02/17.88 | | % 129.02/17.88 | | BETA: splitting (85) gives: % 129.02/17.88 | | % 129.02/17.88 | | Case 1: % 129.02/17.88 | | | % 129.02/17.88 | | | (110) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = % 129.02/17.88 | | | e3) % 129.02/17.88 | | | % 129.02/17.88 | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (15), (16), (17), (18), % 129.02/17.88 | | | (20), (24), (26), (36), (37), (41), (43), (44), (45), (46), % 129.02/17.88 | | | (51), (53), (54), (55), (57), (58), (60), (63), (66), (70), % 129.02/17.88 | | | (77), (78), (80), (81), (83), (87), (90), (93), (100), (101), % 129.02/17.88 | | | (102), (103), (104), (105), (107), (110) are inconsistent by % 129.02/17.88 | | | sub-proof #24. % 129.02/17.88 | | | % 129.02/17.88 | | Case 2: % 129.02/17.88 | | | % 129.02/17.88 | | | (111) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = % 129.02/17.88 | | | e3) | (all_9_23 = e3 & op(e0, e1) = e3) % 129.02/17.88 | | | % 129.02/17.88 | | | BETA: splitting (111) gives: % 129.02/17.88 | | | % 129.02/17.88 | | | Case 1: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (112) all_9_11 = e3 & op(e2, e1) = e3 % 129.02/17.88 | | | | % 129.02/17.88 | | | | ALPHA: (112) implies: % 129.02/17.88 | | | | (113) op(e2, e1) = e3 % 129.02/17.88 | | | | % 129.02/17.88 | | | | REF_CLOSE: (46), (48), (92), (113) are inconsistent by sub-proof #103. % 129.02/17.88 | | | | % 129.02/17.88 | | | Case 2: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (114) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) % 129.02/17.88 | | | | = e3) % 129.02/17.88 | | | | % 129.02/17.88 | | | | BETA: splitting (114) gives: % 129.02/17.88 | | | | % 129.02/17.88 | | | | Case 1: % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | (115) all_9_15 = e3 & op(e1, e1) = e3 % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | ALPHA: (115) implies: % 129.02/17.88 | | | | | (116) all_9_15 = e3 % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | BETA: splitting (74) gives: % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | Case 1: % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | (117) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, % 129.02/17.88 | | | | | | e3) = e3) % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | REF_CLOSE: (36), (38), (45), (86), (117) are inconsistent by % 129.02/17.88 | | | | | | sub-proof #139. % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | Case 2: % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | (118) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, % 129.02/17.88 | | | | | | e1) = e3) | (all_9_16 = e3 & op(e4, e0) = e3) % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | BETA: splitting (118) gives: % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | | Case 1: % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | | (119) all_9_4 = e3 & op(e4, e2) = e3 % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (14), % 129.02/17.88 | | | | | | | (17), (20), (23), (25), (27), (29), (30), (32), (33), % 129.02/17.88 | | | | | | | (34), (35), (36), (39), (42), (43), (46), (47), (53), % 129.02/17.88 | | | | | | | (54), (57), (59), (60), (65), (66), (67), (68), (70), % 129.02/17.88 | | | | | | | (71), (73), (80), (82), (84), (87), (88), (89), (90), % 129.02/17.88 | | | | | | | (93), (94), (96), (98), (100), (101), (102), (103), % 129.02/17.88 | | | | | | | (104), (105), (109), (119) are inconsistent by % 129.02/17.88 | | | | | | | sub-proof #28. % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | Case 2: % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | | (120) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & % 129.02/17.88 | | | | | | | op(e4, e0) = e3) % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), % 129.02/17.88 | | | | | | | (11), (13), (15), (16), (17), (18), (19), (20), (21), % 129.02/17.88 | | | | | | | (22), (24), (26), (28), (29), (31), (32), (33), (36), % 129.02/17.88 | | | | | | | (37), (39), (40), (41), (42), (43), (44), (45), (46), % 129.02/17.88 | | | | | | | (47), (49), (50), (51), (52), (53), (54), (55), (56), % 129.02/17.88 | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), % 129.02/17.88 | | | | | | | (66), (67), (69), (70), (71), (72), (73), (76), (77), % 129.02/17.88 | | | | | | | (78), (79), (80), (81), (82), (83), (84), (87), (88), % 129.02/17.88 | | | | | | | (89), (90), (91), (93), (94), (95), (96), (98), (99), % 129.02/17.88 | | | | | | | (100), (101), (102), (103), (104), (105), (106), (107), % 129.02/17.88 | | | | | | | (116), (120) are inconsistent by sub-proof #15. % 129.02/17.88 | | | | | | | % 129.02/17.88 | | | | | | End of split % 129.02/17.88 | | | | | | % 129.02/17.88 | | | | | End of split % 129.02/17.88 | | | | | % 129.02/17.88 | | | | Case 2: % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | (121) all_9_23 = e3 & op(e0, e1) = e3 % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | ALPHA: (121) implies: % 129.02/17.88 | | | | | (122) all_9_23 = e3 % 129.02/17.88 | | | | | % 129.02/17.88 | | | | | REF_CLOSE: (2), (28), (31), (40), (41), (49), (61), (64), (70), (72), % 129.02/17.88 | | | | | (79), (106), (122) are inconsistent by sub-proof #26. % 129.02/17.88 | | | | | % 129.02/17.88 | | | | End of split % 129.02/17.88 | | | | % 129.02/17.88 | | | End of split % 129.02/17.88 | | | % 129.02/17.88 | | End of split % 129.02/17.88 | | % 129.02/17.88 | Case 2: % 129.02/17.88 | | % 129.02/17.88 | | (123) (all_9_10 = e0 & op(e3, e1) = e0) | (all_9_17 = e0 & op(e3, e0) = % 129.02/17.88 | | e0) % 129.02/17.88 | | % 129.02/17.88 | | BETA: splitting (123) gives: % 129.02/17.88 | | % 129.02/17.88 | | Case 1: % 129.02/17.88 | | | % 129.02/17.88 | | | (124) all_9_10 = e0 & op(e3, e1) = e0 % 129.02/17.88 | | | % 129.02/17.88 | | | ALPHA: (124) implies: % 129.02/17.88 | | | (125) all_9_10 = e0 % 129.02/17.88 | | | % 129.02/17.88 | | | BETA: splitting (85) gives: % 129.02/17.88 | | | % 129.02/17.88 | | | Case 1: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (126) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) % 129.02/17.88 | | | | = e3) % 129.02/17.88 | | | | % 129.02/17.88 | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (15), (16), (17), (18), % 129.02/17.88 | | | | (20), (24), (26), (36), (37), (41), (43), (44), (45), (46), % 129.02/17.88 | | | | (51), (53), (54), (55), (57), (58), (60), (63), (66), (70), % 129.02/17.88 | | | | (77), (78), (80), (81), (83), (87), (90), (93), (100), (101), % 129.02/17.88 | | | | (102), (103), (104), (105), (107), (126) are inconsistent by % 129.02/17.88 | | | | sub-proof #24. % 129.02/17.88 | | | | % 129.02/17.88 | | | Case 2: % 129.02/17.88 | | | | % 129.02/17.88 | | | | (127) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) % 129.02/17.88 | | | | = e3) | (all_9_23 = e3 & op(e0, e1) = e3) % 129.02/17.89 | | | | % 129.02/17.89 | | | | BETA: splitting (127) gives: % 129.02/17.89 | | | | % 129.02/17.89 | | | | Case 1: % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | (128) all_9_11 = e3 & op(e2, e1) = e3 % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | ALPHA: (128) implies: % 129.02/17.89 | | | | | (129) op(e2, e1) = e3 % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | REF_CLOSE: (46), (48), (92), (129) are inconsistent by sub-proof #103. % 129.02/17.89 | | | | | % 129.02/17.89 | | | | Case 2: % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | (130) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, % 129.02/17.89 | | | | | e1) = e3) % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | BETA: splitting (130) gives: % 129.02/17.89 | | | | | % 129.02/17.89 | | | | | Case 1: % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | (131) all_9_15 = e3 & op(e1, e1) = e3 % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | ALPHA: (131) implies: % 129.02/17.89 | | | | | | (132) all_9_15 = e3 % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | BETA: splitting (19) gives: % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | Case 1: % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | (133) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, % 129.02/17.89 | | | | | | | e3) = e0) % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | BETA: splitting (133) gives: % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | (134) all_9_6 = e0 & op(e2, e4) = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | ALPHA: (134) implies: % 129.02/17.89 | | | | | | | | (135) all_9_6 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | REF_CLOSE: (36), (56), (135) are inconsistent by sub-proof #14. % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | (136) all_9_7 = e0 & op(e2, e3) = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | ALPHA: (136) implies: % 129.02/17.89 | | | | | | | | (137) all_9_7 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | COMBINE_EQS: (50), (137) imply: % 129.02/17.89 | | | | | | | | (138) e1 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (17), (20), (29), % 129.02/17.89 | | | | | | | | (32), (33), (36), (39), (42), (43), (46), (47), (57), % 129.02/17.89 | | | | | | | | (59), (60), (65), (66), (67), (70), (71), (73), (80), % 129.02/17.89 | | | | | | | | (82), (84), (88), (89), (90), (93), (94), (96), (98), % 129.02/17.89 | | | | | | | | (101), (103), (104), (105), (138) are inconsistent by % 129.02/17.89 | | | | | | | | sub-proof #264. % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | End of split % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | Case 2: % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | (139) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & % 129.02/17.89 | | | | | | | op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) = e0) % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | BETA: splitting (139) gives: % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | (140) all_9_8 = e0 & op(e2, e2) = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | ALPHA: (140) implies: % 129.02/17.89 | | | | | | | | (141) all_9_8 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | COMBINE_EQS: (1), (141) imply: % 129.02/17.89 | | | | | | | | (142) e4 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | SIMP: (142) implies: % 129.02/17.89 | | | | | | | | (143) e4 = e0 % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | REDUCE: (5), (143) imply: % 129.02/17.89 | | | | | | | | (144) $false % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | CLOSE: (144) is inconsistent. % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | (145) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 & % 129.02/17.89 | | | | | | | | op(e2, e0) = e0) % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | BETA: splitting (145) gives: % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | (146) all_9_11 = e0 & op(e2, e1) = e0 % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | ALPHA: (146) implies: % 129.02/17.89 | | | | | | | | | (147) all_9_11 = e0 % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | BETA: splitting (91) gives: % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | (148) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & % 129.02/17.89 | | | | | | | | | | op(e3, e1) = e4) % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | BETA: splitting (148) gives: % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | (149) all_9_9 = e4 & op(e4, e1) = e4 % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | ALPHA: (149) implies: % 129.02/17.89 | | | | | | | | | | | (150) op(e4, e1) = e4 % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | REF_CLOSE: (21), (69), (95), (150) are inconsistent by % 129.02/17.89 | | | | | | | | | | | sub-proof #92. % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | (151) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | REF_CLOSE: (5), (125), (151) are inconsistent by sub-proof % 129.02/17.89 | | | | | | | | | | | #13. % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | End of split % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | (152) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 % 129.02/17.89 | | | | | | | | | | & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) % 129.02/17.89 | | | | | | | | | | = e4) % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | BETA: splitting (152) gives: % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | Case 1: % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | (153) all_9_11 = e4 & op(e2, e1) = e4 % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | REF_CLOSE: (5), (147), (153) are inconsistent by sub-proof % 129.02/17.89 | | | | | | | | | | | #66. % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | (154) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 % 129.02/17.89 | | | | | | | | | | | & op(e0, e1) = e4) % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (17), (46), (52), (54), % 129.02/17.89 | | | | | | | | | | | (66), (76), (80), (90), (101), (102), (132), (154) % 129.02/17.89 | | | | | | | | | | | are inconsistent by sub-proof #12. % 129.02/17.89 | | | | | | | | | | | % 129.02/17.89 | | | | | | | | | | End of split % 129.02/17.89 | | | | | | | | | | % 129.02/17.89 | | | | | | | | | End of split % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | Case 2: % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | (155) all_9_18 = e0 & op(e2, e0) = e0 % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | ALPHA: (155) implies: % 129.02/17.89 | | | | | | | | | (156) op(e2, e0) = e0 % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | | REF_CLOSE: (13), (22), (62), (156) are inconsistent by % 129.02/17.89 | | | | | | | | | sub-proof #150. % 129.02/17.89 | | | | | | | | | % 129.02/17.89 | | | | | | | | End of split % 129.02/17.89 | | | | | | | | % 129.02/17.89 | | | | | | | End of split % 129.02/17.89 | | | | | | | % 129.02/17.89 | | | | | | End of split % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | Case 2: % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | (157) all_9_23 = e3 & op(e0, e1) = e3 % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | ALPHA: (157) implies: % 129.02/17.89 | | | | | | (158) all_9_23 = e3 % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | | REF_CLOSE: (2), (28), (31), (40), (41), (49), (61), (64), (70), % 129.02/17.89 | | | | | | (72), (79), (106), (158) are inconsistent by sub-proof % 129.02/17.89 | | | | | | #26. % 129.02/17.89 | | | | | | % 129.02/17.89 | | | | | End of split % 129.02/17.89 | | | | | % 129.02/17.89 | | | | End of split % 129.02/17.89 | | | | % 129.02/17.89 | | | End of split % 129.02/17.89 | | | % 129.02/17.89 | | Case 2: % 129.02/17.89 | | | % 129.02/17.89 | | | (159) all_9_17 = e0 & op(e3, e0) = e0 % 129.02/17.89 | | | % 129.02/17.89 | | | REF_CLOSE: (75), (97), (159) are inconsistent by sub-proof #11. % 129.02/17.89 | | | % 129.02/17.89 | | End of split % 129.02/17.89 | | % 129.02/17.89 | End of split % 129.02/17.89 | % 129.02/17.89 End of proof % 129.02/17.89 % 129.02/17.89 Sub-proof #11 shows that the following formulas are inconsistent: % 129.02/17.89 ---------------------------------------------------------------- % 129.02/17.89 (1) all_9_17 = e0 & op(e3, e0) = e0 % 129.02/17.89 (2) all_4_21 = e0 | ~ (op(e3, e0) = e0) % 129.02/17.89 (3) ~ (all_4_21 = e0) % 129.02/17.89 % 129.02/17.89 Begin of proof % 129.02/17.89 | % 129.02/17.89 | ALPHA: (1) implies: % 129.02/17.89 | (4) op(e3, e0) = e0 % 129.02/17.89 | % 129.02/17.89 | BETA: splitting (2) gives: % 129.02/17.89 | % 129.02/17.89 | Case 1: % 129.02/17.89 | | % 129.02/17.89 | | (5) ~ (op(e3, e0) = e0) % 129.02/17.89 | | % 129.02/17.89 | | PRED_UNIFY: (4), (5) imply: % 129.02/17.89 | | (6) $false % 129.02/17.89 | | % 129.02/17.89 | | CLOSE: (6) is inconsistent. % 129.02/17.89 | | % 129.02/17.89 | Case 2: % 129.02/17.89 | | % 129.02/17.89 | | (7) all_4_21 = e0 % 129.02/17.89 | | % 129.02/17.89 | | REDUCE: (3), (7) imply: % 129.02/17.89 | | (8) $false % 129.02/17.89 | | % 129.02/17.89 | | CLOSE: (8) is inconsistent. % 129.02/17.89 | | % 129.02/17.89 | End of split % 129.02/17.89 | % 129.02/17.89 End of proof % 129.02/17.89 % 129.02/17.89 Sub-proof #12 shows that the following formulas are inconsistent: % 129.02/17.89 ---------------------------------------------------------------- % 129.02/17.89 (1) all_6_5 = e1 % 129.02/17.89 (2) ~ (e4 = e0) % 129.02/17.89 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.89 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.89 (5) ~ (e4 = e2) % 129.02/17.89 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.89 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.02/17.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.02/17.89 (8) ~ (all_4_19 = e4) % 129.02/17.89 (9) all_9_12 = e2 % 129.02/17.89 (10) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) % 129.02/17.89 (11) ~ (e4 = e1) % 129.02/17.89 (12) all_9_15 = e3 % 129.02/17.89 (13) op(e0, e1) = all_4_19 % 129.02/17.89 (14) ~ (e4 = e3) % 129.02/17.89 (15) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.02/17.89 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.02/17.89 (all_9_20 = e4 & op(e0, e4) = e4) % 129.02/17.89 (16) all_4_0 = e0 % 129.02/17.89 (17) all_9_20 = e4 % 129.02/17.89 % 129.02/17.89 Begin of proof % 129.02/17.89 | % 129.02/17.89 | BETA: splitting (10) gives: % 129.02/17.89 | % 129.02/17.89 | Case 1: % 129.02/17.89 | | % 129.02/17.89 | | (18) all_9_15 = e4 & op(e1, e1) = e4 % 129.02/17.89 | | % 129.02/17.89 | | ALPHA: (18) implies: % 129.02/17.89 | | (19) all_9_15 = e4 % 129.02/17.89 | | % 129.02/17.89 | | COMBINE_EQS: (12), (19) imply: % 129.02/17.89 | | (20) e4 = e3 % 129.02/17.89 | | % 129.02/17.89 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (14), (15), (16), (17), % 129.02/17.89 | | (20) are inconsistent by sub-proof #89. % 129.02/17.89 | | % 129.02/17.89 | Case 2: % 129.02/17.89 | | % 129.02/17.89 | | (21) all_9_23 = e4 & op(e0, e1) = e4 % 129.02/17.89 | | % 129.02/17.89 | | REF_CLOSE: (7), (8), (13), (21) are inconsistent by sub-proof #65. % 129.02/17.89 | | % 129.02/17.89 | End of split % 129.02/17.89 | % 129.02/17.89 End of proof % 129.02/17.89 % 129.02/17.89 Sub-proof #13 shows that the following formulas are inconsistent: % 129.02/17.89 ---------------------------------------------------------------- % 129.02/17.89 (1) all_9_10 = e4 & op(e3, e1) = e4 % 129.02/17.89 (2) all_9_10 = e0 % 129.02/17.89 (3) ~ (e4 = e0) % 129.02/17.89 % 129.02/17.89 Begin of proof % 129.02/17.89 | % 129.02/17.89 | ALPHA: (1) implies: % 129.02/17.89 | (4) all_9_10 = e4 % 129.02/17.89 | % 129.02/17.89 | COMBINE_EQS: (2), (4) imply: % 129.02/17.89 | (5) e4 = e0 % 129.02/17.89 | % 129.02/17.89 | REDUCE: (3), (5) imply: % 129.02/17.89 | (6) $false % 129.02/17.89 | % 129.02/17.89 | CLOSE: (6) is inconsistent. % 129.02/17.89 | % 129.02/17.89 End of proof % 129.02/17.89 % 129.02/17.89 Sub-proof #14 shows that the following formulas are inconsistent: % 129.02/17.89 ---------------------------------------------------------------- % 129.02/17.89 (1) all_9_6 = e3 % 129.02/17.89 (2) all_9_6 = e0 % 129.02/17.89 (3) ~ (e3 = e0) % 129.02/17.89 % 129.02/17.89 Begin of proof % 129.02/17.89 | % 129.02/17.89 | COMBINE_EQS: (1), (2) imply: % 129.02/17.89 | (4) e3 = e0 % 129.02/17.89 | % 129.02/17.89 | SIMP: (4) implies: % 129.02/17.89 | (5) e3 = e0 % 129.02/17.89 | % 129.02/17.89 | REDUCE: (3), (5) imply: % 129.02/17.89 | (6) $false % 129.02/17.89 | % 129.02/17.89 | CLOSE: (6) is inconsistent. % 129.02/17.89 | % 129.02/17.89 End of proof % 129.02/17.89 % 129.02/17.89 Sub-proof #15 shows that the following formulas are inconsistent: % 129.02/17.89 ---------------------------------------------------------------- % 129.02/17.89 (1) all_9_8 = e4 % 129.02/17.89 (2) ~ (op(e4, e1) = e1) % 129.02/17.89 (3) ~ (all_4_16 = e3) % 129.02/17.89 (4) all_6_5 = e1 % 129.02/17.89 (5) ~ (e4 = e0) % 129.02/17.89 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.02/17.89 (7) all_6_10 = e3 % 129.02/17.89 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.02/17.89 (9) ~ (all_4_3 = all_4_4) % 129.02/17.89 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.02/17.89 (11) ~ (e4 = e2) % 129.02/17.89 (12) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 129.02/17.89 (13) ~ (all_4_6 = e3) % 129.02/17.89 (14) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.02/17.89 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 129.02/17.89 (16) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.02/17.89 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.02/17.89 (all_9_16 = e2 & op(e4, e0) = e2) % 129.02/17.89 (17) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 129.02/17.89 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 129.02/17.89 (all_9_18 = e0 & op(e2, e0) = e0) % 129.02/17.89 (18) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.89 (19) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.02/17.89 (20) ~ (all_4_22 = e0) % 129.02/17.89 (21) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.02/17.89 (22) all_9_17 = e3 % 129.02/17.89 (23) ~ (all_4_18 = e1) % 129.02/17.89 (24) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.02/17.89 (25) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.02/17.89 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.02/17.89 (all_9_23 = e1 & op(e0, e1) = e1) % 129.02/17.89 (26) ~ (all_4_3 = e3) % 129.02/17.89 (27) all_6_20 = all_4_4 % 129.02/17.89 (28) ~ (e3 = e0) % 129.02/17.89 (29) ~ (all_4_11 = e3) % 129.02/17.89 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.02/17.89 (31) ~ (all_4_17 = e1) % 129.02/17.89 (32) all_6_8 = all_4_16 % 129.02/17.89 (33) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.02/17.89 = e0 % 129.02/17.89 (34) ~ (e2 = e0) % 129.02/17.89 (35) all_9_22 = e2 % 129.02/17.89 (36) all_9_0 = e0 % 129.02/17.89 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.02/17.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.02/17.89 (38) ~ (all_4_4 = e3) % 129.02/17.89 (39) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.02/17.89 (40) all_9_7 = e1 % 129.02/17.89 (41) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.02/17.89 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.02/17.89 (all_9_22 = e3 & op(e0, e2) = e3) % 129.02/17.89 (42) ~ (all_4_19 = e4) % 129.02/17.89 (43) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.02/17.89 (44) all_9_12 = e2 % 129.02/17.89 (45) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.02/17.89 (46) all_9_6 = e3 % 129.02/17.89 (47) ~ (e1 = e0) % 129.02/17.89 (48) all_6_7 = all_4_11 % 129.02/17.89 (49) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.02/17.89 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.02/17.89 (all_9_20 = e3 & op(e0, e4) = e3) % 129.02/17.89 (50) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = e3) % 129.02/17.89 (51) ~ (e3 = e2) % 129.02/17.89 (52) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.02/17.89 (53) all_6_14 = all_4_22 % 129.02/17.89 (54) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.02/17.89 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.02/17.89 (all_9_17 = e3 & op(e3, e0) = e3) % 129.02/17.89 (55) all_6_13 = all_4_17 % 129.02/17.89 (56) op(e0, e4) = all_4_4 % 129.02/17.89 (57) ~ (e4 = e1) % 129.02/17.89 (58) ~ (all_4_3 = e0) % 129.02/17.89 (59) ~ (all_4_15 = e4) % 129.02/17.89 (60) all_9_15 = e3 % 129.02/17.89 (61) ~ (e3 = e1) % 129.02/17.89 (62) op(e1, e4) = all_4_3 % 129.02/17.89 (63) all_6_18 = all_4_18 % 129.02/17.89 (64) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.02/17.89 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.02/17.89 (all_9_20 = e2 & op(e0, e4) = e2) % 129.02/17.89 (65) op(e0, e1) = all_4_19 % 129.02/17.89 (66) ~ (all_4_3 = e4) % 129.02/17.89 (67) op(e2, e2) = e4 % 129.02/17.89 (68) ~ (all_4_16 = e1) % 129.02/17.89 (69) ~ (e4 = e3) % 129.02/17.89 (70) all_9_14 = e0 % 129.02/17.89 (71) ~ (all_4_4 = e0) % 129.02/17.89 (72) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.02/17.89 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.02/17.89 (all_9_16 = e1 & op(e4, e0) = e1) % 129.02/17.89 (73) ~ (all_4_3 = e1) % 129.02/17.89 (74) all_6_2 = all_4_10 % 129.27/17.89 (75) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.89 (76) op(e2, e4) = e3 % 129.27/17.89 (77) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.89 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.89 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.89 (78) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.89 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.89 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.89 (79) all_9_2 = e1 % 129.27/17.89 (80) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.89 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.89 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.89 (81) all_6_3 = all_4_15 % 129.27/17.89 (82) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.89 = e0 % 129.27/17.89 (83) ~ (all_4_4 = e1) % 129.27/17.89 (84) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 129.27/17.89 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 129.27/17.89 (all_9_23 = e2 & op(e0, e1) = e2) % 129.27/17.89 (85) ~ (all_4_10 = e2) % 129.27/17.89 (86) all_4_0 = e0 % 129.27/17.89 (87) all_9_20 = e4 % 129.27/17.89 (88) ~ (e2 = e1) % 129.27/17.89 (89) all_6_15 = all_4_3 % 129.27/17.89 (90) op(e4, e4) = e0 % 129.27/17.89 (91) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.89 (92) all_9_16 = e4 % 129.27/17.89 % 129.27/17.89 Begin of proof % 129.27/17.89 | % 129.27/17.89 | BETA: splitting (50) gives: % 129.27/17.89 | % 129.27/17.89 | Case 1: % 129.27/17.89 | | % 129.27/17.89 | | (93) all_9_9 = e3 & op(e4, e1) = e3 % 129.27/17.89 | | % 129.27/17.89 | | ALPHA: (93) implies: % 129.27/17.89 | | (94) all_9_9 = e3 % 129.27/17.89 | | % 129.27/17.89 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.27/17.89 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 129.27/17.89 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 129.27/17.89 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 129.27/17.89 | | (46), (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), % 129.27/17.89 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 129.27/17.89 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 129.27/17.89 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), % 129.27/17.89 | | (91), (92), (94) are inconsistent by sub-proof #16. % 129.27/17.89 | | % 129.27/17.90 | Case 2: % 129.27/17.90 | | % 129.27/17.90 | | (95) all_9_16 = e3 & op(e4, e0) = e3 % 129.27/17.90 | | % 129.27/17.90 | | REF_CLOSE: (4), (5), (8), (10), (11), (15), (44), (57), (69), (77), (86), % 129.27/17.90 | | (87), (92), (95) are inconsistent by sub-proof #80. % 129.27/17.90 | | % 129.27/17.90 | End of split % 129.27/17.90 | % 129.27/17.90 End of proof % 129.27/17.90 % 129.27/17.90 Sub-proof #16 shows that the following formulas are inconsistent: % 129.27/17.90 ---------------------------------------------------------------- % 129.27/17.90 (1) all_9_8 = e4 % 129.27/17.90 (2) ~ (op(e4, e1) = e1) % 129.27/17.90 (3) ~ (all_4_16 = e3) % 129.27/17.90 (4) all_6_5 = e1 % 129.27/17.90 (5) ~ (e4 = e0) % 129.27/17.90 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.27/17.90 (7) all_6_10 = e3 % 129.27/17.90 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.90 (9) ~ (all_4_3 = all_4_4) % 129.27/17.90 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.90 (11) ~ (e4 = e2) % 129.27/17.90 (12) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 129.27/17.90 (13) ~ (all_4_6 = e3) % 129.27/17.90 (14) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.90 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.90 (16) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.90 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.90 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.90 (17) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 129.27/17.90 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 129.27/17.90 (all_9_18 = e0 & op(e2, e0) = e0) % 129.27/17.90 (18) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.90 (19) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.27/17.90 (20) ~ (all_4_22 = e0) % 129.27/17.90 (21) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.90 (22) all_9_17 = e3 % 129.27/17.90 (23) ~ (all_4_18 = e1) % 129.27/17.90 (24) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.27/17.90 (25) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.27/17.90 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.27/17.90 (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.90 (26) ~ (all_4_3 = e3) % 129.27/17.90 (27) all_6_20 = all_4_4 % 129.27/17.90 (28) ~ (e3 = e0) % 129.27/17.90 (29) ~ (all_4_11 = e3) % 129.27/17.90 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.90 (31) ~ (all_4_17 = e1) % 129.27/17.90 (32) all_6_8 = all_4_16 % 129.27/17.90 (33) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.27/17.90 = e0 % 129.27/17.90 (34) ~ (e2 = e0) % 129.27/17.90 (35) all_9_22 = e2 % 129.27/17.90 (36) all_9_0 = e0 % 129.27/17.90 (37) all_9_9 = e3 % 129.27/17.90 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.90 (39) ~ (all_4_4 = e3) % 129.27/17.90 (40) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.90 (41) all_9_7 = e1 % 129.27/17.90 (42) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.27/17.90 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.27/17.90 (all_9_22 = e3 & op(e0, e2) = e3) % 129.27/17.90 (43) ~ (all_4_19 = e4) % 129.27/17.90 (44) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.90 (45) all_9_12 = e2 % 129.27/17.90 (46) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.90 (47) all_9_6 = e3 % 129.27/17.90 (48) ~ (e1 = e0) % 129.27/17.90 (49) all_6_7 = all_4_11 % 129.27/17.90 (50) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.27/17.90 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.27/17.90 (all_9_20 = e3 & op(e0, e4) = e3) % 129.27/17.90 (51) ~ (e3 = e2) % 129.27/17.90 (52) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.27/17.90 (53) all_6_14 = all_4_22 % 129.27/17.90 (54) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.90 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.90 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.90 (55) all_6_13 = all_4_17 % 129.27/17.90 (56) op(e0, e4) = all_4_4 % 129.27/17.90 (57) ~ (e4 = e1) % 129.27/17.90 (58) ~ (all_4_3 = e0) % 129.27/17.90 (59) ~ (all_4_15 = e4) % 129.27/17.90 (60) all_9_15 = e3 % 129.27/17.90 (61) ~ (e3 = e1) % 129.27/17.90 (62) op(e1, e4) = all_4_3 % 129.27/17.90 (63) all_6_18 = all_4_18 % 129.27/17.90 (64) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.27/17.90 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.27/17.90 (all_9_20 = e2 & op(e0, e4) = e2) % 129.27/17.90 (65) op(e0, e1) = all_4_19 % 129.27/17.90 (66) ~ (all_4_3 = e4) % 129.27/17.90 (67) op(e2, e2) = e4 % 129.27/17.90 (68) ~ (all_4_16 = e1) % 129.27/17.90 (69) ~ (e4 = e3) % 129.27/17.90 (70) all_9_14 = e0 % 129.27/17.90 (71) ~ (all_4_4 = e0) % 129.27/17.90 (72) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.90 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.90 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.90 (73) ~ (all_4_3 = e1) % 129.27/17.90 (74) all_6_2 = all_4_10 % 129.27/17.90 (75) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.90 (76) op(e2, e4) = e3 % 129.27/17.90 (77) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.90 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.90 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.90 (78) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.90 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.90 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.90 (79) all_9_2 = e1 % 129.27/17.90 (80) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.90 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.90 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.90 (81) all_6_3 = all_4_15 % 129.27/17.90 (82) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.90 = e0 % 129.27/17.90 (83) ~ (all_4_4 = e1) % 129.27/17.90 (84) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 129.27/17.90 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 129.27/17.90 (all_9_23 = e2 & op(e0, e1) = e2) % 129.27/17.90 (85) ~ (all_4_10 = e2) % 129.27/17.90 (86) all_4_0 = e0 % 129.27/17.90 (87) all_9_20 = e4 % 129.27/17.90 (88) ~ (e2 = e1) % 129.27/17.90 (89) all_6_15 = all_4_3 % 129.27/17.90 (90) op(e4, e4) = e0 % 129.27/17.90 (91) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.90 (92) all_9_16 = e4 % 129.27/17.90 % 129.27/17.90 Begin of proof % 129.27/17.90 | % 129.27/17.90 | BETA: splitting (17) gives: % 129.27/17.90 | % 129.27/17.90 | Case 1: % 129.27/17.90 | | % 129.27/17.90 | | (93) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) % 129.27/17.90 | | % 129.27/17.90 | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (15), (18), (24), (26), (27), % 129.27/17.90 | | (28), (30), (33), (34), (38), (39), (41), (47), (48), (50), (51), % 129.27/17.90 | | (56), (57), (58), (61), (62), (64), (69), (71), (73), (75), (76), % 129.27/17.90 | | (77), (79), (80), (82), (83), (86), (88), (89), (90), (93) are % 129.27/17.90 | | inconsistent by sub-proof #78. % 129.27/17.90 | | % 129.27/17.90 | Case 2: % 129.27/17.90 | | % 129.27/17.90 | | (94) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) % 129.27/17.90 | | | (all_9_18 = e0 & op(e2, e0) = e0) % 129.27/17.90 | | % 129.27/17.90 | | BETA: splitting (94) gives: % 129.27/17.90 | | % 129.27/17.90 | | Case 1: % 129.27/17.90 | | | % 129.27/17.90 | | | (95) all_9_8 = e0 & op(e2, e2) = e0 % 129.27/17.90 | | | % 129.27/17.90 | | | REF_CLOSE: (1), (5), (95) are inconsistent by sub-proof #151. % 129.27/17.90 | | | % 129.27/17.90 | | Case 2: % 129.27/17.90 | | | % 129.27/17.90 | | | (96) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) = % 129.27/17.90 | | | e0) % 129.27/17.90 | | | % 129.27/17.90 | | | BETA: splitting (96) gives: % 129.27/17.90 | | | % 129.27/17.90 | | | Case 1: % 129.27/17.90 | | | | % 129.27/17.90 | | | | (97) all_9_11 = e0 & op(e2, e1) = e0 % 129.27/17.90 | | | | % 129.27/17.90 | | | | ALPHA: (97) implies: % 129.27/17.90 | | | | (98) all_9_11 = e0 % 129.27/17.90 | | | | % 129.27/17.90 | | | | BETA: splitting (84) gives: % 129.27/17.90 | | | | % 129.27/17.90 | | | | Case 1: % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | (99) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) % 129.27/17.90 | | | | | = e2) % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | BETA: splitting (99) gives: % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | Case 1: % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | (100) all_9_9 = e2 & op(e4, e1) = e2 % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | REF_CLOSE: (3), (13), (14), (21), (22), (29), (32), (37), (46), % 129.27/17.90 | | | | | | (49), (51), (54), (61), (79), (100) are inconsistent by % 129.27/17.90 | | | | | | sub-proof #77. % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | Case 2: % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | (101) all_9_10 = e2 & op(e3, e1) = e2 % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | ALPHA: (101) implies: % 129.27/17.90 | | | | | | (102) all_9_10 = e2 % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | BETA: splitting (16) gives: % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | Case 1: % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | | (103) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, % 129.27/17.90 | | | | | | | e3) = e2) % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | | BETA: splitting (103) gives: % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | | Case 1: % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | | (104) all_9_0 = e2 & op(e4, e4) = e2 % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | | REF_CLOSE: (34), (36), (104) are inconsistent by sub-proof #314. % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | Case 2: % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | | (105) all_9_1 = e2 & op(e4, e3) = e2 % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | | ALPHA: (105) implies: % 129.27/17.90 | | | | | | | | (106) all_9_1 = e2 % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (13), (14), % 129.27/17.90 | | | | | | | | (15), (18), (19), (21), (22), (29), (32), (35), (38), % 129.27/17.90 | | | | | | | | (42), (43), (45), (46), (48), (49), (51), (54), (57), % 129.27/17.90 | | | | | | | | (59), (60), (61), (65), (66), (67), (69), (70), (72), % 129.27/17.90 | | | | | | | | (77), (78), (79), (81), (86), (87), (88), (89), (90), % 129.27/17.90 | | | | | | | | (92), (98), (102), (106) are inconsistent by % 129.27/17.90 | | | | | | | | sub-proof #18. % 129.27/17.90 | | | | | | | | % 129.27/17.90 | | | | | | | End of split % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | Case 2: % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | | (107) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, % 129.27/17.90 | | | | | | | e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | | REF_CLOSE: (3), (4), (5), (8), (10), (11), (13), (14), (15), (18), % 129.27/17.90 | | | | | | | (21), (22), (29), (32), (37), (44), (46), (49), (51), % 129.27/17.90 | | | | | | | (54), (57), (61), (66), (69), (74), (77), (79), (85), % 129.27/17.90 | | | | | | | (86), (87), (89), (92), (107) are inconsistent by % 129.27/17.90 | | | | | | | sub-proof #81. % 129.27/17.90 | | | | | | | % 129.27/17.90 | | | | | | End of split % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | End of split % 129.27/17.90 | | | | | % 129.27/17.90 | | | | Case 2: % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | (108) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, % 129.27/17.90 | | | | | e1) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | BETA: splitting (108) gives: % 129.27/17.90 | | | | | % 129.27/17.90 | | | | | Case 1: % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | (109) all_9_11 = e2 & op(e2, e1) = e2 % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | REF_CLOSE: (34), (98), (109) are inconsistent by sub-proof #117. % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | Case 2: % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | (110) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, % 129.27/17.90 | | | | | | e1) = e2) % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | | REF_CLOSE: (2), (3), (13), (14), (21), (22), (23), (25), (29), (31), % 129.27/17.90 | | | | | | (32), (40), (46), (49), (51), (52), (54), (55), (60), % 129.27/17.90 | | | | | | (61), (63), (68), (79), (88), (91), (110) are % 129.27/17.90 | | | | | | inconsistent by sub-proof #27. % 129.27/17.90 | | | | | | % 129.27/17.90 | | | | | End of split % 129.27/17.90 | | | | | % 129.27/17.90 | | | | End of split % 129.27/17.90 | | | | % 129.27/17.90 | | | Case 2: % 129.27/17.90 | | | | % 129.27/17.90 | | | | (111) all_9_18 = e0 & op(e2, e0) = e0 % 129.27/17.90 | | | | % 129.27/17.90 | | | | ALPHA: (111) implies: % 129.27/17.90 | | | | (112) op(e2, e0) = e0 % 129.27/17.90 | | | | % 129.27/17.90 | | | | REF_CLOSE: (12), (20), (53), (112) are inconsistent by sub-proof #150. % 129.27/17.90 | | | | % 129.27/17.90 | | | End of split % 129.27/17.90 | | | % 129.27/17.90 | | End of split % 129.27/17.90 | | % 129.27/17.90 | End of split % 129.27/17.90 | % 129.27/17.90 End of proof % 129.27/17.90 % 129.27/17.90 Sub-proof #17 shows that the following formulas are inconsistent: % 129.27/17.90 ---------------------------------------------------------------- % 129.27/17.90 (1) ~ (op(e4, e1) = e1) % 129.27/17.90 (2) ~ (all_4_16 = e3) % 129.27/17.90 (3) all_6_5 = e1 % 129.27/17.90 (4) ~ (e4 = e0) % 129.27/17.90 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.90 (6) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 129.27/17.90 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.90 (8) ~ (e4 = e2) % 129.27/17.90 (9) ~ (all_4_6 = e3) % 129.27/17.90 (10) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.90 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.90 (12) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.90 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.90 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.90 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.90 (14) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.90 (15) all_9_17 = e3 % 129.27/17.90 (16) all_9_4 = e3 % 129.27/17.90 (17) ~ (all_4_11 = e3) % 129.27/17.90 (18) all_6_8 = all_4_16 % 129.27/17.90 (19) ~ (e2 = e0) % 129.27/17.90 (20) all_9_0 = e0 % 129.27/17.90 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.90 (22) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.90 (23) all_9_12 = e2 % 129.27/17.90 (24) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.90 (25) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 129.27/17.90 (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 129.27/17.90 (all_9_21 = e2 & op(e0, e3) = e2) % 129.27/17.90 (26) ~ (e1 = e0) % 129.27/17.90 (27) all_6_7 = all_4_11 % 129.27/17.90 (28) all_9_3 = e0 % 129.27/17.90 (29) ~ (e3 = e2) % 129.27/17.90 (30) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.90 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.90 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.90 (31) ~ (e4 = e1) % 129.27/17.90 (32) all_9_15 = e3 % 129.27/17.90 (33) ~ (e3 = e1) % 129.27/17.90 (34) all_9_21 = e3 % 129.27/17.90 (35) ~ (op(e1, e4) = e4) % 129.27/17.90 (36) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 129.27/17.90 (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.90 (all_9_19 = e4 & op(e1, e0) = e4) % 129.27/17.90 (37) ~ (all_4_3 = e4) % 129.27/17.90 (38) ~ (e4 = e3) % 129.27/17.90 (39) ~ (all_4_7 = e2) % 129.27/17.90 (40) all_9_14 = e0 % 129.27/17.90 (41) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.90 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.90 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.90 (42) all_9_19 = e2 % 129.27/17.90 (43) all_6_2 = all_4_10 % 129.27/17.90 (44) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.90 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.90 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.90 (45) all_9_2 = e1 % 129.27/17.90 (46) ~ (all_4_10 = e2) % 129.27/17.90 (47) all_4_0 = e0 % 129.27/17.90 (48) all_9_20 = e4 % 129.27/17.90 (49) ~ (e2 = e1) % 129.27/17.90 (50) all_6_15 = all_4_3 % 129.27/17.90 (51) op(e4, e4) = e0 % 129.27/17.90 (52) all_9_16 = e4 % 129.27/17.90 % 129.27/17.90 Begin of proof % 129.27/17.90 | % 129.27/17.90 | BETA: splitting (36) gives: % 129.27/17.90 | % 129.27/17.90 | Case 1: % 129.27/17.90 | | % 129.27/17.90 | | (53) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = % 129.27/17.90 | | e4) % 129.27/17.90 | | % 129.27/17.90 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.27/17.90 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 129.27/17.90 | | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), % 129.27/17.90 | | (37), (38), (39), (41), (43), (44), (45), (46), (47), (48), (49), % 129.27/17.90 | | (50), (51), (52), (53) are inconsistent by sub-proof #20. % 129.27/17.90 | | % 129.27/17.90 | Case 2: % 129.27/17.90 | | % 129.27/17.90 | | (54) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = % 129.27/17.90 | | e4) | (all_9_19 = e4 & op(e1, e0) = e4) % 129.27/17.90 | | % 129.27/17.90 | | BETA: splitting (54) gives: % 129.27/17.90 | | % 129.27/17.90 | | Case 1: % 129.27/17.90 | | | % 129.27/17.90 | | | (55) all_9_14 = e4 & op(e1, e2) = e4 % 129.27/17.90 | | | % 129.27/17.90 | | | REF_CLOSE: (4), (40), (55) are inconsistent by sub-proof #19. % 129.27/17.90 | | | % 129.27/17.90 | | Case 2: % 129.27/17.90 | | | % 129.27/17.90 | | | (56) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) = % 129.27/17.90 | | | e4) % 129.27/17.90 | | | % 129.27/17.90 | | | BETA: splitting (56) gives: % 129.27/17.90 | | | % 129.27/17.90 | | | Case 1: % 129.27/17.90 | | | | % 129.27/17.90 | | | | (57) all_9_15 = e4 & op(e1, e1) = e4 % 129.27/17.91 | | | | % 129.27/17.91 | | | | ALPHA: (57) implies: % 129.27/17.91 | | | | (58) all_9_15 = e4 % 129.27/17.91 | | | | % 129.27/17.91 | | | | COMBINE_EQS: (32), (58) imply: % 129.27/17.91 | | | | (59) e4 = e3 % 129.27/17.91 | | | | % 129.27/17.91 | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (23), (31), (38), (44), (47), % 129.27/17.91 | | | | (48), (59) are inconsistent by sub-proof #89. % 129.27/17.91 | | | | % 129.27/17.91 | | | Case 2: % 129.27/17.91 | | | | % 129.27/17.91 | | | | (60) all_9_19 = e4 & op(e1, e0) = e4 % 129.27/17.91 | | | | % 129.27/17.91 | | | | ALPHA: (60) implies: % 129.27/17.91 | | | | (61) all_9_19 = e4 % 129.27/17.91 | | | | % 129.27/17.91 | | | | COMBINE_EQS: (42), (61) imply: % 129.27/17.91 | | | | (62) e4 = e2 % 129.27/17.91 | | | | % 129.27/17.91 | | | | SIMP: (62) implies: % 129.27/17.91 | | | | (63) e4 = e2 % 129.27/17.91 | | | | % 129.27/17.91 | | | | COMBINE_EQS: (48), (63) imply: % 129.27/17.91 | | | | (64) all_9_20 = e2 % 129.27/17.91 | | | | % 129.27/17.91 | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (13), (31), (37), (38), (44), % 129.27/17.91 | | | | (47), (50), (64) are inconsistent by sub-proof #90. % 129.27/17.91 | | | | % 129.27/17.91 | | | End of split % 129.27/17.91 | | | % 129.27/17.91 | | End of split % 129.27/17.91 | | % 129.27/17.91 | End of split % 129.27/17.91 | % 129.27/17.91 End of proof % 129.27/17.91 % 129.27/17.91 Sub-proof #18 shows that the following formulas are inconsistent: % 129.27/17.91 ---------------------------------------------------------------- % 129.27/17.91 (1) ~ (op(e4, e1) = e1) % 129.27/17.91 (2) ~ (all_4_16 = e3) % 129.27/17.91 (3) all_6_5 = e1 % 129.27/17.91 (4) ~ (e4 = e0) % 129.27/17.91 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.91 (6) all_9_1 = e2 % 129.27/17.91 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.91 (8) ~ (e4 = e2) % 129.27/17.91 (9) ~ (all_4_6 = e3) % 129.27/17.91 (10) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.91 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.91 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.91 (13) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.27/17.91 (14) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.91 (15) all_9_17 = e3 % 129.27/17.91 (16) ~ (all_4_11 = e3) % 129.27/17.91 (17) all_9_10 = e2 % 129.27/17.91 (18) all_6_8 = all_4_16 % 129.27/17.91 (19) all_9_22 = e2 % 129.27/17.91 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.91 (21) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.27/17.91 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.27/17.91 (all_9_22 = e3 & op(e0, e2) = e3) % 129.27/17.91 (22) ~ (all_4_19 = e4) % 129.27/17.91 (23) all_9_12 = e2 % 129.27/17.91 (24) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.91 (25) ~ (e1 = e0) % 129.27/17.91 (26) all_6_7 = all_4_11 % 129.27/17.91 (27) ~ (e3 = e2) % 129.27/17.91 (28) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.91 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.91 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.91 (29) ~ (e4 = e1) % 129.27/17.91 (30) ~ (all_4_15 = e4) % 129.27/17.91 (31) all_9_15 = e3 % 129.27/17.91 (32) ~ (e3 = e1) % 129.27/17.91 (33) op(e0, e1) = all_4_19 % 129.27/17.91 (34) ~ (all_4_3 = e4) % 129.27/17.91 (35) op(e2, e2) = e4 % 129.27/17.91 (36) ~ (e4 = e3) % 129.27/17.91 (37) all_9_14 = e0 % 129.27/17.91 (38) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.91 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.91 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.91 (39) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.91 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.91 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.91 (40) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.91 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.91 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.91 (41) all_9_2 = e1 % 129.27/17.91 (42) all_9_11 = e0 % 129.27/17.91 (43) all_6_3 = all_4_15 % 129.27/17.91 (44) all_4_0 = e0 % 129.27/17.91 (45) all_9_20 = e4 % 129.27/17.91 (46) ~ (e2 = e1) % 129.27/17.91 (47) all_6_15 = all_4_3 % 129.27/17.91 (48) op(e4, e4) = e0 % 129.27/17.91 (49) all_9_16 = e4 % 129.27/17.91 % 129.27/17.91 Begin of proof % 129.27/17.91 | % 129.27/17.91 | BETA: splitting (21) gives: % 129.27/17.91 | % 129.27/17.91 | Case 1: % 129.27/17.91 | | % 129.27/17.91 | | (50) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 129.27/17.91 | | % 129.27/17.91 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (16), (20), (23), (24), % 129.27/17.91 | | (25), (26), (29), (32), (36), (38), (39), (44), (45), (46), (48), % 129.27/17.91 | | (49), (50) are inconsistent by sub-proof #50. % 129.27/17.91 | | % 129.27/17.91 | Case 2: % 129.27/17.91 | | % 129.27/17.91 | | (51) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) % 129.27/17.91 | | | (all_9_22 = e3 & op(e0, e2) = e3) % 129.27/17.91 | | % 129.27/17.91 | | BETA: splitting (51) gives: % 129.27/17.91 | | % 129.27/17.91 | | Case 1: % 129.27/17.91 | | | % 129.27/17.91 | | | (52) all_9_8 = e3 & op(e2, e2) = e3 % 129.27/17.91 | | | % 129.27/17.91 | | | REF_CLOSE: (20), (35), (36), (52) are inconsistent by sub-proof #126. % 129.27/17.91 | | | % 129.27/17.91 | | Case 2: % 129.27/17.91 | | | % 129.27/17.91 | | | (53) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) = % 129.27/17.91 | | | e3) % 129.27/17.91 | | | % 129.27/17.91 | | | BETA: splitting (53) gives: % 129.27/17.91 | | | % 129.27/17.91 | | | Case 1: % 129.27/17.91 | | | | % 129.27/17.91 | | | | (54) all_9_14 = e3 & op(e1, e2) = e3 % 129.27/17.91 | | | | % 129.27/17.91 | | | | ALPHA: (54) implies: % 129.27/17.91 | | | | (55) all_9_14 = e3 % 129.27/17.91 | | | | % 129.27/17.91 | | | | COMBINE_EQS: (37), (55) imply: % 129.27/17.91 | | | | (56) e3 = e0 % 129.27/17.91 | | | | % 129.27/17.91 | | | | COMBINE_EQS: (31), (56) imply: % 129.27/17.91 | | | | (57) all_9_15 = e0 % 129.27/17.91 | | | | % 129.27/17.91 | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (12), (13), (17), (20), (22), % 129.27/17.91 | | | | (29), (30), (33), (34), (36), (39), (40), (42), (43), (44), % 129.27/17.91 | | | | (45), (47), (57) are inconsistent by sub-proof #64. % 129.27/17.91 | | | | % 129.27/17.91 | | | Case 2: % 129.27/17.91 | | | | % 129.27/17.91 | | | | (58) all_9_22 = e3 & op(e0, e2) = e3 % 129.27/17.91 | | | | % 129.27/17.91 | | | | REF_CLOSE: (2), (9), (10), (14), (15), (16), (18), (19), (24), (26), % 129.27/17.91 | | | | (27), (28), (32), (41), (58) are inconsistent by sub-proof % 129.27/17.91 | | | | #70. % 129.27/17.91 | | | | % 129.27/17.91 | | | End of split % 129.27/17.91 | | | % 129.27/17.91 | | End of split % 129.27/17.91 | | % 129.27/17.91 | End of split % 129.27/17.91 | % 129.27/17.91 End of proof % 129.27/17.91 % 129.27/17.91 Sub-proof #19 shows that the following formulas are inconsistent: % 129.27/17.91 ---------------------------------------------------------------- % 129.27/17.91 (1) all_9_14 = e4 & op(e1, e2) = e4 % 129.27/17.91 (2) all_9_14 = e0 % 129.27/17.91 (3) ~ (e4 = e0) % 129.27/17.91 % 129.27/17.91 Begin of proof % 129.27/17.91 | % 129.27/17.91 | ALPHA: (1) implies: % 129.27/17.91 | (4) all_9_14 = e4 % 129.27/17.91 | % 129.27/17.91 | COMBINE_EQS: (2), (4) imply: % 129.27/17.91 | (5) e4 = e0 % 129.27/17.91 | % 129.27/17.91 | SIMP: (5) implies: % 129.27/17.91 | (6) e4 = e0 % 129.27/17.91 | % 129.27/17.91 | REDUCE: (3), (6) imply: % 129.27/17.91 | (7) $false % 129.27/17.91 | % 129.27/17.91 | CLOSE: (7) is inconsistent. % 129.27/17.91 | % 129.27/17.91 End of proof % 129.27/17.91 % 129.27/17.91 Sub-proof #20 shows that the following formulas are inconsistent: % 129.27/17.91 ---------------------------------------------------------------- % 129.27/17.91 (1) ~ (op(e4, e1) = e1) % 129.27/17.91 (2) ~ (all_4_16 = e3) % 129.27/17.91 (3) all_6_5 = e1 % 129.27/17.91 (4) ~ (e4 = e0) % 129.27/17.91 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.91 (6) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 129.27/17.91 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.91 (8) ~ (e4 = e2) % 129.27/17.91 (9) ~ (all_4_6 = e3) % 129.27/17.91 (10) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.91 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.91 (12) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.91 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.91 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.91 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.91 (14) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.91 (15) all_9_17 = e3 % 129.27/17.91 (16) all_9_4 = e3 % 129.27/17.91 (17) ~ (all_4_11 = e3) % 129.27/17.91 (18) all_6_8 = all_4_16 % 129.27/17.91 (19) ~ (e2 = e0) % 129.27/17.91 (20) all_9_0 = e0 % 129.27/17.91 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.91 (22) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.91 (23) all_9_12 = e2 % 129.27/17.91 (24) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.91 (25) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 129.27/17.91 (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 129.27/17.91 (all_9_21 = e2 & op(e0, e3) = e2) % 129.27/17.91 (26) ~ (e1 = e0) % 129.27/17.91 (27) all_6_7 = all_4_11 % 129.27/17.91 (28) all_9_3 = e0 % 129.27/17.91 (29) ~ (e3 = e2) % 129.27/17.91 (30) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.91 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.91 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.91 (31) ~ (e4 = e1) % 129.27/17.91 (32) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) % 129.27/17.91 (33) ~ (e3 = e1) % 129.27/17.91 (34) all_9_21 = e3 % 129.27/17.91 (35) ~ (op(e1, e4) = e4) % 129.27/17.91 (36) ~ (all_4_3 = e4) % 129.27/17.91 (37) ~ (e4 = e3) % 129.27/17.91 (38) ~ (all_4_7 = e2) % 129.27/17.91 (39) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.91 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.91 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.91 (40) all_6_2 = all_4_10 % 129.27/17.91 (41) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.91 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.91 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.91 (42) all_9_2 = e1 % 129.27/17.91 (43) ~ (all_4_10 = e2) % 129.27/17.91 (44) all_4_0 = e0 % 129.27/17.91 (45) all_9_20 = e4 % 129.27/17.91 (46) ~ (e2 = e1) % 129.27/17.91 (47) all_6_15 = all_4_3 % 129.27/17.91 (48) op(e4, e4) = e0 % 129.27/17.91 (49) all_9_16 = e4 % 129.27/17.91 % 129.27/17.91 Begin of proof % 129.27/17.91 | % 129.27/17.91 | BETA: splitting (32) gives: % 129.27/17.91 | % 129.27/17.91 | Case 1: % 129.27/17.91 | | % 129.27/17.91 | | (50) all_9_12 = e4 & op(e1, e4) = e4 % 129.27/17.91 | | % 129.27/17.91 | | REF_CLOSE: (35), (50) are inconsistent by sub-proof #74. % 129.27/17.91 | | % 129.27/17.91 | Case 2: % 129.27/17.91 | | % 129.27/17.91 | | (51) all_9_13 = e4 & op(e1, e3) = e4 % 129.27/17.91 | | % 129.27/17.91 | | ALPHA: (51) implies: % 129.27/17.91 | | (52) all_9_13 = e4 % 129.27/17.91 | | % 129.27/17.91 | | BETA: splitting (12) gives: % 129.27/17.91 | | % 129.27/17.91 | | Case 1: % 129.27/17.91 | | | % 129.27/17.91 | | | (53) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = % 129.27/17.91 | | | e2) % 129.27/17.91 | | | % 129.27/17.91 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (11), (16), (19), (20), (21), % 129.27/17.91 | | | (23), (26), (31), (33), (37), (39), (41), (44), (45), (46), % 129.27/17.91 | | | (48), (49), (53) are inconsistent by sub-proof #58. % 129.27/17.91 | | | % 129.27/17.91 | | Case 2: % 129.27/17.91 | | | % 129.27/17.91 | | | (54) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = % 129.27/17.91 | | | e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.91 | | | % 129.27/17.91 | | | BETA: splitting (54) gives: % 129.27/17.91 | | | % 129.27/17.91 | | | Case 1: % 129.27/17.91 | | | | % 129.27/17.91 | | | | (55) all_9_4 = e2 & op(e4, e2) = e2 % 129.27/17.91 | | | | % 129.27/17.91 | | | | ALPHA: (55) implies: % 129.27/17.91 | | | | (56) op(e4, e2) = e2 % 129.27/17.91 | | | | % 129.27/17.91 | | | | REF_CLOSE: (22), (40), (43), (56) are inconsistent by sub-proof #261. % 129.27/17.91 | | | | % 129.27/17.91 | | | Case 2: % 129.27/17.91 | | | | % 129.27/17.91 | | | | (57) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 129.27/17.91 | | | | e2) % 129.27/17.91 | | | | % 129.27/17.91 | | | | BETA: splitting (57) gives: % 129.27/17.91 | | | | % 129.27/17.91 | | | | Case 1: % 129.27/17.91 | | | | | % 129.27/17.91 | | | | | (58) all_9_9 = e2 & op(e4, e1) = e2 % 129.27/17.91 | | | | | % 129.27/17.91 | | | | | ALPHA: (58) implies: % 129.27/17.91 | | | | | (59) all_9_9 = e2 % 129.27/17.91 | | | | | % 129.27/17.91 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 129.27/17.91 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 129.27/17.91 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), % 129.27/17.91 | | | | | (33), (34), (36), (37), (38), (39), (40), (41), (42), (43), % 129.27/17.91 | | | | | (44), (45), (46), (47), (48), (49), (52), (59) are % 129.27/17.91 | | | | | inconsistent by sub-proof #21. % 129.27/17.91 | | | | | % 129.27/17.91 | | | | Case 2: % 129.27/17.91 | | | | | % 129.27/17.91 | | | | | (60) all_9_16 = e2 & op(e4, e0) = e2 % 129.27/17.91 | | | | | % 129.27/17.91 | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (13), (31), (36), (37), % 129.27/17.91 | | | | | (41), (44), (45), (47), (49), (60) are inconsistent by % 129.27/17.91 | | | | | sub-proof #88. % 129.27/17.91 | | | | | % 129.27/17.91 | | | | End of split % 129.27/17.91 | | | | % 129.27/17.91 | | | End of split % 129.27/17.91 | | | % 129.27/17.91 | | End of split % 129.27/17.91 | | % 129.27/17.91 | End of split % 129.27/17.91 | % 129.27/17.91 End of proof % 129.27/17.91 % 129.27/17.91 Sub-proof #21 shows that the following formulas are inconsistent: % 129.27/17.91 ---------------------------------------------------------------- % 129.27/17.91 (1) ~ (op(e4, e1) = e1) % 129.27/17.91 (2) all_9_9 = e2 % 129.27/17.91 (3) ~ (all_4_16 = e3) % 129.27/17.91 (4) all_6_5 = e1 % 129.27/17.91 (5) ~ (e4 = e0) % 129.27/17.91 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.91 (7) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 129.27/17.91 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.91 (9) ~ (e4 = e2) % 129.27/17.91 (10) ~ (all_4_6 = e3) % 129.27/17.91 (11) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.91 (12) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.91 (13) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.91 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.91 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.91 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.91 (15) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.91 (16) all_9_17 = e3 % 129.27/17.91 (17) all_9_4 = e3 % 129.27/17.91 (18) ~ (all_4_11 = e3) % 129.27/17.91 (19) all_6_8 = all_4_16 % 129.27/17.91 (20) ~ (e2 = e0) % 129.27/17.91 (21) all_9_0 = e0 % 129.27/17.91 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.91 (23) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.91 (24) all_9_12 = e2 % 129.27/17.91 (25) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.91 (26) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 129.27/17.91 (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 129.27/17.91 (all_9_21 = e2 & op(e0, e3) = e2) % 129.27/17.91 (27) ~ (e1 = e0) % 129.27/17.91 (28) all_6_7 = all_4_11 % 129.27/17.91 (29) all_9_3 = e0 % 129.27/17.91 (30) ~ (e3 = e2) % 129.27/17.91 (31) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.91 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.91 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.91 (32) ~ (e4 = e1) % 129.27/17.91 (33) ~ (e3 = e1) % 129.27/17.91 (34) all_9_21 = e3 % 129.27/17.91 (35) ~ (all_4_3 = e4) % 129.27/17.91 (36) all_9_13 = e4 % 129.27/17.91 (37) ~ (e4 = e3) % 129.27/17.91 (38) ~ (all_4_7 = e2) % 129.27/17.91 (39) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.91 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.91 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.91 (40) all_6_2 = all_4_10 % 129.27/17.91 (41) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.91 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.91 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.91 (42) all_9_2 = e1 % 129.27/17.91 (43) ~ (all_4_10 = e2) % 129.27/17.91 (44) all_4_0 = e0 % 129.27/17.91 (45) all_9_20 = e4 % 129.27/17.91 (46) ~ (e2 = e1) % 129.27/17.91 (47) all_6_15 = all_4_3 % 129.27/17.91 (48) op(e4, e4) = e0 % 129.27/17.91 (49) all_9_16 = e4 % 129.27/17.91 % 129.27/17.91 Begin of proof % 129.27/17.91 | % 129.27/17.91 | BETA: splitting (26) gives: % 129.27/17.91 | % 129.27/17.91 | Case 1: % 129.27/17.92 | | % 129.27/17.92 | | (50) (all_9_1 = e2 & op(e4, e3) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) % 129.27/17.92 | | % 129.27/17.92 | | BETA: splitting (50) gives: % 129.27/17.92 | | % 129.27/17.92 | | Case 1: % 129.27/17.92 | | | % 129.27/17.92 | | | (51) all_9_1 = e2 & op(e4, e3) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | ALPHA: (51) implies: % 129.27/17.92 | | | (52) all_9_1 = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (12), (17), (22), (24), (27), % 129.27/17.92 | | | (32), (33), (37), (39), (41), (44), (45), (46), (48), (49), % 129.27/17.92 | | | (52) are inconsistent by sub-proof #59. % 129.27/17.92 | | | % 129.27/17.92 | | Case 2: % 129.27/17.92 | | | % 129.27/17.92 | | | (53) all_9_3 = e2 & op(e3, e3) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (12), (13), (14), (17), % 129.27/17.92 | | | (20), (21), (22), (23), (24), (27), (29), (32), (33), (35), % 129.27/17.92 | | | (37), (39), (40), (41), (43), (44), (45), (46), (47), (48), % 129.27/17.92 | | | (49), (53) are inconsistent by sub-proof #22. % 129.27/17.92 | | | % 129.27/17.92 | | End of split % 129.27/17.92 | | % 129.27/17.92 | Case 2: % 129.27/17.92 | | % 129.27/17.92 | | (54) (all_9_7 = e2 & op(e2, e3) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 129.27/17.92 | | | (all_9_21 = e2 & op(e0, e3) = e2) % 129.27/17.92 | | % 129.27/17.92 | | BETA: splitting (54) gives: % 129.27/17.92 | | % 129.27/17.92 | | Case 1: % 129.27/17.92 | | | % 129.27/17.92 | | | (55) all_9_7 = e2 & op(e2, e3) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | ALPHA: (55) implies: % 129.27/17.92 | | | (56) op(e2, e3) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (7), (38), (56) are inconsistent by sub-proof #308. % 129.27/17.92 | | | % 129.27/17.92 | | Case 2: % 129.27/17.92 | | | % 129.27/17.92 | | | (57) (all_9_13 = e2 & op(e1, e3) = e2) | (all_9_21 = e2 & op(e0, e3) = % 129.27/17.92 | | | e2) % 129.27/17.92 | | | % 129.27/17.92 | | | BETA: splitting (57) gives: % 129.27/17.92 | | | % 129.27/17.92 | | | Case 1: % 129.27/17.92 | | | | % 129.27/17.92 | | | | (58) all_9_13 = e2 & op(e1, e3) = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | ALPHA: (58) implies: % 129.27/17.92 | | | | (59) all_9_13 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | COMBINE_EQS: (36), (59) imply: % 129.27/17.92 | | | | (60) e4 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | SIMP: (60) implies: % 129.27/17.92 | | | | (61) e4 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | COMBINE_EQS: (45), (61) imply: % 129.27/17.92 | | | | (62) all_9_20 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (14), (32), (35), (37), (41), % 129.27/17.92 | | | | (44), (47), (62) are inconsistent by sub-proof #90. % 129.27/17.92 | | | | % 129.27/17.92 | | | Case 2: % 129.27/17.92 | | | | % 129.27/17.92 | | | | (63) all_9_21 = e2 & op(e0, e3) = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | ALPHA: (63) implies: % 129.27/17.92 | | | | (64) all_9_21 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | COMBINE_EQS: (34), (64) imply: % 129.27/17.92 | | | | (65) e3 = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | REF_CLOSE: (3), (10), (11), (15), (16), (18), (19), (25), (28), (30), % 129.27/17.92 | | | | (31), (33), (42), (65) are inconsistent by sub-proof #82. % 129.27/17.92 | | | | % 129.27/17.92 | | | End of split % 129.27/17.92 | | | % 129.27/17.92 | | End of split % 129.27/17.92 | | % 129.27/17.92 | End of split % 129.27/17.92 | % 129.27/17.92 End of proof % 129.27/17.92 % 129.27/17.92 Sub-proof #22 shows that the following formulas are inconsistent: % 129.27/17.92 ---------------------------------------------------------------- % 129.27/17.92 (1) ~ (op(e4, e1) = e1) % 129.27/17.92 (2) all_9_9 = e2 % 129.27/17.92 (3) all_6_5 = e1 % 129.27/17.92 (4) ~ (e4 = e0) % 129.27/17.92 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.92 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.92 (7) ~ (e4 = e2) % 129.27/17.92 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.92 (9) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.92 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.92 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.92 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.92 (11) all_9_4 = e3 % 129.27/17.92 (12) ~ (e2 = e0) % 129.27/17.92 (13) all_9_0 = e0 % 129.27/17.92 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.92 (15) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.92 (16) all_9_12 = e2 % 129.27/17.92 (17) ~ (e1 = e0) % 129.27/17.92 (18) all_9_3 = e0 % 129.27/17.92 (19) ~ (e4 = e1) % 129.27/17.92 (20) ~ (e3 = e1) % 129.27/17.92 (21) ~ (all_4_3 = e4) % 129.27/17.92 (22) ~ (e4 = e3) % 129.27/17.92 (23) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.92 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.92 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.92 (24) all_9_3 = e2 & op(e3, e3) = e2 % 129.27/17.92 (25) all_6_2 = all_4_10 % 129.27/17.92 (26) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.92 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.92 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.92 (27) ~ (all_4_10 = e2) % 129.27/17.92 (28) all_4_0 = e0 % 129.27/17.92 (29) all_9_20 = e4 % 129.27/17.92 (30) ~ (e2 = e1) % 129.27/17.92 (31) all_6_15 = all_4_3 % 129.27/17.92 (32) op(e4, e4) = e0 % 129.27/17.92 (33) all_9_16 = e4 % 129.27/17.92 % 129.27/17.92 Begin of proof % 129.27/17.92 | % 129.27/17.92 | ALPHA: (24) implies: % 129.27/17.92 | (34) all_9_3 = e2 % 129.27/17.92 | % 129.27/17.92 | COMBINE_EQS: (18), (34) imply: % 129.27/17.92 | (35) e2 = e0 % 129.27/17.92 | % 129.27/17.92 | SIMP: (35) implies: % 129.27/17.92 | (36) e2 = e0 % 129.27/17.92 | % 129.27/17.92 | COMBINE_EQS: (2), (36) imply: % 129.27/17.92 | (37) all_9_9 = e0 % 129.27/17.92 | % 129.27/17.92 | BETA: splitting (9) gives: % 129.27/17.92 | % 129.27/17.92 | Case 1: % 129.27/17.92 | | % 129.27/17.92 | | (38) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) % 129.27/17.92 | | % 129.27/17.92 | | BETA: splitting (38) gives: % 129.27/17.92 | | % 129.27/17.92 | | Case 1: % 129.27/17.92 | | | % 129.27/17.92 | | | (39) all_9_0 = e2 & op(e4, e4) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (12), (13), (39) are inconsistent by sub-proof #314. % 129.27/17.92 | | | % 129.27/17.92 | | Case 2: % 129.27/17.92 | | | % 129.27/17.92 | | | (40) all_9_1 = e2 & op(e4, e3) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | ALPHA: (40) implies: % 129.27/17.92 | | | (41) all_9_1 = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (14), (16), (17), % 129.27/17.92 | | | (19), (20), (22), (23), (26), (28), (29), (30), (32), (33), % 129.27/17.92 | | | (41) are inconsistent by sub-proof #59. % 129.27/17.92 | | | % 129.27/17.92 | | End of split % 129.27/17.92 | | % 129.27/17.92 | Case 2: % 129.27/17.92 | | % 129.27/17.92 | | (42) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) % 129.27/17.92 | | | (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.92 | | % 129.27/17.92 | | BETA: splitting (42) gives: % 129.27/17.92 | | % 129.27/17.92 | | Case 1: % 129.27/17.92 | | | % 129.27/17.92 | | | (43) all_9_4 = e2 & op(e4, e2) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | ALPHA: (43) implies: % 129.27/17.92 | | | (44) op(e4, e2) = e2 % 129.27/17.92 | | | % 129.27/17.92 | | | REF_CLOSE: (15), (25), (27), (44) are inconsistent by sub-proof #261. % 129.27/17.92 | | | % 129.27/17.92 | | Case 2: % 129.27/17.92 | | | % 129.27/17.92 | | | (45) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = % 129.27/17.92 | | | e2) % 129.27/17.92 | | | % 129.27/17.92 | | | BETA: splitting (45) gives: % 129.27/17.92 | | | % 129.27/17.92 | | | Case 1: % 129.27/17.92 | | | | % 129.27/17.92 | | | | (46) all_9_9 = e2 & op(e4, e1) = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | REDUCE: (12), (36) imply: % 129.27/17.92 | | | | (47) $false % 129.27/17.92 | | | | % 129.27/17.92 | | | | CLOSE: (47) is inconsistent. % 129.27/17.92 | | | | % 129.27/17.92 | | | Case 2: % 129.27/17.92 | | | | % 129.27/17.92 | | | | (48) all_9_16 = e2 & op(e4, e0) = e2 % 129.27/17.92 | | | | % 129.27/17.92 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (19), (21), (22), (26), % 129.27/17.92 | | | | (28), (29), (31), (33), (48) are inconsistent by sub-proof % 129.27/17.92 | | | | #88. % 129.27/17.92 | | | | % 129.27/17.92 | | | End of split % 129.27/17.92 | | | % 129.27/17.92 | | End of split % 129.27/17.92 | | % 129.27/17.92 | End of split % 129.27/17.92 | % 129.27/17.92 End of proof % 129.27/17.92 % 129.27/17.92 Sub-proof #23 shows that the following formulas are inconsistent: % 129.27/17.92 ---------------------------------------------------------------- % 129.27/17.92 (1) ~ (op(e4, e1) = e1) % 129.27/17.92 (2) ~ (all_4_16 = e3) % 129.27/17.92 (3) all_6_5 = e1 % 129.27/17.92 (4) ~ (e4 = e0) % 129.27/17.92 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.27/17.92 (6) all_6_10 = e3 % 129.27/17.92 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.92 (8) ~ (all_4_3 = all_4_4) % 129.27/17.92 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.92 (10) ~ (e4 = e2) % 129.27/17.92 (11) ~ (all_4_6 = e3) % 129.27/17.92 (12) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.92 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.92 (14) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.92 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.92 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.92 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.92 (16) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.92 (17) all_9_17 = e3 % 129.27/17.92 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.27/17.92 (19) ~ (all_4_3 = e3) % 129.27/17.92 (20) all_6_20 = all_4_4 % 129.27/17.92 (21) all_9_4 = e3 % 129.27/17.92 (22) ~ (e3 = e0) % 129.27/17.92 (23) ~ (all_4_11 = e3) % 129.27/17.92 (24) ~ (all_4_5 = e3) % 129.27/17.92 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.92 (26) all_6_8 = all_4_16 % 129.27/17.92 (27) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.27/17.92 = e0 % 129.27/17.92 (28) ~ (e2 = e0) % 129.27/17.92 (29) all_9_0 = e0 % 129.27/17.92 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.92 (31) ~ (all_4_4 = e3) % 129.27/17.92 (32) all_9_7 = e1 % 129.27/17.92 (33) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.92 (34) all_9_12 = e2 % 129.27/17.92 (35) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.92 (36) all_9_6 = e3 % 129.27/17.92 (37) ~ (e1 = e0) % 129.27/17.92 (38) all_6_7 = all_4_11 % 129.27/17.92 (39) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.27/17.92 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.27/17.92 (all_9_20 = e3 & op(e0, e4) = e3) % 129.27/17.92 (40) ~ (e3 = e2) % 129.27/17.92 (41) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.92 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.92 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.92 (42) op(e0, e4) = all_4_4 % 129.27/17.92 (43) ~ (e4 = e1) % 129.27/17.92 (44) ~ (all_4_3 = e0) % 129.27/17.92 (45) ~ (e3 = e1) % 129.27/17.92 (46) op(e1, e4) = all_4_3 % 129.27/17.92 (47) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.27/17.92 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.27/17.92 (all_9_20 = e2 & op(e0, e4) = e2) % 129.27/17.92 (48) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 129.27/17.92 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 129.27/17.92 (all_9_16 = e3 & op(e4, e0) = e3) % 129.27/17.92 (49) ~ (all_4_3 = e4) % 129.27/17.92 (50) ~ (e4 = e3) % 129.27/17.92 (51) ~ (all_4_4 = e0) % 129.27/17.92 (52) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.92 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.92 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.92 (53) ~ (all_4_3 = e1) % 129.27/17.92 (54) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 129.27/17.92 (55) all_6_2 = all_4_10 % 129.27/17.92 (56) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.92 (57) op(e2, e4) = e3 % 129.27/17.92 (58) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.92 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.92 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.92 (59) all_9_2 = e1 % 129.27/17.92 (60) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.92 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.92 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.92 (61) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.92 = e0 % 129.27/17.92 (62) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) % 129.27/17.92 (63) ~ (all_4_4 = e1) % 129.27/17.92 (64) ~ (all_4_10 = e2) % 129.27/17.92 (65) all_4_0 = e0 % 129.27/17.92 (66) all_9_20 = e4 % 129.27/17.92 (67) ~ (e2 = e1) % 129.27/17.92 (68) all_6_15 = all_4_3 % 129.27/17.92 (69) op(e4, e4) = e0 % 129.27/17.92 (70) all_9_16 = e4 % 129.27/17.92 % 129.27/17.92 Begin of proof % 129.27/17.92 | % 129.27/17.92 | BETA: splitting (62) gives: % 129.27/17.92 | % 129.27/17.92 | Case 1: % 129.27/17.92 | | % 129.27/17.92 | | (71) all_9_6 = e0 & op(e2, e4) = e0 % 129.27/17.92 | | % 129.27/17.92 | | ALPHA: (71) implies: % 129.27/17.92 | | (72) all_9_6 = e0 % 129.27/17.92 | | % 129.27/17.92 | | COMBINE_EQS: (36), (72) imply: % 129.27/17.92 | | (73) e3 = e0 % 129.27/17.92 | | % 129.27/17.92 | | COMBINE_EQS: (21), (73) imply: % 129.27/17.92 | | (74) all_9_4 = e0 % 129.27/17.92 | | % 129.27/17.92 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.27/17.92 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 129.27/17.92 | | (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (37), % 129.27/17.92 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 129.27/17.92 | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), % 129.27/17.92 | | (60), (61), (63), (64), (65), (66), (67), (68), (69), (70), (74) % 129.27/17.92 | | are inconsistent by sub-proof #79. % 129.27/17.92 | | % 129.27/17.92 | Case 2: % 129.27/17.92 | | % 129.27/17.92 | | (75) all_9_7 = e0 & op(e2, e3) = e0 % 129.27/17.92 | | % 129.27/17.92 | | ALPHA: (75) implies: % 129.27/17.92 | | (76) all_9_7 = e0 % 129.27/17.92 | | % 129.27/17.92 | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (13), (15), (18), (19), (20), % 129.27/17.92 | | (22), (25), (27), (28), (30), (31), (32), (37), (39), (40), (42), % 129.27/17.92 | | (43), (44), (45), (46), (47), (50), (51), (53), (56), (57), (58), % 129.27/17.92 | | (59), (60), (61), (63), (65), (67), (68), (69), (76) are % 129.27/17.92 | | inconsistent by sub-proof #222. % 129.27/17.92 | | % 129.27/17.92 | End of split % 129.27/17.92 | % 129.27/17.92 End of proof % 129.27/17.92 % 129.27/17.92 Sub-proof #24 shows that the following formulas are inconsistent: % 129.27/17.92 ---------------------------------------------------------------- % 129.27/17.92 (1) ~ (op(e4, e1) = e1) % 129.27/17.92 (2) ~ (all_4_16 = e3) % 129.27/17.92 (3) all_6_5 = e1 % 129.27/17.92 (4) ~ (e4 = e0) % 129.27/17.92 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.92 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.92 (7) ~ (e4 = e2) % 129.27/17.92 (8) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 129.27/17.92 (9) ~ (all_4_6 = e3) % 129.27/17.92 (10) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.92 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.92 (12) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.27/17.92 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.27/17.92 (all_9_16 = e2 & op(e4, e0) = e2) % 129.27/17.92 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.92 (14) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.92 (15) all_9_17 = e3 % 129.27/17.92 (16) ~ (e3 = e0) % 129.27/17.92 (17) ~ (all_4_11 = e3) % 129.27/17.92 (18) all_6_8 = all_4_16 % 129.27/17.92 (19) ~ (e2 = e0) % 129.27/17.92 (20) all_9_22 = e2 % 129.27/17.92 (21) all_9_0 = e0 % 129.27/17.92 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.92 (23) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.27/17.92 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.27/17.92 (all_9_22 = e3 & op(e0, e2) = e3) % 129.27/17.92 (24) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.92 (25) all_9_12 = e2 % 129.27/17.92 (26) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.92 (27) ~ (e1 = e0) % 129.27/17.92 (28) all_6_7 = all_4_11 % 129.27/17.92 (29) ~ (e3 = e2) % 129.27/17.92 (30) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.92 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.92 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.92 (31) ~ (e4 = e1) % 129.27/17.92 (32) ~ (e3 = e1) % 129.27/17.92 (33) ~ (all_4_3 = e4) % 129.27/17.92 (34) op(e2, e2) = e4 % 129.27/17.92 (35) ~ (e4 = e3) % 129.27/17.92 (36) all_9_14 = e0 % 129.27/17.92 (37) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.27/17.92 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.27/17.92 (all_9_16 = e1 & op(e4, e0) = e1) % 129.27/17.92 (38) all_6_2 = all_4_10 % 129.27/17.92 (39) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.92 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.92 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.92 (40) all_9_2 = e1 % 129.27/17.92 (41) ~ (all_4_10 = e2) % 129.27/17.92 (42) all_4_0 = e0 % 129.27/17.92 (43) all_9_20 = e4 % 129.27/17.92 (44) ~ (e2 = e1) % 129.27/17.92 (45) all_6_15 = all_4_3 % 129.27/17.92 (46) op(e4, e4) = e0 % 129.27/17.92 (47) all_9_16 = e4 % 129.27/17.92 % 129.27/17.92 Begin of proof % 129.27/17.92 | % 129.27/17.92 | BETA: splitting (8) gives: % 129.27/17.92 | % 129.27/17.92 | Case 1: % 129.27/17.92 | | % 129.27/17.92 | | (48) all_9_9 = e3 & op(e4, e1) = e3 % 129.27/17.92 | | % 129.27/17.92 | | ALPHA: (48) implies: % 129.27/17.92 | | (49) all_9_9 = e3 % 129.27/17.92 | | % 129.27/17.92 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 129.27/17.92 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 129.27/17.92 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 129.27/17.92 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 129.27/17.92 | | (47), (49) are inconsistent by sub-proof #56. % 129.27/17.92 | | % 129.27/17.92 | Case 2: % 129.27/17.92 | | % 129.27/17.92 | | (50) all_9_10 = e3 & op(e3, e1) = e3 % 129.27/17.92 | | % 129.27/17.92 | | ALPHA: (50) implies: % 129.27/17.93 | | (51) op(e3, e1) = e3 % 129.27/17.93 | | % 129.27/17.93 | | REF_CLOSE: (2), (10), (18), (51) are inconsistent by sub-proof #87. % 129.27/17.93 | | % 129.27/17.93 | End of split % 129.27/17.93 | % 129.27/17.93 End of proof % 129.27/17.93 % 129.27/17.93 Sub-proof #25 shows that the following formulas are inconsistent: % 129.27/17.93 ---------------------------------------------------------------- % 129.27/17.93 (1) all_9_8 = e4 % 129.27/17.93 (2) ~ (op(e4, e1) = e1) % 129.27/17.93 (3) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 129.27/17.93 (all_9_23 = e3 & op(e0, e1) = e3) % 129.27/17.93 (4) ~ (all_4_16 = e3) % 129.27/17.93 (5) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 129.27/17.93 (6) all_6_5 = e1 % 129.27/17.93 (7) ~ (e4 = e0) % 129.27/17.93 (8) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.27/17.93 (9) all_6_10 = e3 % 129.27/17.93 (10) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.93 (11) ~ (all_4_3 = all_4_4) % 129.27/17.93 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.93 (13) ~ (e4 = e2) % 129.27/17.93 (14) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 129.27/17.93 (15) all_6_17 = all_4_13 % 129.27/17.93 (16) ~ (all_4_6 = e3) % 129.27/17.93 (17) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.93 (18) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.93 (19) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) | % 129.27/17.93 (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & op(e2, e1) = e0) | % 129.27/17.93 (all_9_18 = e0 & op(e2, e0) = e0) % 129.27/17.93 (20) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.93 (21) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.27/17.93 (22) ~ (all_4_22 = e0) % 129.27/17.93 (23) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.27/17.93 (24) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.93 (25) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) | % 129.27/17.93 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) | % 129.27/17.93 (all_9_22 = e1 & op(e0, e2) = e1) % 129.27/17.93 (26) all_9_17 = e3 % 129.27/17.93 (27) ~ (all_4_13 = e2) % 129.27/17.93 (28) ~ (all_4_18 = e1) % 129.27/17.93 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.27/17.93 (30) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 129.27/17.93 (31) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.27/17.93 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.27/17.93 (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.93 (32) ~ (all_4_3 = e3) % 129.27/17.93 (33) all_6_20 = all_4_4 % 129.27/17.93 (34) e4 = e2 | ~ (op(e2, e2) = e2) % 129.27/17.93 (35) ~ (all_4_13 = e1) % 129.27/17.93 (36) ~ (e3 = e0) % 129.27/17.93 (37) ~ (all_4_11 = e3) % 129.27/17.93 (38) ~ (all_4_17 = e2) % 129.27/17.93 (39) ~ (all_4_5 = e3) % 129.27/17.93 (40) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.93 (41) ~ (all_4_17 = e1) % 129.27/17.93 (42) all_6_8 = all_4_16 % 129.27/17.93 (43) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.27/17.93 = e0 % 129.27/17.93 (44) ~ (e2 = e0) % 129.27/17.93 (45) all_9_0 = e0 % 129.27/17.93 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.93 (47) ~ (all_4_4 = e3) % 129.27/17.93 (48) ~ (all_4_17 = e3) % 129.27/17.93 (49) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.93 (50) all_9_7 = e1 % 129.27/17.93 (51) ~ (all_4_19 = e4) % 129.27/17.93 (52) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.93 (53) all_9_12 = e2 % 129.27/17.93 (54) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.93 (55) all_9_6 = e3 % 129.27/17.93 (56) ~ (e1 = e0) % 129.27/17.93 (57) all_6_7 = all_4_11 % 129.27/17.93 (58) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.27/17.93 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.27/17.93 (all_9_20 = e3 & op(e0, e4) = e3) % 129.27/17.93 (59) ~ (e3 = e2) % 129.27/17.93 (60) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.27/17.93 (61) all_6_14 = all_4_22 % 129.27/17.93 (62) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.93 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.93 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.93 (63) all_6_13 = all_4_17 % 129.27/17.93 (64) op(e0, e4) = all_4_4 % 129.27/17.93 (65) ~ (e4 = e1) % 129.27/17.93 (66) ~ (all_4_3 = e0) % 129.27/17.93 (67) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.27/17.93 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.27/17.93 (all_9_22 = e2 & op(e0, e2) = e2) % 129.27/17.93 (68) ~ (all_4_15 = e4) % 129.27/17.93 (69) all_9_5 = e0 % 129.27/17.93 (70) ~ (e3 = e1) % 129.27/17.93 (71) op(e1, e4) = all_4_3 % 129.27/17.93 (72) all_6_18 = all_4_18 % 129.27/17.93 (73) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.27/17.93 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.27/17.93 (all_9_20 = e2 & op(e0, e4) = e2) % 129.27/17.93 (74) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 129.27/17.93 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 129.27/17.93 (all_9_16 = e3 & op(e4, e0) = e3) % 129.27/17.93 (75) op(e0, e1) = all_4_19 % 129.27/17.93 (76) ~ (all_4_3 = e4) % 129.27/17.93 (77) ~ (all_4_16 = e1) % 129.27/17.93 (78) ~ (e4 = e3) % 129.27/17.93 (79) ~ (all_4_4 = e0) % 129.27/17.93 (80) ~ (all_4_3 = e1) % 129.27/17.93 (81) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 129.27/17.93 (82) all_6_2 = all_4_10 % 129.27/17.93 (83) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.93 (84) op(e2, e4) = e3 % 129.27/17.93 (85) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.93 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.93 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.93 (86) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.93 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.93 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.93 (87) op(e2, e1) = all_4_17 % 129.27/17.93 (88) all_9_2 = e1 % 129.27/17.93 (89) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.93 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.93 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.93 (90) all_6_3 = all_4_15 % 129.27/17.93 (91) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.93 = e0 % 129.27/17.93 (92) ~ (all_4_4 = e1) % 129.27/17.93 (93) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 129.27/17.93 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 129.27/17.93 (all_9_23 = e2 & op(e0, e1) = e2) % 129.27/17.93 (94) ~ (all_4_10 = e2) % 129.27/17.93 (95) all_4_0 = e0 % 129.27/17.93 (96) all_9_20 = e4 % 129.27/17.93 (97) ~ (e2 = e1) % 129.27/17.93 (98) all_6_15 = all_4_3 % 129.27/17.93 (99) op(e4, e4) = e0 % 129.27/17.93 (100) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.93 (101) all_9_16 = e4 % 129.27/17.93 % 129.27/17.93 Begin of proof % 129.27/17.93 | % 129.27/17.93 | BETA: splitting (3) gives: % 129.27/17.93 | % 129.27/17.93 | Case 1: % 129.27/17.93 | | % 129.27/17.93 | | (102) all_9_11 = e3 & op(e2, e1) = e3 % 129.27/17.93 | | % 129.27/17.93 | | ALPHA: (102) implies: % 129.27/17.93 | | (103) op(e2, e1) = e3 % 129.27/17.93 | | % 129.27/17.93 | | REF_CLOSE: (46), (48), (87), (103) are inconsistent by sub-proof #103. % 129.27/17.93 | | % 129.27/17.93 | Case 2: % 129.27/17.93 | | % 129.27/17.93 | | (104) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) = % 129.27/17.93 | | e3) % 129.27/17.93 | | % 129.27/17.93 | | BETA: splitting (104) gives: % 129.27/17.93 | | % 129.27/17.93 | | Case 1: % 129.27/17.93 | | | % 129.27/17.93 | | | (105) all_9_15 = e3 & op(e1, e1) = e3 % 129.27/17.93 | | | % 129.27/17.93 | | | ALPHA: (105) implies: % 129.27/17.93 | | | (106) all_9_15 = e3 % 129.27/17.93 | | | % 129.27/17.93 | | | BETA: splitting (74) gives: % 129.27/17.93 | | | % 129.27/17.93 | | | Case 1: % 129.27/17.93 | | | | % 129.27/17.93 | | | | (107) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = % 129.27/17.93 | | | | e3) % 129.27/17.93 | | | | % 129.27/17.93 | | | | REF_CLOSE: (36), (39), (45), (81), (107) are inconsistent by sub-proof % 129.27/17.93 | | | | #139. % 129.27/17.93 | | | | % 129.27/17.93 | | | Case 2: % 129.27/17.93 | | | | % 129.27/17.93 | | | | (108) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = % 129.27/17.93 | | | | e3) | (all_9_16 = e3 & op(e4, e0) = e3) % 129.27/17.93 | | | | % 129.27/17.93 | | | | BETA: splitting (108) gives: % 129.27/17.93 | | | | % 129.27/17.93 | | | | Case 1: % 129.27/17.93 | | | | | % 129.27/17.93 | | | | | (109) all_9_4 = e3 & op(e4, e2) = e3 % 129.27/17.93 | | | | | % 129.27/17.93 | | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (15), % 129.27/17.93 | | | | | (18), (20), (23), (25), (27), (29), (30), (32), (33), (34), % 129.27/17.93 | | | | | (35), (36), (40), (43), (44), (46), (47), (52), (53), (56), % 129.27/17.93 | | | | | (58), (59), (64), (65), (66), (67), (69), (70), (71), (73), % 129.27/17.93 | | | | | (78), (79), (80), (82), (83), (84), (85), (88), (89), (91), % 129.27/17.93 | | | | | (92), (94), (95), (96), (97), (98), (99), (109) are % 129.27/17.93 | | | | | inconsistent by sub-proof #28. % 129.27/17.93 | | | | | % 129.27/17.93 | | | | Case 2: % 129.27/17.93 | | | | | % 129.27/17.93 | | | | | (110) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, % 129.27/17.93 | | | | | e0) = e3) % 129.27/17.93 | | | | | % 129.27/17.93 | | | | | BETA: splitting (110) gives: % 129.27/17.93 | | | | | % 129.27/17.93 | | | | | Case 1: % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | (111) all_9_9 = e3 & op(e4, e1) = e3 % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | ALPHA: (111) implies: % 129.27/17.93 | | | | | | (112) all_9_9 = e3 % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | BETA: splitting (19) gives: % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | Case 1: % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | | (113) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, % 129.27/17.93 | | | | | | | e3) = e0) % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | | REF_CLOSE: (7), (8), (9), (11), (12), (13), (18), (20), (29), % 129.27/17.93 | | | | | | | (32), (33), (36), (40), (43), (44), (46), (47), (50), % 129.27/17.93 | | | | | | | (55), (56), (58), (59), (64), (65), (66), (70), (71), % 129.27/17.93 | | | | | | | (73), (78), (79), (80), (83), (84), (85), (88), (89), % 129.27/17.93 | | | | | | | (91), (92), (95), (97), (98), (99), (113) are % 129.27/17.93 | | | | | | | inconsistent by sub-proof #78. % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | Case 2: % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | | (114) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_11 = e0 & % 129.27/17.93 | | | | | | | op(e2, e1) = e0) | (all_9_18 = e0 & op(e2, e0) = e0) % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | | BETA: splitting (114) gives: % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | | Case 1: % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | | (115) all_9_8 = e0 & op(e2, e2) = e0 % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | | REF_CLOSE: (1), (7), (115) are inconsistent by sub-proof #151. % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | Case 2: % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | | (116) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_18 = e0 & % 129.27/17.93 | | | | | | | | op(e2, e0) = e0) % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | | BETA: splitting (116) gives: % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | | Case 1: % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | (117) all_9_11 = e0 & op(e2, e1) = e0 % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | ALPHA: (117) implies: % 129.27/17.93 | | | | | | | | | (118) all_9_11 = e0 % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | BETA: splitting (93) gives: % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | Case 1: % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | (119) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & % 129.27/17.93 | | | | | | | | | | op(e3, e1) = e2) % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | BETA: splitting (119) gives: % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | Case 1: % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | (120) all_9_9 = e2 & op(e4, e1) = e2 % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | REF_CLOSE: (4), (16), (17), (24), (26), (37), (42), (54), % 129.27/17.93 | | | | | | | | | | | (57), (59), (62), (70), (88), (112), (120) are % 129.27/17.93 | | | | | | | | | | | inconsistent by sub-proof #77. % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | Case 2: % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | (121) all_9_10 = e2 & op(e3, e1) = e2 % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | ALPHA: (121) implies: % 129.27/17.93 | | | | | | | | | | | (122) all_9_10 = e2 % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (12), (13), (18), (20), (21), % 129.27/17.93 | | | | | | | | | | | (46), (51), (53), (65), (68), (75), (76), (78), % 129.27/17.93 | | | | | | | | | | | (85), (86), (90), (95), (96), (98), (106), (118), % 129.27/17.93 | | | | | | | | | | | (122) are inconsistent by sub-proof #33. % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | End of split % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | Case 2: % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | (123) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 % 129.27/17.93 | | | | | | | | | | & op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) % 129.27/17.93 | | | | | | | | | | = e2) % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | BETA: splitting (123) gives: % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | Case 1: % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | (124) all_9_11 = e2 & op(e2, e1) = e2 % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | ALPHA: (124) implies: % 129.27/17.93 | | | | | | | | | | | (125) op(e2, e1) = e2 % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | REF_CLOSE: (5), (38), (63), (125) are inconsistent by % 129.27/17.93 | | | | | | | | | | | sub-proof #44. % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | Case 2: % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | (126) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 % 129.27/17.93 | | | | | | | | | | | & op(e0, e1) = e2) % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (17), (24), (26), (28), (31), % 129.27/17.93 | | | | | | | | | | | (37), (41), (42), (49), (54), (57), (59), (60), % 129.27/17.93 | | | | | | | | | | | (62), (63), (70), (72), (77), (88), (97), (100), % 129.27/17.93 | | | | | | | | | | | (106), (126) are inconsistent by sub-proof #27. % 129.27/17.93 | | | | | | | | | | | % 129.27/17.93 | | | | | | | | | | End of split % 129.27/17.93 | | | | | | | | | | % 129.27/17.93 | | | | | | | | | End of split % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | Case 2: % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | (127) all_9_18 = e0 & op(e2, e0) = e0 % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | ALPHA: (127) implies: % 129.27/17.93 | | | | | | | | | (128) op(e2, e0) = e0 % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | | REF_CLOSE: (14), (22), (61), (128) are inconsistent by % 129.27/17.93 | | | | | | | | | sub-proof #150. % 129.27/17.93 | | | | | | | | | % 129.27/17.93 | | | | | | | | End of split % 129.27/17.93 | | | | | | | | % 129.27/17.93 | | | | | | | End of split % 129.27/17.93 | | | | | | | % 129.27/17.93 | | | | | | End of split % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | Case 2: % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | (129) all_9_16 = e3 & op(e4, e0) = e3 % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | | REF_CLOSE: (6), (7), (10), (12), (13), (18), (53), (65), (78), (85), % 129.27/17.93 | | | | | | (95), (96), (101), (129) are inconsistent by sub-proof % 129.27/17.93 | | | | | | #80. % 129.27/17.93 | | | | | | % 129.27/17.93 | | | | | End of split % 129.27/17.93 | | | | | % 129.27/17.93 | | | | End of split % 129.27/17.93 | | | | % 129.27/17.93 | | | End of split % 129.27/17.93 | | | % 129.27/17.93 | | Case 2: % 129.27/17.93 | | | % 129.27/17.93 | | | (130) all_9_23 = e3 & op(e0, e1) = e3 % 129.27/17.93 | | | % 129.27/17.93 | | | ALPHA: (130) implies: % 129.27/17.93 | | | (131) all_9_23 = e3 % 129.27/17.93 | | | % 129.27/17.93 | | | REF_CLOSE: (2), (28), (31), (41), (42), (49), (60), (63), (70), (72), % 129.27/17.93 | | | (77), (100), (131) are inconsistent by sub-proof #26. % 129.27/17.93 | | | % 129.27/17.93 | | End of split % 129.27/17.93 | | % 129.27/17.93 | End of split % 129.27/17.93 | % 129.27/17.93 End of proof % 129.27/17.93 % 129.27/17.93 Sub-proof #26 shows that the following formulas are inconsistent: % 129.27/17.93 ---------------------------------------------------------------- % 129.27/17.93 (1) ~ (op(e4, e1) = e1) % 129.27/17.93 (2) ~ (all_4_18 = e1) % 129.27/17.93 (3) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.27/17.93 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.27/17.93 (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.93 (4) ~ (all_4_17 = e1) % 129.27/17.93 (5) all_6_8 = all_4_16 % 129.27/17.93 (6) all_9_23 = e3 % 129.27/17.93 (7) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.93 (8) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.27/17.93 (9) all_6_13 = all_4_17 % 129.27/17.93 (10) ~ (e3 = e1) % 129.27/17.93 (11) all_6_18 = all_4_18 % 129.27/17.93 (12) ~ (all_4_16 = e1) % 129.27/17.93 (13) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.93 % 129.27/17.93 Begin of proof % 129.27/17.93 | % 129.27/17.93 | BETA: splitting (3) gives: % 129.27/17.93 | % 129.27/17.93 | Case 1: % 129.27/17.93 | | % 129.27/17.93 | | (14) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) % 129.27/17.93 | | % 129.27/17.93 | | BETA: splitting (14) gives: % 129.27/17.93 | | % 129.27/17.93 | | Case 1: % 129.27/17.93 | | | % 129.27/17.93 | | | (15) all_9_9 = e1 & op(e4, e1) = e1 % 129.27/17.93 | | | % 129.27/17.93 | | | REF_CLOSE: (1), (15) are inconsistent by sub-proof #84. % 129.27/17.93 | | | % 129.27/17.93 | | Case 2: % 129.27/17.93 | | | % 129.27/17.93 | | | (16) all_9_10 = e1 & op(e3, e1) = e1 % 129.27/17.93 | | | % 129.27/17.93 | | | REF_CLOSE: (5), (12), (13), (16) are inconsistent by sub-proof #106. % 129.27/17.93 | | | % 129.27/17.93 | | End of split % 129.27/17.93 | | % 129.27/17.93 | Case 2: % 129.27/17.93 | | % 129.27/17.93 | | (17) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = % 129.27/17.93 | | e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.93 | | % 129.27/17.93 | | BETA: splitting (17) gives: % 129.27/17.93 | | % 129.27/17.93 | | Case 1: % 129.27/17.93 | | | % 129.27/17.93 | | | (18) all_9_11 = e1 & op(e2, e1) = e1 % 129.27/17.93 | | | % 129.27/17.93 | | | ALPHA: (18) implies: % 129.27/17.93 | | | (19) op(e2, e1) = e1 % 129.27/17.93 | | | % 129.27/17.93 | | | REF_CLOSE: (4), (8), (9), (19) are inconsistent by sub-proof #45. % 129.27/17.93 | | | % 129.27/17.93 | | Case 2: % 129.27/17.93 | | | % 129.27/17.93 | | | (20) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, e1) = % 129.27/17.93 | | | e1) % 129.27/17.93 | | | % 129.27/17.93 | | | BETA: splitting (20) gives: % 129.27/17.93 | | | % 129.27/17.93 | | | Case 1: % 129.27/17.93 | | | | % 129.27/17.93 | | | | (21) all_9_15 = e1 & op(e1, e1) = e1 % 129.27/17.93 | | | | % 129.27/17.93 | | | | REF_CLOSE: (2), (7), (11), (21) are inconsistent by sub-proof #31. % 129.27/17.93 | | | | % 129.27/17.93 | | | Case 2: % 129.27/17.93 | | | | % 129.27/17.93 | | | | (22) all_9_23 = e1 & op(e0, e1) = e1 % 129.27/17.93 | | | | % 129.27/17.93 | | | | ALPHA: (22) implies: % 129.27/17.93 | | | | (23) all_9_23 = e1 % 129.27/17.93 | | | | % 129.27/17.93 | | | | COMBINE_EQS: (6), (23) imply: % 129.27/17.93 | | | | (24) e3 = e1 % 129.27/17.93 | | | | % 129.27/17.93 | | | | SIMP: (24) implies: % 129.27/17.93 | | | | (25) e3 = e1 % 129.27/17.93 | | | | % 129.27/17.93 | | | | REDUCE: (10), (25) imply: % 129.27/17.93 | | | | (26) $false % 129.27/17.93 | | | | % 129.27/17.93 | | | | CLOSE: (26) is inconsistent. % 129.27/17.93 | | | | % 129.27/17.93 | | | End of split % 129.27/17.93 | | | % 129.27/17.93 | | End of split % 129.27/17.93 | | % 129.27/17.93 | End of split % 129.27/17.93 | % 129.27/17.93 End of proof % 129.27/17.93 % 129.27/17.93 Sub-proof #27 shows that the following formulas are inconsistent: % 129.27/17.93 ---------------------------------------------------------------- % 129.27/17.93 (1) ~ (op(e4, e1) = e1) % 129.27/17.93 (2) ~ (all_4_16 = e3) % 129.27/17.93 (3) ~ (all_4_6 = e3) % 129.27/17.93 (4) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.27/17.93 (5) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.27/17.93 (6) all_9_17 = e3 % 129.27/17.93 (7) ~ (all_4_18 = e1) % 129.27/17.93 (8) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.27/17.93 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.27/17.93 (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.93 (9) ~ (all_4_11 = e3) % 129.27/17.93 (10) ~ (all_4_17 = e1) % 129.27/17.93 (11) all_6_8 = all_4_16 % 129.27/17.94 (12) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) % 129.27/17.94 (13) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.94 (14) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.27/17.94 (15) all_6_7 = all_4_11 % 129.27/17.94 (16) ~ (e3 = e2) % 129.27/17.94 (17) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.27/17.94 (18) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.27/17.94 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.27/17.94 (all_9_17 = e3 & op(e3, e0) = e3) % 129.27/17.94 (19) all_6_13 = all_4_17 % 129.27/17.94 (20) all_9_15 = e3 % 129.27/17.94 (21) ~ (e3 = e1) % 129.27/17.94 (22) all_6_18 = all_4_18 % 129.27/17.94 (23) ~ (all_4_16 = e1) % 129.27/17.94 (24) all_9_2 = e1 % 129.27/17.94 (25) ~ (e2 = e1) % 129.27/17.94 (26) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | BETA: splitting (12) gives: % 129.27/17.94 | % 129.27/17.94 | Case 1: % 129.27/17.94 | | % 129.27/17.94 | | (27) all_9_15 = e2 & op(e1, e1) = e2 % 129.27/17.94 | | % 129.27/17.94 | | ALPHA: (27) implies: % 129.27/17.94 | | (28) all_9_15 = e2 % 129.27/17.94 | | % 129.27/17.94 | | COMBINE_EQS: (20), (28) imply: % 129.27/17.94 | | (29) e3 = e2 % 129.27/17.94 | | % 129.27/17.94 | | COMBINE_EQS: (6), (29) imply: % 129.27/17.94 | | (30) all_9_17 = e2 % 129.27/17.94 | | % 129.27/17.94 | | REF_CLOSE: (2), (3), (4), (5), (9), (11), (14), (15), (16), (18), (21), % 129.27/17.94 | | (24), (30) are inconsistent by sub-proof #86. % 129.27/17.94 | | % 129.27/17.94 | Case 2: % 129.27/17.94 | | % 129.27/17.94 | | (31) all_9_23 = e2 & op(e0, e1) = e2 % 129.27/17.94 | | % 129.27/17.94 | | REF_CLOSE: (1), (7), (8), (10), (11), (13), (17), (19), (22), (23), (25), % 129.27/17.94 | | (26), (31) are inconsistent by sub-proof #30. % 129.27/17.94 | | % 129.27/17.94 | End of split % 129.27/17.94 | % 129.27/17.94 End of proof % 129.27/17.94 % 129.27/17.94 Sub-proof #28 shows that the following formulas are inconsistent: % 129.27/17.94 ---------------------------------------------------------------- % 129.27/17.94 (1) all_9_8 = e4 % 129.27/17.94 (2) all_6_5 = e1 % 129.27/17.94 (3) ~ (e4 = e0) % 129.27/17.94 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.27/17.94 (5) all_6_10 = e3 % 129.27/17.94 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.94 (7) ~ (all_4_3 = all_4_4) % 129.27/17.94 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.94 (9) ~ (e4 = e2) % 129.27/17.94 (10) all_6_17 = all_4_13 % 129.27/17.94 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.94 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.94 (13) all_9_4 = e3 & op(e4, e2) = e3 % 129.27/17.94 (14) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.27/17.94 (15) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) | % 129.27/17.94 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) | % 129.27/17.94 (all_9_22 = e1 & op(e0, e2) = e1) % 129.27/17.94 (16) ~ (all_4_13 = e2) % 129.27/17.94 (17) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.27/17.94 (18) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 129.27/17.94 (19) ~ (all_4_3 = e3) % 129.27/17.94 (20) all_6_20 = all_4_4 % 129.27/17.94 (21) e4 = e2 | ~ (op(e2, e2) = e2) % 129.27/17.94 (22) ~ (all_4_13 = e1) % 129.27/17.94 (23) ~ (e3 = e0) % 129.27/17.94 (24) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.94 (25) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.27/17.94 = e0 % 129.27/17.94 (26) ~ (e2 = e0) % 129.27/17.94 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.94 (28) ~ (all_4_4 = e3) % 129.27/17.94 (29) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.94 (30) all_9_12 = e2 % 129.27/17.94 (31) ~ (e1 = e0) % 129.27/17.94 (32) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.27/17.94 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.27/17.94 (all_9_20 = e3 & op(e0, e4) = e3) % 129.27/17.94 (33) ~ (e3 = e2) % 129.27/17.94 (34) op(e0, e4) = all_4_4 % 129.27/17.94 (35) ~ (e4 = e1) % 129.27/17.94 (36) ~ (all_4_3 = e0) % 129.27/17.94 (37) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.27/17.94 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.27/17.94 (all_9_22 = e2 & op(e0, e2) = e2) % 129.27/17.94 (38) all_9_5 = e0 % 129.27/17.94 (39) ~ (e3 = e1) % 129.27/17.94 (40) op(e1, e4) = all_4_3 % 129.27/17.94 (41) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.27/17.94 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.27/17.94 (all_9_20 = e2 & op(e0, e4) = e2) % 129.27/17.94 (42) ~ (e4 = e3) % 129.27/17.94 (43) ~ (all_4_4 = e0) % 129.27/17.94 (44) ~ (all_4_3 = e1) % 129.27/17.94 (45) all_6_2 = all_4_10 % 129.27/17.94 (46) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.94 (47) op(e2, e4) = e3 % 129.27/17.94 (48) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.94 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.94 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.94 (49) all_9_2 = e1 % 129.27/17.94 (50) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.94 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.94 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.94 (51) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.94 = e0 % 129.27/17.94 (52) ~ (all_4_4 = e1) % 129.27/17.94 (53) ~ (all_4_10 = e2) % 129.27/17.94 (54) all_4_0 = e0 % 129.27/17.94 (55) all_9_20 = e4 % 129.27/17.94 (56) ~ (e2 = e1) % 129.27/17.94 (57) all_6_15 = all_4_3 % 129.27/17.94 (58) op(e4, e4) = e0 % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | ALPHA: (13) implies: % 129.27/17.94 | (59) all_9_4 = e3 % 129.27/17.94 | % 129.27/17.94 | BETA: splitting (15) gives: % 129.27/17.94 | % 129.27/17.94 | Case 1: % 129.27/17.94 | | % 129.27/17.94 | | (60) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_5 = e1 & op(e3, e2) = e1) % 129.27/17.94 | | % 129.27/17.94 | | BETA: splitting (60) gives: % 129.27/17.94 | | % 129.27/17.94 | | Case 1: % 129.27/17.94 | | | % 129.27/17.94 | | | (61) all_9_4 = e1 & op(e4, e2) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | REF_CLOSE: (39), (59), (61) are inconsistent by sub-proof #72. % 129.27/17.94 | | | % 129.27/17.94 | | Case 2: % 129.27/17.94 | | | % 129.27/17.94 | | | (62) all_9_5 = e1 & op(e3, e2) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | ALPHA: (62) implies: % 129.27/17.94 | | | (63) all_9_5 = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (11), (12), (17), (19), (20), % 129.27/17.94 | | | (23), (24), (25), (26), (27), (28), (31), (32), (33), (34), % 129.27/17.94 | | | (35), (36), (38), (39), (40), (41), (42), (43), (44), (46), % 129.27/17.94 | | | (47), (48), (49), (50), (51), (52), (54), (56), (57), (58), % 129.27/17.94 | | | (63) are inconsistent by sub-proof #101. % 129.27/17.94 | | | % 129.27/17.94 | | End of split % 129.27/17.94 | | % 129.27/17.94 | Case 2: % 129.27/17.94 | | % 129.27/17.94 | | (64) (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_14 = e1 & op(e1, e2) = e1) % 129.27/17.94 | | | (all_9_22 = e1 & op(e0, e2) = e1) % 129.27/17.94 | | % 129.27/17.94 | | BETA: splitting (64) gives: % 129.27/17.94 | | % 129.27/17.94 | | Case 1: % 129.27/17.94 | | | % 129.27/17.94 | | | (65) all_9_8 = e1 & op(e2, e2) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (11), (30), (35), (42), (48), % 129.27/17.94 | | | (54), (55), (65) are inconsistent by sub-proof #29. % 129.27/17.94 | | | % 129.27/17.94 | | Case 2: % 129.27/17.94 | | | % 129.27/17.94 | | | (66) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_22 = e1 & op(e0, e2) = % 129.27/17.94 | | | e1) % 129.27/17.94 | | | % 129.27/17.94 | | | BETA: splitting (66) gives: % 129.27/17.94 | | | % 129.27/17.94 | | | Case 1: % 129.27/17.94 | | | | % 129.27/17.94 | | | | (67) all_9_14 = e1 & op(e1, e2) = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | REF_CLOSE: (10), (18), (22), (67) are inconsistent by sub-proof #99. % 129.27/17.94 | | | | % 129.27/17.94 | | | Case 2: % 129.27/17.94 | | | | % 129.27/17.94 | | | | (68) all_9_22 = e1 & op(e0, e2) = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | ALPHA: (68) implies: % 129.27/17.94 | | | | (69) all_9_22 = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | REF_CLOSE: (9), (14), (16), (21), (26), (29), (37), (38), (45), (53), % 129.27/17.94 | | | | (56), (69) are inconsistent by sub-proof #73. % 129.27/17.94 | | | | % 129.27/17.94 | | | End of split % 129.27/17.94 | | | % 129.27/17.94 | | End of split % 129.27/17.94 | | % 129.27/17.94 | End of split % 129.27/17.94 | % 129.27/17.94 End of proof % 129.27/17.94 % 129.27/17.94 Sub-proof #29 shows that the following formulas are inconsistent: % 129.27/17.94 ---------------------------------------------------------------- % 129.27/17.94 (1) all_9_8 = e4 % 129.27/17.94 (2) all_6_5 = e1 % 129.27/17.94 (3) ~ (e4 = e0) % 129.27/17.94 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.94 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.94 (6) ~ (e4 = e2) % 129.27/17.94 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.94 (8) all_9_12 = e2 % 129.27/17.94 (9) ~ (e4 = e1) % 129.27/17.94 (10) all_9_8 = e1 & op(e2, e2) = e1 % 129.27/17.94 (11) ~ (e4 = e3) % 129.27/17.94 (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.94 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.94 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.94 (13) all_4_0 = e0 % 129.27/17.94 (14) all_9_20 = e4 % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | ALPHA: (10) implies: % 129.27/17.94 | (15) all_9_8 = e1 % 129.27/17.94 | % 129.27/17.94 | COMBINE_EQS: (1), (15) imply: % 129.27/17.94 | (16) e4 = e1 % 129.27/17.94 | % 129.27/17.94 | COMBINE_EQS: (14), (16) imply: % 129.27/17.94 | (17) all_9_20 = e1 % 129.27/17.94 | % 129.27/17.94 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (17) are % 129.27/17.94 | inconsistent by sub-proof #286. % 129.27/17.94 | % 129.27/17.94 End of proof % 129.27/17.94 % 129.27/17.94 Sub-proof #30 shows that the following formulas are inconsistent: % 129.27/17.94 ---------------------------------------------------------------- % 129.27/17.94 (1) ~ (op(e4, e1) = e1) % 129.27/17.94 (2) all_9_23 = e2 & op(e0, e1) = e2 % 129.27/17.94 (3) ~ (all_4_18 = e1) % 129.27/17.94 (4) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.27/17.94 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.27/17.94 (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.94 (5) ~ (all_4_17 = e1) % 129.27/17.94 (6) all_6_8 = all_4_16 % 129.27/17.94 (7) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.94 (8) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.27/17.94 (9) all_6_13 = all_4_17 % 129.27/17.94 (10) all_6_18 = all_4_18 % 129.27/17.94 (11) ~ (all_4_16 = e1) % 129.27/17.94 (12) ~ (e2 = e1) % 129.27/17.94 (13) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | ALPHA: (2) implies: % 129.27/17.94 | (14) all_9_23 = e2 % 129.27/17.94 | % 129.27/17.94 | BETA: splitting (4) gives: % 129.27/17.94 | % 129.27/17.94 | Case 1: % 129.27/17.94 | | % 129.27/17.94 | | (15) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) % 129.27/17.94 | | % 129.27/17.94 | | BETA: splitting (15) gives: % 129.27/17.94 | | % 129.27/17.94 | | Case 1: % 129.27/17.94 | | | % 129.27/17.94 | | | (16) all_9_9 = e1 & op(e4, e1) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | ALPHA: (16) implies: % 129.27/17.94 | | | (17) op(e4, e1) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | PRED_UNIFY: (1), (17) imply: % 129.27/17.94 | | | (18) $false % 129.27/17.94 | | | % 129.27/17.94 | | | CLOSE: (18) is inconsistent. % 129.27/17.94 | | | % 129.27/17.94 | | Case 2: % 129.27/17.94 | | | % 129.27/17.94 | | | (19) all_9_10 = e1 & op(e3, e1) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | REF_CLOSE: (6), (11), (13), (19) are inconsistent by sub-proof #106. % 129.27/17.94 | | | % 129.27/17.94 | | End of split % 129.27/17.94 | | % 129.27/17.94 | Case 2: % 129.27/17.94 | | % 129.27/17.94 | | (20) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = % 129.27/17.94 | | e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 129.27/17.94 | | % 129.27/17.94 | | BETA: splitting (20) gives: % 129.27/17.94 | | % 129.27/17.94 | | Case 1: % 129.27/17.94 | | | % 129.27/17.94 | | | (21) all_9_11 = e1 & op(e2, e1) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | ALPHA: (21) implies: % 129.27/17.94 | | | (22) op(e2, e1) = e1 % 129.27/17.94 | | | % 129.27/17.94 | | | REF_CLOSE: (5), (8), (9), (22) are inconsistent by sub-proof #45. % 129.27/17.94 | | | % 129.27/17.94 | | Case 2: % 129.27/17.94 | | | % 129.27/17.94 | | | (23) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, e1) = % 129.27/17.94 | | | e1) % 129.27/17.94 | | | % 129.27/17.94 | | | BETA: splitting (23) gives: % 129.27/17.94 | | | % 129.27/17.94 | | | Case 1: % 129.27/17.94 | | | | % 129.27/17.94 | | | | (24) all_9_15 = e1 & op(e1, e1) = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | REF_CLOSE: (3), (7), (10), (24) are inconsistent by sub-proof #31. % 129.27/17.94 | | | | % 129.27/17.94 | | | Case 2: % 129.27/17.94 | | | | % 129.27/17.94 | | | | (25) all_9_23 = e1 & op(e0, e1) = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | ALPHA: (25) implies: % 129.27/17.94 | | | | (26) all_9_23 = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | COMBINE_EQS: (14), (26) imply: % 129.27/17.94 | | | | (27) e2 = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | SIMP: (27) implies: % 129.27/17.94 | | | | (28) e2 = e1 % 129.27/17.94 | | | | % 129.27/17.94 | | | | REDUCE: (12), (28) imply: % 129.27/17.94 | | | | (29) $false % 129.27/17.94 | | | | % 129.27/17.94 | | | | CLOSE: (29) is inconsistent. % 129.27/17.94 | | | | % 129.27/17.94 | | | End of split % 129.27/17.94 | | | % 129.27/17.94 | | End of split % 129.27/17.94 | | % 129.27/17.94 | End of split % 129.27/17.94 | % 129.27/17.94 End of proof % 129.27/17.94 % 129.27/17.94 Sub-proof #31 shows that the following formulas are inconsistent: % 129.27/17.94 ---------------------------------------------------------------- % 129.27/17.94 (1) all_9_15 = e1 & op(e1, e1) = e1 % 129.27/17.94 (2) all_6_18 = e1 | ~ (op(e1, e1) = e1) % 129.27/17.94 (3) all_6_18 = all_4_18 % 129.27/17.94 (4) ~ (all_4_18 = e1) % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | ALPHA: (1) implies: % 129.27/17.94 | (5) op(e1, e1) = e1 % 129.27/17.94 | % 129.27/17.94 | BETA: splitting (2) gives: % 129.27/17.94 | % 129.27/17.94 | Case 1: % 129.27/17.94 | | % 129.27/17.94 | | (6) ~ (op(e1, e1) = e1) % 129.27/17.94 | | % 129.27/17.94 | | PRED_UNIFY: (5), (6) imply: % 129.27/17.94 | | (7) $false % 129.27/17.94 | | % 129.27/17.94 | | CLOSE: (7) is inconsistent. % 129.27/17.94 | | % 129.27/17.94 | Case 2: % 129.27/17.94 | | % 129.27/17.94 | | (8) all_6_18 = e1 % 129.27/17.94 | | % 129.27/17.94 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #36. % 129.27/17.94 | | % 129.27/17.94 | End of split % 129.27/17.94 | % 129.27/17.94 End of proof % 129.27/17.94 % 129.27/17.94 Sub-proof #32 shows that the following formulas are inconsistent: % 129.27/17.94 ---------------------------------------------------------------- % 129.27/17.94 (1) all_6_5 = e1 % 129.27/17.94 (2) ~ (e4 = e0) % 129.27/17.94 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.27/17.94 (4) all_6_10 = e3 % 129.27/17.94 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.94 (6) ~ (all_4_3 = all_4_4) % 129.27/17.94 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.94 (8) ~ (e4 = e2) % 129.27/17.94 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.94 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.94 (11) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.27/17.94 (12) all_9_17 = e3 % 129.27/17.94 (13) ~ (all_4_13 = e2) % 129.27/17.94 (14) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.27/17.94 (15) all_9_24 = e0 % 129.27/17.94 (16) ~ (all_4_3 = e3) % 129.27/17.94 (17) all_6_20 = all_4_4 % 129.27/17.94 (18) e4 = e2 | ~ (op(e2, e2) = e2) % 129.27/17.94 (19) all_9_18 = e2 % 129.27/17.94 (20) ~ (e3 = e0) % 129.27/17.94 (21) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.94 (22) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.27/17.94 = e0 % 129.27/17.94 (23) ~ (e2 = e0) % 129.27/17.94 (24) all_9_22 = e2 % 129.27/17.94 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.94 (26) ~ (all_4_4 = e3) % 129.27/17.94 (27) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.27/17.94 (28) all_9_12 = e2 % 129.27/17.94 (29) ~ (e1 = e0) % 129.27/17.94 (30) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.27/17.94 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.27/17.94 (all_9_20 = e3 & op(e0, e4) = e3) % 129.27/17.94 (31) ~ (e3 = e2) % 129.27/17.94 (32) op(e0, e4) = all_4_4 % 129.27/17.94 (33) ~ (e4 = e1) % 129.27/17.94 (34) ~ (all_4_3 = e0) % 129.27/17.94 (35) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.27/17.94 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.27/17.94 (all_9_22 = e2 & op(e0, e2) = e2) % 129.27/17.94 (36) all_9_5 = e0 % 129.27/17.94 (37) ~ (e3 = e1) % 129.27/17.94 (38) op(e1, e4) = all_4_3 % 129.27/17.94 (39) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) | % 129.27/17.94 (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = e1) | % 129.27/17.94 (all_9_24 = e1 & op(e0, e0) = e1) % 129.27/17.94 (40) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.27/17.94 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.27/17.94 (all_9_20 = e2 & op(e0, e4) = e2) % 129.27/17.94 (41) ~ (e4 = e3) % 129.27/17.94 (42) ~ (all_4_4 = e0) % 129.27/17.94 (43) ~ (all_4_3 = e1) % 129.27/17.94 (44) all_9_19 = e3 % 129.27/17.94 (45) all_6_2 = all_4_10 % 129.27/17.94 (46) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.27/17.94 (47) op(e2, e4) = e3 % 129.27/17.94 (48) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.94 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.94 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.94 (49) all_9_2 = e1 % 129.27/17.94 (50) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.27/17.94 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.27/17.94 (all_9_20 = e1 & op(e0, e4) = e1) % 129.27/17.94 (51) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.27/17.94 = e0 % 129.27/17.94 (52) ~ (all_4_4 = e1) % 129.27/17.94 (53) ~ (all_4_10 = e2) % 129.27/17.94 (54) all_4_0 = e0 % 129.27/17.94 (55) all_9_20 = e4 % 129.27/17.94 (56) ~ (e2 = e1) % 129.27/17.94 (57) all_6_15 = all_4_3 % 129.27/17.94 (58) op(e4, e4) = e0 % 129.27/17.94 (59) all_9_16 = e4 % 129.27/17.94 % 129.27/17.94 Begin of proof % 129.27/17.94 | % 129.27/17.94 | BETA: splitting (39) gives: % 129.27/17.94 | % 129.27/17.94 | Case 1: % 129.27/17.94 | | % 129.27/17.94 | | (60) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = % 129.27/17.95 | | e1) % 129.27/17.95 | | % 129.27/17.95 | | BETA: splitting (60) gives: % 129.27/17.95 | | % 129.27/17.95 | | Case 1: % 129.27/17.95 | | | % 129.27/17.95 | | | (61) all_9_16 = e1 & op(e4, e0) = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | ALPHA: (61) implies: % 129.27/17.95 | | | (62) all_9_16 = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | COMBINE_EQS: (59), (62) imply: % 129.27/17.95 | | | (63) e4 = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | COMBINE_EQS: (55), (63) imply: % 129.27/17.95 | | | (64) all_9_20 = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (28), (33), (41), (48), (54), % 129.27/17.95 | | | (64) are inconsistent by sub-proof #286. % 129.27/17.95 | | | % 129.27/17.95 | | Case 2: % 129.27/17.95 | | | % 129.27/17.95 | | | (65) all_9_17 = e1 & op(e3, e0) = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | REF_CLOSE: (12), (37), (65) are inconsistent by sub-proof #63. % 129.27/17.95 | | | % 129.27/17.95 | | End of split % 129.27/17.95 | | % 129.27/17.95 | Case 2: % 129.27/17.95 | | % 129.27/17.95 | | (66) (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = % 129.27/17.95 | | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 129.27/17.95 | | % 129.27/17.95 | | BETA: splitting (66) gives: % 129.27/17.95 | | % 129.27/17.95 | | Case 1: % 129.27/17.95 | | | % 129.27/17.95 | | | (67) all_9_18 = e1 & op(e2, e0) = e1 % 129.27/17.95 | | | % 129.27/17.95 | | | REF_CLOSE: (8), (11), (13), (18), (19), (23), (24), (27), (35), (36), % 129.27/17.95 | | | (45), (53), (56), (67) are inconsistent by sub-proof #62. % 129.27/17.95 | | | % 129.27/17.95 | | Case 2: % 129.27/17.95 | | | % 129.27/17.95 | | | (68) (all_9_19 = e1 & op(e1, e0) = e1) | (all_9_24 = e1 & op(e0, e0) = % 129.27/17.95 | | | e1) % 129.27/17.95 | | | % 129.27/17.95 | | | BETA: splitting (68) gives: % 129.27/17.95 | | | % 129.27/17.95 | | | Case 1: % 129.27/17.95 | | | | % 129.27/17.95 | | | | (69) all_9_19 = e1 & op(e1, e0) = e1 % 129.27/17.95 | | | | % 129.27/17.95 | | | | ALPHA: (69) implies: % 129.27/17.95 | | | | (70) all_9_19 = e1 % 129.27/17.95 | | | | % 129.27/17.95 | | | | COMBINE_EQS: (44), (70) imply: % 129.27/17.95 | | | | (71) e3 = e1 % 129.27/17.95 | | | | % 129.27/17.95 | | | | SIMP: (71) implies: % 129.27/17.95 | | | | (72) e3 = e1 % 129.27/17.95 | | | | % 129.27/17.95 | | | | REDUCE: (37), (72) imply: % 129.27/17.95 | | | | (73) $false % 129.27/17.95 | | | | % 129.27/17.95 | | | | CLOSE: (73) is inconsistent. % 129.27/17.95 | | | | % 129.27/17.95 | | | Case 2: % 129.27/17.95 | | | | % 129.27/17.95 | | | | (74) all_9_24 = e1 & op(e0, e0) = e1 % 129.27/17.95 | | | | % 129.27/17.95 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (14), (15), (16), % 129.27/17.95 | | | | (17), (20), (21), (22), (23), (25), (26), (29), (30), (31), % 129.27/17.95 | | | | (32), (33), (34), (37), (38), (40), (41), (42), (43), (46), % 129.27/17.95 | | | | (47), (48), (49), (50), (51), (52), (54), (56), (57), (58), % 129.27/17.95 | | | | (74) are inconsistent by sub-proof #61. % 129.27/17.95 | | | | % 129.27/17.95 | | | End of split % 129.27/17.95 | | | % 129.27/17.95 | | End of split % 129.27/17.95 | | % 129.27/17.95 | End of split % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #33 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_6_5 = e1 % 129.27/17.95 (2) ~ (e4 = e0) % 129.27/17.95 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.95 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.95 (5) ~ (e4 = e2) % 129.27/17.95 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.95 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.95 (8) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.27/17.95 (9) all_9_10 = e2 % 129.27/17.95 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (11) ~ (all_4_19 = e4) % 129.27/17.95 (12) all_9_12 = e2 % 129.27/17.95 (13) ~ (e4 = e1) % 129.27/17.95 (14) ~ (all_4_15 = e4) % 129.27/17.95 (15) all_9_15 = e3 % 129.27/17.95 (16) op(e0, e1) = all_4_19 % 129.27/17.95 (17) ~ (all_4_3 = e4) % 129.27/17.95 (18) ~ (e4 = e3) % 129.27/17.95 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.95 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.95 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.95 (20) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.95 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.95 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.95 (21) all_9_11 = e0 % 129.27/17.95 (22) all_6_3 = all_4_15 % 129.27/17.95 (23) all_4_0 = e0 % 129.27/17.95 (24) all_9_20 = e4 % 129.27/17.95 (25) all_6_15 = all_4_3 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | BETA: splitting (20) gives: % 129.27/17.95 | % 129.27/17.95 | Case 1: % 129.27/17.95 | | % 129.27/17.95 | | (26) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 129.27/17.95 | | % 129.27/17.95 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (13), (14), (17), % 129.27/17.95 | | (18), (19), (22), (23), (24), (25), (26) are inconsistent by % 129.27/17.95 | | sub-proof #67. % 129.27/17.95 | | % 129.27/17.95 | Case 2: % 129.27/17.95 | | % 129.27/17.95 | | (27) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = % 129.27/17.95 | | e4) | (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.95 | | % 129.27/17.95 | | BETA: splitting (27) gives: % 129.27/17.95 | | % 129.27/17.95 | | Case 1: % 129.27/17.95 | | | % 129.27/17.95 | | | (28) all_9_11 = e4 & op(e2, e1) = e4 % 129.27/17.95 | | | % 129.27/17.95 | | | REF_CLOSE: (2), (21), (28) are inconsistent by sub-proof #66. % 129.27/17.95 | | | % 129.27/17.95 | | Case 2: % 129.27/17.95 | | | % 129.27/17.95 | | | (29) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) = % 129.27/17.95 | | | e4) % 129.27/17.95 | | | % 129.27/17.95 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (13), (15), % 129.27/17.95 | | | (16), (18), (19), (23), (24), (29) are inconsistent by % 129.27/17.95 | | | sub-proof #34. % 129.27/17.95 | | | % 129.27/17.95 | | End of split % 129.27/17.95 | | % 129.27/17.95 | End of split % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #34 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_6_5 = e1 % 129.27/17.95 (2) ~ (e4 = e0) % 129.27/17.95 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.95 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.95 (5) ~ (e4 = e2) % 129.27/17.95 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.95 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (8) ~ (all_4_19 = e4) % 129.27/17.95 (9) all_9_12 = e2 % 129.27/17.95 (10) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.95 (11) ~ (e4 = e1) % 129.27/17.95 (12) all_9_15 = e3 % 129.27/17.95 (13) op(e0, e1) = all_4_19 % 129.27/17.95 (14) ~ (e4 = e3) % 129.27/17.95 (15) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.95 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.95 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.95 (16) all_4_0 = e0 % 129.27/17.95 (17) all_9_20 = e4 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | BETA: splitting (10) gives: % 129.27/17.95 | % 129.27/17.95 | Case 1: % 129.27/17.95 | | % 129.27/17.95 | | (18) all_9_15 = e4 & op(e1, e1) = e4 % 129.27/17.95 | | % 129.27/17.95 | | ALPHA: (18) implies: % 129.27/17.95 | | (19) all_9_15 = e4 % 129.27/17.95 | | % 129.27/17.95 | | COMBINE_EQS: (12), (19) imply: % 129.27/17.95 | | (20) e4 = e3 % 129.27/17.95 | | % 129.27/17.95 | | COMBINE_EQS: (17), (20) imply: % 129.27/17.95 | | (21) all_9_20 = e3 % 129.27/17.95 | | % 129.27/17.95 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (14), (15), (16), (21) % 129.27/17.95 | | are inconsistent by sub-proof #202. % 129.27/17.95 | | % 129.27/17.95 | Case 2: % 129.27/17.95 | | % 129.27/17.95 | | (22) all_9_23 = e4 & op(e0, e1) = e4 % 129.27/17.95 | | % 129.27/17.95 | | REF_CLOSE: (7), (8), (13), (22) are inconsistent by sub-proof #65. % 129.27/17.95 | | % 129.27/17.95 | End of split % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #35 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_6_5 = e1 % 129.27/17.95 (2) ~ (e4 = e0) % 129.27/17.95 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.95 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.95 (5) ~ (e4 = e2) % 129.27/17.95 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.95 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.95 (8) all_9_10 = e4 % 129.27/17.95 (9) all_9_10 = e2 % 129.27/17.95 (10) ~ (e4 = e1) % 129.27/17.95 (11) ~ (all_4_3 = e4) % 129.27/17.95 (12) ~ (e4 = e3) % 129.27/17.95 (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.95 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.95 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.95 (14) all_4_0 = e0 % 129.27/17.95 (15) all_9_20 = e4 % 129.27/17.95 (16) all_6_15 = all_4_3 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | COMBINE_EQS: (8), (9) imply: % 129.27/17.95 | (17) e4 = e2 % 129.27/17.95 | % 129.27/17.95 | SIMP: (17) implies: % 129.27/17.95 | (18) e4 = e2 % 129.27/17.95 | % 129.27/17.95 | COMBINE_EQS: (15), (18) imply: % 129.27/17.95 | (19) all_9_20 = e2 % 129.27/17.95 | % 129.27/17.95 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), % 129.27/17.95 | (16), (19) are inconsistent by sub-proof #90. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #36 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_6_18 = all_4_18 % 129.27/17.95 (2) all_6_18 = e1 % 129.27/17.95 (3) ~ (all_4_18 = e1) % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | COMBINE_EQS: (1), (2) imply: % 129.27/17.95 | (4) all_4_18 = e1 % 129.27/17.95 | % 129.27/17.95 | SIMP: (4) implies: % 129.27/17.95 | (5) all_4_18 = e1 % 129.27/17.95 | % 129.27/17.95 | REDUCE: (3), (5) imply: % 129.27/17.95 | (6) $false % 129.27/17.95 | % 129.27/17.95 | CLOSE: (6) is inconsistent. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #37 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) op(e0, e1) = e1 % 129.27/17.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (3) ~ (all_8_87 = all_8_99) % 129.27/17.95 (4) op(e0, e1) = all_8_87 % 129.27/17.95 (5) op(e1, e0) = all_8_99 % 129.27/17.95 (6) op(e1, e0) = e1 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (2) with e1, all_8_87, e1, e0, simplifying with % 129.27/17.95 | (1), (4) gives: % 129.27/17.95 | (7) all_8_87 = e1 % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (2) with e1, all_8_99, e0, e1, simplifying with % 129.27/17.95 | (5), (6) gives: % 129.27/17.95 | (8) all_8_99 = e1 % 129.27/17.95 | % 129.27/17.95 | REDUCE: (3), (7), (8) imply: % 129.27/17.95 | (9) $false % 129.27/17.95 | % 129.27/17.95 | CLOSE: (9) is inconsistent. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #38 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) op(e2, e0) = all_8_96 % 129.27/17.95 (2) op(e0, e2) = all_8_75 % 129.27/17.95 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (4) op(e2, e0) = e2 % 129.27/17.95 (5) ~ (all_8_75 = all_8_96) % 129.27/17.95 (6) op(e0, e2) = e2 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (3) with e2, all_8_75, e2, e0, simplifying with % 129.27/17.95 | (2), (6) gives: % 129.27/17.95 | (7) all_8_75 = e2 % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (3) with e2, all_8_96, e0, e2, simplifying with % 129.27/17.95 | (1), (4) gives: % 129.27/17.95 | (8) all_8_96 = e2 % 129.27/17.95 | % 129.27/17.95 | REDUCE: (5), (7), (8) imply: % 129.27/17.95 | (9) $false % 129.27/17.95 | % 129.27/17.95 | CLOSE: (9) is inconsistent. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #39 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 129.27/17.95 (2) op(e3, e2) = e2 % 129.27/17.95 (3) all_4_11 = e0 % 129.27/17.95 (4) ~ (e2 = e0) % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | BETA: splitting (1) gives: % 129.27/17.95 | % 129.27/17.95 | Case 1: % 129.27/17.95 | | % 129.27/17.95 | | (5) ~ (op(e3, e2) = e2) % 129.27/17.95 | | % 129.27/17.95 | | PRED_UNIFY: (2), (5) imply: % 129.27/17.95 | | (6) $false % 129.27/17.95 | | % 129.27/17.95 | | CLOSE: (6) is inconsistent. % 129.27/17.95 | | % 129.27/17.95 | Case 2: % 129.27/17.95 | | % 129.27/17.95 | | (7) all_4_11 = e2 % 129.27/17.95 | | % 129.27/17.95 | | COMBINE_EQS: (3), (7) imply: % 129.27/17.95 | | (8) e2 = e0 % 129.27/17.95 | | % 129.27/17.95 | | REDUCE: (4), (8) imply: % 129.27/17.95 | | (9) $false % 129.27/17.95 | | % 129.27/17.95 | | CLOSE: (9) is inconsistent. % 129.27/17.95 | | % 129.27/17.95 | End of split % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #40 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (2) op(e3, e0) = e3 % 129.27/17.95 (3) op(e0, e3) = all_8_63 % 129.27/17.95 (4) op(e0, e3) = e3 % 129.27/17.95 (5) op(e3, e0) = all_8_93 % 129.27/17.95 (6) ~ (all_8_63 = all_8_93) % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (1) with e3, all_8_63, e3, e0, simplifying with % 129.27/17.95 | (3), (4) gives: % 129.27/17.95 | (7) all_8_63 = e3 % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (1) with e3, all_8_93, e0, e3, simplifying with % 129.27/17.95 | (2), (5) gives: % 129.27/17.95 | (8) all_8_93 = e3 % 129.27/17.95 | % 129.27/17.95 | REDUCE: (6), (7), (8) imply: % 129.27/17.95 | (9) $false % 129.27/17.95 | % 129.27/17.95 | CLOSE: (9) is inconsistent. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #41 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) op(e0, e4) = e4 % 129.27/17.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (3) op(e0, e4) = all_8_51 % 129.27/17.95 (4) op(e4, e0) = all_8_90 % 129.27/17.95 (5) op(e4, e0) = e4 % 129.27/17.95 (6) ~ (all_8_51 = all_8_90) % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (2) with e4, all_8_51, e4, e0, simplifying with % 129.27/17.95 | (1), (3) gives: % 129.27/17.95 | (7) all_8_51 = e4 % 129.27/17.95 | % 129.27/17.95 | GROUND_INST: instantiating (2) with e4, all_8_90, e0, e4, simplifying with % 129.27/17.95 | (4), (5) gives: % 129.27/17.95 | (8) all_8_90 = e4 % 129.27/17.95 | % 129.27/17.95 | REDUCE: (6), (7), (8) imply: % 129.27/17.95 | (9) $false % 129.27/17.95 | % 129.27/17.95 | CLOSE: (9) is inconsistent. % 129.27/17.95 | % 129.27/17.95 End of proof % 129.27/17.95 % 129.27/17.95 Sub-proof #42 shows that the following formulas are inconsistent: % 129.27/17.95 ---------------------------------------------------------------- % 129.27/17.95 (1) all_6_5 = e1 % 129.27/17.95 (2) ~ (e4 = e0) % 129.27/17.95 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.27/17.95 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.27/17.95 (5) ~ (e4 = e2) % 129.27/17.95 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.27/17.95 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.27/17.95 (8) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.27/17.95 (9) (all_8_58 = e1 & ~ (all_8_59 = e3) & op(e3, all_8_60) = e1 & op(e1, % 129.27/17.95 all_8_60) = all_8_59 & op(e1, e3) = all_8_60 & $i(all_8_59) & % 129.27/17.95 $i(all_8_60)) | (all_8_61 = e0 & ~ (all_8_62 = e3) & op(e3, all_8_63) % 129.27/17.95 = e0 & op(e0, all_8_63) = all_8_62 & op(e0, e3) = all_8_63 & % 129.27/17.95 $i(all_8_62) & $i(all_8_63)) % 129.27/17.95 (10) all_9_10 = e2 % 129.27/17.95 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.27/17.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.27/17.95 (12) ~ (all_4_19 = e4) % 129.27/17.95 (13) op(e3, e3) = e4 % 129.27/17.95 (14) op(e3, e0) = e3 % 129.27/17.95 (15) op(e0, e3) = e3 % 129.27/17.95 (16) ~ (all_4_15 = e0) % 129.27/17.95 (17) ~ (e4 = e1) % 129.27/17.95 (18) ~ (all_4_15 = e4) % 129.27/17.95 (19) ~ (e3 = e1) % 129.27/17.95 (20) op(e1, e3) = e0 % 129.27/17.95 (21) all_9_15 = e4 % 129.27/17.95 (22) all_6_3 = e3 | all_6_3 = e1 | all_6_3 = e0 % 129.27/17.95 (23) op(e0, e1) = all_4_19 % 129.27/17.95 (24) ~ (all_4_15 = e1) % 129.27/17.95 (25) ~ (all_4_3 = e4) % 129.27/17.95 (26) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.27/17.95 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.27/17.95 (all_9_20 = e4 & op(e0, e4) = e4) % 129.27/17.95 (27) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.27/17.95 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.27/17.95 (all_9_23 = e4 & op(e0, e1) = e4) % 129.27/17.95 (28) all_9_11 = e0 % 129.27/17.95 (29) all_6_3 = all_4_15 % 129.27/17.95 (30) all_4_0 = e0 % 129.27/17.95 (31) all_9_20 = e4 % 129.27/17.95 (32) all_6_15 = all_4_3 % 129.27/17.95 % 129.27/17.95 Begin of proof % 129.27/17.95 | % 129.27/17.95 | BETA: splitting (9) gives: % 129.27/17.95 | % 129.27/17.95 | Case 1: % 129.27/17.95 | | % 129.27/17.96 | | (33) all_8_58 = e1 & ~ (all_8_59 = e3) & op(e3, all_8_60) = e1 & op(e1, % 129.27/17.96 | | all_8_60) = all_8_59 & op(e1, e3) = all_8_60 & $i(all_8_59) & % 129.27/17.96 | | $i(all_8_60) % 129.27/17.96 | | % 129.27/17.96 | | ALPHA: (33) implies: % 129.27/17.96 | | (34) op(e1, e3) = all_8_60 % 129.53/17.96 | | (35) op(e3, all_8_60) = e1 % 129.53/17.96 | | % 129.53/17.96 | | GROUND_INST: instantiating (11) with e0, all_8_60, e3, e1, simplifying with % 129.53/17.96 | | (20), (34) gives: % 129.53/17.96 | | (36) all_8_60 = e0 % 129.53/17.96 | | % 129.53/17.99 | | GROUND_INST: instantiating (11) with e3, e1, e0, e3, simplifying with (14) % 129.53/17.99 | | gives: % 129.53/17.99 | | (37) e3 = e1 | ~ (op(e3, e0) = e1) % 129.53/17.99 | | % 129.53/17.99 | | REDUCE: (35), (36) imply: % 129.53/17.99 | | (38) op(e3, e0) = e1 % 129.53/17.99 | | % 129.53/17.99 | | BETA: splitting (37) gives: % 129.53/17.99 | | % 129.53/17.99 | | Case 1: % 129.53/17.99 | | | % 129.53/17.99 | | | (39) ~ (op(e3, e0) = e1) % 129.53/17.99 | | | % 129.53/17.99 | | | PRED_UNIFY: (38), (39) imply: % 129.53/17.99 | | | (40) $false % 129.53/17.99 | | | % 129.53/17.99 | | | CLOSE: (40) is inconsistent. % 129.53/17.99 | | | % 129.53/17.99 | | Case 2: % 129.53/17.99 | | | % 129.53/17.99 | | | (41) e3 = e1 % 129.53/17.99 | | | % 129.53/17.99 | | | REDUCE: (19), (41) imply: % 129.53/17.99 | | | (42) $false % 129.53/17.99 | | | % 129.53/17.99 | | | CLOSE: (42) is inconsistent. % 129.53/17.99 | | | % 129.53/17.99 | | End of split % 129.53/17.99 | | % 129.53/17.99 | Case 2: % 129.53/17.99 | | % 129.53/17.99 | | (43) all_8_61 = e0 & ~ (all_8_62 = e3) & op(e3, all_8_63) = e0 & op(e0, % 129.53/17.99 | | all_8_63) = all_8_62 & op(e0, e3) = all_8_63 & $i(all_8_62) & % 129.53/17.99 | | $i(all_8_63) % 129.53/17.99 | | % 129.53/17.99 | | ALPHA: (43) implies: % 129.53/17.99 | | (44) op(e0, e3) = all_8_63 % 129.53/17.99 | | (45) op(e3, all_8_63) = e0 % 129.53/17.99 | | % 129.53/17.99 | | BETA: splitting (22) gives: % 129.53/17.99 | | % 129.53/17.99 | | Case 1: % 129.53/17.99 | | | % 129.53/17.99 | | | (46) all_6_3 = e3 % 129.53/17.99 | | | % 129.53/17.99 | | | COMBINE_EQS: (29), (46) imply: % 129.53/17.99 | | | (47) all_4_15 = e3 % 129.53/17.99 | | | % 129.53/17.99 | | | REDUCE: (18), (47) imply: % 129.53/17.99 | | | (48) ~ (e4 = e3) % 129.53/17.99 | | | % 129.53/17.99 | | | SIMP: (48) implies: % 129.53/17.99 | | | (49) ~ (e4 = e3) % 129.53/17.99 | | | % 129.53/17.99 | | | GROUND_INST: instantiating (11) with e3, all_8_63, e3, e0, simplifying % 129.53/17.99 | | | with (15), (44) gives: % 129.53/17.99 | | | (50) all_8_63 = e3 % 129.53/17.99 | | | % 129.53/17.99 | | | GROUND_INST: instantiating (11) with e4, e0, e3, e3, simplifying with (13) % 129.53/17.99 | | | gives: % 129.53/17.99 | | | (51) e4 = e0 | ~ (op(e3, e3) = e0) % 129.53/17.99 | | | % 129.53/17.99 | | | REDUCE: (45), (50) imply: % 129.53/17.99 | | | (52) op(e3, e3) = e0 % 129.53/17.99 | | | % 129.53/17.99 | | | BETA: splitting (51) gives: % 129.53/17.99 | | | % 129.53/17.99 | | | Case 1: % 129.53/17.99 | | | | % 129.53/17.99 | | | | (53) ~ (op(e3, e3) = e0) % 129.53/17.99 | | | | % 129.53/17.99 | | | | PRED_UNIFY: (52), (53) imply: % 129.53/17.99 | | | | (54) $false % 129.53/17.99 | | | | % 129.53/17.99 | | | | CLOSE: (54) is inconsistent. % 129.53/17.99 | | | | % 129.53/17.99 | | | Case 2: % 129.53/17.99 | | | | % 129.53/17.99 | | | | (55) e4 = e0 % 129.53/17.99 | | | | % 129.53/17.99 | | | | COMBINE_EQS: (21), (55) imply: % 129.53/17.99 | | | | (56) all_9_15 = e0 % 129.53/17.99 | | | | % 129.53/17.99 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), % 129.53/17.99 | | | | (17), (18), (23), (25), (26), (27), (28), (29), (30), (31), % 129.53/17.99 | | | | (32), (49), (56) are inconsistent by sub-proof #64. % 129.53/17.99 | | | | % 129.53/17.99 | | | End of split % 129.53/17.99 | | | % 129.53/17.99 | | Case 2: % 129.53/17.99 | | | % 129.53/17.99 | | | (57) all_6_3 = e1 | all_6_3 = e0 % 129.53/17.99 | | | % 129.53/17.99 | | | REF_CLOSE: (16), (24), (29), (57) are inconsistent by sub-proof #43. % 129.53/17.99 | | | % 129.53/17.99 | | End of split % 129.53/17.99 | | % 129.53/17.99 | End of split % 129.78/17.99 | % 129.78/17.99 End of proof % 129.78/17.99 % 129.78/17.99 Sub-proof #43 shows that the following formulas are inconsistent: % 129.78/17.99 ---------------------------------------------------------------- % 129.78/17.99 (1) all_6_3 = e1 | all_6_3 = e0 % 129.78/17.99 (2) all_6_3 = all_4_15 % 129.78/17.99 (3) ~ (all_4_15 = e1) % 129.78/17.99 (4) ~ (all_4_15 = e0) % 129.78/17.99 % 129.78/17.99 Begin of proof % 129.78/17.99 | % 129.78/17.99 | BETA: splitting (1) gives: % 129.78/17.99 | % 129.78/17.99 | Case 1: % 129.78/17.99 | | % 129.78/17.99 | | (5) all_6_3 = e1 % 129.78/17.99 | | % 129.78/17.99 | | COMBINE_EQS: (2), (5) imply: % 129.78/17.99 | | (6) all_4_15 = e1 % 129.78/17.99 | | % 129.78/17.99 | | REDUCE: (3), (6) imply: % 129.78/17.99 | | (7) $false % 129.78/17.99 | | % 129.78/17.99 | | CLOSE: (7) is inconsistent. % 129.78/17.99 | | % 129.78/17.99 | Case 2: % 129.78/17.99 | | % 129.78/17.99 | | (8) all_6_3 = e0 % 129.78/17.99 | | % 129.78/17.99 | | COMBINE_EQS: (2), (8) imply: % 129.78/17.99 | | (9) all_4_15 = e0 % 129.78/17.99 | | % 129.78/17.99 | | REDUCE: (4), (9) imply: % 129.78/17.99 | | (10) $false % 129.78/17.99 | | % 129.78/17.99 | | CLOSE: (10) is inconsistent. % 129.78/17.99 | | % 129.78/17.99 | End of split % 129.78/17.99 | % 129.78/17.99 End of proof % 129.78/17.99 % 129.78/17.99 Sub-proof #44 shows that the following formulas are inconsistent: % 129.78/17.99 ---------------------------------------------------------------- % 129.78/17.99 (1) all_6_13 = e2 | ~ (op(e2, e1) = e2) % 129.78/17.99 (2) op(e2, e1) = e2 % 129.78/17.99 (3) all_6_13 = all_4_17 % 129.78/17.99 (4) ~ (all_4_17 = e2) % 129.78/17.99 % 129.78/17.99 Begin of proof % 129.78/17.99 | % 129.78/17.99 | BETA: splitting (1) gives: % 129.78/17.99 | % 129.78/17.99 | Case 1: % 129.78/17.99 | | % 129.78/17.99 | | (5) ~ (op(e2, e1) = e2) % 129.78/17.99 | | % 129.78/17.99 | | PRED_UNIFY: (2), (5) imply: % 129.78/17.99 | | (6) $false % 129.78/17.99 | | % 129.78/17.99 | | CLOSE: (6) is inconsistent. % 129.78/17.99 | | % 129.78/17.99 | Case 2: % 129.78/17.99 | | % 129.78/17.99 | | (7) all_6_13 = e2 % 129.78/17.99 | | % 129.78/17.99 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #76. % 129.78/17.99 | | % 129.78/17.99 | End of split % 129.78/17.99 | % 129.78/17.99 End of proof % 129.78/17.99 % 129.78/17.99 Sub-proof #45 shows that the following formulas are inconsistent: % 129.78/17.99 ---------------------------------------------------------------- % 129.78/17.99 (1) all_6_13 = e1 | ~ (op(e2, e1) = e1) % 129.78/17.99 (2) op(e2, e1) = e1 % 129.78/17.99 (3) all_6_13 = all_4_17 % 129.78/17.99 (4) ~ (all_4_17 = e1) % 129.78/17.99 % 129.78/17.99 Begin of proof % 129.78/17.99 | % 129.78/17.99 | BETA: splitting (1) gives: % 129.78/17.99 | % 129.78/17.99 | Case 1: % 129.78/17.99 | | % 129.78/17.99 | | (5) ~ (op(e2, e1) = e1) % 129.78/17.99 | | % 129.78/17.99 | | PRED_UNIFY: (2), (5) imply: % 129.78/17.99 | | (6) $false % 129.78/17.99 | | % 129.78/17.99 | | CLOSE: (6) is inconsistent. % 129.78/17.99 | | % 129.78/17.99 | Case 2: % 129.78/17.99 | | % 129.78/17.99 | | (7) all_6_13 = e1 % 129.78/17.99 | | % 129.78/17.99 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #52. % 129.78/17.99 | | % 129.78/17.99 | End of split % 129.78/17.99 | % 129.78/17.99 End of proof % 129.78/17.99 % 129.78/17.99 Sub-proof #46 shows that the following formulas are inconsistent: % 129.78/17.99 ---------------------------------------------------------------- % 129.78/17.99 (1) ~ (op(e4, e1) = e1) % 129.78/17.99 (2) ~ (all_4_16 = e3) % 129.78/17.99 (3) all_6_5 = e1 % 129.78/17.99 (4) ~ (e4 = e0) % 129.78/17.99 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.78/17.99 (6) all_6_10 = e3 % 129.78/17.99 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/17.99 (8) ~ (all_4_3 = all_4_4) % 129.78/17.99 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.00 (10) ~ (e4 = e2) % 129.78/18.00 (11) ~ (all_4_6 = e3) % 129.78/18.00 (12) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.00 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.00 (14) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.78/18.00 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.78/18.00 (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.00 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.00 (16) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.78/18.00 (17) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.00 (18) all_9_17 = e3 % 129.78/18.00 (19) all_9_15 = e2 % 129.78/18.00 (20) ~ (all_4_13 = e2) % 129.78/18.00 (21) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.78/18.00 (22) all_9_24 = e0 % 129.78/18.00 (23) ~ (all_4_3 = e3) % 129.78/18.00 (24) all_6_20 = all_4_4 % 129.78/18.00 (25) e4 = e2 | ~ (op(e2, e2) = e2) % 129.78/18.00 (26) all_9_18 = e2 % 129.78/18.00 (27) ~ (e3 = e0) % 129.78/18.00 (28) ~ (all_4_11 = e3) % 129.78/18.00 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.00 (30) all_6_8 = all_4_16 % 129.78/18.00 (31) ~ (op(e1, e0) = e0) % 129.78/18.00 (32) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.78/18.00 = e0 % 129.78/18.00 (33) ~ (e2 = e0) % 129.78/18.00 (34) all_9_22 = e2 % 129.78/18.00 (35) all_9_0 = e0 % 129.78/18.00 (36) all_9_9 = e3 % 129.78/18.00 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.00 (38) ~ (all_4_4 = e3) % 129.78/18.00 (39) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.78/18.00 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.78/18.00 (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.00 (40) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.00 (41) all_9_12 = e2 % 129.78/18.00 (42) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.00 (43) ~ (e1 = e0) % 129.78/18.00 (44) all_6_7 = all_4_11 % 129.78/18.00 (45) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.78/18.00 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.78/18.00 (all_9_20 = e3 & op(e0, e4) = e3) % 129.78/18.00 (46) ~ (e3 = e2) % 129.78/18.00 (47) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.00 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.00 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.00 (48) op(e0, e4) = all_4_4 % 129.78/18.00 (49) ~ (e4 = e1) % 129.78/18.00 (50) ~ (all_4_3 = e0) % 129.78/18.00 (51) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.78/18.00 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.78/18.00 (all_9_22 = e2 & op(e0, e2) = e2) % 129.78/18.00 (52) all_9_5 = e0 % 129.78/18.00 (53) ~ (e3 = e1) % 129.78/18.00 (54) ~ (op(e1, e4) = e4) % 129.78/18.00 (55) op(e1, e4) = all_4_3 % 129.78/18.00 (56) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = e4) | % 129.78/18.00 (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.78/18.00 (all_9_19 = e4 & op(e1, e0) = e4) % 129.78/18.00 (57) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) | % 129.78/18.00 (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = e1) | % 129.78/18.00 (all_9_24 = e1 & op(e0, e0) = e1) % 129.78/18.00 (58) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.78/18.00 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.78/18.00 (all_9_20 = e2 & op(e0, e4) = e2) % 129.78/18.00 (59) ~ (all_4_3 = e4) % 129.78/18.00 (60) op(e2, e2) = e4 % 129.78/18.00 (61) ~ (e4 = e3) % 129.78/18.00 (62) ~ (all_4_4 = e0) % 129.78/18.00 (63) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.00 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.00 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.00 (64) ~ (all_4_3 = e1) % 129.78/18.00 (65) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) | % 129.78/18.00 (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 129.78/18.00 (all_9_19 = e0 & op(e1, e0) = e0) % 129.78/18.00 (66) all_6_2 = all_4_10 % 129.78/18.00 (67) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.78/18.00 (68) op(e2, e4) = e3 % 129.78/18.00 (69) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.00 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.00 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.00 (70) all_9_2 = e1 % 129.78/18.00 (71) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.78/18.00 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.78/18.00 (all_9_20 = e1 & op(e0, e4) = e1) % 129.78/18.00 (72) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.78/18.00 = e0 % 129.78/18.00 (73) ~ (all_4_4 = e1) % 129.78/18.00 (74) ~ (all_4_10 = e2) % 129.78/18.00 (75) all_4_0 = e0 % 129.78/18.00 (76) all_9_20 = e4 % 129.78/18.00 (77) ~ (e2 = e1) % 129.78/18.00 (78) all_6_15 = all_4_3 % 129.78/18.00 (79) op(e4, e4) = e0 % 129.78/18.00 (80) all_9_16 = e4 % 129.78/18.00 % 129.78/18.00 Begin of proof % 129.78/18.00 | % 129.78/18.00 | BETA: splitting (56) gives: % 129.78/18.00 | % 129.78/18.00 | Case 1: % 129.78/18.00 | | % 129.78/18.00 | | (81) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_13 = e4 & op(e1, e3) = % 129.78/18.00 | | e4) % 129.78/18.00 | | % 129.78/18.00 | | BETA: splitting (81) gives: % 129.78/18.00 | | % 129.78/18.00 | | Case 1: % 129.78/18.00 | | | % 129.78/18.00 | | | (82) all_9_12 = e4 & op(e1, e4) = e4 % 129.78/18.00 | | | % 129.78/18.00 | | | REF_CLOSE: (54), (82) are inconsistent by sub-proof #74. % 129.78/18.00 | | | % 129.78/18.00 | | Case 2: % 129.78/18.00 | | | % 129.78/18.00 | | | (83) all_9_13 = e4 & op(e1, e3) = e4 % 129.78/18.00 | | | % 129.78/18.00 | | | ALPHA: (83) implies: % 129.78/18.00 | | | (84) all_9_13 = e4 % 129.78/18.00 | | | % 129.78/18.00 | | | BETA: splitting (14) gives: % 129.78/18.00 | | | % 129.78/18.00 | | | Case 1: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (85) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = % 129.78/18.00 | | | | e2) % 129.78/18.00 | | | | % 129.78/18.00 | | | | BETA: splitting (85) gives: % 129.78/18.00 | | | | % 129.78/18.00 | | | | Case 1: % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | (86) all_9_0 = e2 & op(e4, e4) = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | REF_CLOSE: (33), (35), (86) are inconsistent by sub-proof #314. % 129.78/18.00 | | | | | % 129.78/18.00 | | | | Case 2: % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | (87) all_9_1 = e2 & op(e4, e3) = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | ALPHA: (87) implies: % 129.78/18.00 | | | | | (88) all_9_1 = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | BETA: splitting (39) gives: % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | Case 1: % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | | (89) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, % 129.78/18.00 | | | | | | e2) = e3) % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (10), (13), (28), (37), (41), % 129.78/18.00 | | | | | | (42), (43), (44), (49), (53), (61), (63), (69), (75), % 129.78/18.00 | | | | | | (76), (77), (79), (80), (88), (89) are inconsistent by % 129.78/18.00 | | | | | | sub-proof #50. % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | Case 2: % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | | (90) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, % 129.78/18.00 | | | | | | e2) = e3) | (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | | REF_CLOSE: (2), (4), (11), (12), (17), (18), (19), (27), (28), (30), % 129.78/18.00 | | | | | | (31), (33), (34), (37), (41), (42), (44), (46), (47), % 129.78/18.00 | | | | | | (53), (60), (61), (65), (70), (84), (90) are inconsistent % 129.78/18.00 | | | | | | by sub-proof #49. % 129.78/18.00 | | | | | | % 129.78/18.00 | | | | | End of split % 129.78/18.00 | | | | | % 129.78/18.00 | | | | End of split % 129.78/18.00 | | | | % 129.78/18.00 | | | Case 2: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (91) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = % 129.78/18.00 | | | | e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.00 | | | | % 129.78/18.00 | | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (12), (13), (15), (17), % 129.78/18.00 | | | | (18), (28), (30), (36), (40), (42), (44), (46), (47), (49), % 129.78/18.00 | | | | (53), (59), (61), (66), (69), (70), (74), (75), (76), (78), % 129.78/18.00 | | | | (80), (91) are inconsistent by sub-proof #81. % 129.78/18.00 | | | | % 129.78/18.00 | | | End of split % 129.78/18.00 | | | % 129.78/18.00 | | End of split % 129.78/18.00 | | % 129.78/18.00 | Case 2: % 129.78/18.00 | | % 129.78/18.00 | | (92) (all_9_14 = e4 & op(e1, e2) = e4) | (all_9_15 = e4 & op(e1, e1) = % 129.78/18.00 | | e4) | (all_9_19 = e4 & op(e1, e0) = e4) % 129.78/18.00 | | % 129.78/18.00 | | BETA: splitting (92) gives: % 129.78/18.00 | | % 129.78/18.00 | | Case 1: % 129.78/18.00 | | | % 129.78/18.00 | | | (93) all_9_14 = e4 & op(e1, e2) = e4 % 129.78/18.00 | | | % 129.78/18.00 | | | ALPHA: (93) implies: % 129.78/18.00 | | | (94) all_9_14 = e4 % 129.78/18.00 | | | % 129.78/18.00 | | | BETA: splitting (14) gives: % 129.78/18.00 | | | % 129.78/18.00 | | | Case 1: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (95) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = % 129.78/18.00 | | | | e2) % 129.78/18.00 | | | | % 129.78/18.00 | | | | BETA: splitting (95) gives: % 129.78/18.00 | | | | % 129.78/18.00 | | | | Case 1: % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | (96) all_9_0 = e2 & op(e4, e4) = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | REF_CLOSE: (33), (35), (96) are inconsistent by sub-proof #314. % 129.78/18.00 | | | | | % 129.78/18.00 | | | | Case 2: % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | (97) all_9_1 = e2 & op(e4, e3) = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | ALPHA: (97) implies: % 129.78/18.00 | | | | | (98) all_9_1 = e2 % 129.78/18.00 | | | | | % 129.78/18.00 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (16), % 129.78/18.00 | | | | | (17), (18), (20), (25), (28), (30), (33), (34), (37), (39), % 129.78/18.00 | | | | | (40), (41), (42), (43), (44), (46), (47), (49), (51), (52), % 129.78/18.00 | | | | | (53), (60), (61), (63), (66), (69), (70), (74), (75), (76), % 129.78/18.00 | | | | | (77), (79), (80), (94), (98) are inconsistent by sub-proof % 129.78/18.00 | | | | | #69. % 129.78/18.00 | | | | | % 129.78/18.00 | | | | End of split % 129.78/18.00 | | | | % 129.78/18.00 | | | Case 2: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (99) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = % 129.78/18.00 | | | | e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.00 | | | | % 129.78/18.00 | | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (12), (13), (15), (17), % 129.78/18.00 | | | | (18), (28), (30), (36), (40), (42), (44), (46), (47), (49), % 129.78/18.00 | | | | (53), (59), (61), (66), (69), (70), (74), (75), (76), (78), % 129.78/18.00 | | | | (80), (99) are inconsistent by sub-proof #48. % 129.78/18.00 | | | | % 129.78/18.00 | | | End of split % 129.78/18.00 | | | % 129.78/18.00 | | Case 2: % 129.78/18.00 | | | % 129.78/18.00 | | | (100) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_19 = e4 & op(e1, e0) = % 129.78/18.00 | | | e4) % 129.78/18.00 | | | % 129.78/18.00 | | | BETA: splitting (100) gives: % 129.78/18.00 | | | % 129.78/18.00 | | | Case 1: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (101) all_9_15 = e4 & op(e1, e1) = e4 % 129.78/18.00 | | | | % 129.78/18.00 | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (15), (19), (49), (59), (61), % 129.78/18.00 | | | | (69), (75), (76), (78), (101) are inconsistent by sub-proof % 129.78/18.00 | | | | #47. % 129.78/18.00 | | | | % 129.78/18.00 | | | Case 2: % 129.78/18.00 | | | | % 129.78/18.00 | | | | (102) all_9_19 = e4 & op(e1, e0) = e4 % 129.78/18.00 | | | | % 129.78/18.00 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (13), (15), (16), % 129.78/18.00 | | | | (18), (20), (21), (22), (23), (24), (25), (26), (27), (29), % 129.78/18.00 | | | | (32), (33), (34), (37), (38), (40), (41), (43), (45), (46), % 129.78/18.00 | | | | (48), (49), (50), (51), (52), (53), (55), (57), (58), (61), % 129.78/18.00 | | | | (62), (64), (66), (67), (68), (69), (70), (71), (72), (73), % 129.78/18.00 | | | | (74), (75), (76), (77), (78), (79), (80), (102) are % 129.78/18.00 | | | | inconsistent by sub-proof #60. % 129.78/18.00 | | | | % 129.78/18.00 | | | End of split % 129.78/18.00 | | | % 129.78/18.00 | | End of split % 129.78/18.00 | | % 129.78/18.00 | End of split % 129.78/18.00 | % 129.78/18.00 End of proof % 129.78/18.00 % 129.78/18.00 Sub-proof #47 shows that the following formulas are inconsistent: % 129.78/18.00 ---------------------------------------------------------------- % 129.78/18.00 (1) all_6_5 = e1 % 129.78/18.00 (2) ~ (e4 = e0) % 129.78/18.00 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.00 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.00 (5) ~ (e4 = e2) % 129.78/18.00 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.00 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.00 (8) all_9_15 = e2 % 129.78/18.00 (9) ~ (e4 = e1) % 129.78/18.00 (10) ~ (all_4_3 = e4) % 129.78/18.00 (11) ~ (e4 = e3) % 129.78/18.00 (12) all_9_15 = e4 & op(e1, e1) = e4 % 129.78/18.00 (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.00 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.00 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.00 (14) all_4_0 = e0 % 129.78/18.00 (15) all_9_20 = e4 % 129.78/18.00 (16) all_6_15 = all_4_3 % 129.78/18.00 % 129.78/18.00 Begin of proof % 129.78/18.00 | % 129.78/18.00 | ALPHA: (12) implies: % 129.78/18.00 | (17) all_9_15 = e4 % 129.78/18.00 | % 129.78/18.00 | COMBINE_EQS: (8), (17) imply: % 129.78/18.00 | (18) e4 = e2 % 129.78/18.00 | % 129.78/18.00 | COMBINE_EQS: (15), (18) imply: % 129.78/18.00 | (19) all_9_20 = e2 % 129.78/18.00 | % 129.78/18.00 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), % 129.78/18.00 | (16), (19) are inconsistent by sub-proof #90. % 129.78/18.00 | % 129.78/18.00 End of proof % 129.78/18.00 % 129.78/18.00 Sub-proof #48 shows that the following formulas are inconsistent: % 129.78/18.00 ---------------------------------------------------------------- % 129.78/18.00 (1) ~ (all_4_16 = e3) % 129.78/18.00 (2) all_6_5 = e1 % 129.78/18.00 (3) ~ (e4 = e0) % 129.78/18.00 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.00 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.00 (6) ~ (e4 = e2) % 129.78/18.00 (7) ~ (all_4_6 = e3) % 129.78/18.00 (8) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.00 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.00 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.00 (11) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.00 (12) all_9_17 = e3 % 129.78/18.00 (13) ~ (all_4_11 = e3) % 129.78/18.00 (14) all_6_8 = all_4_16 % 129.78/18.00 (15) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.78/18.00 (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.00 (16) all_9_9 = e3 % 129.78/18.00 (17) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.00 (18) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.00 (19) all_6_7 = all_4_11 % 129.78/18.00 (20) ~ (e3 = e2) % 129.78/18.00 (21) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.00 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.00 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.00 (22) ~ (e4 = e1) % 129.78/18.00 (23) ~ (e3 = e1) % 129.78/18.00 (24) ~ (all_4_3 = e4) % 129.78/18.00 (25) ~ (e4 = e3) % 129.78/18.00 (26) all_6_2 = all_4_10 % 129.78/18.00 (27) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.00 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.00 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.00 (28) all_9_2 = e1 % 129.78/18.00 (29) ~ (all_4_10 = e2) % 129.78/18.00 (30) all_4_0 = e0 % 129.78/18.00 (31) all_9_20 = e4 % 129.78/18.00 (32) all_6_15 = all_4_3 % 129.78/18.00 (33) all_9_16 = e4 % 129.78/18.00 % 129.78/18.00 Begin of proof % 129.78/18.00 | % 129.78/18.00 | BETA: splitting (15) gives: % 129.78/18.00 | % 129.78/18.00 | Case 1: % 129.78/18.00 | | % 129.78/18.00 | | (34) all_9_4 = e2 & op(e4, e2) = e2 % 129.78/18.00 | | % 129.78/18.00 | | ALPHA: (34) implies: % 129.78/18.00 | | (35) op(e4, e2) = e2 % 129.78/18.00 | | % 129.78/18.00 | | REF_CLOSE: (17), (26), (29), (35) are inconsistent by sub-proof #261. % 129.78/18.00 | | % 129.78/18.00 | Case 2: % 129.78/18.00 | | % 129.78/18.00 | | (36) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.00 | | % 129.78/18.00 | | BETA: splitting (36) gives: % 129.78/18.00 | | % 129.78/18.00 | | Case 1: % 129.78/18.00 | | | % 129.78/18.00 | | | (37) all_9_9 = e2 & op(e4, e1) = e2 % 129.78/18.00 | | | % 129.78/18.00 | | | REF_CLOSE: (1), (7), (8), (11), (12), (13), (14), (16), (18), (19), (20), % 129.78/18.00 | | | (21), (23), (28), (37) are inconsistent by sub-proof #77. % 129.78/18.00 | | | % 129.78/18.00 | | Case 2: % 129.78/18.00 | | | % 129.78/18.00 | | | (38) all_9_16 = e2 & op(e4, e0) = e2 % 129.78/18.00 | | | % 129.78/18.00 | | | ALPHA: (38) implies: % 129.78/18.00 | | | (39) all_9_16 = e2 % 129.78/18.00 | | | % 129.78/18.00 | | | COMBINE_EQS: (33), (39) imply: % 129.78/18.00 | | | (40) e4 = e2 % 129.78/18.00 | | | % 129.78/18.00 | | | COMBINE_EQS: (31), (40) imply: % 129.78/18.00 | | | (41) all_9_20 = e2 % 129.78/18.00 | | | % 129.78/18.00 | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (22), (24), (25), (27), % 129.78/18.00 | | | (30), (32), (41) are inconsistent by sub-proof #90. % 129.78/18.00 | | | % 129.78/18.00 | | End of split % 129.78/18.00 | | % 129.78/18.00 | End of split % 129.78/18.00 | % 129.78/18.00 End of proof % 129.78/18.00 % 129.78/18.00 Sub-proof #49 shows that the following formulas are inconsistent: % 129.78/18.00 ---------------------------------------------------------------- % 129.78/18.00 (1) ~ (all_4_16 = e3) % 129.78/18.00 (2) ~ (e4 = e0) % 129.78/18.00 (3) ~ (all_4_6 = e3) % 129.78/18.00 (4) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.00 (5) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.00 (6) all_9_17 = e3 % 129.78/18.00 (7) all_9_15 = e2 % 129.78/18.00 (8) ~ (e3 = e0) % 129.78/18.00 (9) ~ (all_4_11 = e3) % 129.78/18.00 (10) all_6_8 = all_4_16 % 129.78/18.00 (11) ~ (op(e1, e0) = e0) % 129.78/18.00 (12) ~ (e2 = e0) % 129.78/18.00 (13) all_9_22 = e2 % 129.78/18.00 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.00 (15) all_9_12 = e2 % 129.78/18.00 (16) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.00 (17) all_6_7 = all_4_11 % 129.78/18.00 (18) ~ (e3 = e2) % 129.78/18.00 (19) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.00 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.00 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.00 (20) ~ (e3 = e1) % 129.78/18.00 (21) op(e2, e2) = e4 % 129.78/18.00 (22) all_9_13 = e4 % 129.78/18.00 (23) ~ (e4 = e3) % 129.78/18.00 (24) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) = e0) | % 129.78/18.00 (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 129.78/18.00 (all_9_19 = e0 & op(e1, e0) = e0) % 129.78/18.00 (25) all_9_2 = e1 % 129.78/18.00 (26) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.78/18.00 (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.00 % 129.78/18.00 Begin of proof % 129.78/18.00 | % 129.78/18.00 | BETA: splitting (26) gives: % 129.78/18.00 | % 129.78/18.00 | Case 1: % 129.78/18.00 | | % 129.78/18.00 | | (27) all_9_8 = e3 & op(e2, e2) = e3 % 129.78/18.00 | | % 129.78/18.00 | | REF_CLOSE: (14), (21), (23), (27) are inconsistent by sub-proof #126. % 129.78/18.00 | | % 129.78/18.00 | Case 2: % 129.78/18.00 | | % 129.78/18.00 | | (28) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) = % 129.78/18.00 | | e3) % 129.78/18.01 | | % 129.78/18.01 | | BETA: splitting (28) gives: % 129.78/18.01 | | % 129.78/18.01 | | Case 1: % 129.78/18.01 | | | % 129.78/18.01 | | | (29) all_9_14 = e3 & op(e1, e2) = e3 % 129.78/18.01 | | | % 129.78/18.01 | | | ALPHA: (29) implies: % 129.78/18.01 | | | (30) all_9_14 = e3 % 129.78/18.01 | | | % 129.78/18.01 | | | BETA: splitting (24) gives: % 129.78/18.01 | | | % 129.78/18.01 | | | Case 1: % 129.78/18.01 | | | | % 129.78/18.01 | | | | (31) (all_9_12 = e0 & op(e1, e4) = e0) | (all_9_13 = e0 & op(e1, e3) % 129.78/18.01 | | | | = e0) % 129.78/18.01 | | | | % 129.78/18.01 | | | | BETA: splitting (31) gives: % 129.78/18.01 | | | | % 129.78/18.01 | | | | Case 1: % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | (32) all_9_12 = e0 & op(e1, e4) = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | REF_CLOSE: (12), (15), (32) are inconsistent by sub-proof #75. % 129.78/18.01 | | | | | % 129.78/18.01 | | | | Case 2: % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | (33) all_9_13 = e0 & op(e1, e3) = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | ALPHA: (33) implies: % 129.78/18.01 | | | | | (34) all_9_13 = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | COMBINE_EQS: (22), (34) imply: % 129.78/18.01 | | | | | (35) e4 = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | SIMP: (35) implies: % 129.78/18.01 | | | | | (36) e4 = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | REDUCE: (2), (36) imply: % 129.78/18.01 | | | | | (37) $false % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | CLOSE: (37) is inconsistent. % 129.78/18.01 | | | | | % 129.78/18.01 | | | | End of split % 129.78/18.01 | | | | % 129.78/18.01 | | | Case 2: % 129.78/18.01 | | | | % 129.78/18.01 | | | | (38) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) % 129.78/18.01 | | | | = e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 129.78/18.01 | | | | % 129.78/18.01 | | | | BETA: splitting (38) gives: % 129.78/18.01 | | | | % 129.78/18.01 | | | | Case 1: % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | (39) all_9_14 = e0 & op(e1, e2) = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | ALPHA: (39) implies: % 129.78/18.01 | | | | | (40) all_9_14 = e0 % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | REF_CLOSE: (8), (30), (40) are inconsistent by sub-proof #57. % 129.78/18.01 | | | | | % 129.78/18.01 | | | | Case 2: % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | (41) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, % 129.78/18.01 | | | | | e0) = e0) % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | BETA: splitting (41) gives: % 129.78/18.01 | | | | | % 129.78/18.01 | | | | | Case 1: % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | (42) all_9_15 = e0 & op(e1, e1) = e0 % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | ALPHA: (42) implies: % 129.78/18.01 | | | | | | (43) all_9_15 = e0 % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | COMBINE_EQS: (7), (43) imply: % 129.78/18.01 | | | | | | (44) e2 = e0 % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | REDUCE: (12), (44) imply: % 129.78/18.01 | | | | | | (45) $false % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | CLOSE: (45) is inconsistent. % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | Case 2: % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | (46) all_9_19 = e0 & op(e1, e0) = e0 % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | | REF_CLOSE: (11), (46) are inconsistent by sub-proof #55. % 129.78/18.01 | | | | | | % 129.78/18.01 | | | | | End of split % 129.78/18.01 | | | | | % 129.78/18.01 | | | | End of split % 129.78/18.01 | | | | % 129.78/18.01 | | | End of split % 129.78/18.01 | | | % 129.78/18.01 | | Case 2: % 129.78/18.01 | | | % 129.78/18.01 | | | (47) all_9_22 = e3 & op(e0, e2) = e3 % 129.78/18.01 | | | % 129.78/18.01 | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (13), (16), (17), (18), % 129.78/18.01 | | | (19), (20), (25), (47) are inconsistent by sub-proof #70. % 129.78/18.01 | | | % 129.78/18.01 | | End of split % 129.78/18.01 | | % 129.78/18.01 | End of split % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #50 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) ~ (op(e4, e1) = e1) % 129.78/18.01 (2) all_6_5 = e1 % 129.78/18.01 (3) ~ (e4 = e0) % 129.78/18.01 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.01 (5) all_9_1 = e2 % 129.78/18.01 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.01 (7) ~ (e4 = e2) % 129.78/18.01 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.01 (9) ~ (all_4_11 = e3) % 129.78/18.01 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.01 (11) all_9_12 = e2 % 129.78/18.01 (12) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.01 (13) ~ (e1 = e0) % 129.78/18.01 (14) all_6_7 = all_4_11 % 129.78/18.01 (15) ~ (e4 = e1) % 129.78/18.01 (16) ~ (e3 = e1) % 129.78/18.01 (17) ~ (e4 = e3) % 129.78/18.01 (18) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.01 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.01 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.01 (19) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 129.78/18.01 (20) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.01 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.01 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.01 (21) all_4_0 = e0 % 129.78/18.01 (22) all_9_20 = e4 % 129.78/18.01 (23) ~ (e2 = e1) % 129.78/18.01 (24) op(e4, e4) = e0 % 129.78/18.01 (25) all_9_16 = e4 % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | BETA: splitting (19) gives: % 129.78/18.01 | % 129.78/18.01 | Case 1: % 129.78/18.01 | | % 129.78/18.01 | | (26) all_9_4 = e3 & op(e4, e2) = e3 % 129.78/18.01 | | % 129.78/18.01 | | ALPHA: (26) implies: % 129.78/18.01 | | (27) all_9_4 = e3 % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (15), % 129.78/18.01 | | (16), (17), (18), (20), (21), (22), (23), (24), (25), (27) are % 129.78/18.01 | | inconsistent by sub-proof #59. % 129.78/18.01 | | % 129.78/18.01 | Case 2: % 129.78/18.01 | | % 129.78/18.01 | | (28) all_9_5 = e3 & op(e3, e2) = e3 % 129.78/18.01 | | % 129.78/18.01 | | ALPHA: (28) implies: % 129.78/18.01 | | (29) op(e3, e2) = e3 % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (9), (12), (14), (29) are inconsistent by sub-proof #292. % 129.78/18.01 | | % 129.78/18.01 | End of split % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #51 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) ~ (e4 = e0) % 129.78/18.01 (2) op(e4, e3) = e2 % 129.78/18.01 (3) op(e3, e2) = e0 % 129.78/18.01 (4) all_8_52 = e4 & ~ (all_8_53 = e3) & op(e4, all_8_54) = all_8_53 & op(e4, % 129.78/18.01 e3) = all_8_54 & op(e3, all_8_54) = e4 & $i(all_8_53) & $i(all_8_54) % 129.78/18.01 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | ALPHA: (4) implies: % 129.78/18.01 | (6) op(e3, all_8_54) = e4 % 129.78/18.01 | (7) op(e4, e3) = all_8_54 % 129.78/18.01 | % 129.78/18.01 | GROUND_INST: instantiating (5) with e0, e4, e2, e3, simplifying with (3) % 129.78/18.01 | gives: % 129.78/18.01 | (8) e4 = e0 | ~ (op(e3, e2) = e4) % 129.78/18.01 | % 129.78/18.01 | GROUND_INST: instantiating (5) with e2, all_8_54, e3, e4, simplifying with % 129.78/18.01 | (2), (7) gives: % 129.78/18.01 | (9) all_8_54 = e2 % 129.78/18.01 | % 129.78/18.01 | REDUCE: (6), (9) imply: % 129.78/18.01 | (10) op(e3, e2) = e4 % 129.78/18.01 | % 129.78/18.01 | BETA: splitting (8) gives: % 129.78/18.01 | % 129.78/18.01 | Case 1: % 129.78/18.01 | | % 129.78/18.01 | | (11) ~ (op(e3, e2) = e4) % 129.78/18.01 | | % 129.78/18.01 | | PRED_UNIFY: (10), (11) imply: % 129.78/18.01 | | (12) $false % 129.78/18.01 | | % 129.78/18.01 | | CLOSE: (12) is inconsistent. % 129.78/18.01 | | % 129.78/18.01 | Case 2: % 129.78/18.01 | | % 129.78/18.01 | | (13) e4 = e0 % 129.78/18.01 | | % 129.78/18.01 | | REDUCE: (1), (13) imply: % 129.78/18.01 | | (14) $false % 129.78/18.01 | | % 129.78/18.01 | | CLOSE: (14) is inconsistent. % 129.78/18.01 | | % 129.78/18.01 | End of split % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #52 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) all_6_13 = all_4_17 % 129.78/18.01 (2) all_6_13 = e1 % 129.78/18.01 (3) ~ (all_4_17 = e1) % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | COMBINE_EQS: (1), (2) imply: % 129.78/18.01 | (4) all_4_17 = e1 % 129.78/18.01 | % 129.78/18.01 | SIMP: (4) implies: % 129.78/18.01 | (5) all_4_17 = e1 % 129.78/18.01 | % 129.78/18.01 | REDUCE: (3), (5) imply: % 129.78/18.01 | (6) $false % 129.78/18.01 | % 129.78/18.01 | CLOSE: (6) is inconsistent. % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #53 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) ~ (op(e4, e1) = e1) % 129.78/18.01 (2) ~ (all_4_16 = e3) % 129.78/18.01 (3) all_6_5 = e1 % 129.78/18.01 (4) ~ (e4 = e0) % 129.78/18.01 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.01 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.01 (7) ~ (e4 = e2) % 129.78/18.01 (8) ~ (all_4_6 = e3) % 129.78/18.01 (9) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.01 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.01 (11) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.78/18.01 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.78/18.01 (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.01 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.01 (13) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.78/18.01 (14) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.01 (15) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 129.78/18.01 (all_9_19 = e0 & op(e1, e0) = e0) % 129.78/18.01 (16) all_9_17 = e3 % 129.78/18.01 (17) ~ (e3 = e0) % 129.78/18.01 (18) ~ (all_4_11 = e3) % 129.78/18.01 (19) all_9_10 = e2 % 129.78/18.01 (20) all_6_8 = all_4_16 % 129.78/18.01 (21) ~ (op(e1, e0) = e0) % 129.78/18.01 (22) ~ (e2 = e0) % 129.78/18.01 (23) all_9_22 = e2 % 129.78/18.01 (24) all_9_0 = e0 % 129.78/18.01 (25) all_9_9 = e3 % 129.78/18.01 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.01 (27) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.78/18.01 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.78/18.01 (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.01 (28) ~ (all_4_19 = e4) % 129.78/18.01 (29) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.01 (30) all_9_12 = e2 % 129.78/18.01 (31) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.01 (32) ~ (e1 = e0) % 129.78/18.01 (33) all_6_7 = all_4_11 % 129.78/18.01 (34) ~ (e3 = e2) % 129.78/18.01 (35) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.01 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.01 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.01 (36) ~ (e4 = e1) % 129.78/18.01 (37) ~ (all_4_15 = e4) % 129.78/18.01 (38) ~ (e3 = e1) % 129.78/18.01 (39) op(e0, e1) = all_4_19 % 129.78/18.01 (40) ~ (all_4_3 = e4) % 129.78/18.01 (41) op(e2, e2) = e4 % 129.78/18.01 (42) ~ (e4 = e3) % 129.78/18.01 (43) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.01 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.01 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.01 (44) all_6_2 = all_4_10 % 129.78/18.01 (45) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.01 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.01 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.01 (46) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.78/18.01 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.78/18.01 (all_9_23 = e4 & op(e0, e1) = e4) % 129.78/18.01 (47) all_9_2 = e1 % 129.78/18.01 (48) all_9_11 = e0 % 129.78/18.01 (49) all_6_3 = all_4_15 % 129.78/18.01 (50) ~ (all_4_10 = e2) % 129.78/18.01 (51) all_4_0 = e0 % 129.78/18.01 (52) all_9_20 = e4 % 129.78/18.01 (53) ~ (e2 = e1) % 129.78/18.01 (54) all_6_15 = all_4_3 % 129.78/18.01 (55) op(e4, e4) = e0 % 129.78/18.01 (56) all_9_16 = e4 % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | BETA: splitting (15) gives: % 129.78/18.01 | % 129.78/18.01 | Case 1: % 129.78/18.01 | | % 129.78/18.01 | | (57) all_9_14 = e0 & op(e1, e2) = e0 % 129.78/18.01 | | % 129.78/18.01 | | ALPHA: (57) implies: % 129.78/18.01 | | (58) all_9_14 = e0 % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.78/18.01 | | (14), (16), (17), (18), (20), (22), (23), (24), (25), (26), (27), % 129.78/18.01 | | (29), (30), (31), (32), (33), (34), (35), (36), (38), (40), (41), % 129.78/18.01 | | (42), (43), (44), (45), (47), (50), (51), (52), (53), (54), (55), % 129.78/18.01 | | (56), (58) are inconsistent by sub-proof #56. % 129.78/18.01 | | % 129.78/18.01 | Case 2: % 129.78/18.01 | | % 129.78/18.01 | | (59) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) = % 129.78/18.01 | | e0) % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (12), (13), (19), (21), (26), % 129.78/18.01 | | (28), (36), (37), (39), (40), (42), (45), (46), (48), (49), (51), % 129.78/18.01 | | (52), (54), (59) are inconsistent by sub-proof #54. % 129.78/18.01 | | % 129.78/18.01 | End of split % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #54 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_19 = e0 & op(e1, e0) = e0) % 129.78/18.01 (2) all_6_5 = e1 % 129.78/18.01 (3) ~ (e4 = e0) % 129.78/18.01 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.01 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.01 (6) ~ (e4 = e2) % 129.78/18.01 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.01 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.01 (9) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.78/18.01 (10) all_9_10 = e2 % 129.78/18.01 (11) ~ (op(e1, e0) = e0) % 129.78/18.01 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.01 (13) ~ (all_4_19 = e4) % 129.78/18.01 (14) ~ (e4 = e1) % 129.78/18.01 (15) ~ (all_4_15 = e4) % 129.78/18.01 (16) op(e0, e1) = all_4_19 % 129.78/18.01 (17) ~ (all_4_3 = e4) % 129.78/18.01 (18) ~ (e4 = e3) % 129.78/18.01 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.01 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.01 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.01 (20) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.78/18.01 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.78/18.01 (all_9_23 = e4 & op(e0, e1) = e4) % 129.78/18.01 (21) all_9_11 = e0 % 129.78/18.01 (22) all_6_3 = all_4_15 % 129.78/18.01 (23) all_4_0 = e0 % 129.78/18.01 (24) all_9_20 = e4 % 129.78/18.01 (25) all_6_15 = all_4_3 % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | BETA: splitting (1) gives: % 129.78/18.01 | % 129.78/18.01 | Case 1: % 129.78/18.01 | | % 129.78/18.01 | | (26) all_9_15 = e0 & op(e1, e1) = e0 % 129.78/18.01 | | % 129.78/18.01 | | ALPHA: (26) implies: % 129.78/18.01 | | (27) all_9_15 = e0 % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 129.78/18.01 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 129.78/18.01 | | (27) are inconsistent by sub-proof #64. % 129.78/18.01 | | % 129.78/18.01 | Case 2: % 129.78/18.01 | | % 129.78/18.01 | | (28) all_9_19 = e0 & op(e1, e0) = e0 % 129.78/18.01 | | % 129.78/18.01 | | REF_CLOSE: (11), (28) are inconsistent by sub-proof #55. % 129.78/18.01 | | % 129.78/18.01 | End of split % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #55 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) all_9_19 = e0 & op(e1, e0) = e0 % 129.78/18.01 (2) ~ (op(e1, e0) = e0) % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | ALPHA: (1) implies: % 129.78/18.01 | (3) op(e1, e0) = e0 % 129.78/18.01 | % 129.78/18.01 | PRED_UNIFY: (2), (3) imply: % 129.78/18.01 | (4) $false % 129.78/18.01 | % 129.78/18.01 | CLOSE: (4) is inconsistent. % 129.78/18.01 | % 129.78/18.01 End of proof % 129.78/18.01 % 129.78/18.01 Sub-proof #56 shows that the following formulas are inconsistent: % 129.78/18.01 ---------------------------------------------------------------- % 129.78/18.01 (1) ~ (op(e4, e1) = e1) % 129.78/18.01 (2) ~ (all_4_16 = e3) % 129.78/18.01 (3) all_6_5 = e1 % 129.78/18.01 (4) ~ (e4 = e0) % 129.78/18.01 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.01 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.01 (7) ~ (e4 = e2) % 129.78/18.01 (8) ~ (all_4_6 = e3) % 129.78/18.01 (9) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.01 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.01 (11) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.78/18.01 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.78/18.01 (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.01 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.01 (13) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.01 (14) all_9_17 = e3 % 129.78/18.01 (15) ~ (e3 = e0) % 129.78/18.01 (16) ~ (all_4_11 = e3) % 129.78/18.01 (17) all_6_8 = all_4_16 % 129.78/18.01 (18) ~ (e2 = e0) % 129.78/18.01 (19) all_9_22 = e2 % 129.78/18.01 (20) all_9_0 = e0 % 129.78/18.01 (21) all_9_9 = e3 % 129.78/18.01 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.01 (23) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.78/18.01 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.78/18.01 (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.01 (24) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.01 (25) all_9_12 = e2 % 129.78/18.01 (26) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.01 (27) ~ (e1 = e0) % 129.78/18.01 (28) all_6_7 = all_4_11 % 129.78/18.01 (29) ~ (e3 = e2) % 129.78/18.01 (30) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.01 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.01 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.01 (31) ~ (e4 = e1) % 129.78/18.01 (32) ~ (e3 = e1) % 129.78/18.01 (33) ~ (all_4_3 = e4) % 129.78/18.01 (34) op(e2, e2) = e4 % 129.78/18.01 (35) ~ (e4 = e3) % 129.78/18.01 (36) all_9_14 = e0 % 129.78/18.01 (37) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.01 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.01 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.01 (38) all_6_2 = all_4_10 % 129.78/18.01 (39) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.01 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.01 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.01 (40) all_9_2 = e1 % 129.78/18.01 (41) ~ (all_4_10 = e2) % 129.78/18.01 (42) all_4_0 = e0 % 129.78/18.01 (43) all_9_20 = e4 % 129.78/18.01 (44) ~ (e2 = e1) % 129.78/18.01 (45) all_6_15 = all_4_3 % 129.78/18.01 (46) op(e4, e4) = e0 % 129.78/18.01 (47) all_9_16 = e4 % 129.78/18.01 % 129.78/18.01 Begin of proof % 129.78/18.01 | % 129.78/18.01 | BETA: splitting (23) gives: % 129.78/18.01 | % 129.78/18.01 | Case 1: % 129.78/18.01 | | % 129.78/18.01 | | (48) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 129.78/18.01 | | % 129.78/18.01 | | BETA: splitting (48) gives: % 129.78/18.02 | | % 129.78/18.02 | | Case 1: % 129.78/18.02 | | | % 129.78/18.02 | | | (49) all_9_4 = e3 & op(e4, e2) = e3 % 129.78/18.02 | | | % 129.78/18.02 | | | ALPHA: (49) implies: % 129.78/18.02 | | | (50) all_9_4 = e3 % 129.78/18.02 | | | % 129.78/18.02 | | | BETA: splitting (11) gives: % 129.78/18.02 | | | % 129.78/18.02 | | | Case 1: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (51) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = % 129.78/18.02 | | | | e2) % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (18), (20), (22), (25), % 129.78/18.02 | | | | (27), (31), (32), (35), (37), (39), (42), (43), (44), (46), % 129.78/18.02 | | | | (47), (50), (51) are inconsistent by sub-proof #58. % 129.78/18.02 | | | | % 129.78/18.02 | | | Case 2: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (52) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = % 129.78/18.02 | | | | e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), % 129.78/18.02 | | | | (14), (16), (17), (21), (24), (26), (28), (29), (30), (31), % 129.78/18.02 | | | | (32), (33), (35), (38), (39), (40), (41), (42), (43), (45), % 129.78/18.02 | | | | (47), (52) are inconsistent by sub-proof #81. % 129.78/18.02 | | | | % 129.78/18.02 | | | End of split % 129.78/18.02 | | | % 129.78/18.02 | | Case 2: % 129.78/18.02 | | | % 129.78/18.02 | | | (53) all_9_5 = e3 & op(e3, e2) = e3 % 129.78/18.02 | | | % 129.78/18.02 | | | ALPHA: (53) implies: % 129.78/18.02 | | | (54) op(e3, e2) = e3 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (16), (26), (28), (54) are inconsistent by sub-proof #292. % 129.78/18.02 | | | % 129.78/18.02 | | End of split % 129.78/18.02 | | % 129.78/18.02 | Case 2: % 129.78/18.02 | | % 129.78/18.02 | | (55) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) % 129.78/18.02 | | | (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.02 | | % 129.78/18.02 | | BETA: splitting (55) gives: % 129.78/18.02 | | % 129.78/18.02 | | Case 1: % 129.78/18.02 | | | % 129.78/18.02 | | | (56) all_9_8 = e3 & op(e2, e2) = e3 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (22), (34), (35), (56) are inconsistent by sub-proof #126. % 129.78/18.02 | | | % 129.78/18.02 | | Case 2: % 129.78/18.02 | | | % 129.78/18.02 | | | (57) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) = % 129.78/18.02 | | | e3) % 129.78/18.02 | | | % 129.78/18.02 | | | BETA: splitting (57) gives: % 129.78/18.02 | | | % 129.78/18.02 | | | Case 1: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (58) all_9_14 = e3 & op(e1, e2) = e3 % 129.78/18.02 | | | | % 129.78/18.02 | | | | ALPHA: (58) implies: % 129.78/18.02 | | | | (59) all_9_14 = e3 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (15), (36), (59) are inconsistent by sub-proof #57. % 129.78/18.02 | | | | % 129.78/18.02 | | | Case 2: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (60) all_9_22 = e3 & op(e0, e2) = e3 % 129.78/18.02 | | | | % 129.78/18.02 | | | | ALPHA: (60) implies: % 129.78/18.02 | | | | (61) all_9_22 = e3 % 129.78/18.02 | | | | % 129.78/18.02 | | | | COMBINE_EQS: (19), (61) imply: % 129.78/18.02 | | | | (62) e3 = e2 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (2), (8), (9), (13), (14), (16), (17), (26), (28), (29), % 129.78/18.02 | | | | (30), (32), (40), (62) are inconsistent by sub-proof #82. % 129.78/18.02 | | | | % 129.78/18.02 | | | End of split % 129.78/18.02 | | | % 129.78/18.02 | | End of split % 129.78/18.02 | | % 129.78/18.02 | End of split % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #57 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) all_9_14 = e3 % 129.78/18.02 (2) all_9_14 = e0 % 129.78/18.02 (3) ~ (e3 = e0) % 129.78/18.02 % 129.78/18.02 Begin of proof % 129.78/18.02 | % 129.78/18.02 | COMBINE_EQS: (1), (2) imply: % 129.78/18.02 | (4) e3 = e0 % 129.78/18.02 | % 129.78/18.02 | SIMP: (4) implies: % 129.78/18.02 | (5) e3 = e0 % 129.78/18.02 | % 129.78/18.02 | REDUCE: (3), (5) imply: % 129.78/18.02 | (6) $false % 129.78/18.02 | % 129.78/18.02 | CLOSE: (6) is inconsistent. % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #58 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) ~ (op(e4, e1) = e1) % 129.78/18.02 (2) all_6_5 = e1 % 129.78/18.02 (3) ~ (e4 = e0) % 129.78/18.02 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.02 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.02 (6) ~ (e4 = e2) % 129.78/18.02 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.02 (8) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) % 129.78/18.02 (9) all_9_4 = e3 % 129.78/18.02 (10) ~ (e2 = e0) % 129.78/18.02 (11) all_9_0 = e0 % 129.78/18.02 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.02 (13) all_9_12 = e2 % 129.78/18.02 (14) ~ (e1 = e0) % 129.78/18.02 (15) ~ (e4 = e1) % 129.78/18.02 (16) ~ (e3 = e1) % 129.78/18.02 (17) ~ (e4 = e3) % 129.78/18.02 (18) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.02 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.02 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.02 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.02 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.02 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.02 (20) all_4_0 = e0 % 129.78/18.02 (21) all_9_20 = e4 % 129.78/18.02 (22) ~ (e2 = e1) % 129.78/18.02 (23) op(e4, e4) = e0 % 129.78/18.02 (24) all_9_16 = e4 % 129.78/18.02 % 129.78/18.02 Begin of proof % 129.78/18.02 | % 129.78/18.02 | BETA: splitting (8) gives: % 129.78/18.02 | % 129.78/18.02 | Case 1: % 129.78/18.02 | | % 129.78/18.02 | | (25) all_9_0 = e2 & op(e4, e4) = e2 % 129.78/18.02 | | % 129.78/18.02 | | REF_CLOSE: (10), (11), (25) are inconsistent by sub-proof #314. % 129.78/18.02 | | % 129.78/18.02 | Case 2: % 129.78/18.02 | | % 129.78/18.02 | | (26) all_9_1 = e2 & op(e4, e3) = e2 % 129.78/18.02 | | % 129.78/18.02 | | ALPHA: (26) implies: % 129.78/18.02 | | (27) all_9_1 = e2 % 129.78/18.02 | | % 129.78/18.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (14), (15), % 129.78/18.02 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (27) are % 129.78/18.02 | | inconsistent by sub-proof #59. % 129.78/18.02 | | % 129.78/18.02 | End of split % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #59 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) ~ (op(e4, e1) = e1) % 129.78/18.02 (2) all_6_5 = e1 % 129.78/18.02 (3) ~ (e4 = e0) % 129.78/18.02 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.02 (5) all_9_1 = e2 % 129.78/18.02 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.02 (7) ~ (e4 = e2) % 129.78/18.02 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.02 (9) all_9_4 = e3 % 129.78/18.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.02 (11) all_9_12 = e2 % 129.78/18.02 (12) ~ (e1 = e0) % 129.78/18.02 (13) ~ (e4 = e1) % 129.78/18.02 (14) ~ (e3 = e1) % 129.78/18.02 (15) ~ (e4 = e3) % 129.78/18.02 (16) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.02 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.02 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.02 (17) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.02 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.02 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.02 (18) all_4_0 = e0 % 129.78/18.02 (19) all_9_20 = e4 % 129.78/18.02 (20) ~ (e2 = e1) % 129.78/18.02 (21) op(e4, e4) = e0 % 129.78/18.02 (22) all_9_16 = e4 % 129.78/18.02 % 129.78/18.02 Begin of proof % 129.78/18.02 | % 129.78/18.02 | BETA: splitting (16) gives: % 129.78/18.02 | % 129.78/18.02 | Case 1: % 129.78/18.02 | | % 129.78/18.02 | | (23) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) % 129.78/18.02 | | % 129.78/18.02 | | REF_CLOSE: (5), (10), (12), (20), (21), (23) are inconsistent by sub-proof % 129.78/18.02 | | #85. % 129.78/18.02 | | % 129.78/18.02 | Case 2: % 129.78/18.02 | | % 129.78/18.02 | | (24) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) % 129.78/18.02 | | | (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.02 | | % 129.78/18.02 | | BETA: splitting (24) gives: % 129.78/18.02 | | % 129.78/18.02 | | Case 1: % 129.78/18.02 | | | % 129.78/18.02 | | | (25) all_9_4 = e1 & op(e4, e2) = e1 % 129.78/18.02 | | | % 129.78/18.02 | | | ALPHA: (25) implies: % 129.78/18.02 | | | (26) all_9_4 = e1 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (9), (14), (26) are inconsistent by sub-proof #138. % 129.78/18.02 | | | % 129.78/18.02 | | Case 2: % 129.78/18.02 | | | % 129.78/18.02 | | | (27) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 129.78/18.02 | | | e1) % 129.78/18.02 | | | % 129.78/18.02 | | | BETA: splitting (27) gives: % 129.78/18.02 | | | % 129.78/18.02 | | | Case 1: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (28) all_9_9 = e1 & op(e4, e1) = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (1), (28) are inconsistent by sub-proof #84. % 129.78/18.02 | | | | % 129.78/18.02 | | | Case 2: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (29) all_9_16 = e1 & op(e4, e0) = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (11), (13), (15), (17), (18), % 129.78/18.02 | | | | (19), (22), (29) are inconsistent by sub-proof #83. % 129.78/18.02 | | | | % 129.78/18.02 | | | End of split % 129.78/18.02 | | | % 129.78/18.02 | | End of split % 129.78/18.02 | | % 129.78/18.02 | End of split % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #60 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) all_6_5 = e1 % 129.78/18.02 (2) ~ (e4 = e0) % 129.78/18.02 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.78/18.02 (4) all_6_10 = e3 % 129.78/18.02 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.02 (6) ~ (all_4_3 = all_4_4) % 129.78/18.02 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.02 (8) ~ (e4 = e2) % 129.78/18.02 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.02 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.02 (11) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.78/18.02 (12) all_9_17 = e3 % 129.78/18.02 (13) ~ (all_4_13 = e2) % 129.78/18.02 (14) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.78/18.02 (15) all_9_24 = e0 % 129.78/18.02 (16) all_9_19 = e4 & op(e1, e0) = e4 % 129.78/18.02 (17) ~ (all_4_3 = e3) % 129.78/18.02 (18) all_6_20 = all_4_4 % 129.78/18.02 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 129.78/18.02 (20) all_9_18 = e2 % 129.78/18.02 (21) ~ (e3 = e0) % 129.78/18.02 (22) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.02 (23) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.78/18.02 = e0 % 129.78/18.02 (24) ~ (e2 = e0) % 129.78/18.02 (25) all_9_22 = e2 % 129.78/18.02 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.02 (27) ~ (all_4_4 = e3) % 129.78/18.02 (28) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.02 (29) all_9_12 = e2 % 129.78/18.02 (30) ~ (e1 = e0) % 129.78/18.02 (31) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.78/18.02 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.78/18.02 (all_9_20 = e3 & op(e0, e4) = e3) % 129.78/18.02 (32) ~ (e3 = e2) % 129.78/18.02 (33) op(e0, e4) = all_4_4 % 129.78/18.02 (34) ~ (e4 = e1) % 129.78/18.02 (35) ~ (all_4_3 = e0) % 129.78/18.02 (36) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.78/18.02 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.78/18.02 (all_9_22 = e2 & op(e0, e2) = e2) % 129.78/18.02 (37) all_9_5 = e0 % 129.78/18.02 (38) ~ (e3 = e1) % 129.78/18.02 (39) op(e1, e4) = all_4_3 % 129.78/18.02 (40) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = e1) | % 129.78/18.02 (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = e1) | % 129.78/18.02 (all_9_24 = e1 & op(e0, e0) = e1) % 129.78/18.02 (41) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.78/18.02 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.78/18.02 (all_9_20 = e2 & op(e0, e4) = e2) % 129.78/18.02 (42) ~ (e4 = e3) % 129.78/18.02 (43) ~ (all_4_4 = e0) % 129.78/18.02 (44) ~ (all_4_3 = e1) % 129.78/18.02 (45) all_6_2 = all_4_10 % 129.78/18.02 (46) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.78/18.02 (47) op(e2, e4) = e3 % 129.78/18.02 (48) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.02 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.02 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.02 (49) all_9_2 = e1 % 129.78/18.02 (50) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.78/18.02 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.78/18.02 (all_9_20 = e1 & op(e0, e4) = e1) % 129.78/18.02 (51) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.78/18.02 = e0 % 129.78/18.02 (52) ~ (all_4_4 = e1) % 129.78/18.02 (53) ~ (all_4_10 = e2) % 129.78/18.02 (54) all_4_0 = e0 % 129.78/18.02 (55) all_9_20 = e4 % 129.78/18.02 (56) ~ (e2 = e1) % 129.78/18.02 (57) all_6_15 = all_4_3 % 129.78/18.02 (58) op(e4, e4) = e0 % 129.78/18.02 (59) all_9_16 = e4 % 129.78/18.02 % 129.78/18.02 Begin of proof % 129.78/18.02 | % 129.78/18.02 | ALPHA: (16) implies: % 129.78/18.02 | (60) all_9_19 = e4 % 129.78/18.02 | % 129.78/18.02 | BETA: splitting (40) gives: % 129.78/18.02 | % 129.78/18.02 | Case 1: % 129.78/18.02 | | % 129.78/18.02 | | (61) (all_9_16 = e1 & op(e4, e0) = e1) | (all_9_17 = e1 & op(e3, e0) = % 129.78/18.02 | | e1) % 129.78/18.02 | | % 129.78/18.02 | | BETA: splitting (61) gives: % 129.78/18.02 | | % 129.78/18.02 | | Case 1: % 129.78/18.02 | | | % 129.78/18.02 | | | (62) all_9_16 = e1 & op(e4, e0) = e1 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (29), (34), (42), (48), (54), % 129.78/18.02 | | | (55), (59), (62) are inconsistent by sub-proof #83. % 129.78/18.02 | | | % 129.78/18.02 | | Case 2: % 129.78/18.02 | | | % 129.78/18.02 | | | (63) all_9_17 = e1 & op(e3, e0) = e1 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (12), (38), (63) are inconsistent by sub-proof #63. % 129.78/18.02 | | | % 129.78/18.02 | | End of split % 129.78/18.02 | | % 129.78/18.02 | Case 2: % 129.78/18.02 | | % 129.78/18.02 | | (64) (all_9_18 = e1 & op(e2, e0) = e1) | (all_9_19 = e1 & op(e1, e0) = % 129.78/18.02 | | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 129.78/18.02 | | % 129.78/18.02 | | BETA: splitting (64) gives: % 129.78/18.02 | | % 129.78/18.02 | | Case 1: % 129.78/18.02 | | | % 129.78/18.02 | | | (65) all_9_18 = e1 & op(e2, e0) = e1 % 129.78/18.02 | | | % 129.78/18.02 | | | REF_CLOSE: (8), (11), (13), (19), (20), (24), (25), (28), (36), (37), % 129.78/18.02 | | | (45), (53), (56), (65) are inconsistent by sub-proof #62. % 129.78/18.02 | | | % 129.78/18.02 | | Case 2: % 129.78/18.02 | | | % 129.78/18.02 | | | (66) (all_9_19 = e1 & op(e1, e0) = e1) | (all_9_24 = e1 & op(e0, e0) = % 129.78/18.02 | | | e1) % 129.78/18.02 | | | % 129.78/18.02 | | | BETA: splitting (66) gives: % 129.78/18.02 | | | % 129.78/18.02 | | | Case 1: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (67) all_9_19 = e1 & op(e1, e0) = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | ALPHA: (67) implies: % 129.78/18.02 | | | | (68) all_9_19 = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | COMBINE_EQS: (60), (68) imply: % 129.78/18.02 | | | | (69) e4 = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | SIMP: (69) implies: % 129.78/18.02 | | | | (70) e4 = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | COMBINE_EQS: (55), (70) imply: % 129.78/18.02 | | | | (71) all_9_20 = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (29), (34), (42), (48), (54), % 129.78/18.02 | | | | (71) are inconsistent by sub-proof #286. % 129.78/18.02 | | | | % 129.78/18.02 | | | Case 2: % 129.78/18.02 | | | | % 129.78/18.02 | | | | (72) all_9_24 = e1 & op(e0, e0) = e1 % 129.78/18.02 | | | | % 129.78/18.02 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (14), (15), (17), % 129.78/18.02 | | | | (18), (21), (22), (23), (24), (26), (27), (30), (31), (32), % 129.78/18.02 | | | | (33), (34), (35), (38), (39), (41), (42), (43), (44), (46), % 129.78/18.02 | | | | (47), (48), (49), (50), (51), (52), (54), (56), (57), (58), % 129.78/18.02 | | | | (72) are inconsistent by sub-proof #61. % 129.78/18.02 | | | | % 129.78/18.02 | | | End of split % 129.78/18.02 | | | % 129.78/18.02 | | End of split % 129.78/18.02 | | % 129.78/18.02 | End of split % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #61 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) ~ (e4 = e0) % 129.78/18.02 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.78/18.02 (3) all_6_10 = e3 % 129.78/18.02 (4) ~ (all_4_3 = all_4_4) % 129.78/18.02 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.02 (6) ~ (e4 = e2) % 129.78/18.02 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.02 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.02 (9) all_9_24 = e1 & op(e0, e0) = e1 % 129.78/18.02 (10) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.78/18.02 (11) all_9_24 = e0 % 129.78/18.02 (12) ~ (all_4_3 = e3) % 129.78/18.02 (13) all_6_20 = all_4_4 % 129.78/18.02 (14) ~ (e3 = e0) % 129.78/18.02 (15) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.02 (16) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.78/18.02 = e0 % 129.78/18.02 (17) ~ (e2 = e0) % 129.78/18.02 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.02 (19) ~ (all_4_4 = e3) % 129.78/18.02 (20) ~ (e1 = e0) % 129.78/18.02 (21) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.78/18.02 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.78/18.02 (all_9_20 = e3 & op(e0, e4) = e3) % 129.78/18.02 (22) ~ (e3 = e2) % 129.78/18.02 (23) op(e0, e4) = all_4_4 % 129.78/18.02 (24) ~ (e4 = e1) % 129.78/18.02 (25) ~ (all_4_3 = e0) % 129.78/18.02 (26) ~ (e3 = e1) % 129.78/18.02 (27) op(e1, e4) = all_4_3 % 129.78/18.02 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.78/18.02 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.78/18.02 (all_9_20 = e2 & op(e0, e4) = e2) % 129.78/18.02 (29) ~ (e4 = e3) % 129.78/18.02 (30) ~ (all_4_4 = e0) % 129.78/18.02 (31) ~ (all_4_3 = e1) % 129.78/18.02 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.78/18.02 (33) op(e2, e4) = e3 % 129.78/18.02 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.02 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.02 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.02 (35) all_9_2 = e1 % 129.78/18.02 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.78/18.02 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.78/18.02 (all_9_20 = e1 & op(e0, e4) = e1) % 129.78/18.02 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.78/18.02 = e0 % 129.78/18.02 (38) ~ (all_4_4 = e1) % 129.78/18.02 (39) all_4_0 = e0 % 129.78/18.02 (40) ~ (e2 = e1) % 129.78/18.02 (41) all_6_15 = all_4_3 % 129.78/18.02 (42) op(e4, e4) = e0 % 129.78/18.02 % 129.78/18.02 Begin of proof % 129.78/18.02 | % 129.78/18.02 | ALPHA: (9) implies: % 129.78/18.02 | (43) all_9_24 = e1 % 129.78/18.02 | % 129.78/18.02 | COMBINE_EQS: (11), (43) imply: % 129.78/18.02 | (44) e1 = e0 % 129.78/18.02 | % 129.78/18.02 | COMBINE_EQS: (35), (44) imply: % 129.78/18.02 | (45) all_9_2 = e0 % 129.78/18.02 | % 129.78/18.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), % 129.78/18.02 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 129.78/18.02 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 129.78/18.02 | (38), (39), (40), (41), (42), (45) are inconsistent by sub-proof % 129.78/18.02 | #265. % 129.78/18.02 | % 129.78/18.02 End of proof % 129.78/18.02 % 129.78/18.02 Sub-proof #62 shows that the following formulas are inconsistent: % 129.78/18.02 ---------------------------------------------------------------- % 129.78/18.02 (1) ~ (e4 = e2) % 129.78/18.02 (2) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.78/18.02 (3) ~ (all_4_13 = e2) % 129.78/18.02 (4) e4 = e2 | ~ (op(e2, e2) = e2) % 129.78/18.02 (5) all_9_18 = e2 % 129.78/18.02 (6) ~ (e2 = e0) % 129.78/18.02 (7) all_9_22 = e2 % 129.78/18.02 (8) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.02 (9) all_9_18 = e1 & op(e2, e0) = e1 % 129.78/18.03 (10) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.78/18.03 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.78/18.03 (all_9_22 = e2 & op(e0, e2) = e2) % 129.78/18.03 (11) all_9_5 = e0 % 129.78/18.03 (12) all_6_2 = all_4_10 % 129.78/18.03 (13) ~ (all_4_10 = e2) % 129.78/18.03 (14) ~ (e2 = e1) % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (9) implies: % 129.78/18.03 | (15) all_9_18 = e1 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (5), (15) imply: % 129.78/18.03 | (16) e2 = e1 % 129.78/18.03 | % 129.78/18.03 | SIMP: (16) implies: % 129.78/18.03 | (17) e2 = e1 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (7), (17) imply: % 129.78/18.03 | (18) all_9_22 = e1 % 129.78/18.03 | % 129.78/18.03 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (13), (14), (18) % 129.78/18.03 | are inconsistent by sub-proof #73. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #63 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_9_17 = e1 & op(e3, e0) = e1 % 129.78/18.03 (2) all_9_17 = e3 % 129.78/18.03 (3) ~ (e3 = e1) % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (1) implies: % 129.78/18.03 | (4) all_9_17 = e1 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (2), (4) imply: % 129.78/18.03 | (5) e3 = e1 % 129.78/18.03 | % 129.78/18.03 | REDUCE: (3), (5) imply: % 129.78/18.03 | (6) $false % 129.78/18.03 | % 129.78/18.03 | CLOSE: (6) is inconsistent. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #64 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_6_5 = e1 % 129.78/18.03 (2) ~ (e4 = e0) % 129.78/18.03 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.03 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.03 (5) ~ (e4 = e2) % 129.78/18.03 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.03 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.03 (8) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.78/18.03 (9) all_9_10 = e2 % 129.78/18.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.03 (11) ~ (all_4_19 = e4) % 129.78/18.03 (12) ~ (e4 = e1) % 129.78/18.03 (13) ~ (all_4_15 = e4) % 129.78/18.03 (14) op(e0, e1) = all_4_19 % 129.78/18.03 (15) ~ (all_4_3 = e4) % 129.78/18.03 (16) ~ (e4 = e3) % 129.78/18.03 (17) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.03 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.03 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.03 (18) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 129.78/18.03 (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = e4) | % 129.78/18.03 (all_9_23 = e4 & op(e0, e1) = e4) % 129.78/18.03 (19) all_9_11 = e0 % 129.78/18.03 (20) all_6_3 = all_4_15 % 129.78/18.03 (21) all_4_0 = e0 % 129.78/18.03 (22) all_9_15 = e0 % 129.78/18.03 (23) all_9_20 = e4 % 129.78/18.03 (24) all_6_15 = all_4_3 % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | BETA: splitting (18) gives: % 129.78/18.03 | % 129.78/18.03 | Case 1: % 129.78/18.03 | | % 129.78/18.03 | | (25) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 129.78/18.03 | | % 129.78/18.03 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (15), % 129.78/18.03 | | (16), (17), (20), (21), (23), (24), (25) are inconsistent by % 129.78/18.03 | | sub-proof #67. % 129.78/18.03 | | % 129.78/18.03 | Case 2: % 129.78/18.03 | | % 129.78/18.03 | | (26) (all_9_11 = e4 & op(e2, e1) = e4) | (all_9_15 = e4 & op(e1, e1) = % 129.78/18.03 | | e4) | (all_9_23 = e4 & op(e0, e1) = e4) % 129.78/18.03 | | % 129.78/18.03 | | BETA: splitting (26) gives: % 129.78/18.03 | | % 129.78/18.03 | | Case 1: % 129.78/18.03 | | | % 129.78/18.03 | | | (27) all_9_11 = e4 & op(e2, e1) = e4 % 129.78/18.03 | | | % 129.78/18.03 | | | REF_CLOSE: (2), (19), (27) are inconsistent by sub-proof #66. % 129.78/18.03 | | | % 129.78/18.03 | | Case 2: % 129.78/18.03 | | | % 129.78/18.03 | | | (28) (all_9_15 = e4 & op(e1, e1) = e4) | (all_9_23 = e4 & op(e0, e1) = % 129.78/18.03 | | | e4) % 129.78/18.03 | | | % 129.78/18.03 | | | BETA: splitting (28) gives: % 129.78/18.03 | | | % 129.78/18.03 | | | Case 1: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (29) all_9_15 = e4 & op(e1, e1) = e4 % 129.78/18.03 | | | | % 129.78/18.03 | | | | ALPHA: (29) implies: % 129.78/18.03 | | | | (30) all_9_15 = e4 % 129.78/18.03 | | | | % 129.78/18.03 | | | | COMBINE_EQS: (22), (30) imply: % 129.78/18.03 | | | | (31) e4 = e0 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REDUCE: (2), (31) imply: % 129.78/18.03 | | | | (32) $false % 129.78/18.03 | | | | % 129.78/18.03 | | | | CLOSE: (32) is inconsistent. % 129.78/18.03 | | | | % 129.78/18.03 | | | Case 2: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (33) all_9_23 = e4 & op(e0, e1) = e4 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (10), (11), (14), (33) are inconsistent by sub-proof #65. % 129.78/18.03 | | | | % 129.78/18.03 | | | End of split % 129.78/18.03 | | | % 129.78/18.03 | | End of split % 129.78/18.03 | | % 129.78/18.03 | End of split % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #65 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_9_23 = e4 & op(e0, e1) = e4 % 129.78/18.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.03 (3) op(e0, e1) = all_4_19 % 129.78/18.03 (4) ~ (all_4_19 = e4) % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (1) implies: % 129.78/18.03 | (5) op(e0, e1) = e4 % 129.78/18.03 | % 129.78/18.03 | GROUND_INST: instantiating (2) with all_4_19, e4, e1, e0, simplifying with % 129.78/18.03 | (3), (5) gives: % 129.78/18.03 | (6) all_4_19 = e4 % 129.78/18.03 | % 129.78/18.03 | REDUCE: (4), (6) imply: % 129.78/18.03 | (7) $false % 129.78/18.03 | % 129.78/18.03 | CLOSE: (7) is inconsistent. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #66 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_9_11 = e4 & op(e2, e1) = e4 % 129.78/18.03 (2) all_9_11 = e0 % 129.78/18.03 (3) ~ (e4 = e0) % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (1) implies: % 129.78/18.03 | (4) all_9_11 = e4 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (2), (4) imply: % 129.78/18.03 | (5) e4 = e0 % 129.78/18.03 | % 129.78/18.03 | REDUCE: (3), (5) imply: % 129.78/18.03 | (6) $false % 129.78/18.03 | % 129.78/18.03 | CLOSE: (6) is inconsistent. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #67 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_6_5 = e1 % 129.78/18.03 (2) ~ (e4 = e0) % 129.78/18.03 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.03 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.03 (5) ~ (e4 = e2) % 129.78/18.03 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.03 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.03 (8) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.78/18.03 (9) all_9_10 = e2 % 129.78/18.03 (10) ~ (e4 = e1) % 129.78/18.03 (11) ~ (all_4_15 = e4) % 129.78/18.03 (12) ~ (all_4_3 = e4) % 129.78/18.03 (13) ~ (e4 = e3) % 129.78/18.03 (14) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.03 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.03 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.03 (15) all_6_3 = all_4_15 % 129.78/18.03 (16) all_4_0 = e0 % 129.78/18.03 (17) all_9_20 = e4 % 129.78/18.03 (18) all_6_15 = all_4_3 % 129.78/18.03 (19) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | BETA: splitting (19) gives: % 129.78/18.03 | % 129.78/18.03 | Case 1: % 129.78/18.03 | | % 129.78/18.03 | | (20) all_9_9 = e4 & op(e4, e1) = e4 % 129.78/18.03 | | % 129.78/18.03 | | ALPHA: (20) implies: % 129.78/18.03 | | (21) op(e4, e1) = e4 % 129.78/18.03 | | % 129.78/18.03 | | REF_CLOSE: (8), (11), (15), (21) are inconsistent by sub-proof #92. % 129.78/18.03 | | % 129.78/18.03 | Case 2: % 129.78/18.03 | | % 129.78/18.03 | | (22) all_9_10 = e4 & op(e3, e1) = e4 % 129.78/18.03 | | % 129.78/18.03 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), % 129.78/18.03 | | (16), (17), (18), (22) are inconsistent by sub-proof #68. % 129.78/18.03 | | % 129.78/18.03 | End of split % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #68 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) all_6_5 = e1 % 129.78/18.03 (2) ~ (e4 = e0) % 129.78/18.03 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.03 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.03 (5) ~ (e4 = e2) % 129.78/18.03 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.03 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.78/18.03 (8) all_9_10 = e2 % 129.78/18.03 (9) ~ (e4 = e1) % 129.78/18.03 (10) all_9_10 = e4 & op(e3, e1) = e4 % 129.78/18.03 (11) ~ (all_4_3 = e4) % 129.78/18.03 (12) ~ (e4 = e3) % 129.78/18.03 (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.03 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.03 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.03 (14) all_4_0 = e0 % 129.78/18.03 (15) all_9_20 = e4 % 129.78/18.03 (16) all_6_15 = all_4_3 % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (10) implies: % 129.78/18.03 | (17) all_9_10 = e4 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (8), (17) imply: % 129.78/18.03 | (18) e4 = e2 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (15), (18) imply: % 129.78/18.03 | (19) all_9_20 = e2 % 129.78/18.03 | % 129.78/18.03 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13), (14), % 129.78/18.03 | (16), (19) are inconsistent by sub-proof #90. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #69 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) ~ (op(e4, e1) = e1) % 129.78/18.03 (2) ~ (all_4_16 = e3) % 129.78/18.03 (3) all_6_5 = e1 % 129.78/18.03 (4) ~ (e4 = e0) % 129.78/18.03 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.03 (6) all_9_1 = e2 % 129.78/18.03 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.03 (8) ~ (e4 = e2) % 129.78/18.03 (9) ~ (all_4_6 = e3) % 129.78/18.03 (10) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.03 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.03 (12) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.78/18.03 (13) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.03 (14) all_9_17 = e3 % 129.78/18.03 (15) ~ (all_4_13 = e2) % 129.78/18.03 (16) e4 = e2 | ~ (op(e2, e2) = e2) % 129.78/18.03 (17) ~ (all_4_11 = e3) % 129.78/18.03 (18) all_6_8 = all_4_16 % 129.78/18.03 (19) ~ (e2 = e0) % 129.78/18.03 (20) all_9_22 = e2 % 129.78/18.03 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.03 (22) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 129.78/18.03 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 129.78/18.03 (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.03 (23) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.03 (24) all_9_12 = e2 % 129.78/18.03 (25) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.03 (26) ~ (e1 = e0) % 129.78/18.03 (27) all_6_7 = all_4_11 % 129.78/18.03 (28) ~ (e3 = e2) % 129.78/18.03 (29) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.03 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.03 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.03 (30) ~ (e4 = e1) % 129.78/18.03 (31) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.78/18.03 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.78/18.03 (all_9_22 = e2 & op(e0, e2) = e2) % 129.78/18.03 (32) all_9_5 = e0 % 129.78/18.03 (33) ~ (e3 = e1) % 129.78/18.03 (34) op(e2, e2) = e4 % 129.78/18.03 (35) ~ (e4 = e3) % 129.78/18.03 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.03 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.03 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.03 (37) all_9_14 = e4 % 129.78/18.03 (38) all_6_2 = all_4_10 % 129.78/18.03 (39) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.03 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.03 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.03 (40) all_9_2 = e1 % 129.78/18.03 (41) ~ (all_4_10 = e2) % 129.78/18.03 (42) all_4_0 = e0 % 129.78/18.03 (43) all_9_20 = e4 % 129.78/18.03 (44) ~ (e2 = e1) % 129.78/18.03 (45) op(e4, e4) = e0 % 129.78/18.03 (46) all_9_16 = e4 % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | BETA: splitting (22) gives: % 129.78/18.03 | % 129.78/18.03 | Case 1: % 129.78/18.03 | | % 129.78/18.03 | | (47) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 129.78/18.03 | | % 129.78/18.03 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (12), (15), (16), (17), % 129.78/18.03 | | (19), (20), (21), (23), (24), (25), (26), (27), (30), (31), (32), % 129.78/18.03 | | (33), (35), (36), (38), (39), (41), (42), (43), (44), (45), (46), % 129.78/18.03 | | (47) are inconsistent by sub-proof #71. % 129.78/18.03 | | % 129.78/18.03 | Case 2: % 129.78/18.03 | | % 129.78/18.03 | | (48) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) % 129.78/18.03 | | | (all_9_22 = e3 & op(e0, e2) = e3) % 129.78/18.03 | | % 129.78/18.03 | | BETA: splitting (48) gives: % 129.78/18.03 | | % 129.78/18.03 | | Case 1: % 129.78/18.03 | | | % 129.78/18.03 | | | (49) all_9_8 = e3 & op(e2, e2) = e3 % 129.78/18.03 | | | % 129.78/18.03 | | | REF_CLOSE: (21), (34), (35), (49) are inconsistent by sub-proof #126. % 129.78/18.03 | | | % 129.78/18.03 | | Case 2: % 129.78/18.03 | | | % 129.78/18.03 | | | (50) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) = % 129.78/18.03 | | | e3) % 129.78/18.03 | | | % 129.78/18.03 | | | BETA: splitting (50) gives: % 129.78/18.03 | | | % 129.78/18.03 | | | Case 1: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (51) all_9_14 = e3 & op(e1, e2) = e3 % 129.78/18.03 | | | | % 129.78/18.03 | | | | ALPHA: (51) implies: % 129.78/18.03 | | | | (52) all_9_14 = e3 % 129.78/18.03 | | | | % 129.78/18.03 | | | | COMBINE_EQS: (37), (52) imply: % 129.78/18.03 | | | | (53) e4 = e3 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (24), (30), (35), (39), (42), % 129.78/18.03 | | | | (43), (53) are inconsistent by sub-proof #89. % 129.78/18.03 | | | | % 129.78/18.03 | | | Case 2: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (54) all_9_22 = e3 & op(e0, e2) = e3 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (2), (9), (10), (13), (14), (17), (18), (20), (25), (27), % 129.78/18.03 | | | | (28), (29), (33), (40), (54) are inconsistent by sub-proof % 129.78/18.03 | | | | #70. % 129.78/18.03 | | | | % 129.78/18.03 | | | End of split % 129.78/18.03 | | | % 129.78/18.03 | | End of split % 129.78/18.03 | | % 129.78/18.03 | End of split % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #70 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) ~ (all_4_16 = e3) % 129.78/18.03 (2) ~ (all_4_6 = e3) % 129.78/18.03 (3) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.78/18.03 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.78/18.03 (5) all_9_17 = e3 % 129.78/18.03 (6) ~ (all_4_11 = e3) % 129.78/18.03 (7) all_6_8 = all_4_16 % 129.78/18.03 (8) all_9_22 = e2 % 129.78/18.03 (9) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.03 (10) all_6_7 = all_4_11 % 129.78/18.03 (11) ~ (e3 = e2) % 129.78/18.03 (12) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.78/18.03 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.78/18.03 (all_9_17 = e3 & op(e3, e0) = e3) % 129.78/18.03 (13) ~ (e3 = e1) % 129.78/18.03 (14) all_9_22 = e3 & op(e0, e2) = e3 % 129.78/18.03 (15) all_9_2 = e1 % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | ALPHA: (14) implies: % 129.78/18.03 | (16) all_9_22 = e3 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (8), (16) imply: % 129.78/18.03 | (17) e3 = e2 % 129.78/18.03 | % 129.78/18.03 | COMBINE_EQS: (5), (17) imply: % 129.78/18.03 | (18) all_9_17 = e2 % 129.78/18.03 | % 129.78/18.03 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15), % 129.78/18.03 | (18) are inconsistent by sub-proof #86. % 129.78/18.03 | % 129.78/18.03 End of proof % 129.78/18.03 % 129.78/18.03 Sub-proof #71 shows that the following formulas are inconsistent: % 129.78/18.03 ---------------------------------------------------------------- % 129.78/18.03 (1) ~ (op(e4, e1) = e1) % 129.78/18.03 (2) all_6_5 = e1 % 129.78/18.03 (3) ~ (e4 = e0) % 129.78/18.03 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.78/18.03 (5) all_9_1 = e2 % 129.78/18.03 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.78/18.03 (7) ~ (e4 = e2) % 129.78/18.03 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 129.78/18.03 (9) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.78/18.03 (10) ~ (all_4_13 = e2) % 129.78/18.03 (11) e4 = e2 | ~ (op(e2, e2) = e2) % 129.78/18.03 (12) ~ (all_4_11 = e3) % 129.78/18.03 (13) ~ (e2 = e0) % 129.78/18.03 (14) all_9_22 = e2 % 129.78/18.03 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.78/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.78/18.03 (16) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.78/18.03 (17) all_9_12 = e2 % 129.78/18.03 (18) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.78/18.03 (19) ~ (e1 = e0) % 129.78/18.03 (20) all_6_7 = all_4_11 % 129.78/18.03 (21) ~ (e4 = e1) % 129.78/18.03 (22) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.78/18.03 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.78/18.03 (all_9_22 = e2 & op(e0, e2) = e2) % 129.78/18.03 (23) all_9_5 = e0 % 129.78/18.03 (24) ~ (e3 = e1) % 129.78/18.03 (25) ~ (e4 = e3) % 129.78/18.03 (26) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.78/18.03 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.78/18.03 (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.03 (27) all_6_2 = all_4_10 % 129.78/18.03 (28) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 129.78/18.03 (29) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.78/18.03 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.78/18.03 (all_9_20 = e4 & op(e0, e4) = e4) % 129.78/18.03 (30) ~ (all_4_10 = e2) % 129.78/18.03 (31) all_4_0 = e0 % 129.78/18.03 (32) all_9_20 = e4 % 129.78/18.03 (33) ~ (e2 = e1) % 129.78/18.03 (34) op(e4, e4) = e0 % 129.78/18.03 (35) all_9_16 = e4 % 129.78/18.03 % 129.78/18.03 Begin of proof % 129.78/18.03 | % 129.78/18.03 | BETA: splitting (28) gives: % 129.78/18.03 | % 129.78/18.03 | Case 1: % 129.78/18.03 | | % 129.78/18.03 | | (36) all_9_4 = e3 & op(e4, e2) = e3 % 129.78/18.03 | | % 129.78/18.03 | | ALPHA: (36) implies: % 129.78/18.03 | | (37) all_9_4 = e3 % 129.78/18.03 | | % 129.78/18.03 | | BETA: splitting (26) gives: % 129.78/18.03 | | % 129.78/18.03 | | Case 1: % 129.78/18.03 | | | % 129.78/18.03 | | | (38) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = % 129.78/18.03 | | | e1) % 129.78/18.03 | | | % 129.78/18.03 | | | BETA: splitting (38) gives: % 129.78/18.03 | | | % 129.78/18.03 | | | Case 1: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (39) all_9_0 = e1 & op(e4, e4) = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | ALPHA: (39) implies: % 129.78/18.03 | | | | (40) op(e4, e4) = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (15), (19), (34), (40) are inconsistent by sub-proof #321. % 129.78/18.03 | | | | % 129.78/18.03 | | | Case 2: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (41) all_9_1 = e1 & op(e4, e3) = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | ALPHA: (41) implies: % 129.78/18.03 | | | | (42) all_9_1 = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | COMBINE_EQS: (5), (42) imply: % 129.78/18.03 | | | | (43) e2 = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | COMBINE_EQS: (14), (43) imply: % 129.78/18.03 | | | | (44) all_9_22 = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (7), (9), (10), (11), (13), (16), (22), (23), (27), (30), % 129.78/18.03 | | | | (33), (44) are inconsistent by sub-proof #73. % 129.78/18.03 | | | | % 129.78/18.03 | | | End of split % 129.78/18.03 | | | % 129.78/18.03 | | Case 2: % 129.78/18.03 | | | % 129.78/18.03 | | | (45) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = % 129.78/18.03 | | | e1) | (all_9_16 = e1 & op(e4, e0) = e1) % 129.78/18.03 | | | % 129.78/18.03 | | | BETA: splitting (45) gives: % 129.78/18.03 | | | % 129.78/18.03 | | | Case 1: % 129.78/18.03 | | | | % 129.78/18.03 | | | | (46) all_9_4 = e1 & op(e4, e2) = e1 % 129.78/18.03 | | | | % 129.78/18.03 | | | | REF_CLOSE: (24), (37), (46) are inconsistent by sub-proof #72. % 129.78/18.03 | | | | % 129.78/18.03 | | | Case 2: % 129.78/18.03 | | | | % 129.95/18.03 | | | | (47) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 129.95/18.03 | | | | e1) % 129.95/18.03 | | | | % 129.95/18.03 | | | | BETA: splitting (47) gives: % 129.95/18.03 | | | | % 129.95/18.03 | | | | Case 1: % 129.95/18.03 | | | | | % 129.95/18.03 | | | | | (48) all_9_9 = e1 & op(e4, e1) = e1 % 129.95/18.03 | | | | | % 129.95/18.03 | | | | | REF_CLOSE: (1), (48) are inconsistent by sub-proof #84. % 129.95/18.03 | | | | | % 129.95/18.03 | | | | Case 2: % 129.95/18.03 | | | | | % 129.95/18.04 | | | | | (49) all_9_16 = e1 & op(e4, e0) = e1 % 129.95/18.04 | | | | | % 129.95/18.04 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (17), (21), (25), (29), (31), % 129.95/18.04 | | | | | (32), (35), (49) are inconsistent by sub-proof #83. % 129.95/18.04 | | | | | % 129.95/18.04 | | | | End of split % 129.95/18.04 | | | | % 129.95/18.04 | | | End of split % 129.95/18.04 | | | % 129.95/18.04 | | End of split % 129.95/18.04 | | % 129.95/18.04 | Case 2: % 129.95/18.04 | | % 129.95/18.04 | | (50) all_9_5 = e3 & op(e3, e2) = e3 % 129.95/18.04 | | % 129.95/18.04 | | ALPHA: (50) implies: % 129.95/18.04 | | (51) op(e3, e2) = e3 % 129.95/18.04 | | % 129.95/18.04 | | REF_CLOSE: (12), (18), (20), (51) are inconsistent by sub-proof #292. % 129.95/18.04 | | % 129.95/18.04 | End of split % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #72 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) all_9_4 = e1 & op(e4, e2) = e1 % 129.95/18.04 (2) all_9_4 = e3 % 129.95/18.04 (3) ~ (e3 = e1) % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | ALPHA: (1) implies: % 129.95/18.04 | (4) all_9_4 = e1 % 129.95/18.04 | % 129.95/18.04 | COMBINE_EQS: (2), (4) imply: % 129.95/18.04 | (5) e3 = e1 % 129.95/18.04 | % 129.95/18.04 | REDUCE: (3), (5) imply: % 129.95/18.04 | (6) $false % 129.95/18.04 | % 129.95/18.04 | CLOSE: (6) is inconsistent. % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #73 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) ~ (e4 = e2) % 129.95/18.04 (2) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.95/18.04 (3) ~ (all_4_13 = e2) % 129.95/18.04 (4) e4 = e2 | ~ (op(e2, e2) = e2) % 129.95/18.04 (5) ~ (e2 = e0) % 129.95/18.04 (6) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.95/18.04 (7) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 129.95/18.04 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 129.95/18.04 (all_9_22 = e2 & op(e0, e2) = e2) % 129.95/18.04 (8) all_9_5 = e0 % 129.95/18.04 (9) all_9_22 = e1 % 129.95/18.04 (10) all_6_2 = all_4_10 % 129.95/18.04 (11) ~ (all_4_10 = e2) % 129.95/18.04 (12) ~ (e2 = e1) % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | BETA: splitting (7) gives: % 129.95/18.04 | % 129.95/18.04 | Case 1: % 129.95/18.04 | | % 129.95/18.04 | | (13) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) % 129.95/18.04 | | % 129.95/18.04 | | BETA: splitting (13) gives: % 129.95/18.04 | | % 129.95/18.04 | | Case 1: % 129.95/18.04 | | | % 129.95/18.04 | | | (14) all_9_4 = e2 & op(e4, e2) = e2 % 129.95/18.04 | | | % 129.95/18.04 | | | ALPHA: (14) implies: % 129.95/18.04 | | | (15) op(e4, e2) = e2 % 129.95/18.04 | | | % 129.95/18.04 | | | REF_CLOSE: (6), (10), (11), (15) are inconsistent by sub-proof #261. % 129.95/18.04 | | | % 129.95/18.04 | | Case 2: % 129.95/18.04 | | | % 129.95/18.04 | | | (16) all_9_5 = e2 & op(e3, e2) = e2 % 129.95/18.04 | | | % 129.95/18.04 | | | ALPHA: (16) implies: % 129.95/18.04 | | | (17) all_9_5 = e2 % 129.95/18.04 | | | % 129.95/18.04 | | | COMBINE_EQS: (8), (17) imply: % 129.95/18.04 | | | (18) e2 = e0 % 129.95/18.04 | | | % 129.95/18.04 | | | SIMP: (18) implies: % 129.95/18.04 | | | (19) e2 = e0 % 129.95/18.04 | | | % 129.95/18.04 | | | REDUCE: (5), (19) imply: % 129.95/18.04 | | | (20) $false % 129.95/18.04 | | | % 129.95/18.04 | | | CLOSE: (20) is inconsistent. % 129.95/18.04 | | | % 129.95/18.04 | | End of split % 129.95/18.04 | | % 129.95/18.04 | Case 2: % 129.95/18.04 | | % 129.95/18.04 | | (21) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 129.95/18.04 | | | (all_9_22 = e2 & op(e0, e2) = e2) % 129.95/18.04 | | % 129.95/18.04 | | BETA: splitting (21) gives: % 129.95/18.04 | | % 129.95/18.04 | | Case 1: % 129.95/18.04 | | | % 129.95/18.04 | | | (22) all_9_8 = e2 & op(e2, e2) = e2 % 129.95/18.04 | | | % 129.95/18.04 | | | REF_CLOSE: (1), (4), (22) are inconsistent by sub-proof #306. % 129.95/18.04 | | | % 129.95/18.04 | | Case 2: % 129.95/18.04 | | | % 129.95/18.04 | | | (23) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) = % 129.95/18.04 | | | e2) % 129.95/18.04 | | | % 129.95/18.04 | | | BETA: splitting (23) gives: % 129.95/18.04 | | | % 129.95/18.04 | | | Case 1: % 129.95/18.04 | | | | % 129.95/18.04 | | | | (24) all_9_14 = e2 & op(e1, e2) = e2 % 129.95/18.04 | | | | % 129.95/18.04 | | | | ALPHA: (24) implies: % 129.95/18.04 | | | | (25) op(e1, e2) = e2 % 129.95/18.04 | | | | % 129.95/18.04 | | | | REF_CLOSE: (2), (3), (25) are inconsistent by sub-proof #96. % 129.95/18.04 | | | | % 129.95/18.04 | | | Case 2: % 129.95/18.04 | | | | % 129.95/18.04 | | | | (26) all_9_22 = e2 & op(e0, e2) = e2 % 129.95/18.04 | | | | % 129.95/18.04 | | | | ALPHA: (26) implies: % 129.95/18.04 | | | | (27) all_9_22 = e2 % 129.95/18.04 | | | | % 129.95/18.04 | | | | COMBINE_EQS: (9), (27) imply: % 129.95/18.04 | | | | (28) e2 = e1 % 129.95/18.04 | | | | % 129.95/18.04 | | | | SIMP: (28) implies: % 129.95/18.04 | | | | (29) e2 = e1 % 129.95/18.04 | | | | % 129.95/18.04 | | | | REDUCE: (12), (29) imply: % 129.95/18.04 | | | | (30) $false % 129.95/18.04 | | | | % 129.95/18.04 | | | | CLOSE: (30) is inconsistent. % 129.95/18.04 | | | | % 129.95/18.04 | | | End of split % 129.95/18.04 | | | % 129.95/18.04 | | End of split % 129.95/18.04 | | % 129.95/18.04 | End of split % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #74 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) all_9_12 = e4 & op(e1, e4) = e4 % 129.95/18.04 (2) ~ (op(e1, e4) = e4) % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | ALPHA: (1) implies: % 129.95/18.04 | (3) op(e1, e4) = e4 % 129.95/18.04 | % 129.95/18.04 | PRED_UNIFY: (2), (3) imply: % 129.95/18.04 | (4) $false % 129.95/18.04 | % 129.95/18.04 | CLOSE: (4) is inconsistent. % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #75 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) all_9_12 = e0 & op(e1, e4) = e0 % 129.95/18.04 (2) all_9_12 = e2 % 129.95/18.04 (3) ~ (e2 = e0) % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | ALPHA: (1) implies: % 129.95/18.04 | (4) all_9_12 = e0 % 129.95/18.04 | % 129.95/18.04 | COMBINE_EQS: (2), (4) imply: % 129.95/18.04 | (5) e2 = e0 % 129.95/18.04 | % 129.95/18.04 | SIMP: (5) implies: % 129.95/18.04 | (6) e2 = e0 % 129.95/18.04 | % 129.95/18.04 | REDUCE: (3), (6) imply: % 129.95/18.04 | (7) $false % 129.95/18.04 | % 129.95/18.04 | CLOSE: (7) is inconsistent. % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #76 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) all_6_13 = all_4_17 % 129.95/18.04 (2) all_6_13 = e2 % 129.95/18.04 (3) ~ (all_4_17 = e2) % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | COMBINE_EQS: (1), (2) imply: % 129.95/18.04 | (4) all_4_17 = e2 % 129.95/18.04 | % 129.95/18.04 | SIMP: (4) implies: % 129.95/18.04 | (5) all_4_17 = e2 % 129.95/18.04 | % 129.95/18.04 | REDUCE: (3), (5) imply: % 129.95/18.04 | (6) $false % 129.95/18.04 | % 129.95/18.04 | CLOSE: (6) is inconsistent. % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #77 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) ~ (all_4_16 = e3) % 129.95/18.04 (2) all_9_9 = e2 & op(e4, e1) = e2 % 129.95/18.04 (3) ~ (all_4_6 = e3) % 129.95/18.04 (4) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.04 (5) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.04 (6) all_9_17 = e3 % 129.95/18.04 (7) ~ (all_4_11 = e3) % 129.95/18.04 (8) all_6_8 = all_4_16 % 129.95/18.04 (9) all_9_9 = e3 % 129.95/18.04 (10) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.95/18.04 (11) all_6_7 = all_4_11 % 129.95/18.04 (12) ~ (e3 = e2) % 129.95/18.04 (13) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.95/18.04 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.95/18.04 (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.04 (14) ~ (e3 = e1) % 129.95/18.04 (15) all_9_2 = e1 % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | ALPHA: (2) implies: % 129.95/18.04 | (16) all_9_9 = e2 % 129.95/18.04 | % 129.95/18.04 | COMBINE_EQS: (9), (16) imply: % 129.95/18.04 | (17) e3 = e2 % 129.95/18.04 | % 129.95/18.04 | COMBINE_EQS: (6), (17) imply: % 129.95/18.04 | (18) all_9_17 = e2 % 129.95/18.04 | % 129.95/18.04 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15), % 129.95/18.04 | (18) are inconsistent by sub-proof #86. % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #78 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) ~ (e4 = e0) % 129.95/18.04 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.95/18.04 (3) all_6_10 = e3 % 129.95/18.04 (4) ~ (all_4_3 = all_4_4) % 129.95/18.04 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.04 (6) ~ (e4 = e2) % 129.95/18.04 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.04 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.04 (9) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.95/18.04 (10) ~ (all_4_3 = e3) % 129.95/18.04 (11) all_6_20 = all_4_4 % 129.95/18.04 (12) ~ (e3 = e0) % 129.95/18.04 (13) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.04 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.95/18.04 = e0 % 129.95/18.04 (15) ~ (e2 = e0) % 129.95/18.04 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.95/18.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.95/18.04 (17) ~ (all_4_4 = e3) % 129.95/18.04 (18) all_9_7 = e1 % 129.95/18.04 (19) all_9_6 = e3 % 129.95/18.04 (20) ~ (e1 = e0) % 129.95/18.04 (21) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.95/18.04 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.95/18.04 (all_9_20 = e3 & op(e0, e4) = e3) % 129.95/18.04 (22) ~ (e3 = e2) % 129.95/18.04 (23) op(e0, e4) = all_4_4 % 129.95/18.04 (24) ~ (e4 = e1) % 129.95/18.04 (25) ~ (all_4_3 = e0) % 129.95/18.04 (26) ~ (e3 = e1) % 129.95/18.04 (27) op(e1, e4) = all_4_3 % 129.95/18.04 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.95/18.04 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.95/18.04 (all_9_20 = e2 & op(e0, e4) = e2) % 129.95/18.04 (29) ~ (e4 = e3) % 129.95/18.04 (30) ~ (all_4_4 = e0) % 129.95/18.04 (31) ~ (all_4_3 = e1) % 129.95/18.04 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.95/18.04 (33) op(e2, e4) = e3 % 129.95/18.04 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.04 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.04 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.04 (35) all_9_2 = e1 % 129.95/18.04 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.95/18.04 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.95/18.04 (all_9_20 = e1 & op(e0, e4) = e1) % 129.95/18.04 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.95/18.04 = e0 % 129.95/18.04 (38) (all_9_6 = e0 & op(e2, e4) = e0) | (all_9_7 = e0 & op(e2, e3) = e0) % 129.95/18.04 (39) ~ (all_4_4 = e1) % 129.95/18.04 (40) all_4_0 = e0 % 129.95/18.04 (41) ~ (e2 = e1) % 129.95/18.04 (42) all_6_15 = all_4_3 % 129.95/18.04 (43) op(e4, e4) = e0 % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | BETA: splitting (38) gives: % 129.95/18.04 | % 129.95/18.04 | Case 1: % 129.95/18.04 | | % 129.95/18.04 | | (44) all_9_6 = e0 & op(e2, e4) = e0 % 129.95/18.04 | | % 129.95/18.04 | | REF_CLOSE: (12), (19), (44) are inconsistent by sub-proof #256. % 129.95/18.04 | | % 129.95/18.04 | Case 2: % 129.95/18.04 | | % 129.95/18.04 | | (45) all_9_7 = e0 & op(e2, e3) = e0 % 129.95/18.04 | | % 129.95/18.04 | | ALPHA: (45) implies: % 129.95/18.04 | | (46) all_9_7 = e0 % 129.95/18.04 | | % 129.95/18.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.95/18.04 | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 129.95/18.04 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 129.95/18.04 | | (36), (37), (39), (40), (41), (42), (43), (46) are inconsistent % 129.95/18.04 | | by sub-proof #222. % 129.95/18.04 | | % 129.95/18.04 | End of split % 129.95/18.04 | % 129.95/18.04 End of proof % 129.95/18.04 % 129.95/18.04 Sub-proof #79 shows that the following formulas are inconsistent: % 129.95/18.04 ---------------------------------------------------------------- % 129.95/18.04 (1) ~ (op(e4, e1) = e1) % 129.95/18.04 (2) ~ (all_4_16 = e3) % 129.95/18.04 (3) all_6_5 = e1 % 129.95/18.04 (4) ~ (e4 = e0) % 129.95/18.04 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.95/18.04 (6) all_6_10 = e3 % 129.95/18.04 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.04 (8) ~ (all_4_3 = all_4_4) % 129.95/18.04 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.04 (10) ~ (e4 = e2) % 129.95/18.04 (11) ~ (all_4_6 = e3) % 129.95/18.04 (12) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.04 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.04 (14) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 129.95/18.04 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.95/18.04 (all_9_16 = e2 & op(e4, e0) = e2) % 129.95/18.04 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.04 (16) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.04 (17) all_9_17 = e3 % 129.95/18.04 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.95/18.04 (19) ~ (all_4_3 = e3) % 129.95/18.04 (20) all_6_20 = all_4_4 % 129.95/18.04 (21) ~ (e3 = e0) % 129.95/18.04 (22) ~ (all_4_11 = e3) % 129.95/18.04 (23) ~ (all_4_5 = e3) % 129.95/18.04 (24) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.04 (25) all_6_8 = all_4_16 % 129.95/18.04 (26) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.95/18.04 = e0 % 129.95/18.04 (27) ~ (e2 = e0) % 129.95/18.04 (28) all_9_0 = e0 % 129.95/18.04 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.95/18.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.95/18.04 (30) ~ (all_4_4 = e3) % 129.95/18.04 (31) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.95/18.04 (32) all_9_12 = e2 % 129.95/18.04 (33) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.95/18.04 (34) ~ (e1 = e0) % 129.95/18.04 (35) all_6_7 = all_4_11 % 129.95/18.04 (36) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.95/18.04 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.95/18.04 (all_9_20 = e3 & op(e0, e4) = e3) % 129.95/18.04 (37) ~ (e3 = e2) % 129.95/18.04 (38) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.95/18.04 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.95/18.04 (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.04 (39) op(e0, e4) = all_4_4 % 129.95/18.04 (40) ~ (e4 = e1) % 129.95/18.04 (41) ~ (all_4_3 = e0) % 129.95/18.04 (42) ~ (e3 = e1) % 129.95/18.04 (43) op(e1, e4) = all_4_3 % 129.95/18.04 (44) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.95/18.04 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.95/18.04 (all_9_20 = e2 & op(e0, e4) = e2) % 129.95/18.04 (45) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 129.95/18.04 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 129.95/18.04 (all_9_16 = e3 & op(e4, e0) = e3) % 129.95/18.04 (46) ~ (all_4_3 = e4) % 129.95/18.04 (47) ~ (e4 = e3) % 129.95/18.04 (48) ~ (all_4_4 = e0) % 129.95/18.04 (49) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 129.95/18.04 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 129.95/18.04 (all_9_16 = e1 & op(e4, e0) = e1) % 129.95/18.04 (50) ~ (all_4_3 = e1) % 129.95/18.04 (51) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 129.95/18.04 (52) all_6_2 = all_4_10 % 129.95/18.04 (53) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.95/18.04 (54) op(e2, e4) = e3 % 129.95/18.04 (55) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.04 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.04 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.04 (56) all_9_4 = e0 % 129.95/18.04 (57) all_9_2 = e1 % 129.95/18.04 (58) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.95/18.04 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.95/18.04 (all_9_20 = e1 & op(e0, e4) = e1) % 129.95/18.04 (59) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.95/18.04 = e0 % 129.95/18.04 (60) ~ (all_4_4 = e1) % 129.95/18.04 (61) ~ (all_4_10 = e2) % 129.95/18.04 (62) all_4_0 = e0 % 129.95/18.04 (63) all_9_20 = e4 % 129.95/18.04 (64) ~ (e2 = e1) % 129.95/18.04 (65) all_6_15 = all_4_3 % 129.95/18.04 (66) op(e4, e4) = e0 % 129.95/18.04 (67) all_9_16 = e4 % 129.95/18.04 % 129.95/18.04 Begin of proof % 129.95/18.04 | % 129.95/18.04 | BETA: splitting (45) gives: % 129.95/18.04 | % 129.95/18.04 | Case 1: % 129.95/18.04 | | % 129.95/18.04 | | (68) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) % 129.95/18.04 | | % 129.95/18.04 | | REF_CLOSE: (21), (23), (28), (51), (68) are inconsistent by sub-proof #139. % 129.95/18.04 | | % 129.95/18.04 | Case 2: % 129.95/18.04 | | % 129.95/18.04 | | (69) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) % 129.95/18.04 | | | (all_9_16 = e3 & op(e4, e0) = e3) % 129.95/18.04 | | % 129.95/18.04 | | BETA: splitting (69) gives: % 129.95/18.04 | | % 129.95/18.04 | | Case 1: % 129.95/18.04 | | | % 129.95/18.04 | | | (70) all_9_4 = e3 & op(e4, e2) = e3 % 129.95/18.04 | | | % 129.95/18.04 | | | REF_CLOSE: (21), (56), (70) are inconsistent by sub-proof #290. % 129.95/18.04 | | | % 129.95/18.04 | | Case 2: % 129.95/18.04 | | | % 129.95/18.04 | | | (71) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 129.95/18.04 | | | e3) % 129.95/18.04 | | | % 129.95/18.04 | | | BETA: splitting (71) gives: % 129.95/18.04 | | | % 129.95/18.04 | | | Case 1: % 129.95/18.04 | | | | % 129.95/18.04 | | | | (72) all_9_9 = e3 & op(e4, e1) = e3 % 129.95/18.04 | | | | % 129.95/18.04 | | | | ALPHA: (72) implies: % 129.95/18.04 | | | | (73) all_9_9 = e3 % 129.95/18.04 | | | | % 129.95/18.04 | | | | BETA: splitting (14) gives: % 129.95/18.04 | | | | % 129.95/18.04 | | | | Case 1: % 129.95/18.04 | | | | | % 129.95/18.04 | | | | | (74) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) % 129.95/18.04 | | | | | = e2) % 129.95/18.04 | | | | | % 129.95/18.04 | | | | | BETA: splitting (74) gives: % 129.95/18.04 | | | | | % 129.95/18.04 | | | | | Case 1: % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | (75) all_9_0 = e2 & op(e4, e4) = e2 % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | REF_CLOSE: (27), (28), (75) are inconsistent by sub-proof #314. % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | Case 2: % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | (76) all_9_1 = e2 & op(e4, e3) = e2 % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | ALPHA: (76) implies: % 129.95/18.04 | | | | | | (77) all_9_1 = e2 % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | BETA: splitting (49) gives: % 129.95/18.04 | | | | | | % 129.95/18.04 | | | | | | Case 1: % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | | (78) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, % 129.95/18.04 | | | | | | | e3) = e1) % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | | REF_CLOSE: (29), (34), (64), (66), (77), (78) are inconsistent by % 129.95/18.04 | | | | | | | sub-proof #85. % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | Case 2: % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | | (79) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, % 129.95/18.04 | | | | | | | e1) = e1) | (all_9_16 = e1 & op(e4, e0) = e1) % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | | BETA: splitting (79) gives: % 129.95/18.04 | | | | | | | % 129.95/18.04 | | | | | | | Case 1: % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | (80) all_9_4 = e1 & op(e4, e2) = e1 % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | ALPHA: (80) implies: % 129.95/18.04 | | | | | | | | (81) all_9_4 = e1 % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | COMBINE_EQS: (56), (81) imply: % 129.95/18.04 | | | | | | | | (82) e1 = e0 % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (13), (15), (18), % 129.95/18.04 | | | | | | | | (19), (20), (21), (24), (26), (27), (29), (30), (34), % 129.95/18.04 | | | | | | | | (36), (37), (39), (40), (41), (42), (43), (44), (47), % 129.95/18.04 | | | | | | | | (48), (50), (53), (54), (55), (57), (58), (59), (60), % 129.95/18.04 | | | | | | | | (62), (64), (65), (66), (82) are inconsistent by % 129.95/18.04 | | | | | | | | sub-proof #264. % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | Case 2: % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | (83) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 & % 129.95/18.04 | | | | | | | | op(e4, e0) = e1) % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | BETA: splitting (83) gives: % 129.95/18.04 | | | | | | | | % 129.95/18.04 | | | | | | | | Case 1: % 129.95/18.04 | | | | | | | | | % 129.95/18.04 | | | | | | | | | (84) all_9_9 = e1 & op(e4, e1) = e1 % 129.95/18.04 | | | | | | | | | % 129.95/18.04 | | | | | | | | | REF_CLOSE: (1), (84) are inconsistent by sub-proof #84. % 129.95/18.04 | | | | | | | | | % 129.95/18.04 | | | | | | | | Case 2: % 129.95/18.04 | | | | | | | | | % 129.95/18.04 | | | | | | | | | (85) all_9_16 = e1 & op(e4, e0) = e1 % 129.95/18.04 | | | | | | | | | % 129.95/18.04 | | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (32), (40), (47), % 129.95/18.04 | | | | | | | | | (55), (62), (63), (67), (85) are inconsistent by % 129.95/18.04 | | | | | | | | | sub-proof #83. % 129.95/18.05 | | | | | | | | | % 129.95/18.05 | | | | | | | | End of split % 129.95/18.05 | | | | | | | | % 129.95/18.05 | | | | | | | End of split % 129.95/18.05 | | | | | | | % 129.95/18.05 | | | | | | End of split % 129.95/18.05 | | | | | | % 129.95/18.05 | | | | | End of split % 129.95/18.05 | | | | | % 129.95/18.05 | | | | Case 2: % 129.95/18.05 | | | | | % 129.95/18.05 | | | | | (86) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) % 129.95/18.05 | | | | | = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.95/18.05 | | | | | % 129.95/18.05 | | | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (12), (13), (15), % 129.95/18.05 | | | | | (16), (17), (22), (25), (31), (33), (35), (37), (38), (40), % 129.95/18.05 | | | | | (42), (46), (47), (52), (55), (57), (61), (62), (63), (65), % 129.95/18.05 | | | | | (67), (73), (86) are inconsistent by sub-proof #81. % 129.95/18.05 | | | | | % 129.95/18.05 | | | | End of split % 129.95/18.05 | | | | % 129.95/18.05 | | | Case 2: % 129.95/18.05 | | | | % 129.95/18.05 | | | | (87) all_9_16 = e3 & op(e4, e0) = e3 % 129.95/18.05 | | | | % 129.95/18.05 | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (32), (40), (47), (55), (62), % 129.95/18.05 | | | | (63), (67), (87) are inconsistent by sub-proof #80. % 129.95/18.05 | | | | % 129.95/18.05 | | | End of split % 129.95/18.05 | | | % 129.95/18.05 | | End of split % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #80 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_9_16 = e3 & op(e4, e0) = e3 % 129.95/18.05 (2) all_6_5 = e1 % 129.95/18.05 (3) ~ (e4 = e0) % 129.95/18.05 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (6) ~ (e4 = e2) % 129.95/18.05 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (8) all_9_12 = e2 % 129.95/18.05 (9) ~ (e4 = e1) % 129.95/18.05 (10) ~ (e4 = e3) % 129.95/18.05 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (12) all_4_0 = e0 % 129.95/18.05 (13) all_9_20 = e4 % 129.95/18.05 (14) all_9_16 = e4 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | ALPHA: (1) implies: % 129.95/18.05 | (15) all_9_16 = e3 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (14), (15) imply: % 129.95/18.05 | (16) e4 = e3 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (13), (16) imply: % 129.95/18.05 | (17) all_9_20 = e3 % 129.95/18.05 | % 129.95/18.05 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (17) are % 129.95/18.05 | inconsistent by sub-proof #202. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #81 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) ~ (all_4_16 = e3) % 129.95/18.05 (2) all_6_5 = e1 % 129.95/18.05 (3) ~ (e4 = e0) % 129.95/18.05 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (6) ~ (e4 = e2) % 129.95/18.05 (7) ~ (all_4_6 = e3) % 129.95/18.05 (8) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.05 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.05 (11) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.05 (12) all_9_17 = e3 % 129.95/18.05 (13) ~ (all_4_11 = e3) % 129.95/18.05 (14) all_6_8 = all_4_16 % 129.95/18.05 (15) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 129.95/18.05 (all_9_16 = e2 & op(e4, e0) = e2) % 129.95/18.05 (16) all_9_9 = e3 % 129.95/18.05 (17) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 129.95/18.05 (18) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.95/18.05 (19) all_6_7 = all_4_11 % 129.95/18.05 (20) ~ (e3 = e2) % 129.95/18.05 (21) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.95/18.05 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.95/18.05 (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.05 (22) ~ (e4 = e1) % 129.95/18.05 (23) ~ (e3 = e1) % 129.95/18.05 (24) ~ (all_4_3 = e4) % 129.95/18.05 (25) ~ (e4 = e3) % 129.95/18.05 (26) all_6_2 = all_4_10 % 129.95/18.05 (27) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (28) all_9_2 = e1 % 129.95/18.05 (29) ~ (all_4_10 = e2) % 129.95/18.05 (30) all_4_0 = e0 % 129.95/18.05 (31) all_9_20 = e4 % 129.95/18.05 (32) all_6_15 = all_4_3 % 129.95/18.05 (33) all_9_16 = e4 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (15) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (34) all_9_4 = e2 & op(e4, e2) = e2 % 129.95/18.05 | | % 129.95/18.05 | | ALPHA: (34) implies: % 129.95/18.05 | | (35) op(e4, e2) = e2 % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (17), (26), (29), (35) are inconsistent by sub-proof #261. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (36) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 129.95/18.05 | | % 129.95/18.05 | | BETA: splitting (36) gives: % 129.95/18.05 | | % 129.95/18.05 | | Case 1: % 129.95/18.05 | | | % 129.95/18.05 | | | (37) all_9_9 = e2 & op(e4, e1) = e2 % 129.95/18.05 | | | % 129.95/18.05 | | | ALPHA: (37) implies: % 129.95/18.05 | | | (38) all_9_9 = e2 % 129.95/18.05 | | | % 129.95/18.05 | | | COMBINE_EQS: (16), (38) imply: % 129.95/18.05 | | | (39) e3 = e2 % 129.95/18.05 | | | % 129.95/18.05 | | | REF_CLOSE: (1), (7), (8), (11), (12), (13), (14), (18), (19), (20), (21), % 129.95/18.05 | | | (23), (28), (39) are inconsistent by sub-proof #82. % 129.95/18.05 | | | % 129.95/18.05 | | Case 2: % 129.95/18.05 | | | % 129.95/18.05 | | | (40) all_9_16 = e2 & op(e4, e0) = e2 % 129.95/18.05 | | | % 129.95/18.05 | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (22), (24), (25), (27), % 129.95/18.05 | | | (30), (31), (32), (33), (40) are inconsistent by sub-proof #88. % 129.95/18.05 | | | % 129.95/18.05 | | End of split % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #82 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) ~ (all_4_16 = e3) % 129.95/18.05 (2) ~ (all_4_6 = e3) % 129.95/18.05 (3) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.05 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.05 (5) all_9_17 = e3 % 129.95/18.05 (6) ~ (all_4_11 = e3) % 129.95/18.05 (7) all_6_8 = all_4_16 % 129.95/18.05 (8) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.95/18.05 (9) all_6_7 = all_4_11 % 129.95/18.05 (10) ~ (e3 = e2) % 129.95/18.05 (11) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.95/18.05 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.95/18.05 (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.05 (12) e3 = e2 % 129.95/18.05 (13) ~ (e3 = e1) % 129.95/18.05 (14) all_9_2 = e1 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | SIMP: (12) implies: % 129.95/18.05 | (15) e3 = e2 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (5), (15) imply: % 129.95/18.05 | (16) all_9_17 = e2 % 129.95/18.05 | % 129.95/18.05 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), % 129.95/18.05 | (16) are inconsistent by sub-proof #86. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #83 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_5 = e1 % 129.95/18.05 (2) ~ (e4 = e0) % 129.95/18.05 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (5) ~ (e4 = e2) % 129.95/18.05 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (7) all_9_12 = e2 % 129.95/18.05 (8) ~ (e4 = e1) % 129.95/18.05 (9) ~ (e4 = e3) % 129.95/18.05 (10) all_9_16 = e1 & op(e4, e0) = e1 % 129.95/18.05 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (12) all_4_0 = e0 % 129.95/18.05 (13) all_9_20 = e4 % 129.95/18.05 (14) all_9_16 = e4 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | ALPHA: (10) implies: % 129.95/18.05 | (15) all_9_16 = e1 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (14), (15) imply: % 129.95/18.05 | (16) e4 = e1 % 129.95/18.05 | % 129.95/18.05 | SIMP: (16) implies: % 129.95/18.05 | (17) e4 = e1 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (13), (17) imply: % 129.95/18.05 | (18) all_9_20 = e1 % 129.95/18.05 | % 129.95/18.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (18) are % 129.95/18.05 | inconsistent by sub-proof #286. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #84 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_9_9 = e1 & op(e4, e1) = e1 % 129.95/18.05 (2) ~ (op(e4, e1) = e1) % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | ALPHA: (1) implies: % 129.95/18.05 | (3) op(e4, e1) = e1 % 129.95/18.05 | % 129.95/18.05 | PRED_UNIFY: (2), (3) imply: % 129.95/18.05 | (4) $false % 129.95/18.05 | % 129.95/18.05 | CLOSE: (4) is inconsistent. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #85 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_9_1 = e2 % 129.95/18.05 (2) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) % 129.95/18.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.95/18.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.95/18.05 (4) ~ (e1 = e0) % 129.95/18.05 (5) ~ (e2 = e1) % 129.95/18.05 (6) op(e4, e4) = e0 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (2) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (7) all_9_0 = e1 & op(e4, e4) = e1 % 129.95/18.05 | | % 129.95/18.05 | | ALPHA: (7) implies: % 129.95/18.05 | | (8) op(e4, e4) = e1 % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #321. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (9) all_9_1 = e1 & op(e4, e3) = e1 % 129.95/18.05 | | % 129.95/18.05 | | ALPHA: (9) implies: % 129.95/18.05 | | (10) all_9_1 = e1 % 129.95/18.05 | | % 129.95/18.05 | | COMBINE_EQS: (1), (10) imply: % 129.95/18.05 | | (11) e2 = e1 % 129.95/18.05 | | % 129.95/18.05 | | REDUCE: (5), (11) imply: % 129.95/18.05 | | (12) $false % 129.95/18.05 | | % 129.95/18.05 | | CLOSE: (12) is inconsistent. % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #86 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) ~ (all_4_16 = e3) % 129.95/18.05 (2) ~ (all_4_6 = e3) % 129.95/18.05 (3) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.05 (4) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.05 (5) ~ (all_4_11 = e3) % 129.95/18.05 (6) all_9_17 = e2 % 129.95/18.05 (7) all_6_8 = all_4_16 % 129.95/18.05 (8) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 129.95/18.05 (9) all_6_7 = all_4_11 % 129.95/18.05 (10) ~ (e3 = e2) % 129.95/18.05 (11) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 129.95/18.05 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 129.95/18.05 (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.05 (12) ~ (e3 = e1) % 129.95/18.05 (13) all_9_2 = e1 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (11) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (14) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (2), (4), (12), (13), (14) are inconsistent by sub-proof #293. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (15) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 129.95/18.05 | | | (all_9_17 = e3 & op(e3, e0) = e3) % 129.95/18.05 | | % 129.95/18.05 | | BETA: splitting (15) gives: % 129.95/18.05 | | % 129.95/18.05 | | Case 1: % 129.95/18.05 | | | % 129.95/18.05 | | | (16) all_9_5 = e3 & op(e3, e2) = e3 % 129.95/18.05 | | | % 129.95/18.05 | | | ALPHA: (16) implies: % 129.95/18.05 | | | (17) op(e3, e2) = e3 % 129.95/18.05 | | | % 129.95/18.05 | | | REF_CLOSE: (5), (8), (9), (17) are inconsistent by sub-proof #292. % 129.95/18.05 | | | % 129.95/18.05 | | Case 2: % 129.95/18.05 | | | % 129.95/18.05 | | | (18) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) = % 129.95/18.05 | | | e3) % 129.95/18.05 | | | % 129.95/18.05 | | | BETA: splitting (18) gives: % 129.95/18.05 | | | % 129.95/18.05 | | | Case 1: % 129.95/18.05 | | | | % 129.95/18.05 | | | | (19) all_9_10 = e3 & op(e3, e1) = e3 % 129.95/18.05 | | | | % 129.95/18.05 | | | | ALPHA: (19) implies: % 129.95/18.05 | | | | (20) op(e3, e1) = e3 % 129.95/18.05 | | | | % 129.95/18.05 | | | | REF_CLOSE: (1), (3), (7), (20) are inconsistent by sub-proof #87. % 129.95/18.05 | | | | % 129.95/18.05 | | | Case 2: % 129.95/18.05 | | | | % 129.95/18.05 | | | | (21) all_9_17 = e3 & op(e3, e0) = e3 % 129.95/18.05 | | | | % 129.95/18.05 | | | | REF_CLOSE: (6), (10), (21) are inconsistent by sub-proof #119. % 129.95/18.05 | | | | % 129.95/18.05 | | | End of split % 129.95/18.05 | | | % 129.95/18.05 | | End of split % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #87 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_8 = e3 | ~ (op(e3, e1) = e3) % 129.95/18.05 (2) op(e3, e1) = e3 % 129.95/18.05 (3) all_6_8 = all_4_16 % 129.95/18.05 (4) ~ (all_4_16 = e3) % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (1) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (5) ~ (op(e3, e1) = e3) % 129.95/18.05 | | % 129.95/18.05 | | PRED_UNIFY: (2), (5) imply: % 129.95/18.05 | | (6) $false % 129.95/18.05 | | % 129.95/18.05 | | CLOSE: (6) is inconsistent. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (7) all_6_8 = e3 % 129.95/18.05 | | % 129.95/18.05 | | COMBINE_EQS: (3), (7) imply: % 129.95/18.05 | | (8) all_4_16 = e3 % 129.95/18.05 | | % 129.95/18.05 | | REDUCE: (4), (8) imply: % 129.95/18.05 | | (9) $false % 129.95/18.05 | | % 129.95/18.05 | | CLOSE: (9) is inconsistent. % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #88 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_5 = e1 % 129.95/18.05 (2) ~ (e4 = e0) % 129.95/18.05 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (5) ~ (e4 = e2) % 129.95/18.05 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (7) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.05 (8) all_9_16 = e2 & op(e4, e0) = e2 % 129.95/18.05 (9) ~ (e4 = e1) % 129.95/18.05 (10) ~ (all_4_3 = e4) % 129.95/18.05 (11) ~ (e4 = e3) % 129.95/18.05 (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (13) all_4_0 = e0 % 129.95/18.05 (14) all_9_20 = e4 % 129.95/18.05 (15) all_6_15 = all_4_3 % 129.95/18.05 (16) all_9_16 = e4 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | ALPHA: (8) implies: % 129.95/18.05 | (17) all_9_16 = e2 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (16), (17) imply: % 129.95/18.05 | (18) e4 = e2 % 129.95/18.05 | % 129.95/18.05 | SIMP: (18) implies: % 129.95/18.05 | (19) e4 = e2 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (14), (19) imply: % 129.95/18.05 | (20) all_9_20 = e2 % 129.95/18.05 | % 129.95/18.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 129.95/18.05 | (15), (20) are inconsistent by sub-proof #90. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #89 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_5 = e1 % 129.95/18.05 (2) ~ (e4 = e0) % 129.95/18.05 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (5) ~ (e4 = e2) % 129.95/18.05 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (7) all_9_12 = e2 % 129.95/18.05 (8) ~ (e4 = e1) % 129.95/18.05 (9) ~ (e4 = e3) % 129.95/18.05 (10) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (11) e4 = e3 % 129.95/18.05 (12) all_4_0 = e0 % 129.95/18.05 (13) all_9_20 = e4 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | SIMP: (11) implies: % 129.95/18.05 | (14) e4 = e3 % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (13), (14) imply: % 129.95/18.05 | (15) all_9_20 = e3 % 129.95/18.05 | % 129.95/18.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15) are % 129.95/18.05 | inconsistent by sub-proof #202. % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #90 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_5 = e1 % 129.95/18.05 (2) ~ (e4 = e0) % 129.95/18.05 (3) all_9_20 = e2 % 129.95/18.05 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.05 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.05 (6) ~ (e4 = e2) % 129.95/18.05 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.05 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.05 (9) ~ (e4 = e1) % 129.95/18.05 (10) ~ (all_4_3 = e4) % 129.95/18.05 (11) ~ (e4 = e3) % 129.95/18.05 (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.05 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.05 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 (13) all_4_0 = e0 % 129.95/18.05 (14) all_6_15 = all_4_3 % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (12) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (15) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (1), (2), (4), (5), (9), (13), (15) are inconsistent by sub-proof % 129.95/18.05 | | #315. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (16) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 129.95/18.05 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.05 | | % 129.95/18.05 | | BETA: splitting (16) gives: % 129.95/18.05 | | % 129.95/18.05 | | Case 1: % 129.95/18.05 | | | % 129.95/18.05 | | | (17) all_9_6 = e4 & op(e2, e4) = e4 % 129.95/18.05 | | | % 129.95/18.05 | | | ALPHA: (17) implies: % 129.95/18.05 | | | (18) op(e2, e4) = e4 % 129.95/18.05 | | | % 129.95/18.05 | | | REF_CLOSE: (7), (11), (18) are inconsistent by sub-proof #320. % 129.95/18.05 | | | % 129.95/18.05 | | Case 2: % 129.95/18.05 | | | % 129.95/18.05 | | | (19) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 129.95/18.05 | | | e4) % 129.95/18.05 | | | % 129.95/18.05 | | | BETA: splitting (19) gives: % 129.95/18.05 | | | % 129.95/18.05 | | | Case 1: % 129.95/18.05 | | | | % 129.95/18.05 | | | | (20) all_9_12 = e4 & op(e1, e4) = e4 % 129.95/18.05 | | | | % 129.95/18.05 | | | | ALPHA: (20) implies: % 129.95/18.05 | | | | (21) op(e1, e4) = e4 % 129.95/18.05 | | | | % 129.95/18.05 | | | | REF_CLOSE: (8), (10), (14), (21) are inconsistent by sub-proof #91. % 129.95/18.05 | | | | % 129.95/18.05 | | | Case 2: % 129.95/18.05 | | | | % 129.95/18.05 | | | | (22) all_9_20 = e4 & op(e0, e4) = e4 % 129.95/18.05 | | | | % 129.95/18.05 | | | | REF_CLOSE: (3), (6), (22) are inconsistent by sub-proof #304. % 129.95/18.05 | | | | % 129.95/18.05 | | | End of split % 129.95/18.05 | | | % 129.95/18.05 | | End of split % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #91 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.05 (2) op(e1, e4) = e4 % 129.95/18.05 (3) all_6_15 = all_4_3 % 129.95/18.05 (4) ~ (all_4_3 = e4) % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (1) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (5) ~ (op(e1, e4) = e4) % 129.95/18.05 | | % 129.95/18.05 | | PRED_UNIFY: (2), (5) imply: % 129.95/18.05 | | (6) $false % 129.95/18.05 | | % 129.95/18.05 | | CLOSE: (6) is inconsistent. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (7) all_6_15 = e4 % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #278. % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #92 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_3 = e4 | ~ (op(e4, e1) = e4) % 129.95/18.05 (2) op(e4, e1) = e4 % 129.95/18.05 (3) all_6_3 = all_4_15 % 129.95/18.05 (4) ~ (all_4_15 = e4) % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | BETA: splitting (1) gives: % 129.95/18.05 | % 129.95/18.05 | Case 1: % 129.95/18.05 | | % 129.95/18.05 | | (5) ~ (op(e4, e1) = e4) % 129.95/18.05 | | % 129.95/18.05 | | PRED_UNIFY: (2), (5) imply: % 129.95/18.05 | | (6) $false % 129.95/18.05 | | % 129.95/18.05 | | CLOSE: (6) is inconsistent. % 129.95/18.05 | | % 129.95/18.05 | Case 2: % 129.95/18.05 | | % 129.95/18.05 | | (7) all_6_3 = e4 % 129.95/18.05 | | % 129.95/18.05 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #93. % 129.95/18.05 | | % 129.95/18.05 | End of split % 129.95/18.05 | % 129.95/18.05 End of proof % 129.95/18.05 % 129.95/18.05 Sub-proof #93 shows that the following formulas are inconsistent: % 129.95/18.05 ---------------------------------------------------------------- % 129.95/18.05 (1) all_6_3 = all_4_15 % 129.95/18.05 (2) all_6_3 = e4 % 129.95/18.05 (3) ~ (all_4_15 = e4) % 129.95/18.05 % 129.95/18.05 Begin of proof % 129.95/18.05 | % 129.95/18.05 | COMBINE_EQS: (1), (2) imply: % 129.95/18.06 | (4) all_4_15 = e4 % 129.95/18.06 | % 129.95/18.06 | SIMP: (4) implies: % 129.95/18.06 | (5) all_4_15 = e4 % 129.95/18.06 | % 129.95/18.06 | REDUCE: (3), (5) imply: % 129.95/18.06 | (6) $false % 129.95/18.06 | % 129.95/18.06 | CLOSE: (6) is inconsistent. % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #94 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) all_4_5 = e4 | ~ (op(e4, e3) = e4) % 129.95/18.06 (2) op(e4, e3) = e4 % 129.95/18.06 (3) ~ (all_4_5 = e4) % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (1) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (4) ~ (op(e4, e3) = e4) % 129.95/18.06 | | % 129.95/18.06 | | PRED_UNIFY: (2), (4) imply: % 129.95/18.06 | | (5) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (5) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | (6) all_4_5 = e4 % 129.95/18.06 | | % 129.95/18.06 | | REDUCE: (3), (6) imply: % 129.95/18.06 | | (7) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (7) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #95 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) ~ (unit = e2) % 129.95/18.06 (2) ~ (e4 = e0) % 129.95/18.06 (3) op(unit, e4) = e4 % 129.95/18.06 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.06 (5) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.95/18.06 (6) ~ (all_4_13 = e2) % 129.95/18.06 (7) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.95/18.06 (8) ~ (unit = e3) % 129.95/18.06 (9) ~ (unit = e0) % 129.95/18.06 (10) op(unit, e2) = e2 % 129.95/18.06 (11) all_4_0 = e0 % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (4) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (12) ~ (op(e4, e4) = e4) % 129.95/18.06 | | % 129.95/18.06 | | PRED_UNIFY: (3), (12) imply: % 129.95/18.06 | | (13) ~ (unit = e4) % 129.95/18.06 | | % 129.95/18.06 | | BETA: splitting (7) gives: % 129.95/18.06 | | % 129.95/18.06 | | Case 1: % 129.95/18.06 | | | % 129.95/18.06 | | | (14) unit = e4 % 129.95/18.06 | | | % 129.95/18.06 | | | REDUCE: (13), (14) imply: % 129.95/18.06 | | | (15) $false % 129.95/18.06 | | | % 129.95/18.06 | | | CLOSE: (15) is inconsistent. % 129.95/18.06 | | | % 129.95/18.06 | | Case 2: % 129.95/18.06 | | | % 129.95/18.06 | | | (16) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 129.95/18.06 | | | % 129.95/18.06 | | | BETA: splitting (16) gives: % 129.95/18.06 | | | % 129.95/18.06 | | | Case 1: % 129.95/18.06 | | | | % 129.95/18.06 | | | | (17) unit = e2 % 129.95/18.06 | | | | % 129.95/18.06 | | | | REDUCE: (1), (17) imply: % 129.95/18.06 | | | | (18) $false % 129.95/18.06 | | | | % 129.95/18.06 | | | | CLOSE: (18) is inconsistent. % 129.95/18.06 | | | | % 129.95/18.06 | | | Case 2: % 129.95/18.06 | | | | % 129.95/18.06 | | | | (19) unit = e3 | unit = e1 | unit = e0 % 129.95/18.06 | | | | % 129.95/18.06 | | | | BETA: splitting (19) gives: % 129.95/18.06 | | | | % 129.95/18.06 | | | | Case 1: % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | (20) unit = e3 % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | REDUCE: (8), (20) imply: % 129.95/18.06 | | | | | (21) $false % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | CLOSE: (21) is inconsistent. % 129.95/18.06 | | | | | % 129.95/18.06 | | | | Case 2: % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | (22) unit = e1 | unit = e0 % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | BETA: splitting (22) gives: % 129.95/18.06 | | | | | % 129.95/18.06 | | | | | Case 1: % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | | (23) unit = e1 % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | | REDUCE: (10), (23) imply: % 129.95/18.06 | | | | | | (24) op(e1, e2) = e2 % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | | REF_CLOSE: (5), (6), (24) are inconsistent by sub-proof #96. % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | Case 2: % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | | (25) ~ (unit = e1) % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | | REF_CLOSE: (9), (22), (25) are inconsistent by sub-proof #141. % 129.95/18.06 | | | | | | % 129.95/18.06 | | | | | End of split % 129.95/18.06 | | | | | % 129.95/18.06 | | | | End of split % 129.95/18.06 | | | | % 129.95/18.06 | | | End of split % 129.95/18.06 | | | % 129.95/18.06 | | End of split % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | (26) op(e4, e4) = e4 % 129.95/18.06 | | % 129.95/18.06 | | REF_CLOSE: (2), (4), (11), (26) are inconsistent by sub-proof #317. % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #96 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) all_4_13 = e2 | ~ (op(e1, e2) = e2) % 129.95/18.06 (2) op(e1, e2) = e2 % 129.95/18.06 (3) ~ (all_4_13 = e2) % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (1) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (4) ~ (op(e1, e2) = e2) % 129.95/18.06 | | % 129.95/18.06 | | PRED_UNIFY: (2), (4) imply: % 129.95/18.06 | | (5) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (5) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | (6) all_4_13 = e2 % 129.95/18.06 | | % 129.95/18.06 | | REDUCE: (3), (6) imply: % 129.95/18.06 | | (7) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (7) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #97 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) ~ (all_4_24 = e3) % 129.95/18.06 (2) all_6_24 = all_4_24 % 129.95/18.06 (3) ~ (all_4_24 = e1) % 129.95/18.06 (4) ~ (all_4_24 = e0) % 129.95/18.06 (5) ~ (all_4_24 = e2) % 129.95/18.06 (6) all_6_24 = e3 | all_6_24 = e2 | all_6_24 = e1 | all_6_24 = e0 % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (6) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (7) all_6_24 = e2 % 129.95/18.06 | | % 129.95/18.06 | | COMBINE_EQS: (2), (7) imply: % 129.95/18.06 | | (8) all_4_24 = e2 % 129.95/18.06 | | % 129.95/18.06 | | SIMP: (8) implies: % 129.95/18.06 | | (9) all_4_24 = e2 % 129.95/18.06 | | % 129.95/18.06 | | REDUCE: (5), (9) imply: % 129.95/18.06 | | (10) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (10) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | (11) all_6_24 = e3 | all_6_24 = e1 | all_6_24 = e0 % 129.95/18.06 | | % 129.95/18.06 | | BETA: splitting (11) gives: % 129.95/18.06 | | % 129.95/18.06 | | Case 1: % 129.95/18.06 | | | % 129.95/18.06 | | | (12) all_6_24 = e3 % 129.95/18.06 | | | % 129.95/18.06 | | | COMBINE_EQS: (2), (12) imply: % 129.95/18.06 | | | (13) all_4_24 = e3 % 129.95/18.06 | | | % 129.95/18.06 | | | SIMP: (13) implies: % 129.95/18.06 | | | (14) all_4_24 = e3 % 129.95/18.06 | | | % 129.95/18.06 | | | REDUCE: (1), (14) imply: % 129.95/18.06 | | | (15) $false % 129.95/18.06 | | | % 129.95/18.06 | | | CLOSE: (15) is inconsistent. % 129.95/18.06 | | | % 129.95/18.06 | | Case 2: % 129.95/18.06 | | | % 129.95/18.06 | | | (16) all_6_24 = e1 | all_6_24 = e0 % 129.95/18.06 | | | % 129.95/18.06 | | | BETA: splitting (16) gives: % 129.95/18.06 | | | % 129.95/18.06 | | | Case 1: % 129.95/18.06 | | | | % 129.95/18.06 | | | | (17) all_6_24 = e1 % 129.95/18.06 | | | | % 129.95/18.06 | | | | COMBINE_EQS: (2), (17) imply: % 129.95/18.06 | | | | (18) all_4_24 = e1 % 129.95/18.06 | | | | % 129.95/18.06 | | | | SIMP: (18) implies: % 129.95/18.06 | | | | (19) all_4_24 = e1 % 129.95/18.06 | | | | % 129.95/18.06 | | | | REDUCE: (3), (19) imply: % 129.95/18.06 | | | | (20) $false % 129.95/18.06 | | | | % 129.95/18.06 | | | | CLOSE: (20) is inconsistent. % 129.95/18.06 | | | | % 129.95/18.06 | | | Case 2: % 129.95/18.06 | | | | % 129.95/18.06 | | | | (21) all_6_24 = e0 % 129.95/18.06 | | | | % 129.95/18.06 | | | | COMBINE_EQS: (2), (21) imply: % 129.95/18.06 | | | | (22) all_4_24 = e0 % 129.95/18.06 | | | | % 129.95/18.06 | | | | SIMP: (22) implies: % 129.95/18.06 | | | | (23) all_4_24 = e0 % 129.95/18.06 | | | | % 129.95/18.06 | | | | REDUCE: (4), (23) imply: % 129.95/18.06 | | | | (24) $false % 129.95/18.06 | | | | % 129.95/18.06 | | | | CLOSE: (24) is inconsistent. % 129.95/18.06 | | | | % 129.95/18.06 | | | End of split % 129.95/18.06 | | | % 129.95/18.06 | | End of split % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #98 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) all_6_9 = all_4_21 % 129.95/18.06 (2) op(e2, all_8_69) = e3 % 129.95/18.06 (3) op(e3, e2) = e0 % 129.95/18.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.95/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.95/18.06 (5) ~ (all_4_22 = e3) % 129.95/18.06 (6) all_6_9 = e4 | all_6_9 = e3 | all_6_9 = e2 | all_6_9 = e1 | all_6_9 = e0 % 129.95/18.06 (7) ~ (all_4_21 = e4) % 129.95/18.06 (8) op(e2, e0) = all_4_22 % 129.95/18.06 (9) op(e3, e2) = all_8_69 % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (6) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (10) all_6_9 = e4 % 129.95/18.06 | | % 129.95/18.06 | | COMBINE_EQS: (1), (10) imply: % 129.95/18.06 | | (11) all_4_21 = e4 % 129.95/18.06 | | % 129.95/18.06 | | SIMP: (11) implies: % 129.95/18.06 | | (12) all_4_21 = e4 % 129.95/18.06 | | % 129.95/18.06 | | REDUCE: (7), (12) imply: % 129.95/18.06 | | (13) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (13) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | % 129.95/18.06 | | GROUND_INST: instantiating (4) with e0, all_8_69, e2, e3, simplifying with % 129.95/18.06 | | (3), (9) gives: % 129.95/18.06 | | (14) all_8_69 = e0 % 129.95/18.06 | | % 129.95/18.06 | | REDUCE: (2), (14) imply: % 129.95/18.06 | | (15) op(e2, e0) = e3 % 129.95/18.06 | | % 129.95/18.06 | | REF_CLOSE: (4), (5), (8), (15) are inconsistent by sub-proof #226. % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #99 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) all_9_14 = e1 & op(e1, e2) = e1 % 129.95/18.06 (2) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 129.95/18.06 (3) all_6_17 = all_4_13 % 129.95/18.06 (4) ~ (all_4_13 = e1) % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | ALPHA: (1) implies: % 129.95/18.06 | (5) op(e1, e2) = e1 % 129.95/18.06 | % 129.95/18.06 | BETA: splitting (2) gives: % 129.95/18.06 | % 129.95/18.06 | Case 1: % 129.95/18.06 | | % 129.95/18.06 | | (6) ~ (op(e1, e2) = e1) % 129.95/18.06 | | % 129.95/18.06 | | PRED_UNIFY: (5), (6) imply: % 129.95/18.06 | | (7) $false % 129.95/18.06 | | % 129.95/18.06 | | CLOSE: (7) is inconsistent. % 129.95/18.06 | | % 129.95/18.06 | Case 2: % 129.95/18.06 | | % 129.95/18.06 | | (8) all_6_17 = e1 % 129.95/18.06 | | % 129.95/18.06 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #100. % 129.95/18.06 | | % 129.95/18.06 | End of split % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #100 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) all_6_17 = all_4_13 % 129.95/18.06 (2) all_6_17 = e1 % 129.95/18.06 (3) ~ (all_4_13 = e1) % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | COMBINE_EQS: (1), (2) imply: % 129.95/18.06 | (4) all_4_13 = e1 % 129.95/18.06 | % 129.95/18.06 | SIMP: (4) implies: % 129.95/18.06 | (5) all_4_13 = e1 % 129.95/18.06 | % 129.95/18.06 | REDUCE: (3), (5) imply: % 129.95/18.06 | (6) $false % 129.95/18.06 | % 129.95/18.06 | CLOSE: (6) is inconsistent. % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #101 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) ~ (e4 = e0) % 129.95/18.06 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.95/18.06 (3) all_6_10 = e3 % 129.95/18.06 (4) ~ (all_4_3 = all_4_4) % 129.95/18.06 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.06 (6) ~ (e4 = e2) % 129.95/18.06 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.06 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.06 (9) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.95/18.06 (10) ~ (all_4_3 = e3) % 129.95/18.06 (11) all_6_20 = all_4_4 % 129.95/18.06 (12) ~ (e3 = e0) % 129.95/18.06 (13) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.06 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 129.95/18.06 = e0 % 129.95/18.06 (15) ~ (e2 = e0) % 129.95/18.06 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 129.95/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 129.95/18.06 (17) ~ (all_4_4 = e3) % 129.95/18.06 (18) ~ (e1 = e0) % 129.95/18.06 (19) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 129.95/18.06 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 129.95/18.06 (all_9_20 = e3 & op(e0, e4) = e3) % 129.95/18.06 (20) ~ (e3 = e2) % 129.95/18.06 (21) op(e0, e4) = all_4_4 % 129.95/18.06 (22) ~ (e4 = e1) % 129.95/18.06 (23) ~ (all_4_3 = e0) % 129.95/18.06 (24) all_9_5 = e0 % 129.95/18.06 (25) ~ (e3 = e1) % 129.95/18.06 (26) all_9_5 = e1 % 129.95/18.06 (27) op(e1, e4) = all_4_3 % 129.95/18.06 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 129.95/18.06 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 129.95/18.06 (all_9_20 = e2 & op(e0, e4) = e2) % 129.95/18.06 (29) ~ (e4 = e3) % 129.95/18.06 (30) ~ (all_4_4 = e0) % 129.95/18.06 (31) ~ (all_4_3 = e1) % 129.95/18.06 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 129.95/18.06 (33) op(e2, e4) = e3 % 129.95/18.06 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 129.95/18.06 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 129.95/18.06 (all_9_20 = e4 & op(e0, e4) = e4) % 129.95/18.06 (35) all_9_2 = e1 % 129.95/18.06 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 129.95/18.06 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 129.95/18.06 (all_9_20 = e1 & op(e0, e4) = e1) % 129.95/18.06 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 129.95/18.06 = e0 % 129.95/18.06 (38) ~ (all_4_4 = e1) % 129.95/18.06 (39) all_4_0 = e0 % 129.95/18.06 (40) ~ (e2 = e1) % 129.95/18.06 (41) all_6_15 = all_4_3 % 129.95/18.06 (42) op(e4, e4) = e0 % 129.95/18.06 % 129.95/18.06 Begin of proof % 129.95/18.06 | % 129.95/18.06 | COMBINE_EQS: (24), (26) imply: % 129.95/18.06 | (43) e1 = e0 % 129.95/18.06 | % 129.95/18.06 | COMBINE_EQS: (35), (43) imply: % 129.95/18.06 | (44) all_9_2 = e0 % 129.95/18.06 | % 129.95/18.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 129.95/18.06 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 129.95/18.06 | (25), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 129.95/18.06 | (38), (39), (40), (41), (42), (44) are inconsistent by sub-proof % 129.95/18.06 | #265. % 129.95/18.06 | % 129.95/18.06 End of proof % 129.95/18.06 % 129.95/18.06 Sub-proof #102 shows that the following formulas are inconsistent: % 129.95/18.06 ---------------------------------------------------------------- % 129.95/18.06 (1) ~ (all_4_14 = e0) % 129.95/18.06 (2) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 129.95/18.06 (3) all_6_5 = e1 % 129.95/18.06 (4) ~ (e4 = e0) % 129.95/18.06 (5) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 129.95/18.06 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 129.95/18.06 (all_9_16 = e4 & op(e4, e0) = e4) % 129.95/18.06 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 129.95/18.06 (7) all_9_20 = e2 % 129.95/18.06 (8) all_6_10 = e3 % 129.95/18.06 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 129.95/18.06 (10) ~ (all_4_3 = all_4_4) % 129.95/18.06 (11) all_9_3 = e4 % 129.95/18.06 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 129.95/18.06 (13) ~ (e4 = e2) % 129.95/18.06 (14) ~ (all_4_6 = e3) % 129.95/18.06 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 129.95/18.06 (16) all_9_23 = e4 & op(e0, e1) = e4 % 129.95/18.06 (17) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 129.95/18.06 (18) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.06 (19) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 129.95/18.06 (20) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 129.95/18.06 (21) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = e1) | % 129.95/18.06 (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 129.95/18.06 (all_9_23 = e1 & op(e0, e1) = e1) % 129.95/18.06 (22) ~ (all_4_3 = e3) % 129.95/18.06 (23) all_6_20 = all_4_4 % 129.95/18.06 (24) ~ (e3 = e0) % 129.95/18.06 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 129.95/18.06 (26) all_6_8 = all_4_16 % 130.06/18.06 (27) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.06/18.06 = e0 % 130.06/18.06 (28) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 130.06/18.06 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 130.06/18.06 (all_9_17 = e2 & op(e3, e0) = e2) % 130.06/18.06 (29) ~ (op(e4, e3) = e4) % 130.06/18.06 (30) ~ (e2 = e0) % 130.06/18.06 (31) all_9_0 = e0 % 130.06/18.06 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.06 (33) ~ (all_4_4 = e3) % 130.06/18.06 (34) ~ (all_4_17 = e3) % 130.06/18.06 (35) ~ (op(e3, e2) = e2) % 130.06/18.06 (36) (all_9_9 = e0 & op(e4, e1) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) | % 130.06/18.06 (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_15 = e0 & op(e1, e1) = e0) | % 130.06/18.06 (all_9_23 = e0 & op(e0, e1) = e0) % 130.06/18.06 (37) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 130.06/18.06 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 130.06/18.06 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 130.06/18.06 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 130.06/18.06 e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 130.06/18.06 (38) ~ (e1 = e0) % 130.06/18.06 (39) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 130.06/18.06 (40) all_6_24 = all_4_24 % 130.06/18.06 (41) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.06/18.06 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.06/18.06 (all_9_20 = e3 & op(e0, e4) = e3) % 130.06/18.06 (42) ~ (e3 = e2) % 130.06/18.06 (43) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 130.06/18.06 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 130.06/18.06 (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.06 (44) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.06/18.06 (45) all_9_12 = e4 % 130.06/18.06 (46) ~ (all_4_24 = e0) % 130.06/18.06 (47) op(e0, e4) = all_4_4 % 130.06/18.06 (48) ~ (e4 = e1) % 130.06/18.06 (49) ~ (all_4_3 = e0) % 130.06/18.06 (50) ~ (all_4_20 = e4) % 130.06/18.06 (51) ~ (e3 = e1) % 130.06/18.06 (52) op(e3, e4) = e1 % 130.06/18.06 (53) all_9_9 = e4 % 130.06/18.06 (54) all_9_21 = e3 % 130.06/18.06 (55) op(e1, e4) = all_4_3 % 130.06/18.06 (56) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.06 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.06 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.06 (57) ~ (all_4_16 = e1) % 130.06/18.06 (58) ~ (e4 = e3) % 130.06/18.06 (59) all_6_4 = all_4_20 % 130.06/18.06 (60) ~ (all_4_4 = e0) % 130.06/18.06 (61) ~ (all_4_3 = e1) % 130.06/18.06 (62) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 130.06/18.06 (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & op(e1, e1) = e3) | % 130.06/18.06 (all_9_23 = e3 & op(e0, e1) = e3) % 130.06/18.06 (63) all_6_2 = all_4_10 % 130.06/18.06 (64) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.06/18.06 (65) op(e2, e4) = e3 % 130.06/18.06 (66) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.06 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.06 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.06 (67) ~ (all_4_10 = e4) % 130.06/18.06 (68) op(e2, e1) = all_4_17 % 130.06/18.06 (69) all_9_2 = e1 % 130.06/18.06 (70) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.06/18.06 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.06/18.06 (all_9_20 = e1 & op(e0, e4) = e1) % 130.06/18.06 (71) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.06/18.06 = e0 % 130.06/18.06 (72) ~ (all_4_4 = e1) % 130.06/18.06 (73) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 130.06/18.06 (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.06/18.06 (all_9_23 = e2 & op(e0, e1) = e2) % 130.06/18.06 (74) all_4_0 = e0 % 130.06/18.06 (75) ~ (e2 = e1) % 130.06/18.06 (76) all_6_15 = all_4_3 % 130.06/18.06 (77) op(e4, e4) = e0 % 130.06/18.06 (78) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 130.06/18.06 % 130.06/18.06 Begin of proof % 130.06/18.06 | % 130.06/18.06 | ALPHA: (16) implies: % 130.06/18.06 | (79) all_9_23 = e4 % 130.06/18.06 | % 130.06/18.06 | BETA: splitting (36) gives: % 130.06/18.06 | % 130.06/18.06 | Case 1: % 130.06/18.06 | | % 130.06/18.06 | | (80) (all_9_9 = e0 & op(e4, e1) = e0) | (all_9_10 = e0 & op(e3, e1) = e0) % 130.06/18.06 | | % 130.06/18.06 | | BETA: splitting (80) gives: % 130.06/18.06 | | % 130.06/18.06 | | Case 1: % 130.06/18.06 | | | % 130.06/18.06 | | | (81) all_9_9 = e0 & op(e4, e1) = e0 % 130.06/18.06 | | | % 130.06/18.06 | | | ALPHA: (81) implies: % 130.06/18.06 | | | (82) all_9_9 = e0 % 130.06/18.06 | | | % 130.06/18.06 | | | COMBINE_EQS: (53), (82) imply: % 130.06/18.07 | | | (83) e4 = e0 % 130.06/18.07 | | | % 130.06/18.07 | | | REDUCE: (4), (83) imply: % 130.06/18.07 | | | (84) $false % 130.06/18.07 | | | % 130.06/18.07 | | | CLOSE: (84) is inconsistent. % 130.06/18.07 | | | % 130.06/18.07 | | Case 2: % 130.06/18.07 | | | % 130.06/18.07 | | | (85) all_9_10 = e0 & op(e3, e1) = e0 % 130.06/18.07 | | | % 130.06/18.07 | | | ALPHA: (85) implies: % 130.06/18.07 | | | (86) all_9_10 = e0 % 130.06/18.07 | | | % 130.06/18.07 | | | REF_CLOSE: (1), (4), (7), (11), (13), (14), (17), (19), (24), (28), (30), % 130.06/18.07 | | | (32), (35), (37), (39), (40), (42), (43), (46), (51), (52), % 130.06/18.07 | | | (54), (69), (75), (79), (86) are inconsistent by sub-proof % 130.06/18.07 | | | #107. % 130.06/18.07 | | | % 130.06/18.07 | | End of split % 130.06/18.07 | | % 130.06/18.07 | Case 2: % 130.06/18.07 | | % 130.06/18.07 | | (87) (all_9_11 = e0 & op(e2, e1) = e0) | (all_9_15 = e0 & op(e1, e1) = % 130.06/18.07 | | e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 130.06/18.07 | | % 130.06/18.07 | | BETA: splitting (87) gives: % 130.06/18.07 | | % 130.06/18.07 | | Case 1: % 130.06/18.07 | | | % 130.06/18.07 | | | (88) all_9_11 = e0 & op(e2, e1) = e0 % 130.06/18.07 | | | % 130.06/18.07 | | | ALPHA: (88) implies: % 130.06/18.07 | | | (89) all_9_11 = e0 % 130.06/18.07 | | | % 130.06/18.07 | | | BETA: splitting (21) gives: % 130.06/18.07 | | | % 130.06/18.07 | | | Case 1: % 130.06/18.07 | | | | % 130.06/18.07 | | | | (90) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, e1) = % 130.06/18.07 | | | | e1) % 130.06/18.07 | | | | % 130.06/18.07 | | | | BETA: splitting (90) gives: % 130.06/18.07 | | | | % 130.06/18.07 | | | | Case 1: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (91) all_9_9 = e1 & op(e4, e1) = e1 % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | REF_CLOSE: (48), (53), (91) are inconsistent by sub-proof #263. % 130.06/18.07 | | | | | % 130.06/18.07 | | | | Case 2: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (92) all_9_10 = e1 & op(e3, e1) = e1 % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | REF_CLOSE: (26), (57), (78), (92) are inconsistent by sub-proof #106. % 130.06/18.07 | | | | | % 130.06/18.07 | | | | End of split % 130.06/18.07 | | | | % 130.06/18.07 | | | Case 2: % 130.06/18.07 | | | | % 130.06/18.07 | | | | (93) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, e1) % 130.06/18.07 | | | | = e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 130.06/18.07 | | | | % 130.06/18.07 | | | | BETA: splitting (93) gives: % 130.06/18.07 | | | | % 130.06/18.07 | | | | Case 1: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (94) all_9_11 = e1 & op(e2, e1) = e1 % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | REF_CLOSE: (4), (6), (8), (10), (12), (13), (15), (18), (20), (22), % 130.06/18.07 | | | | | (23), (24), (25), (27), (30), (32), (33), (38), (41), (42), % 130.06/18.07 | | | | | (47), (48), (49), (51), (55), (56), (58), (60), (61), (64), % 130.06/18.07 | | | | | (65), (66), (69), (70), (71), (72), (74), (75), (76), (77), % 130.06/18.07 | | | | | (89), (94) are inconsistent by sub-proof #118. % 130.06/18.07 | | | | | % 130.06/18.07 | | | | Case 2: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (95) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, % 130.06/18.07 | | | | | e1) = e1) % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | BETA: splitting (95) gives: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | Case 1: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (96) all_9_15 = e1 & op(e1, e1) = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | ALPHA: (96) implies: % 130.06/18.07 | | | | | | (97) all_9_15 = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | BETA: splitting (73) gives: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | Case 1: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (98) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & op(e3, % 130.06/18.07 | | | | | | | e1) = e2) % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | BETA: splitting (98) gives: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (99) all_9_9 = e2 & op(e4, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | REF_CLOSE: (13), (53), (99) are inconsistent by sub-proof #260. % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (100) all_9_10 = e2 & op(e3, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | ALPHA: (100) implies: % 130.06/18.07 | | | | | | | | (101) all_9_10 = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | BETA: splitting (37) gives: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (102) all_9_24 = e0 & op(e0, e0) = e0 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | ALPHA: (102) implies: % 130.06/18.07 | | | | | | | | | (103) op(e0, e0) = e0 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | REF_CLOSE: (17), (40), (46), (103) are inconsistent by % 130.06/18.07 | | | | | | | | | sub-proof #240. % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (104) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 & % 130.06/18.07 | | | | | | | | | op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 130.06/18.07 | | | | | | | | | e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & % 130.06/18.07 | | | | | | | | | ((all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & % 130.06/18.07 | | | | | | | | | op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = % 130.06/18.07 | | | | | | | | | e0) | (all_9_23 = e0 & op(e0, e1) = e0)) % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | ALPHA: (104) implies: % 130.06/18.07 | | | | | | | | | (105) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & % 130.06/18.07 | | | | | | | | | op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = % 130.06/18.07 | | | | | | | | | e0) | (all_9_23 = e0 & op(e0, e1) = e0) % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | BETA: splitting (105) gives: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (106) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 % 130.06/18.07 | | | | | | | | | | & op(e0, e3) = e0) % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | BETA: splitting (106) gives: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (107) all_9_20 = e0 & op(e0, e4) = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | ALPHA: (107) implies: % 130.06/18.07 | | | | | | | | | | | (108) all_9_20 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (7), (108) imply: % 130.06/18.07 | | | | | | | | | | | (109) e2 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (101), (109) imply: % 130.06/18.07 | | | | | | | | | | | (110) all_9_10 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (11), (13), (14), (17), (19), (24), % 130.06/18.07 | | | | | | | | | | | (28), (30), (32), (35), (37), (39), (40), (42), % 130.06/18.07 | | | | | | | | | | | (43), (46), (51), (52), (54), (69), (75), (79), % 130.06/18.07 | | | | | | | | | | | (110) are inconsistent by sub-proof #107. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (111) all_9_21 = e0 & op(e0, e3) = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REF_CLOSE: (24), (54), (111) are inconsistent by sub-proof % 130.06/18.07 | | | | | | | | | | | #136. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (112) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 % 130.06/18.07 | | | | | | | | | | & op(e0, e1) = e0) % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | BETA: splitting (112) gives: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (113) all_9_22 = e0 & op(e0, e2) = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REF_CLOSE: (1), (39), (113) are inconsistent by sub-proof % 130.06/18.07 | | | | | | | | | | | #238. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (114) all_9_23 = e0 & op(e0, e1) = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | ALPHA: (114) implies: % 130.06/18.07 | | | | | | | | | | | (115) all_9_23 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (79), (115) imply: % 130.06/18.07 | | | | | | | | | | | (116) e4 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | SIMP: (116) implies: % 130.06/18.07 | | | | | | | | | | | (117) e4 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REDUCE: (4), (117) imply: % 130.06/18.07 | | | | | | | | | | | (118) $false % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | CLOSE: (118) is inconsistent. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | End of split % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | End of split % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | Case 2: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (119) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & % 130.06/18.07 | | | | | | | op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | BETA: splitting (119) gives: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (120) all_9_11 = e2 & op(e2, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | ALPHA: (120) implies: % 130.06/18.07 | | | | | | | | (121) all_9_11 = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | COMBINE_EQS: (89), (121) imply: % 130.06/18.07 | | | | | | | | (122) e2 = e0 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | REDUCE: (30), (122) imply: % 130.06/18.07 | | | | | | | | (123) $false % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | CLOSE: (123) is inconsistent. % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (124) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 & % 130.06/18.07 | | | | | | | | op(e0, e1) = e2) % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | BETA: splitting (124) gives: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (125) all_9_15 = e2 & op(e1, e1) = e2 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (12), (13), (15), % 130.06/18.07 | | | | | | | | | (30), (31), (32), (42), (48), (52), (56), (58), % 130.06/18.07 | | | | | | | | | (66), (74), (75), (97), (125) are inconsistent by % 130.06/18.07 | | | | | | | | | sub-proof #250. % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (126) all_9_23 = e2 & op(e0, e1) = e2 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | REF_CLOSE: (13), (79), (126) are inconsistent by sub-proof % 130.06/18.07 | | | | | | | | | #105. % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | End of split % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | End of split % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | End of split % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | Case 2: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (127) all_9_23 = e1 & op(e0, e1) = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | REF_CLOSE: (48), (79), (127) are inconsistent by sub-proof #104. % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | End of split % 130.06/18.07 | | | | | % 130.06/18.07 | | | | End of split % 130.06/18.07 | | | | % 130.06/18.07 | | | End of split % 130.06/18.07 | | | % 130.06/18.07 | | Case 2: % 130.06/18.07 | | | % 130.06/18.07 | | | (128) (all_9_15 = e0 & op(e1, e1) = e0) | (all_9_23 = e0 & op(e0, e1) = % 130.06/18.07 | | | e0) % 130.06/18.07 | | | % 130.06/18.07 | | | BETA: splitting (128) gives: % 130.06/18.07 | | | % 130.06/18.07 | | | Case 1: % 130.06/18.07 | | | | % 130.06/18.07 | | | | (129) all_9_15 = e0 & op(e1, e1) = e0 % 130.06/18.07 | | | | % 130.06/18.07 | | | | ALPHA: (129) implies: % 130.06/18.07 | | | | (130) all_9_15 = e0 % 130.06/18.07 | | | | % 130.06/18.07 | | | | BETA: splitting (21) gives: % 130.06/18.07 | | | | % 130.06/18.07 | | | | Case 1: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (131) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_10 = e1 & op(e3, % 130.06/18.07 | | | | | e1) = e1) % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | BETA: splitting (131) gives: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | Case 1: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (132) all_9_9 = e1 & op(e4, e1) = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | REF_CLOSE: (48), (53), (132) are inconsistent by sub-proof #263. % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | Case 2: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (133) all_9_10 = e1 & op(e3, e1) = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | REF_CLOSE: (26), (57), (78), (133) are inconsistent by sub-proof % 130.06/18.07 | | | | | | #106. % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | End of split % 130.06/18.07 | | | | | % 130.06/18.07 | | | | Case 2: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | (134) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_15 = e1 & op(e1, % 130.06/18.07 | | | | | e1) = e1) | (all_9_23 = e1 & op(e0, e1) = e1) % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | BETA: splitting (134) gives: % 130.06/18.07 | | | | | % 130.06/18.07 | | | | | Case 1: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (135) all_9_11 = e1 & op(e2, e1) = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | ALPHA: (135) implies: % 130.06/18.07 | | | | | | (136) all_9_11 = e1 % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | BETA: splitting (73) gives: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | Case 1: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (137) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_10 = e2 & % 130.06/18.07 | | | | | | | op(e3, e1) = e2) % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | BETA: splitting (137) gives: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (138) all_9_9 = e2 & op(e4, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | REF_CLOSE: (13), (53), (138) are inconsistent by sub-proof #260. % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (139) all_9_10 = e2 & op(e3, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | ALPHA: (139) implies: % 130.06/18.07 | | | | | | | | (140) all_9_10 = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | BETA: splitting (62) gives: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (141) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_10 = e3 & % 130.06/18.07 | | | | | | | | | op(e3, e1) = e3) % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | BETA: splitting (141) gives: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (142) all_9_9 = e3 & op(e4, e1) = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | ALPHA: (142) implies: % 130.06/18.07 | | | | | | | | | | (143) all_9_9 = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (12), (13), (15), % 130.06/18.07 | | | | | | | | | | (29), (44), (45), (48), (50), (58), (59), (63), % 130.06/18.07 | | | | | | | | | | (66), (67), (74), (143) are inconsistent by % 130.06/18.07 | | | | | | | | | | sub-proof #137. % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (144) all_9_10 = e3 & op(e3, e1) = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | ALPHA: (144) implies: % 130.06/18.07 | | | | | | | | | | (145) all_9_10 = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | COMBINE_EQS: (140), (145) imply: % 130.06/18.07 | | | | | | | | | | (146) e3 = e2 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | REDUCE: (42), (146) imply: % 130.06/18.07 | | | | | | | | | | (147) $false % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | CLOSE: (147) is inconsistent. % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (148) (all_9_11 = e3 & op(e2, e1) = e3) | (all_9_15 = e3 & % 130.06/18.07 | | | | | | | | | op(e1, e1) = e3) | (all_9_23 = e3 & op(e0, e1) = % 130.06/18.07 | | | | | | | | | e3) % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | BETA: splitting (148) gives: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (149) all_9_11 = e3 & op(e2, e1) = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | ALPHA: (149) implies: % 130.06/18.07 | | | | | | | | | | (150) op(e2, e1) = e3 % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | REF_CLOSE: (32), (34), (68), (150) are inconsistent by % 130.06/18.07 | | | | | | | | | | sub-proof #103. % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | (151) (all_9_15 = e3 & op(e1, e1) = e3) | (all_9_23 = e3 % 130.06/18.07 | | | | | | | | | | & op(e0, e1) = e3) % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | BETA: splitting (151) gives: % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (152) all_9_15 = e3 & op(e1, e1) = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | ALPHA: (152) implies: % 130.06/18.07 | | | | | | | | | | | (153) all_9_15 = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (130), (153) imply: % 130.06/18.07 | | | | | | | | | | | (154) e3 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | SIMP: (154) implies: % 130.06/18.07 | | | | | | | | | | | (155) e3 = e0 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REDUCE: (24), (155) imply: % 130.06/18.07 | | | | | | | | | | | (156) $false % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | CLOSE: (156) is inconsistent. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | (157) all_9_23 = e3 & op(e0, e1) = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | ALPHA: (157) implies: % 130.06/18.07 | | | | | | | | | | | (158) all_9_23 = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (79), (158) imply: % 130.06/18.07 | | | | | | | | | | | (159) e4 = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | SIMP: (159) implies: % 130.06/18.07 | | | | | | | | | | | (160) e4 = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | COMBINE_EQS: (53), (160) imply: % 130.06/18.07 | | | | | | | | | | | (161) all_9_9 = e3 % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (12), (13), (15), % 130.06/18.07 | | | | | | | | | | | (29), (44), (45), (48), (50), (58), (59), (63), % 130.06/18.07 | | | | | | | | | | | (66), (67), (74), (161) are inconsistent by % 130.06/18.07 | | | | | | | | | | | sub-proof #137. % 130.06/18.07 | | | | | | | | | | | % 130.06/18.07 | | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | | % 130.06/18.07 | | | | | | | | | End of split % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | End of split % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | End of split % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | Case 2: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (162) (all_9_11 = e2 & op(e2, e1) = e2) | (all_9_15 = e2 & % 130.06/18.07 | | | | | | | op(e1, e1) = e2) | (all_9_23 = e2 & op(e0, e1) = e2) % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | BETA: splitting (162) gives: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (163) all_9_11 = e2 & op(e2, e1) = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | ALPHA: (163) implies: % 130.06/18.07 | | | | | | | | (164) all_9_11 = e2 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | COMBINE_EQS: (136), (164) imply: % 130.06/18.07 | | | | | | | | (165) e2 = e1 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | COMBINE_EQS: (7), (165) imply: % 130.06/18.07 | | | | | | | | (166) all_9_20 = e1 % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (9), (12), (13), (15), (30), % 130.06/18.07 | | | | | | | | (31), (32), (42), (48), (52), (56), (58), (66), (74), % 130.06/18.07 | | | | | | | | (75), (166) are inconsistent by sub-proof #283. % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | (167) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_23 = e2 & % 130.06/18.07 | | | | | | | | op(e0, e1) = e2) % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | BETA: splitting (167) gives: % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | | Case 1: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (168) all_9_15 = e2 & op(e1, e1) = e2 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | ALPHA: (168) implies: % 130.06/18.07 | | | | | | | | | (169) all_9_15 = e2 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | COMBINE_EQS: (130), (169) imply: % 130.06/18.07 | | | | | | | | | (170) e2 = e0 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | SIMP: (170) implies: % 130.06/18.07 | | | | | | | | | (171) e2 = e0 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | REDUCE: (30), (171) imply: % 130.06/18.07 | | | | | | | | | (172) $false % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | CLOSE: (172) is inconsistent. % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | Case 2: % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | (173) all_9_23 = e2 & op(e0, e1) = e2 % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | | REF_CLOSE: (13), (79), (173) are inconsistent by sub-proof % 130.06/18.07 | | | | | | | | | #105. % 130.06/18.07 | | | | | | | | | % 130.06/18.07 | | | | | | | | End of split % 130.06/18.07 | | | | | | | | % 130.06/18.07 | | | | | | | End of split % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | End of split % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | Case 2: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | (174) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_23 = e1 & op(e0, % 130.06/18.07 | | | | | | e1) = e1) % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | BETA: splitting (174) gives: % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | | Case 1: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (175) all_9_15 = e1 & op(e1, e1) = e1 % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | ALPHA: (175) implies: % 130.06/18.07 | | | | | | | (176) all_9_15 = e1 % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | COMBINE_EQS: (130), (176) imply: % 130.06/18.07 | | | | | | | (177) e1 = e0 % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | REF_CLOSE: (4), (6), (8), (10), (12), (13), (15), (18), (20), % 130.06/18.07 | | | | | | | (22), (23), (24), (25), (27), (30), (32), (33), (38), % 130.06/18.07 | | | | | | | (41), (42), (47), (48), (49), (51), (55), (56), (58), % 130.06/18.07 | | | | | | | (60), (61), (64), (65), (66), (69), (70), (71), (72), % 130.06/18.07 | | | | | | | (74), (75), (76), (77), (177) are inconsistent by % 130.06/18.07 | | | | | | | sub-proof #264. % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | Case 2: % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | (178) all_9_23 = e1 & op(e0, e1) = e1 % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | | REF_CLOSE: (48), (79), (178) are inconsistent by sub-proof #104. % 130.06/18.07 | | | | | | | % 130.06/18.07 | | | | | | End of split % 130.06/18.07 | | | | | | % 130.06/18.07 | | | | | End of split % 130.06/18.07 | | | | | % 130.06/18.07 | | | | End of split % 130.06/18.07 | | | | % 130.06/18.07 | | | Case 2: % 130.06/18.07 | | | | % 130.06/18.07 | | | | (179) all_9_23 = e0 & op(e0, e1) = e0 % 130.06/18.07 | | | | % 130.06/18.07 | | | | REF_CLOSE: (4), (79), (179) are inconsistent by sub-proof #109. % 130.06/18.07 | | | | % 130.06/18.07 | | | End of split % 130.06/18.07 | | | % 130.06/18.07 | | End of split % 130.06/18.07 | | % 130.06/18.07 | End of split % 130.06/18.07 | % 130.06/18.07 End of proof % 130.06/18.07 % 130.06/18.07 Sub-proof #103 shows that the following formulas are inconsistent: % 130.06/18.07 ---------------------------------------------------------------- % 130.06/18.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.07 (2) op(e2, e1) = all_4_17 % 130.06/18.07 (3) op(e2, e1) = e3 % 130.06/18.07 (4) ~ (all_4_17 = e3) % 130.06/18.07 % 130.06/18.07 Begin of proof % 130.06/18.07 | % 130.06/18.07 | GROUND_INST: instantiating (1) with all_4_17, e3, e1, e2, simplifying with % 130.06/18.07 | (2), (3) gives: % 130.06/18.07 | (5) all_4_17 = e3 % 130.06/18.07 | % 130.06/18.07 | REDUCE: (4), (5) imply: % 130.06/18.07 | (6) $false % 130.06/18.07 | % 130.06/18.07 | CLOSE: (6) is inconsistent. % 130.06/18.07 | % 130.06/18.07 End of proof % 130.06/18.07 % 130.06/18.07 Sub-proof #104 shows that the following formulas are inconsistent: % 130.06/18.07 ---------------------------------------------------------------- % 130.06/18.07 (1) all_9_23 = e1 & op(e0, e1) = e1 % 130.06/18.07 (2) all_9_23 = e4 % 130.06/18.07 (3) ~ (e4 = e1) % 130.06/18.07 % 130.06/18.07 Begin of proof % 130.06/18.07 | % 130.06/18.07 | ALPHA: (1) implies: % 130.06/18.07 | (4) all_9_23 = e1 % 130.06/18.07 | % 130.06/18.07 | COMBINE_EQS: (2), (4) imply: % 130.06/18.07 | (5) e4 = e1 % 130.06/18.07 | % 130.06/18.07 | REDUCE: (3), (5) imply: % 130.06/18.07 | (6) $false % 130.06/18.07 | % 130.06/18.07 | CLOSE: (6) is inconsistent. % 130.06/18.07 | % 130.06/18.07 End of proof % 130.06/18.07 % 130.06/18.07 Sub-proof #105 shows that the following formulas are inconsistent: % 130.06/18.07 ---------------------------------------------------------------- % 130.06/18.07 (1) all_9_23 = e2 & op(e0, e1) = e2 % 130.06/18.07 (2) all_9_23 = e4 % 130.06/18.07 (3) ~ (e4 = e2) % 130.06/18.07 % 130.06/18.07 Begin of proof % 130.06/18.07 | % 130.06/18.07 | ALPHA: (1) implies: % 130.06/18.07 | (4) all_9_23 = e2 % 130.06/18.07 | % 130.06/18.07 | COMBINE_EQS: (2), (4) imply: % 130.06/18.07 | (5) e4 = e2 % 130.06/18.07 | % 130.06/18.07 | SIMP: (5) implies: % 130.06/18.07 | (6) e4 = e2 % 130.06/18.07 | % 130.06/18.07 | REDUCE: (3), (6) imply: % 130.06/18.07 | (7) $false % 130.06/18.07 | % 130.06/18.07 | CLOSE: (7) is inconsistent. % 130.06/18.07 | % 130.06/18.07 End of proof % 130.06/18.07 % 130.06/18.07 Sub-proof #106 shows that the following formulas are inconsistent: % 130.06/18.07 ---------------------------------------------------------------- % 130.06/18.07 (1) all_9_10 = e1 & op(e3, e1) = e1 % 130.06/18.07 (2) all_6_8 = e1 | ~ (op(e3, e1) = e1) % 130.06/18.07 (3) all_6_8 = all_4_16 % 130.06/18.07 (4) ~ (all_4_16 = e1) % 130.06/18.07 % 130.06/18.07 Begin of proof % 130.06/18.07 | % 130.06/18.07 | ALPHA: (1) implies: % 130.06/18.07 | (5) op(e3, e1) = e1 % 130.06/18.07 | % 130.06/18.07 | BETA: splitting (2) gives: % 130.06/18.07 | % 130.06/18.07 | Case 1: % 130.06/18.07 | | % 130.06/18.07 | | (6) ~ (op(e3, e1) = e1) % 130.06/18.07 | | % 130.06/18.07 | | PRED_UNIFY: (5), (6) imply: % 130.06/18.07 | | (7) $false % 130.06/18.07 | | % 130.06/18.07 | | CLOSE: (7) is inconsistent. % 130.06/18.07 | | % 130.06/18.07 | Case 2: % 130.06/18.07 | | % 130.06/18.07 | | (8) all_6_8 = e1 % 130.06/18.07 | | % 130.06/18.07 | | COMBINE_EQS: (3), (8) imply: % 130.06/18.07 | | (9) all_4_16 = e1 % 130.06/18.07 | | % 130.06/18.07 | | REDUCE: (4), (9) imply: % 130.06/18.07 | | (10) $false % 130.06/18.07 | | % 130.06/18.07 | | CLOSE: (10) is inconsistent. % 130.06/18.07 | | % 130.06/18.07 | End of split % 130.06/18.07 | % 130.06/18.07 End of proof % 130.06/18.07 % 130.06/18.07 Sub-proof #107 shows that the following formulas are inconsistent: % 130.06/18.07 ---------------------------------------------------------------- % 130.06/18.07 (1) ~ (all_4_14 = e0) % 130.06/18.07 (2) ~ (e4 = e0) % 130.06/18.07 (3) all_9_20 = e2 % 130.06/18.07 (4) all_9_3 = e4 % 130.06/18.07 (5) ~ (e4 = e2) % 130.06/18.07 (6) ~ (all_4_6 = e3) % 130.06/18.07 (7) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 130.06/18.07 (8) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 130.06/18.07 (9) ~ (e3 = e0) % 130.06/18.07 (10) all_9_10 = e0 % 130.06/18.07 (11) all_9_23 = e4 % 130.06/18.07 (12) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) | % 130.06/18.07 (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) | % 130.06/18.07 (all_9_17 = e2 & op(e3, e0) = e2) % 130.06/18.07 (13) ~ (e2 = e0) % 130.06/18.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.07 (15) ~ (op(e3, e2) = e2) % 130.06/18.07 (16) (all_9_24 = e0 & op(e0, e0) = e0) | (((all_9_16 = e0 & op(e4, e0) = e0) % 130.06/18.07 | (all_9_17 = e0 & op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = % 130.06/18.07 e0) | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 130.06/18.07 op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | (all_9_22 = % 130.06/18.07 e0 & op(e0, e2) = e0) | (all_9_23 = e0 & op(e0, e1) = e0))) % 130.06/18.07 (17) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 130.06/18.07 (18) all_6_24 = all_4_24 % 130.06/18.07 (19) ~ (e3 = e2) % 130.06/18.08 (20) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 130.06/18.08 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 130.06/18.08 (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.08 (21) ~ (all_4_24 = e0) % 130.06/18.08 (22) ~ (e3 = e1) % 130.06/18.08 (23) op(e3, e4) = e1 % 130.06/18.08 (24) all_9_21 = e3 % 130.06/18.08 (25) all_9_2 = e1 % 130.06/18.08 (26) ~ (e2 = e1) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (12) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (27) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) % 130.06/18.08 | | % 130.06/18.08 | | REF_CLOSE: (4), (5), (14), (23), (26), (27) are inconsistent by sub-proof % 130.06/18.08 | | #133. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (28) (all_9_5 = e2 & op(e3, e2) = e2) | (all_9_10 = e2 & op(e3, e1) = e2) % 130.06/18.08 | | | (all_9_17 = e2 & op(e3, e0) = e2) % 130.06/18.08 | | % 130.06/18.08 | | BETA: splitting (28) gives: % 130.06/18.08 | | % 130.06/18.08 | | Case 1: % 130.06/18.08 | | | % 130.06/18.08 | | | (29) all_9_5 = e2 & op(e3, e2) = e2 % 130.06/18.08 | | | % 130.06/18.08 | | | REF_CLOSE: (15), (29) are inconsistent by sub-proof #132. % 130.06/18.08 | | | % 130.06/18.08 | | Case 2: % 130.06/18.08 | | | % 130.06/18.08 | | | (30) (all_9_10 = e2 & op(e3, e1) = e2) | (all_9_17 = e2 & op(e3, e0) = % 130.06/18.08 | | | e2) % 130.06/18.08 | | | % 130.06/18.08 | | | BETA: splitting (30) gives: % 130.06/18.08 | | | % 130.06/18.08 | | | Case 1: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (31) all_9_10 = e2 & op(e3, e1) = e2 % 130.06/18.08 | | | | % 130.06/18.08 | | | | REF_CLOSE: (10), (13), (31) are inconsistent by sub-proof #110. % 130.06/18.08 | | | | % 130.06/18.08 | | | Case 2: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (32) all_9_17 = e2 & op(e3, e0) = e2 % 130.06/18.08 | | | | % 130.06/18.08 | | | | ALPHA: (32) implies: % 130.06/18.08 | | | | (33) all_9_17 = e2 % 130.06/18.08 | | | | % 130.06/18.08 | | | | BETA: splitting (20) gives: % 130.06/18.08 | | | | % 130.06/18.08 | | | | Case 1: % 130.06/18.08 | | | | | % 130.06/18.08 | | | | | (34) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) % 130.06/18.08 | | | | | = e3) % 130.06/18.08 | | | | | % 130.06/18.08 | | | | | REF_CLOSE: (6), (8), (22), (25), (34) are inconsistent by sub-proof % 130.06/18.08 | | | | | #293. % 130.06/18.08 | | | | | % 130.06/18.08 | | | | Case 2: % 130.06/18.08 | | | | | % 130.06/18.08 | | | | | (35) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) % 130.06/18.08 | | | | | = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.08 | | | | | % 130.06/18.08 | | | | | BETA: splitting (35) gives: % 130.06/18.08 | | | | | % 130.06/18.08 | | | | | Case 1: % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | (36) all_9_5 = e3 & op(e3, e2) = e3 % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | ALPHA: (36) implies: % 130.06/18.08 | | | | | | (37) all_9_5 = e3 % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | BETA: splitting (16) gives: % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | Case 1: % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | (38) all_9_24 = e0 & op(e0, e0) = e0 % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | ALPHA: (38) implies: % 130.06/18.08 | | | | | | | (39) op(e0, e0) = e0 % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | REF_CLOSE: (7), (18), (21), (39) are inconsistent by sub-proof % 130.06/18.08 | | | | | | | #240. % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | Case 2: % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | (40) ((all_9_16 = e0 & op(e4, e0) = e0) | (all_9_17 = e0 & % 130.06/18.08 | | | | | | | op(e3, e0) = e0) | (all_9_18 = e0 & op(e2, e0) = e0) | % 130.06/18.08 | | | | | | | (all_9_19 = e0 & op(e1, e0) = e0)) & ((all_9_20 = e0 & % 130.06/18.08 | | | | | | | op(e0, e4) = e0) | (all_9_21 = e0 & op(e0, e3) = e0) | % 130.06/18.08 | | | | | | | (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 130.06/18.08 | | | | | | | op(e0, e1) = e0)) % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | ALPHA: (40) implies: % 130.06/18.08 | | | | | | | (41) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & % 130.06/18.08 | | | | | | | op(e0, e3) = e0) | (all_9_22 = e0 & op(e0, e2) = e0) | % 130.06/18.08 | | | | | | | (all_9_23 = e0 & op(e0, e1) = e0) % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | BETA: splitting (41) gives: % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | | Case 1: % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | (42) (all_9_20 = e0 & op(e0, e4) = e0) | (all_9_21 = e0 & % 130.06/18.08 | | | | | | | | op(e0, e3) = e0) % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | BETA: splitting (42) gives: % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | Case 1: % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | (43) all_9_20 = e0 & op(e0, e4) = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | REF_CLOSE: (3), (13), (43) are inconsistent by sub-proof #239. % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | Case 2: % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | (44) all_9_21 = e0 & op(e0, e3) = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | ALPHA: (44) implies: % 130.06/18.08 | | | | | | | | | (45) all_9_21 = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | COMBINE_EQS: (24), (45) imply: % 130.06/18.08 | | | | | | | | | (46) e3 = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | SIMP: (46) implies: % 130.06/18.08 | | | | | | | | | (47) e3 = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | COMBINE_EQS: (37), (47) imply: % 130.06/18.08 | | | | | | | | | (48) all_9_5 = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (19), (20), (22), (25), (33), % 130.06/18.08 | | | | | | | | | (48) are inconsistent by sub-proof #115. % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | End of split % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | Case 2: % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | (49) (all_9_22 = e0 & op(e0, e2) = e0) | (all_9_23 = e0 & % 130.06/18.08 | | | | | | | | op(e0, e1) = e0) % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | BETA: splitting (49) gives: % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | | Case 1: % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | (50) all_9_22 = e0 & op(e0, e2) = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | REF_CLOSE: (1), (17), (50) are inconsistent by sub-proof #238. % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | Case 2: % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | (51) all_9_23 = e0 & op(e0, e1) = e0 % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | | REF_CLOSE: (2), (11), (51) are inconsistent by sub-proof #109. % 130.06/18.08 | | | | | | | | | % 130.06/18.08 | | | | | | | | End of split % 130.06/18.08 | | | | | | | | % 130.06/18.08 | | | | | | | End of split % 130.06/18.08 | | | | | | | % 130.06/18.08 | | | | | | End of split % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | Case 2: % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | (52) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, % 130.06/18.08 | | | | | | e0) = e3) % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | | REF_CLOSE: (9), (10), (19), (33), (52) are inconsistent by sub-proof % 130.06/18.08 | | | | | | #108. % 130.06/18.08 | | | | | | % 130.06/18.08 | | | | | End of split % 130.06/18.08 | | | | | % 130.06/18.08 | | | | End of split % 130.06/18.08 | | | | % 130.06/18.08 | | | End of split % 130.06/18.08 | | | % 130.06/18.08 | | End of split % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #108 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) ~ (e3 = e0) % 130.06/18.08 (2) all_9_17 = e2 % 130.06/18.08 (3) all_9_10 = e0 % 130.06/18.08 (4) ~ (e3 = e2) % 130.06/18.08 (5) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (5) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (6) all_9_10 = e3 & op(e3, e1) = e3 % 130.06/18.08 | | % 130.06/18.08 | | ALPHA: (6) implies: % 130.06/18.08 | | (7) all_9_10 = e3 % 130.06/18.08 | | % 130.06/18.08 | | COMBINE_EQS: (3), (7) imply: % 130.06/18.08 | | (8) e3 = e0 % 130.06/18.08 | | % 130.06/18.08 | | REDUCE: (1), (8) imply: % 130.06/18.08 | | (9) $false % 130.06/18.08 | | % 130.06/18.08 | | CLOSE: (9) is inconsistent. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (10) all_9_17 = e3 & op(e3, e0) = e3 % 130.06/18.08 | | % 130.06/18.08 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #119. % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #109 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_9_23 = e0 & op(e0, e1) = e0 % 130.06/18.08 (2) all_9_23 = e4 % 130.06/18.08 (3) ~ (e4 = e0) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | ALPHA: (1) implies: % 130.06/18.08 | (4) all_9_23 = e0 % 130.06/18.08 | % 130.06/18.08 | COMBINE_EQS: (2), (4) imply: % 130.06/18.08 | (5) e4 = e0 % 130.06/18.08 | % 130.06/18.08 | REDUCE: (3), (5) imply: % 130.06/18.08 | (6) $false % 130.06/18.08 | % 130.06/18.08 | CLOSE: (6) is inconsistent. % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #110 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_9_10 = e2 & op(e3, e1) = e2 % 130.06/18.08 (2) all_9_10 = e0 % 130.06/18.08 (3) ~ (e2 = e0) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | ALPHA: (1) implies: % 130.06/18.08 | (4) all_9_10 = e2 % 130.06/18.08 | % 130.06/18.08 | COMBINE_EQS: (2), (4) imply: % 130.06/18.08 | (5) e2 = e0 % 130.06/18.08 | % 130.06/18.08 | REDUCE: (3), (5) imply: % 130.06/18.08 | (6) $false % 130.06/18.08 | % 130.06/18.08 | CLOSE: (6) is inconsistent. % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #111 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_6_5 = e1 % 130.06/18.08 (2) ~ (e4 = e0) % 130.06/18.08 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.08 (4) all_9_20 = e2 % 130.06/18.08 (5) all_6_10 = e3 % 130.06/18.08 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.08 (7) ~ (all_4_3 = all_4_4) % 130.06/18.08 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.08 (9) ~ (e4 = e2) % 130.06/18.08 (10) all_6_17 = all_4_13 % 130.06/18.08 (11) ~ (all_4_10 = all_4_11) % 130.06/18.08 (12) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.08 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.08 (14) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.06/18.08 (15) ~ (all_4_10 = all_4_13) % 130.06/18.08 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.08 (17) ~ (all_4_3 = e3) % 130.06/18.08 (18) all_6_20 = all_4_4 % 130.06/18.08 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 130.06/18.08 (20) ~ (e3 = e0) % 130.06/18.08 (21) ~ (all_4_10 = e0) % 130.06/18.08 (22) all_6_22 = all_4_14 % 130.06/18.08 (23) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.08 (24) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.06/18.08 = e0 % 130.06/18.08 (25) ~ (all_4_14 = e2) % 130.06/18.08 (26) ~ (e2 = e0) % 130.06/18.08 (27) all_9_0 = e0 % 130.06/18.08 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.08 (29) ~ (all_4_4 = e3) % 130.06/18.08 (30) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 130.06/18.08 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 130.06/18.08 (all_9_22 = e3 & op(e0, e2) = e3) % 130.06/18.08 (31) all_9_23 = e0 % 130.06/18.08 (32) ~ (op(e3, e2) = e2) % 130.06/18.08 (33) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 130.06/18.08 (34) ~ (e1 = e0) % 130.06/18.08 (35) all_6_7 = all_4_11 % 130.06/18.08 (36) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 130.06/18.08 (37) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.06/18.08 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.06/18.08 (all_9_20 = e3 & op(e0, e4) = e3) % 130.06/18.08 (38) ~ (e3 = e2) % 130.06/18.08 (39) op(e0, e4) = all_4_4 % 130.06/18.08 (40) ~ (e4 = e1) % 130.06/18.08 (41) ~ (all_4_3 = e0) % 130.06/18.08 (42) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.06/18.08 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.06/18.08 (all_9_22 = e2 & op(e0, e2) = e2) % 130.06/18.08 (43) ~ (e3 = e1) % 130.06/18.08 (44) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) | % 130.06/18.08 (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = e1) | % 130.06/18.08 (all_9_24 = e1 & op(e0, e0) = e1) % 130.06/18.08 (45) op(e3, e4) = e1 % 130.06/18.08 (46) all_9_21 = e3 % 130.06/18.08 (47) op(e1, e4) = all_4_3 % 130.06/18.08 (48) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.08 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.08 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.08 (49) all_9_24 = e4 % 130.06/18.08 (50) op(e2, e2) = e4 % 130.06/18.08 (51) ~ (all_4_10 = e1) % 130.06/18.08 (52) ~ (e4 = e3) % 130.06/18.08 (53) ~ (all_4_4 = e0) % 130.06/18.08 (54) ~ (all_4_3 = e1) % 130.06/18.08 (55) all_9_4 = e1 % 130.06/18.08 (56) all_6_2 = all_4_10 % 130.06/18.08 (57) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.06/18.08 (58) op(e2, e4) = e3 % 130.06/18.08 (59) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.08 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.08 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.08 (60) ~ (all_4_10 = e4) % 130.06/18.08 (61) all_9_2 = e1 % 130.06/18.08 (62) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.06/18.08 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.06/18.08 (all_9_20 = e1 & op(e0, e4) = e1) % 130.06/18.08 (63) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.06/18.08 = e0 % 130.06/18.08 (64) ~ (all_4_4 = e1) % 130.06/18.08 (65) all_4_0 = e0 % 130.06/18.08 (66) ~ (e2 = e1) % 130.06/18.08 (67) all_6_15 = all_4_3 % 130.06/18.08 (68) op(e4, e4) = e0 % 130.06/18.08 (69) all_6_17 = e2 | ~ (op(e1, e2) = e2) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (44) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (70) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = % 130.06/18.08 | | e1) % 130.06/18.08 | | % 130.06/18.08 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (12), (26), (27), (28), (38), % 130.06/18.08 | | (40), (43), (45), (46), (48), (52), (59), (65), (66), (70) are % 130.06/18.08 | | inconsistent by sub-proof #128. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (71) (all_9_22 = e1 & op(e0, e2) = e1) | (all_9_23 = e1 & op(e0, e1) = % 130.06/18.08 | | e1) | (all_9_24 = e1 & op(e0, e0) = e1) % 130.06/18.08 | | % 130.06/18.08 | | BETA: splitting (71) gives: % 130.06/18.08 | | % 130.06/18.08 | | Case 1: % 130.06/18.08 | | | % 130.06/18.08 | | | (72) all_9_22 = e1 & op(e0, e2) = e1 % 130.06/18.08 | | | % 130.06/18.08 | | | ALPHA: (72) implies: % 130.06/18.08 | | | (73) all_9_22 = e1 % 130.06/18.08 | | | % 130.06/18.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), % 130.06/18.08 | | | (15), (19), (21), (22), (25), (26), (27), (28), (30), (32), % 130.06/18.08 | | | (33), (35), (36), (38), (40), (42), (45), (48), (50), (51), % 130.06/18.08 | | | (52), (55), (56), (59), (60), (65), (66), (69), (73) are % 130.06/18.08 | | | inconsistent by sub-proof #122. % 130.06/18.08 | | | % 130.06/18.08 | | Case 2: % 130.06/18.08 | | | % 130.06/18.08 | | | (74) (all_9_23 = e1 & op(e0, e1) = e1) | (all_9_24 = e1 & op(e0, e0) = % 130.06/18.08 | | | e1) % 130.06/18.08 | | | % 130.06/18.08 | | | BETA: splitting (74) gives: % 130.06/18.08 | | | % 130.06/18.08 | | | Case 1: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (75) all_9_23 = e1 & op(e0, e1) = e1 % 130.06/18.08 | | | | % 130.06/18.08 | | | | ALPHA: (75) implies: % 130.06/18.08 | | | | (76) all_9_23 = e1 % 130.06/18.08 | | | | % 130.06/18.08 | | | | COMBINE_EQS: (31), (76) imply: % 130.06/18.08 | | | | (77) e1 = e0 % 130.06/18.08 | | | | % 130.06/18.08 | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (12), (13), (16), (17), (18), % 130.06/18.08 | | | | (20), (23), (24), (26), (28), (29), (34), (37), (38), (39), % 130.06/18.08 | | | | (40), (41), (43), (47), (48), (52), (53), (54), (57), (58), % 130.06/18.08 | | | | (59), (61), (62), (63), (64), (65), (66), (67), (68), (77) % 130.06/18.08 | | | | are inconsistent by sub-proof #264. % 130.06/18.08 | | | | % 130.06/18.08 | | | Case 2: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (78) all_9_24 = e1 & op(e0, e0) = e1 % 130.06/18.08 | | | | % 130.06/18.08 | | | | ALPHA: (78) implies: % 130.06/18.08 | | | | (79) all_9_24 = e1 % 130.06/18.08 | | | | % 130.06/18.08 | | | | REF_CLOSE: (40), (49), (79) are inconsistent by sub-proof #208. % 130.06/18.08 | | | | % 130.06/18.08 | | | End of split % 130.06/18.08 | | | % 130.06/18.08 | | End of split % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #112 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_9_16 = e0 & op(e4, e0) = e0 % 130.06/18.08 (2) all_6_4 = e0 | ~ (op(e4, e0) = e0) % 130.06/18.08 (3) all_6_4 = all_4_20 % 130.06/18.08 (4) ~ (all_4_20 = e0) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | ALPHA: (1) implies: % 130.06/18.08 | (5) op(e4, e0) = e0 % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (2) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (6) ~ (op(e4, e0) = e0) % 130.06/18.08 | | % 130.06/18.08 | | PRED_UNIFY: (5), (6) imply: % 130.06/18.08 | | (7) $false % 130.06/18.08 | | % 130.06/18.08 | | CLOSE: (7) is inconsistent. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (8) all_6_4 = e0 % 130.06/18.08 | | % 130.06/18.08 | | COMBINE_EQS: (3), (8) imply: % 130.06/18.08 | | (9) all_4_20 = e0 % 130.06/18.08 | | % 130.06/18.08 | | SIMP: (9) implies: % 130.06/18.08 | | (10) all_4_20 = e0 % 130.06/18.08 | | % 130.06/18.08 | | REDUCE: (4), (10) imply: % 130.06/18.08 | | (11) $false % 130.06/18.08 | | % 130.06/18.08 | | CLOSE: (11) is inconsistent. % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #113 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_9_8 = e4 % 130.06/18.08 (2) ~ (all_4_14 = e0) % 130.06/18.08 (3) ~ (e4 = e0) % 130.06/18.08 (4) ~ (e2 = e0) % 130.06/18.08 (5) (all_9_8 = e0 & op(e2, e2) = e0) | (all_9_14 = e0 & op(e1, e2) = e0) | % 130.06/18.08 (all_9_22 = e0 & op(e0, e2) = e0) % 130.06/18.08 (6) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 130.06/18.08 (7) all_9_14 = e2 % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (5) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (8) all_9_8 = e0 & op(e2, e2) = e0 % 130.06/18.08 | | % 130.06/18.08 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #151. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (9) (all_9_14 = e0 & op(e1, e2) = e0) | (all_9_22 = e0 & op(e0, e2) = e0) % 130.06/18.08 | | % 130.06/18.08 | | BETA: splitting (9) gives: % 130.06/18.08 | | % 130.06/18.08 | | Case 1: % 130.06/18.08 | | | % 130.06/18.08 | | | (10) all_9_14 = e0 & op(e1, e2) = e0 % 130.06/18.08 | | | % 130.06/18.08 | | | REF_CLOSE: (4), (7), (10) are inconsistent by sub-proof #114. % 130.06/18.08 | | | % 130.06/18.08 | | Case 2: % 130.06/18.08 | | | % 130.06/18.08 | | | (11) all_9_22 = e0 & op(e0, e2) = e0 % 130.06/18.08 | | | % 130.06/18.08 | | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #238. % 130.06/18.08 | | | % 130.06/18.08 | | End of split % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #114 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) all_9_14 = e0 & op(e1, e2) = e0 % 130.06/18.08 (2) all_9_14 = e2 % 130.06/18.08 (3) ~ (e2 = e0) % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | ALPHA: (1) implies: % 130.06/18.08 | (4) all_9_14 = e0 % 130.06/18.08 | % 130.06/18.08 | COMBINE_EQS: (2), (4) imply: % 130.06/18.08 | (5) e2 = e0 % 130.06/18.08 | % 130.06/18.08 | REDUCE: (3), (5) imply: % 130.06/18.08 | (6) $false % 130.06/18.08 | % 130.06/18.08 | CLOSE: (6) is inconsistent. % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #115 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) ~ (all_4_6 = e3) % 130.06/18.08 (2) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 130.06/18.08 (3) ~ (e3 = e0) % 130.06/18.08 (4) all_9_17 = e2 % 130.06/18.08 (5) all_9_10 = e0 % 130.06/18.08 (6) ~ (e3 = e2) % 130.06/18.08 (7) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) | % 130.06/18.08 (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) | % 130.06/18.08 (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.08 (8) all_9_5 = e0 % 130.06/18.08 (9) ~ (e3 = e1) % 130.06/18.08 (10) all_9_2 = e1 % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (7) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (11) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) % 130.06/18.08 | | % 130.06/18.08 | | REF_CLOSE: (1), (2), (9), (10), (11) are inconsistent by sub-proof #293. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (12) (all_9_5 = e3 & op(e3, e2) = e3) | (all_9_10 = e3 & op(e3, e1) = e3) % 130.06/18.08 | | | (all_9_17 = e3 & op(e3, e0) = e3) % 130.06/18.08 | | % 130.06/18.08 | | BETA: splitting (12) gives: % 130.06/18.08 | | % 130.06/18.08 | | Case 1: % 130.06/18.08 | | | % 130.06/18.08 | | | (13) all_9_5 = e3 & op(e3, e2) = e3 % 130.06/18.08 | | | % 130.06/18.08 | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #121. % 130.06/18.08 | | | % 130.06/18.08 | | Case 2: % 130.06/18.08 | | | % 130.06/18.08 | | | (14) (all_9_10 = e3 & op(e3, e1) = e3) | (all_9_17 = e3 & op(e3, e0) = % 130.06/18.08 | | | e3) % 130.06/18.08 | | | % 130.06/18.08 | | | BETA: splitting (14) gives: % 130.06/18.08 | | | % 130.06/18.08 | | | Case 1: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (15) all_9_10 = e3 & op(e3, e1) = e3 % 130.06/18.08 | | | | % 130.06/18.08 | | | | ALPHA: (15) implies: % 130.06/18.08 | | | | (16) all_9_10 = e3 % 130.06/18.08 | | | | % 130.06/18.08 | | | | COMBINE_EQS: (5), (16) imply: % 130.06/18.08 | | | | (17) e3 = e0 % 130.06/18.08 | | | | % 130.06/18.08 | | | | SIMP: (17) implies: % 130.06/18.08 | | | | (18) e3 = e0 % 130.06/18.08 | | | | % 130.06/18.08 | | | | REDUCE: (3), (18) imply: % 130.06/18.08 | | | | (19) $false % 130.06/18.08 | | | | % 130.06/18.08 | | | | CLOSE: (19) is inconsistent. % 130.06/18.08 | | | | % 130.06/18.08 | | | Case 2: % 130.06/18.08 | | | | % 130.06/18.08 | | | | (20) all_9_17 = e3 & op(e3, e0) = e3 % 130.06/18.08 | | | | % 130.06/18.08 | | | | REF_CLOSE: (4), (6), (20) are inconsistent by sub-proof #119. % 130.06/18.08 | | | | % 130.06/18.08 | | | End of split % 130.06/18.08 | | | % 130.06/18.08 | | End of split % 130.06/18.08 | | % 130.06/18.08 | End of split % 130.06/18.08 | % 130.06/18.08 End of proof % 130.06/18.08 % 130.06/18.08 Sub-proof #116 shows that the following formulas are inconsistent: % 130.06/18.08 ---------------------------------------------------------------- % 130.06/18.08 (1) ~ (unit = e2) % 130.06/18.08 (2) op(e1, unit) = e1 % 130.06/18.08 (3) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 130.06/18.08 (4) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.08 (5) all_6_19 = all_4_23 % 130.06/18.08 (6) all_6_19 = e0 | ~ (op(e1, e0) = e0) % 130.06/18.08 (7) ~ (all_4_22 = all_4_23) % 130.06/18.08 (8) op(unit, e0) = e0 % 130.06/18.08 (9) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.08 (10) ~ (unit = e3) % 130.06/18.08 (11) all_6_14 = all_4_22 % 130.06/18.08 (12) ~ (unit = e0) % 130.06/18.08 (13) ~ (all_4_3 = e1) % 130.06/18.08 (14) all_9_18 = e0 & op(e2, e0) = e0 % 130.06/18.08 % 130.06/18.08 Begin of proof % 130.06/18.08 | % 130.06/18.08 | ALPHA: (14) implies: % 130.06/18.08 | (15) op(e2, e0) = e0 % 130.06/18.08 | % 130.06/18.08 | BETA: splitting (3) gives: % 130.06/18.08 | % 130.06/18.08 | Case 1: % 130.06/18.08 | | % 130.06/18.08 | | (16) ~ (op(e2, e0) = e0) % 130.06/18.08 | | % 130.06/18.08 | | PRED_UNIFY: (15), (16) imply: % 130.06/18.08 | | (17) $false % 130.06/18.08 | | % 130.06/18.08 | | CLOSE: (17) is inconsistent. % 130.06/18.08 | | % 130.06/18.08 | Case 2: % 130.06/18.08 | | % 130.06/18.08 | | (18) all_6_14 = e0 % 130.06/18.08 | | % 130.06/18.08 | | COMBINE_EQS: (11), (18) imply: % 130.06/18.08 | | (19) all_4_22 = e0 % 130.06/18.08 | | % 130.06/18.08 | | SIMP: (19) implies: % 130.06/18.08 | | (20) all_4_22 = e0 % 130.06/18.09 | | % 130.06/18.09 | | REDUCE: (7), (20) imply: % 130.06/18.09 | | (21) ~ (all_4_23 = e0) % 130.06/18.09 | | % 130.06/18.09 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (13), (21) are % 130.06/18.09 | | inconsistent by sub-proof #130. % 130.06/18.09 | | % 130.06/18.09 | End of split % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #117 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_11 = e2 & op(e2, e1) = e2 % 130.06/18.09 (2) all_9_11 = e0 % 130.06/18.09 (3) ~ (e2 = e0) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (1) implies: % 130.06/18.09 | (4) all_9_11 = e2 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (2), (4) imply: % 130.06/18.09 | (5) e2 = e0 % 130.06/18.09 | % 130.06/18.09 | SIMP: (5) implies: % 130.06/18.09 | (6) e2 = e0 % 130.06/18.09 | % 130.06/18.09 | REDUCE: (3), (6) imply: % 130.06/18.09 | (7) $false % 130.06/18.09 | % 130.06/18.09 | CLOSE: (7) is inconsistent. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #118 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_11 = e1 & op(e2, e1) = e1 % 130.06/18.09 (2) ~ (e4 = e0) % 130.06/18.09 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.09 (4) all_6_10 = e3 % 130.06/18.09 (5) ~ (all_4_3 = all_4_4) % 130.06/18.09 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.09 (7) ~ (e4 = e2) % 130.06/18.09 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.09 (9) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.09 (10) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.09 (11) ~ (all_4_3 = e3) % 130.06/18.09 (12) all_6_20 = all_4_4 % 130.06/18.09 (13) ~ (e3 = e0) % 130.06/18.09 (14) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.09 (15) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.06/18.09 = e0 % 130.06/18.09 (16) ~ (e2 = e0) % 130.06/18.09 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.09 (18) ~ (all_4_4 = e3) % 130.06/18.09 (19) ~ (e1 = e0) % 130.06/18.09 (20) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.06/18.09 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.06/18.09 (all_9_20 = e3 & op(e0, e4) = e3) % 130.06/18.09 (21) ~ (e3 = e2) % 130.06/18.09 (22) op(e0, e4) = all_4_4 % 130.06/18.09 (23) ~ (e4 = e1) % 130.06/18.09 (24) ~ (all_4_3 = e0) % 130.06/18.09 (25) ~ (e3 = e1) % 130.06/18.09 (26) op(e1, e4) = all_4_3 % 130.06/18.09 (27) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.09 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.09 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.09 (28) ~ (e4 = e3) % 130.06/18.09 (29) ~ (all_4_4 = e0) % 130.06/18.09 (30) ~ (all_4_3 = e1) % 130.06/18.09 (31) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.06/18.09 (32) op(e2, e4) = e3 % 130.06/18.09 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.09 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.09 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.09 (34) all_9_2 = e1 % 130.06/18.09 (35) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.06/18.09 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.06/18.09 (all_9_20 = e1 & op(e0, e4) = e1) % 130.06/18.09 (36) all_9_11 = e0 % 130.06/18.09 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.06/18.09 = e0 % 130.06/18.09 (38) ~ (all_4_4 = e1) % 130.06/18.09 (39) all_4_0 = e0 % 130.06/18.09 (40) ~ (e2 = e1) % 130.06/18.09 (41) all_6_15 = all_4_3 % 130.06/18.09 (42) op(e4, e4) = e0 % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (1) implies: % 130.06/18.09 | (43) all_9_11 = e1 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (36), (43) imply: % 130.06/18.09 | (44) e1 = e0 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (34), (44) imply: % 130.06/18.09 | (45) all_9_2 = e0 % 130.06/18.09 | % 130.06/18.09 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.06/18.09 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 130.06/18.09 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (37), % 130.06/18.09 | (38), (39), (40), (41), (42), (45) are inconsistent by sub-proof % 130.06/18.09 | #265. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #119 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_17 = e3 & op(e3, e0) = e3 % 130.06/18.09 (2) all_9_17 = e2 % 130.06/18.09 (3) ~ (e3 = e2) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (1) implies: % 130.06/18.09 | (4) all_9_17 = e3 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (2), (4) imply: % 130.06/18.09 | (5) e3 = e2 % 130.06/18.09 | % 130.06/18.09 | SIMP: (5) implies: % 130.06/18.09 | (6) e3 = e2 % 130.06/18.09 | % 130.06/18.09 | REDUCE: (3), (6) imply: % 130.06/18.09 | (7) $false % 130.06/18.09 | % 130.06/18.09 | CLOSE: (7) is inconsistent. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #120 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_6_5 = e1 % 130.06/18.09 (2) ~ (e4 = e0) % 130.06/18.09 (3) all_9_20 = e2 % 130.06/18.09 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.09 (5) all_9_3 = e4 % 130.06/18.09 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.09 (7) ~ (e4 = e2) % 130.06/18.09 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.09 (9) all_9_18 = e2 & op(e2, e0) = e2 % 130.06/18.09 (10) all_9_17 = e2 % 130.06/18.09 (11) all_9_10 = e3 % 130.06/18.09 (12) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 130.06/18.09 (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 130.06/18.09 (all_9_17 = e4 & op(e3, e0) = e4) % 130.06/18.09 (13) all_9_12 = e4 % 130.06/18.09 (14) ~ (e4 = e1) % 130.06/18.09 (15) all_9_5 = e0 % 130.06/18.09 (16) ~ (e4 = e3) % 130.06/18.09 (17) all_9_18 = e4 % 130.06/18.09 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.09 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.09 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.09 (19) all_4_0 = e0 % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (9) implies: % 130.06/18.09 | (20) all_9_18 = e2 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (17), (20) imply: % 130.06/18.09 | (21) e4 = e2 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (5), (21) imply: % 130.06/18.09 | (22) all_9_3 = e2 % 130.06/18.09 | % 130.06/18.09 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), % 130.06/18.09 | (15), (16), (18), (19), (22) are inconsistent by sub-proof #203. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #121 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_5 = e3 & op(e3, e2) = e3 % 130.06/18.09 (2) all_9_5 = e0 % 130.06/18.09 (3) ~ (e3 = e0) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (1) implies: % 130.06/18.09 | (4) all_9_5 = e3 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (2), (4) imply: % 130.06/18.09 | (5) e3 = e0 % 130.06/18.09 | % 130.06/18.09 | SIMP: (5) implies: % 130.06/18.09 | (6) e3 = e0 % 130.06/18.09 | % 130.06/18.09 | REDUCE: (3), (6) imply: % 130.06/18.09 | (7) $false % 130.06/18.09 | % 130.06/18.09 | CLOSE: (7) is inconsistent. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #122 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_6_5 = e1 % 130.06/18.09 (2) ~ (e4 = e0) % 130.06/18.09 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.09 (4) all_9_20 = e2 % 130.06/18.09 (5) all_6_10 = e3 % 130.06/18.09 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.09 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.09 (8) ~ (e4 = e2) % 130.06/18.09 (9) all_6_17 = all_4_13 % 130.06/18.09 (10) ~ (all_4_10 = all_4_11) % 130.06/18.09 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.09 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.06/18.09 (13) ~ (all_4_10 = all_4_13) % 130.06/18.09 (14) e4 = e2 | ~ (op(e2, e2) = e2) % 130.06/18.09 (15) ~ (all_4_10 = e0) % 130.06/18.09 (16) all_6_22 = all_4_14 % 130.06/18.09 (17) ~ (all_4_14 = e2) % 130.06/18.09 (18) ~ (e2 = e0) % 130.06/18.09 (19) all_9_0 = e0 % 130.06/18.09 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.09 (21) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 130.06/18.09 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 130.06/18.09 (all_9_22 = e3 & op(e0, e2) = e3) % 130.06/18.09 (22) ~ (op(e3, e2) = e2) % 130.06/18.09 (23) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 130.06/18.09 (24) all_6_7 = all_4_11 % 130.06/18.09 (25) all_6_2 = e4 | all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 130.06/18.09 (26) ~ (e3 = e2) % 130.06/18.09 (27) ~ (e4 = e1) % 130.06/18.09 (28) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.06/18.09 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.06/18.09 (all_9_22 = e2 & op(e0, e2) = e2) % 130.06/18.09 (29) op(e3, e4) = e1 % 130.06/18.09 (30) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.09 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.09 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.09 (31) op(e2, e2) = e4 % 130.06/18.09 (32) ~ (all_4_10 = e1) % 130.06/18.09 (33) ~ (e4 = e3) % 130.06/18.09 (34) all_9_22 = e1 % 130.06/18.09 (35) all_9_4 = e1 % 130.06/18.09 (36) all_6_2 = all_4_10 % 130.06/18.09 (37) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.09 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.09 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.09 (38) ~ (all_4_10 = e4) % 130.06/18.09 (39) all_4_0 = e0 % 130.06/18.09 (40) ~ (e2 = e1) % 130.06/18.09 (41) all_6_17 = e2 | ~ (op(e1, e2) = e2) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | BETA: splitting (28) gives: % 130.06/18.09 | % 130.06/18.09 | Case 1: % 130.06/18.09 | | % 130.06/18.09 | | (42) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) % 130.06/18.09 | | % 130.06/18.09 | | BETA: splitting (42) gives: % 130.06/18.09 | | % 130.06/18.09 | | Case 1: % 130.06/18.09 | | | % 130.06/18.09 | | | (43) all_9_4 = e2 & op(e4, e2) = e2 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (18), (19), (20), % 130.06/18.09 | | | (26), (27), (29), (30), (33), (35), (37), (39), (40), (43) are % 130.06/18.09 | | | inconsistent by sub-proof #127. % 130.06/18.09 | | | % 130.06/18.09 | | Case 2: % 130.06/18.09 | | | % 130.06/18.09 | | | (44) all_9_5 = e2 & op(e3, e2) = e2 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (22), (44) are inconsistent by sub-proof #132. % 130.06/18.09 | | | % 130.06/18.09 | | End of split % 130.06/18.09 | | % 130.06/18.09 | Case 2: % 130.06/18.09 | | % 130.06/18.09 | | (45) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 130.06/18.09 | | | (all_9_22 = e2 & op(e0, e2) = e2) % 130.06/18.09 | | % 130.06/18.09 | | BETA: splitting (45) gives: % 130.06/18.09 | | % 130.06/18.09 | | Case 1: % 130.06/18.09 | | | % 130.06/18.09 | | | (46) all_9_8 = e2 & op(e2, e2) = e2 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (8), (14), (46) are inconsistent by sub-proof #306. % 130.06/18.09 | | | % 130.06/18.09 | | Case 2: % 130.06/18.09 | | | % 130.06/18.09 | | | (47) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) = % 130.06/18.09 | | | e2) % 130.06/18.09 | | | % 130.06/18.09 | | | BETA: splitting (47) gives: % 130.06/18.09 | | | % 130.06/18.09 | | | Case 1: % 130.06/18.09 | | | | % 130.06/18.09 | | | | (48) all_9_14 = e2 & op(e1, e2) = e2 % 130.06/18.09 | | | | % 130.06/18.09 | | | | ALPHA: (48) implies: % 130.06/18.09 | | | | (49) all_9_14 = e2 % 130.06/18.09 | | | | (50) op(e1, e2) = e2 % 130.06/18.09 | | | | % 130.06/18.09 | | | | BETA: splitting (41) gives: % 130.06/18.09 | | | | % 130.06/18.09 | | | | Case 1: % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | (51) ~ (op(e1, e2) = e2) % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | PRED_UNIFY: (50), (51) imply: % 130.06/18.09 | | | | | (52) $false % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | CLOSE: (52) is inconsistent. % 130.06/18.09 | | | | | % 130.06/18.09 | | | | Case 2: % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | (53) all_6_17 = e2 % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | COMBINE_EQS: (9), (53) imply: % 130.06/18.09 | | | | | (54) all_4_13 = e2 % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | SIMP: (54) implies: % 130.06/18.09 | | | | | (55) all_4_13 = e2 % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | REDUCE: (13), (55) imply: % 130.06/18.09 | | | | | (56) ~ (all_4_10 = e2) % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | BETA: splitting (25) gives: % 130.06/18.09 | | | | | % 130.06/18.09 | | | | | Case 1: % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | (57) all_6_2 = e4 % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | COMBINE_EQS: (36), (57) imply: % 130.06/18.09 | | | | | | (58) all_4_10 = e4 % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | REDUCE: (38), (58) imply: % 130.06/18.09 | | | | | | (59) $false % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | CLOSE: (59) is inconsistent. % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | Case 2: % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | (60) ~ (all_6_2 = e4) % 130.06/18.09 | | | | | | (61) all_6_2 = e3 | all_6_2 = e2 | all_6_2 = e1 | all_6_2 = e0 % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | BETA: splitting (61) gives: % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | | Case 1: % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | (62) all_6_2 = e2 % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | COMBINE_EQS: (36), (62) imply: % 130.06/18.09 | | | | | | | (63) all_4_10 = e2 % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | REDUCE: (56), (63) imply: % 130.06/18.09 | | | | | | | (64) $false % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | CLOSE: (64) is inconsistent. % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | Case 2: % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | (65) ~ (all_6_2 = e2) % 130.06/18.09 | | | | | | | (66) all_6_2 = e3 | all_6_2 = e1 | all_6_2 = e0 % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | BETA: splitting (66) gives: % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | | Case 1: % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | (67) all_6_2 = e3 % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | COMBINE_EQS: (36), (67) imply: % 130.06/18.09 | | | | | | | | (68) all_4_10 = e3 % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | REDUCE: (10), (68) imply: % 130.06/18.09 | | | | | | | | (69) ~ (all_4_11 = e3) % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | SIMP: (69) implies: % 130.06/18.09 | | | | | | | | (70) ~ (all_4_11 = e3) % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | REDUCE: (38), (68) imply: % 130.06/18.09 | | | | | | | | (71) ~ (e4 = e3) % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | REDUCE: (32), (68) imply: % 130.06/18.09 | | | | | | | | (72) ~ (e3 = e1) % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (31), (33), (34), (35), % 130.06/18.09 | | | | | | | | (49), (70), (72) are inconsistent by sub-proof #124. % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | Case 2: % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | (73) all_6_2 = e1 | all_6_2 = e0 % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | | REF_CLOSE: (15), (32), (36), (73) are inconsistent by sub-proof % 130.06/18.09 | | | | | | | | #123. % 130.06/18.09 | | | | | | | | % 130.06/18.09 | | | | | | | End of split % 130.06/18.09 | | | | | | | % 130.06/18.09 | | | | | | End of split % 130.06/18.09 | | | | | | % 130.06/18.09 | | | | | End of split % 130.06/18.09 | | | | | % 130.06/18.09 | | | | End of split % 130.06/18.09 | | | | % 130.06/18.09 | | | Case 2: % 130.06/18.09 | | | | % 130.06/18.09 | | | | (74) all_9_22 = e2 & op(e0, e2) = e2 % 130.06/18.09 | | | | % 130.06/18.09 | | | | ALPHA: (74) implies: % 130.06/18.09 | | | | (75) op(e0, e2) = e2 % 130.06/18.09 | | | | % 130.06/18.09 | | | | REF_CLOSE: (12), (16), (17), (75) are inconsistent by sub-proof #246. % 130.06/18.09 | | | | % 130.06/18.09 | | | End of split % 130.06/18.09 | | | % 130.06/18.09 | | End of split % 130.06/18.09 | | % 130.06/18.09 | End of split % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #123 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_6_2 = e1 | all_6_2 = e0 % 130.06/18.09 (2) all_6_2 = all_4_10 % 130.06/18.09 (3) ~ (all_4_10 = e1) % 130.06/18.09 (4) ~ (all_4_10 = e0) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | BETA: splitting (1) gives: % 130.06/18.09 | % 130.06/18.09 | Case 1: % 130.06/18.09 | | % 130.06/18.09 | | (5) all_6_2 = e1 % 130.06/18.09 | | % 130.06/18.09 | | COMBINE_EQS: (2), (5) imply: % 130.06/18.09 | | (6) all_4_10 = e1 % 130.06/18.09 | | % 130.06/18.09 | | REDUCE: (3), (6) imply: % 130.06/18.09 | | (7) $false % 130.06/18.09 | | % 130.06/18.09 | | CLOSE: (7) is inconsistent. % 130.06/18.09 | | % 130.06/18.09 | Case 2: % 130.06/18.09 | | % 130.06/18.09 | | (8) all_6_2 = e0 % 130.06/18.09 | | % 130.06/18.09 | | COMBINE_EQS: (2), (8) imply: % 130.06/18.09 | | (9) all_4_10 = e0 % 130.06/18.09 | | % 130.06/18.09 | | REDUCE: (4), (9) imply: % 130.06/18.09 | | (10) $false % 130.06/18.09 | | % 130.06/18.09 | | CLOSE: (10) is inconsistent. % 130.06/18.09 | | % 130.06/18.09 | End of split % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #124 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) ~ (all_4_11 = e3) % 130.06/18.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.09 (3) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) | % 130.06/18.09 (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) | % 130.06/18.09 (all_9_22 = e3 & op(e0, e2) = e3) % 130.06/18.09 (4) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 130.06/18.09 (5) all_6_7 = all_4_11 % 130.06/18.09 (6) ~ (e3 = e2) % 130.06/18.09 (7) all_9_14 = e2 % 130.06/18.09 (8) ~ (e3 = e1) % 130.06/18.09 (9) op(e2, e2) = e4 % 130.06/18.09 (10) ~ (e4 = e3) % 130.06/18.09 (11) all_9_22 = e1 % 130.06/18.09 (12) all_9_4 = e1 % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | BETA: splitting (3) gives: % 130.06/18.09 | % 130.06/18.09 | Case 1: % 130.06/18.09 | | % 130.06/18.09 | | (13) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_5 = e3 & op(e3, e2) = e3) % 130.06/18.09 | | % 130.06/18.09 | | BETA: splitting (13) gives: % 130.06/18.09 | | % 130.06/18.09 | | Case 1: % 130.06/18.09 | | | % 130.06/18.09 | | | (14) all_9_4 = e3 & op(e4, e2) = e3 % 130.06/18.09 | | | % 130.06/18.09 | | | ALPHA: (14) implies: % 130.06/18.09 | | | (15) all_9_4 = e3 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (8), (12), (15) are inconsistent by sub-proof #138. % 130.06/18.09 | | | % 130.06/18.09 | | Case 2: % 130.06/18.09 | | | % 130.06/18.09 | | | (16) all_9_5 = e3 & op(e3, e2) = e3 % 130.06/18.09 | | | % 130.06/18.09 | | | ALPHA: (16) implies: % 130.06/18.09 | | | (17) op(e3, e2) = e3 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (1), (4), (5), (17) are inconsistent by sub-proof #292. % 130.06/18.09 | | | % 130.06/18.09 | | End of split % 130.06/18.09 | | % 130.06/18.09 | Case 2: % 130.06/18.09 | | % 130.06/18.09 | | (18) (all_9_8 = e3 & op(e2, e2) = e3) | (all_9_14 = e3 & op(e1, e2) = e3) % 130.06/18.09 | | | (all_9_22 = e3 & op(e0, e2) = e3) % 130.06/18.09 | | % 130.06/18.09 | | BETA: splitting (18) gives: % 130.06/18.09 | | % 130.06/18.09 | | Case 1: % 130.06/18.09 | | | % 130.06/18.09 | | | (19) all_9_8 = e3 & op(e2, e2) = e3 % 130.06/18.09 | | | % 130.06/18.09 | | | REF_CLOSE: (2), (9), (10), (19) are inconsistent by sub-proof #126. % 130.06/18.09 | | | % 130.06/18.09 | | Case 2: % 130.06/18.09 | | | % 130.06/18.09 | | | (20) (all_9_14 = e3 & op(e1, e2) = e3) | (all_9_22 = e3 & op(e0, e2) = % 130.06/18.09 | | | e3) % 130.06/18.09 | | | % 130.06/18.09 | | | BETA: splitting (20) gives: % 130.06/18.09 | | | % 130.06/18.09 | | | Case 1: % 130.06/18.09 | | | | % 130.06/18.09 | | | | (21) all_9_14 = e3 & op(e1, e2) = e3 % 130.06/18.09 | | | | % 130.06/18.09 | | | | REF_CLOSE: (6), (7), (21) are inconsistent by sub-proof #125. % 130.06/18.09 | | | | % 130.06/18.09 | | | Case 2: % 130.06/18.09 | | | | % 130.06/18.09 | | | | (22) all_9_22 = e3 & op(e0, e2) = e3 % 130.06/18.09 | | | | % 130.06/18.09 | | | | ALPHA: (22) implies: % 130.06/18.09 | | | | (23) all_9_22 = e3 % 130.06/18.09 | | | | % 130.06/18.09 | | | | COMBINE_EQS: (11), (23) imply: % 130.06/18.09 | | | | (24) e3 = e1 % 130.06/18.09 | | | | % 130.06/18.09 | | | | REDUCE: (8), (24) imply: % 130.06/18.09 | | | | (25) $false % 130.06/18.09 | | | | % 130.06/18.09 | | | | CLOSE: (25) is inconsistent. % 130.06/18.09 | | | | % 130.06/18.09 | | | End of split % 130.06/18.09 | | | % 130.06/18.09 | | End of split % 130.06/18.09 | | % 130.06/18.09 | End of split % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #125 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_14 = e3 & op(e1, e2) = e3 % 130.06/18.09 (2) all_9_14 = e2 % 130.06/18.09 (3) ~ (e3 = e2) % 130.06/18.09 % 130.06/18.09 Begin of proof % 130.06/18.09 | % 130.06/18.09 | ALPHA: (1) implies: % 130.06/18.09 | (4) all_9_14 = e3 % 130.06/18.09 | % 130.06/18.09 | COMBINE_EQS: (2), (4) imply: % 130.06/18.09 | (5) e3 = e2 % 130.06/18.09 | % 130.06/18.09 | SIMP: (5) implies: % 130.06/18.09 | (6) e3 = e2 % 130.06/18.09 | % 130.06/18.09 | REDUCE: (3), (6) imply: % 130.06/18.09 | (7) $false % 130.06/18.09 | % 130.06/18.09 | CLOSE: (7) is inconsistent. % 130.06/18.09 | % 130.06/18.09 End of proof % 130.06/18.09 % 130.06/18.09 Sub-proof #126 shows that the following formulas are inconsistent: % 130.06/18.09 ---------------------------------------------------------------- % 130.06/18.09 (1) all_9_8 = e3 & op(e2, e2) = e3 % 130.06/18.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.10 (3) op(e2, e2) = e4 % 130.06/18.10 (4) ~ (e4 = e3) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | ALPHA: (1) implies: % 130.06/18.10 | (5) op(e2, e2) = e3 % 130.06/18.10 | % 130.06/18.10 | GROUND_INST: instantiating (2) with e4, e3, e2, e2, simplifying with (3), (5) % 130.06/18.10 | gives: % 130.06/18.10 | (6) e4 = e3 % 130.06/18.10 | % 130.06/18.10 | REDUCE: (4), (6) imply: % 130.06/18.10 | (7) $false % 130.06/18.10 | % 130.06/18.10 | CLOSE: (7) is inconsistent. % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #127 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_6_5 = e1 % 130.06/18.10 (2) ~ (e4 = e0) % 130.06/18.10 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.10 (4) all_9_20 = e2 % 130.06/18.10 (5) all_6_10 = e3 % 130.06/18.10 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.10 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.10 (8) ~ (e4 = e2) % 130.06/18.10 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.10 (10) ~ (e2 = e0) % 130.06/18.10 (11) all_9_0 = e0 % 130.06/18.10 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.10 (13) ~ (e3 = e2) % 130.06/18.10 (14) ~ (e4 = e1) % 130.06/18.10 (15) op(e3, e4) = e1 % 130.06/18.10 (16) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.10 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.10 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.10 (17) ~ (e4 = e3) % 130.06/18.10 (18) all_9_4 = e1 % 130.06/18.10 (19) all_9_4 = e2 & op(e4, e2) = e2 % 130.06/18.10 (20) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.10 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.10 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.10 (21) all_4_0 = e0 % 130.06/18.10 (22) ~ (e2 = e1) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | ALPHA: (19) implies: % 130.06/18.10 | (23) all_9_4 = e2 % 130.06/18.10 | % 130.06/18.10 | COMBINE_EQS: (18), (23) imply: % 130.06/18.10 | (24) e2 = e1 % 130.06/18.10 | % 130.06/18.10 | SIMP: (24) implies: % 130.06/18.10 | (25) e2 = e1 % 130.06/18.10 | % 130.06/18.10 | COMBINE_EQS: (4), (25) imply: % 130.06/18.10 | (26) all_9_20 = e1 % 130.06/18.10 | % 130.06/18.10 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.06/18.10 | (14), (15), (16), (17), (20), (21), (22), (26) are inconsistent by % 130.06/18.10 | sub-proof #283. % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #128 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_6_5 = e1 % 130.06/18.10 (2) ~ (e4 = e0) % 130.06/18.10 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.10 (4) all_6_10 = e3 % 130.06/18.10 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.10 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.10 (7) ~ (e4 = e2) % 130.06/18.10 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.10 (9) ~ (e2 = e0) % 130.06/18.10 (10) all_9_0 = e0 % 130.06/18.10 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.10 (12) ~ (e3 = e2) % 130.06/18.10 (13) ~ (e4 = e1) % 130.06/18.10 (14) ~ (e3 = e1) % 130.06/18.10 (15) op(e3, e4) = e1 % 130.06/18.10 (16) all_9_21 = e3 % 130.06/18.10 (17) (all_9_20 = e1 & op(e0, e4) = e1) | (all_9_21 = e1 & op(e0, e3) = e1) % 130.06/18.10 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.10 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.10 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.10 (19) ~ (e4 = e3) % 130.06/18.10 (20) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.10 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.10 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.10 (21) all_4_0 = e0 % 130.06/18.10 (22) ~ (e2 = e1) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (17) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (23) all_9_20 = e1 & op(e0, e4) = e1 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (23) implies: % 130.06/18.10 | | (24) all_9_20 = e1 % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.06/18.10 | | (13), (15), (18), (19), (20), (21), (22), (24) are inconsistent % 130.06/18.10 | | by sub-proof #283. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (25) all_9_21 = e1 & op(e0, e3) = e1 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (25) implies: % 130.06/18.10 | | (26) all_9_21 = e1 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (16), (26) imply: % 130.06/18.10 | | (27) e3 = e1 % 130.06/18.10 | | % 130.06/18.10 | | REDUCE: (14), (27) imply: % 130.06/18.10 | | (28) $false % 130.06/18.10 | | % 130.06/18.10 | | CLOSE: (28) is inconsistent. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #129 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) ~ (unit = e2) % 130.06/18.10 (2) op(e1, unit) = e1 % 130.06/18.10 (3) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.10 (4) all_6_19 = all_4_23 % 130.06/18.10 (5) all_6_19 = e0 | ~ (op(e1, e0) = e0) % 130.06/18.10 (6) op(e3, e0) = e0 % 130.06/18.10 (7) op(unit, e0) = e0 % 130.06/18.10 (8) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.10 (9) ~ (unit = e3) % 130.06/18.10 (10) ~ (all_4_21 = all_4_23) % 130.06/18.10 (11) ~ (unit = e0) % 130.06/18.10 (12) ~ (all_4_3 = e1) % 130.06/18.10 (13) all_4_21 = e0 | ~ (op(e3, e0) = e0) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (13) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (14) ~ (op(e3, e0) = e0) % 130.06/18.10 | | % 130.06/18.10 | | PRED_UNIFY: (6), (14) imply: % 130.06/18.10 | | (15) $false % 130.06/18.10 | | % 130.06/18.10 | | CLOSE: (15) is inconsistent. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (16) all_4_21 = e0 % 130.06/18.10 | | % 130.06/18.10 | | REDUCE: (10), (16) imply: % 130.06/18.10 | | (17) ~ (all_4_23 = e0) % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (17) are % 130.06/18.10 | | inconsistent by sub-proof #130. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #130 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) ~ (unit = e2) % 130.06/18.10 (2) op(e1, unit) = e1 % 130.06/18.10 (3) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.10 (4) all_6_19 = all_4_23 % 130.06/18.10 (5) all_6_19 = e0 | ~ (op(e1, e0) = e0) % 130.06/18.10 (6) op(unit, e0) = e0 % 130.06/18.10 (7) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.10 (8) ~ (unit = e3) % 130.06/18.10 (9) ~ (unit = e0) % 130.06/18.10 (10) ~ (all_4_3 = e1) % 130.06/18.10 (11) ~ (all_4_23 = e0) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | SIMP: (11) implies: % 130.06/18.10 | (12) ~ (all_4_23 = e0) % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (5) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (13) ~ (op(e1, e0) = e0) % 130.06/18.10 | | % 130.06/18.10 | | PRED_UNIFY: (6), (13) imply: % 130.06/18.10 | | (14) ~ (unit = e1) % 130.06/18.10 | | % 130.06/18.10 | | BETA: splitting (7) gives: % 130.06/18.10 | | % 130.06/18.10 | | Case 1: % 130.06/18.10 | | | % 130.06/18.10 | | | (15) unit = e4 % 130.06/18.10 | | | % 130.06/18.10 | | | REDUCE: (2), (15) imply: % 130.06/18.10 | | | (16) op(e1, e4) = e1 % 130.06/18.10 | | | % 130.06/18.10 | | | REF_CLOSE: (3), (10), (16) are inconsistent by sub-proof #268. % 130.06/18.10 | | | % 130.06/18.10 | | Case 2: % 130.06/18.10 | | | % 130.06/18.10 | | | (17) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.10 | | | % 130.06/18.10 | | | REF_CLOSE: (1), (8), (9), (14), (17) are inconsistent by sub-proof #140. % 130.06/18.10 | | | % 130.06/18.10 | | End of split % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (18) all_6_19 = e0 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (4), (18) imply: % 130.06/18.10 | | (19) all_4_23 = e0 % 130.06/18.10 | | % 130.06/18.10 | | SIMP: (19) implies: % 130.06/18.10 | | (20) all_4_23 = e0 % 130.06/18.10 | | % 130.06/18.10 | | REDUCE: (12), (20) imply: % 130.06/18.10 | | (21) $false % 130.06/18.10 | | % 130.06/18.10 | | CLOSE: (21) is inconsistent. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #131 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) ~ (e4 = e0) % 130.06/18.10 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.10 (3) all_6_10 = e3 % 130.06/18.10 (4) ~ (all_4_3 = all_4_4) % 130.06/18.10 (5) all_9_3 = e4 % 130.06/18.10 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.10 (7) ~ (e4 = e2) % 130.06/18.10 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.10 (9) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.10 (10) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.06/18.10 (11) ~ (all_4_3 = e3) % 130.06/18.10 (12) all_6_20 = all_4_4 % 130.06/18.10 (13) ~ (e3 = e0) % 130.06/18.10 (14) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.06/18.10 (15) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.06/18.10 = e0 % 130.06/18.10 (16) ~ (e2 = e0) % 130.06/18.10 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.10 (18) ~ (all_4_4 = e3) % 130.06/18.10 (19) (all_9_2 = e0 & op(e3, e4) = e0) | (all_9_3 = e0 & op(e3, e3) = e0) % 130.06/18.10 (20) ~ (e1 = e0) % 130.06/18.10 (21) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.06/18.10 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.06/18.10 (all_9_20 = e3 & op(e0, e4) = e3) % 130.06/18.10 (22) ~ (e3 = e2) % 130.06/18.10 (23) op(e0, e4) = all_4_4 % 130.06/18.10 (24) ~ (e4 = e1) % 130.06/18.10 (25) ~ (all_4_3 = e0) % 130.06/18.10 (26) ~ (e3 = e1) % 130.06/18.10 (27) op(e1, e4) = all_4_3 % 130.06/18.10 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.10 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.10 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.10 (29) ~ (e4 = e3) % 130.06/18.10 (30) ~ (all_4_4 = e0) % 130.06/18.10 (31) ~ (all_4_3 = e1) % 130.06/18.10 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.06/18.10 (33) op(e2, e4) = e3 % 130.06/18.10 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.10 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.10 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.10 (35) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.06/18.10 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.06/18.10 (all_9_20 = e1 & op(e0, e4) = e1) % 130.06/18.10 (36) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.06/18.10 = e0 % 130.06/18.10 (37) ~ (all_4_4 = e1) % 130.06/18.10 (38) all_4_0 = e0 % 130.06/18.10 (39) ~ (e2 = e1) % 130.06/18.10 (40) all_6_15 = all_4_3 % 130.06/18.10 (41) op(e4, e4) = e0 % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (19) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (42) all_9_2 = e0 & op(e3, e4) = e0 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (42) implies: % 130.06/18.10 | | (43) all_9_2 = e0 % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 130.06/18.10 | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), % 130.06/18.10 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.06/18.10 | | (37), (38), (39), (40), (41), (43) are inconsistent by sub-proof % 130.06/18.10 | | #265. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (44) all_9_3 = e0 & op(e3, e3) = e0 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (44) implies: % 130.06/18.10 | | (45) all_9_3 = e0 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (5), (45) imply: % 130.06/18.10 | | (46) e4 = e0 % 130.06/18.10 | | % 130.06/18.10 | | REDUCE: (1), (46) imply: % 130.06/18.10 | | (47) $false % 130.06/18.10 | | % 130.06/18.10 | | CLOSE: (47) is inconsistent. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #132 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_9_5 = e2 & op(e3, e2) = e2 % 130.06/18.10 (2) ~ (op(e3, e2) = e2) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | ALPHA: (1) implies: % 130.06/18.10 | (3) op(e3, e2) = e2 % 130.06/18.10 | % 130.06/18.10 | PRED_UNIFY: (2), (3) imply: % 130.06/18.10 | (4) $false % 130.06/18.10 | % 130.06/18.10 | CLOSE: (4) is inconsistent. % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #133 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_9_3 = e4 % 130.06/18.10 (2) ~ (e4 = e2) % 130.06/18.10 (3) (all_9_2 = e2 & op(e3, e4) = e2) | (all_9_3 = e2 & op(e3, e3) = e2) % 130.06/18.10 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.10 (5) op(e3, e4) = e1 % 130.06/18.10 (6) ~ (e2 = e1) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (3) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (7) all_9_2 = e2 & op(e3, e4) = e2 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (7) implies: % 130.06/18.10 | | (8) op(e3, e4) = e2 % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #313. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (9) all_9_3 = e2 & op(e3, e3) = e2 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (9) implies: % 130.06/18.10 | | (10) all_9_3 = e2 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (1), (10) imply: % 130.06/18.10 | | (11) e4 = e2 % 130.06/18.10 | | % 130.06/18.10 | | REDUCE: (2), (11) imply: % 130.06/18.10 | | (12) $false % 130.06/18.10 | | % 130.06/18.10 | | CLOSE: (12) is inconsistent. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #134 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 130.06/18.10 (2) all_6_5 = e1 % 130.06/18.10 (3) ~ (e4 = e0) % 130.06/18.10 (4) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 130.06/18.10 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 130.06/18.10 (all_9_16 = e4 & op(e4, e0) = e4) % 130.06/18.10 (5) all_9_20 = e2 % 130.06/18.10 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.10 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.10 (8) ~ (e4 = e2) % 130.06/18.10 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.10 (10) ~ (op(e4, e3) = e4) % 130.06/18.10 (11) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.06/18.10 (12) all_9_12 = e4 % 130.06/18.10 (13) (all_9_20 = e4 & op(e0, e4) = e4) | (all_9_21 = e4 & op(e0, e3) = e4) % 130.06/18.10 (14) ~ (e4 = e1) % 130.06/18.10 (15) ~ (all_4_20 = e4) % 130.06/18.10 (16) all_9_9 = e4 % 130.06/18.10 (17) all_9_21 = e3 % 130.06/18.10 (18) ~ (op(e0, e4) = e4) % 130.06/18.10 (19) ~ (e4 = e3) % 130.06/18.10 (20) all_6_4 = all_4_20 % 130.06/18.10 (21) all_6_2 = all_4_10 % 130.06/18.10 (22) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.10 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.10 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.10 (23) ~ (all_4_10 = e4) % 130.06/18.10 (24) all_4_0 = e0 % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (13) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (25) all_9_20 = e4 & op(e0, e4) = e4 % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (18), (25) are inconsistent by sub-proof #135. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (26) all_9_21 = e4 & op(e0, e3) = e4 % 130.06/18.10 | | % 130.06/18.10 | | ALPHA: (26) implies: % 130.06/18.10 | | (27) all_9_21 = e4 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (17), (27) imply: % 130.06/18.10 | | (28) e4 = e3 % 130.06/18.10 | | % 130.06/18.10 | | SIMP: (28) implies: % 130.06/18.10 | | (29) e4 = e3 % 130.06/18.10 | | % 130.06/18.10 | | COMBINE_EQS: (16), (29) imply: % 130.06/18.10 | | (30) all_9_9 = e3 % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.06/18.10 | | (14), (15), (19), (20), (21), (22), (23), (24), (30) are % 130.06/18.10 | | inconsistent by sub-proof #137. % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #135 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_9_20 = e4 & op(e0, e4) = e4 % 130.06/18.10 (2) ~ (op(e0, e4) = e4) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | ALPHA: (1) implies: % 130.06/18.10 | (3) op(e0, e4) = e4 % 130.06/18.10 | % 130.06/18.10 | PRED_UNIFY: (2), (3) imply: % 130.06/18.10 | (4) $false % 130.06/18.10 | % 130.06/18.10 | CLOSE: (4) is inconsistent. % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #136 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_9_21 = e0 & op(e0, e3) = e0 % 130.06/18.10 (2) all_9_21 = e3 % 130.06/18.10 (3) ~ (e3 = e0) % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | ALPHA: (1) implies: % 130.06/18.10 | (4) all_9_21 = e0 % 130.06/18.10 | % 130.06/18.10 | COMBINE_EQS: (2), (4) imply: % 130.06/18.10 | (5) e3 = e0 % 130.06/18.10 | % 130.06/18.10 | REDUCE: (3), (5) imply: % 130.06/18.10 | (6) $false % 130.06/18.10 | % 130.06/18.10 | CLOSE: (6) is inconsistent. % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #137 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 130.06/18.10 (2) all_6_5 = e1 % 130.06/18.10 (3) ~ (e4 = e0) % 130.06/18.10 (4) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) | % 130.06/18.10 (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) | % 130.06/18.10 (all_9_16 = e4 & op(e4, e0) = e4) % 130.06/18.10 (5) all_9_20 = e2 % 130.06/18.10 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.10 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.10 (8) ~ (e4 = e2) % 130.06/18.10 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.10 (10) ~ (op(e4, e3) = e4) % 130.06/18.10 (11) all_9_9 = e3 % 130.06/18.10 (12) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.06/18.10 (13) all_9_12 = e4 % 130.06/18.10 (14) ~ (e4 = e1) % 130.06/18.10 (15) ~ (all_4_20 = e4) % 130.06/18.10 (16) ~ (e4 = e3) % 130.06/18.10 (17) all_6_4 = all_4_20 % 130.06/18.10 (18) all_6_2 = all_4_10 % 130.06/18.10 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.10 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.10 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.10 (20) ~ (all_4_10 = e4) % 130.06/18.10 (21) all_4_0 = e0 % 130.06/18.10 % 130.06/18.10 Begin of proof % 130.06/18.10 | % 130.06/18.10 | BETA: splitting (4) gives: % 130.06/18.10 | % 130.06/18.10 | Case 1: % 130.06/18.10 | | % 130.06/18.10 | | (22) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 130.06/18.10 | | % 130.06/18.10 | | REF_CLOSE: (3), (7), (10), (21), (22) are inconsistent by sub-proof #299. % 130.06/18.10 | | % 130.06/18.10 | Case 2: % 130.06/18.10 | | % 130.06/18.10 | | (23) (all_9_4 = e4 & op(e4, e2) = e4) | (all_9_9 = e4 & op(e4, e1) = e4) % 130.06/18.10 | | | (all_9_16 = e4 & op(e4, e0) = e4) % 130.06/18.10 | | % 130.06/18.10 | | BETA: splitting (23) gives: % 130.06/18.10 | | % 130.06/18.10 | | Case 1: % 130.06/18.10 | | | % 130.06/18.10 | | | (24) all_9_4 = e4 & op(e4, e2) = e4 % 130.06/18.10 | | | % 130.06/18.10 | | | ALPHA: (24) implies: % 130.06/18.10 | | | (25) op(e4, e2) = e4 % 130.06/18.10 | | | % 130.06/18.10 | | | REF_CLOSE: (12), (18), (20), (25) are inconsistent by sub-proof #298. % 130.06/18.10 | | | % 130.06/18.10 | | Case 2: % 130.06/18.10 | | | % 130.06/18.10 | | | (26) (all_9_9 = e4 & op(e4, e1) = e4) | (all_9_16 = e4 & op(e4, e0) = % 130.06/18.10 | | | e4) % 130.06/18.10 | | | % 130.06/18.10 | | | BETA: splitting (26) gives: % 130.06/18.10 | | | % 130.06/18.10 | | | Case 1: % 130.06/18.10 | | | | % 130.06/18.10 | | | | (27) all_9_9 = e4 & op(e4, e1) = e4 % 130.06/18.10 | | | | % 130.06/18.10 | | | | ALPHA: (27) implies: % 130.06/18.10 | | | | (28) all_9_9 = e4 % 130.06/18.10 | | | | % 130.06/18.10 | | | | COMBINE_EQS: (11), (28) imply: % 130.06/18.10 | | | | (29) e4 = e3 % 130.06/18.10 | | | | % 130.06/18.10 | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (13), (14), (16), (19), % 130.06/18.10 | | | | (21), (29) are inconsistent by sub-proof #217. % 130.06/18.10 | | | | % 130.06/18.10 | | | Case 2: % 130.06/18.10 | | | | % 130.06/18.10 | | | | (30) all_9_16 = e4 & op(e4, e0) = e4 % 130.06/18.10 | | | | % 130.06/18.10 | | | | REF_CLOSE: (1), (15), (17), (30) are inconsistent by sub-proof #195. % 130.06/18.10 | | | | % 130.06/18.10 | | | End of split % 130.06/18.10 | | | % 130.06/18.10 | | End of split % 130.06/18.10 | | % 130.06/18.10 | End of split % 130.06/18.10 | % 130.06/18.10 End of proof % 130.06/18.10 % 130.06/18.10 Sub-proof #138 shows that the following formulas are inconsistent: % 130.06/18.10 ---------------------------------------------------------------- % 130.06/18.10 (1) all_9_4 = e3 % 130.06/18.11 (2) all_9_4 = e1 % 130.06/18.11 (3) ~ (e3 = e1) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | COMBINE_EQS: (1), (2) imply: % 130.06/18.11 | (4) e3 = e1 % 130.06/18.11 | % 130.06/18.11 | SIMP: (4) implies: % 130.06/18.11 | (5) e3 = e1 % 130.06/18.11 | % 130.06/18.11 | REDUCE: (3), (5) imply: % 130.06/18.11 | (6) $false % 130.06/18.11 | % 130.06/18.11 | CLOSE: (6) is inconsistent. % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #139 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (e3 = e0) % 130.06/18.11 (2) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) % 130.06/18.11 (3) ~ (all_4_5 = e3) % 130.06/18.11 (4) all_9_0 = e0 % 130.06/18.11 (5) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (2) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (6) all_9_0 = e3 & op(e4, e4) = e3 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #291. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (7) all_9_1 = e3 & op(e4, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | ALPHA: (7) implies: % 130.06/18.11 | | (8) op(e4, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #144. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #140 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (unit = e2) % 130.06/18.11 (2) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.11 (3) ~ (unit = e1) % 130.06/18.11 (4) ~ (unit = e3) % 130.06/18.11 (5) ~ (unit = e0) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (2) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (6) unit = e2 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (1), (6) imply: % 130.06/18.11 | | (7) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (7) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (8) unit = e3 | unit = e1 | unit = e0 % 130.06/18.11 | | % 130.06/18.11 | | BETA: splitting (8) gives: % 130.06/18.11 | | % 130.06/18.11 | | Case 1: % 130.06/18.11 | | | % 130.06/18.11 | | | (9) unit = e3 % 130.06/18.11 | | | % 130.06/18.11 | | | REDUCE: (4), (9) imply: % 130.06/18.11 | | | (10) $false % 130.06/18.11 | | | % 130.06/18.11 | | | CLOSE: (10) is inconsistent. % 130.06/18.11 | | | % 130.06/18.11 | | Case 2: % 130.06/18.11 | | | % 130.06/18.11 | | | (11) unit = e1 | unit = e0 % 130.06/18.11 | | | % 130.06/18.11 | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #141. % 130.06/18.11 | | | % 130.06/18.11 | | End of split % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #141 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) unit = e1 | unit = e0 % 130.06/18.11 (2) ~ (unit = e1) % 130.06/18.11 (3) ~ (unit = e0) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (1) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (4) unit = e1 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (2), (4) imply: % 130.06/18.11 | | (5) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (5) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (6) unit = e0 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (3), (6) imply: % 130.06/18.11 | | (7) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (7) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #142 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_9_13 = e3 & op(e1, e3) = e3 % 130.06/18.11 (2) all_6_16 = e3 | ~ (op(e1, e3) = e3) % 130.06/18.11 (3) all_6_16 = all_4_8 % 130.06/18.11 (4) ~ (all_4_8 = e3) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | ALPHA: (1) implies: % 130.06/18.11 | (5) op(e1, e3) = e3 % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (2) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (6) ~ (op(e1, e3) = e3) % 130.06/18.11 | | % 130.06/18.11 | | PRED_UNIFY: (5), (6) imply: % 130.06/18.11 | | (7) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (7) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (8) all_6_16 = e3 % 130.06/18.11 | | % 130.06/18.11 | | COMBINE_EQS: (3), (8) imply: % 130.06/18.11 | | (9) all_4_8 = e3 % 130.06/18.11 | | % 130.06/18.11 | | SIMP: (9) implies: % 130.06/18.11 | | (10) all_4_8 = e3 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (4), (10) imply: % 130.06/18.11 | | (11) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (11) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #143 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (all_4_6 = e3) % 130.06/18.11 (2) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 130.06/18.11 (3) (all_9_1 = e3 & op(e4, e3) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) % 130.06/18.11 (4) ~ (all_4_5 = e3) % 130.06/18.11 (5) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (3) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (6) all_9_1 = e3 & op(e4, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | ALPHA: (6) implies: % 130.06/18.11 | | (7) op(e4, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #144. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (8) all_9_3 = e3 & op(e3, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | ALPHA: (8) implies: % 130.06/18.11 | | (9) op(e3, e3) = e3 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #295. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #144 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_4_5 = e3 | ~ (op(e4, e3) = e3) % 130.06/18.11 (2) op(e4, e3) = e3 % 130.06/18.11 (3) ~ (all_4_5 = e3) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (1) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (4) ~ (op(e4, e3) = e3) % 130.06/18.11 | | % 130.06/18.11 | | PRED_UNIFY: (2), (4) imply: % 130.06/18.11 | | (5) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (5) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (6) all_4_5 = e3 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (3), (6) imply: % 130.06/18.11 | | (7) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (7) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #145 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.11 (3) ~ (e3 = e2) % 130.06/18.11 (4) op(e2, e4) = all_8_45 % 130.06/18.11 (5) all_4_2 = e4 | ~ (op(e2, e4) = e4) % 130.06/18.11 (6) op(e4, e3) = e3 % 130.06/18.11 (7) ~ (e4 = e3) % 130.06/18.11 (8) op(e4, all_8_45) = e2 % 130.06/18.11 (9) op(e2, e4) = e3 % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (5) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | % 130.06/18.11 | | GROUND_INST: instantiating (2) with e3, all_8_45, e4, e2, simplifying with % 130.06/18.11 | | (4), (9) gives: % 130.06/18.11 | | (10) all_8_45 = e3 % 130.06/18.11 | | % 130.06/18.11 | | GROUND_INST: instantiating (2) with e3, e2, e3, e4, simplifying with (6) % 130.06/18.11 | | gives: % 130.06/18.11 | | (11) e3 = e2 | ~ (op(e4, e3) = e2) % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (8), (10) imply: % 130.06/18.11 | | (12) op(e4, e3) = e2 % 130.06/18.11 | | % 130.06/18.11 | | BETA: splitting (11) gives: % 130.06/18.11 | | % 130.06/18.11 | | Case 1: % 130.06/18.11 | | | % 130.06/18.11 | | | (13) ~ (op(e4, e3) = e2) % 130.06/18.11 | | | % 130.06/18.11 | | | PRED_UNIFY: (12), (13) imply: % 130.06/18.11 | | | (14) $false % 130.06/18.11 | | | % 130.06/18.11 | | | CLOSE: (14) is inconsistent. % 130.06/18.11 | | | % 130.06/18.11 | | Case 2: % 130.06/18.11 | | | % 130.06/18.11 | | | (15) e3 = e2 % 130.06/18.11 | | | % 130.06/18.11 | | | REDUCE: (3), (15) imply: % 130.06/18.11 | | | (16) $false % 130.06/18.11 | | | % 130.06/18.11 | | | CLOSE: (16) is inconsistent. % 130.06/18.11 | | | % 130.06/18.11 | | End of split % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (17) op(e2, e4) = e4 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #320. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #146 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) op(e4, e2) = all_4_10 % 130.06/18.11 (2) ~ (all_4_10 = e0) % 130.06/18.11 (3) op(e1, e4) = e4 % 130.06/18.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.11 (5) ~ (e1 = e0) % 130.06/18.11 (6) op(e0, e4) = e2 % 130.06/18.11 (7) op(e4, e4) = e0 % 130.06/18.11 (8) (all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, all_8_48) = e1 & op(e1, % 130.06/18.11 all_8_48) = all_8_47 & op(e1, e4) = all_8_48 & $i(all_8_47) & % 130.06/18.11 $i(all_8_48)) | (all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, all_8_51) % 130.06/18.11 = e0 & op(e0, all_8_51) = all_8_50 & op(e0, e4) = all_8_51 & % 130.06/18.11 $i(all_8_50) & $i(all_8_51)) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (8) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (9) all_8_46 = e1 & ~ (all_8_47 = e4) & op(e4, all_8_48) = e1 & op(e1, % 130.06/18.11 | | all_8_48) = all_8_47 & op(e1, e4) = all_8_48 & $i(all_8_47) & % 130.06/18.11 | | $i(all_8_48) % 130.06/18.11 | | % 130.06/18.11 | | ALPHA: (9) implies: % 130.06/18.11 | | (10) op(e1, e4) = all_8_48 % 130.06/18.11 | | (11) op(e4, all_8_48) = e1 % 130.06/18.11 | | % 130.06/18.11 | | GROUND_INST: instantiating (4) with e4, all_8_48, e4, e1, simplifying with % 130.06/18.11 | | (3), (10) gives: % 130.06/18.11 | | (12) all_8_48 = e4 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (11), (12) imply: % 130.06/18.11 | | (13) op(e4, e4) = e1 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (4), (5), (7), (13) are inconsistent by sub-proof #321. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (14) all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, all_8_51) = e0 & op(e0, % 130.06/18.11 | | all_8_51) = all_8_50 & op(e0, e4) = all_8_51 & $i(all_8_50) & % 130.06/18.11 | | $i(all_8_51) % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (1), (2), (4), (6), (14) are inconsistent by sub-proof #149. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #147 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (e4 = e2) % 130.06/18.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.11 (3) op(e4, e3) = e4 % 130.06/18.11 (4) op(e2, e4) = all_8_45 % 130.06/18.11 (5) op(e4, all_8_45) = e2 % 130.06/18.11 (6) op(e2, e4) = e3 % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | GROUND_INST: instantiating (2) with e3, all_8_45, e4, e2, simplifying with % 130.06/18.11 | (4), (6) gives: % 130.06/18.11 | (7) all_8_45 = e3 % 130.06/18.11 | % 130.06/18.11 | GROUND_INST: instantiating (2) with e4, e2, e3, e4, simplifying with (3) % 130.06/18.11 | gives: % 130.06/18.11 | (8) e4 = e2 | ~ (op(e4, e3) = e2) % 130.06/18.11 | % 130.06/18.11 | REDUCE: (5), (7) imply: % 130.06/18.11 | (9) op(e4, e3) = e2 % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (8) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (10) ~ (op(e4, e3) = e2) % 130.06/18.11 | | % 130.06/18.11 | | PRED_UNIFY: (9), (10) imply: % 130.06/18.11 | | (11) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (11) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (12) e4 = e2 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (1), (12) imply: % 130.06/18.11 | | (13) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (13) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #148 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (unit = e2) % 130.06/18.11 (2) op(e4, unit) = e4 % 130.06/18.11 (3) all_6_5 = e1 % 130.06/18.11 (4) ~ (e4 = e0) % 130.06/18.11 (5) all_9_20 = e2 % 130.06/18.11 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.11 (7) op(unit, e4) = e4 % 130.06/18.11 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.11 (9) ~ (e4 = e2) % 130.06/18.11 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.11 (11) ~ (op(e3, e4) = e4) % 130.06/18.11 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.11 (13) op(e4, all_8_42) = e3 % 130.06/18.11 (14) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.11 (15) all_9_12 = e4 % 130.06/18.11 (16) op(e3, e4) = e1 % 130.06/18.11 (17) ~ (unit = e0) % 130.06/18.11 (18) ~ (e4 = e3) % 130.06/18.11 (19) ~ (unit = e4) % 130.06/18.11 (20) op(e3, e4) = all_8_42 % 130.06/18.11 (21) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.11 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.11 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.11 (22) all_4_0 = e0 % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | GROUND_INST: instantiating (12) with e1, all_8_42, e4, e3, simplifying with % 130.06/18.11 | (16), (20) gives: % 130.06/18.11 | (23) all_8_42 = e1 % 130.06/18.11 | % 130.06/18.11 | PRED_UNIFY: (7), (11) imply: % 130.06/18.11 | (24) ~ (unit = e3) % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (14) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (25) unit = e4 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (19), (25) imply: % 130.06/18.11 | | (26) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (26) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (27) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.06/18.11 | | % 130.06/18.11 | | BETA: splitting (27) gives: % 130.06/18.11 | | % 130.06/18.11 | | Case 1: % 130.06/18.11 | | | % 130.06/18.11 | | | (28) unit = e2 % 130.06/18.11 | | | % 130.06/18.11 | | | REDUCE: (1), (28) imply: % 130.06/18.11 | | | (29) $false % 130.06/18.11 | | | % 130.06/18.11 | | | CLOSE: (29) is inconsistent. % 130.06/18.11 | | | % 130.06/18.11 | | Case 2: % 130.06/18.11 | | | % 130.06/18.11 | | | (30) unit = e3 | unit = e1 | unit = e0 % 130.06/18.11 | | | % 130.06/18.11 | | | BETA: splitting (30) gives: % 130.06/18.11 | | | % 130.06/18.11 | | | Case 1: % 130.06/18.11 | | | | % 130.06/18.11 | | | | (31) unit = e3 % 130.06/18.11 | | | | % 130.06/18.11 | | | | REDUCE: (24), (31) imply: % 130.06/18.11 | | | | (32) $false % 130.06/18.11 | | | | % 130.06/18.11 | | | | CLOSE: (32) is inconsistent. % 130.06/18.11 | | | | % 130.06/18.11 | | | Case 2: % 130.06/18.11 | | | | % 130.06/18.11 | | | | (33) unit = e1 | unit = e0 % 130.06/18.11 | | | | % 130.06/18.11 | | | | BETA: splitting (33) gives: % 130.06/18.11 | | | | % 130.06/18.11 | | | | Case 1: % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | (34) unit = e1 % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | REDUCE: (2), (34) imply: % 130.06/18.11 | | | | | (35) op(e4, e1) = e4 % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15), % 130.06/18.11 | | | | | (16), (18), (20), (21), (22), (35) are inconsistent by % 130.06/18.11 | | | | | sub-proof #302. % 130.06/18.11 | | | | | % 130.06/18.11 | | | | Case 2: % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | (36) unit = e0 % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | REDUCE: (17), (36) imply: % 130.06/18.11 | | | | | (37) $false % 130.06/18.11 | | | | | % 130.06/18.11 | | | | | CLOSE: (37) is inconsistent. % 130.06/18.11 | | | | | % 130.06/18.11 | | | | End of split % 130.06/18.11 | | | | % 130.06/18.11 | | | End of split % 130.06/18.11 | | | % 130.06/18.11 | | End of split % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #149 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) op(e4, e2) = all_4_10 % 130.06/18.11 (2) ~ (all_4_10 = e0) % 130.06/18.11 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.11 (4) all_8_49 = e0 & ~ (all_8_50 = e4) & op(e4, all_8_51) = e0 & op(e0, % 130.06/18.11 all_8_51) = all_8_50 & op(e0, e4) = all_8_51 & $i(all_8_50) & % 130.06/18.11 $i(all_8_51) % 130.06/18.11 (5) op(e0, e4) = e2 % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | ALPHA: (4) implies: % 130.06/18.11 | (6) op(e0, e4) = all_8_51 % 130.06/18.11 | (7) op(e4, all_8_51) = e0 % 130.06/18.11 | % 130.06/18.11 | GROUND_INST: instantiating (3) with e2, all_8_51, e4, e0, simplifying with % 130.06/18.11 | (5), (6) gives: % 130.06/18.11 | (8) all_8_51 = e2 % 130.06/18.11 | % 130.06/18.11 | GROUND_INST: instantiating (3) with all_4_10, e0, e2, e4, simplifying with (1) % 130.06/18.11 | gives: % 130.06/18.11 | (9) all_4_10 = e0 | ~ (op(e4, e2) = e0) % 130.06/18.11 | % 130.06/18.11 | REDUCE: (7), (8) imply: % 130.06/18.11 | (10) op(e4, e2) = e0 % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (9) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (11) ~ (op(e4, e2) = e0) % 130.06/18.11 | | % 130.06/18.11 | | PRED_UNIFY: (10), (11) imply: % 130.06/18.11 | | (12) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (12) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (13) all_4_10 = e0 % 130.06/18.11 | | % 130.06/18.11 | | REDUCE: (2), (13) imply: % 130.06/18.11 | | (14) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (14) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #150 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_6_14 = e0 | ~ (op(e2, e0) = e0) % 130.06/18.11 (2) op(e2, e0) = e0 % 130.06/18.11 (3) all_6_14 = all_4_22 % 130.06/18.11 (4) ~ (all_4_22 = e0) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (1) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (5) ~ (op(e2, e0) = e0) % 130.06/18.11 | | % 130.06/18.11 | | PRED_UNIFY: (2), (5) imply: % 130.06/18.11 | | (6) $false % 130.06/18.11 | | % 130.06/18.11 | | CLOSE: (6) is inconsistent. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (7) all_6_14 = e0 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #152. % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #151 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_9_8 = e0 & op(e2, e2) = e0 % 130.06/18.11 (2) all_9_8 = e4 % 130.06/18.11 (3) ~ (e4 = e0) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | ALPHA: (1) implies: % 130.06/18.11 | (4) all_9_8 = e0 % 130.06/18.11 | % 130.06/18.11 | COMBINE_EQS: (2), (4) imply: % 130.06/18.11 | (5) e4 = e0 % 130.06/18.11 | % 130.06/18.11 | REDUCE: (3), (5) imply: % 130.06/18.11 | (6) $false % 130.06/18.11 | % 130.06/18.11 | CLOSE: (6) is inconsistent. % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #152 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_6_14 = all_4_22 % 130.06/18.11 (2) all_6_14 = e0 % 130.06/18.11 (3) ~ (all_4_22 = e0) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | COMBINE_EQS: (1), (2) imply: % 130.06/18.11 | (4) all_4_22 = e0 % 130.06/18.11 | % 130.06/18.11 | SIMP: (4) implies: % 130.06/18.11 | (5) all_4_22 = e0 % 130.06/18.11 | % 130.06/18.11 | REDUCE: (3), (5) imply: % 130.06/18.11 | (6) $false % 130.06/18.11 | % 130.06/18.11 | CLOSE: (6) is inconsistent. % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #153 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) ~ (e4 = e2) % 130.06/18.11 (2) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.06/18.11 (all_9_16 = e2 & op(e4, e0) = e2) % 130.06/18.11 (3) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.06/18.11 (4) all_4_20 = e2 | ~ (op(e4, e0) = e2) % 130.06/18.11 (5) all_9_9 = e4 % 130.06/18.11 (6) ~ (all_4_20 = e2) % 130.06/18.11 (7) all_6_2 = all_4_10 % 130.06/18.11 (8) ~ (all_4_10 = e2) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | BETA: splitting (2) gives: % 130.06/18.11 | % 130.06/18.11 | Case 1: % 130.06/18.11 | | % 130.06/18.11 | | (9) all_9_4 = e2 & op(e4, e2) = e2 % 130.06/18.11 | | % 130.06/18.11 | | ALPHA: (9) implies: % 130.06/18.11 | | (10) op(e4, e2) = e2 % 130.06/18.11 | | % 130.06/18.11 | | REF_CLOSE: (3), (7), (8), (10) are inconsistent by sub-proof #261. % 130.06/18.11 | | % 130.06/18.11 | Case 2: % 130.06/18.11 | | % 130.06/18.11 | | (11) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 130.06/18.11 | | % 130.06/18.11 | | BETA: splitting (11) gives: % 130.06/18.11 | | % 130.06/18.11 | | Case 1: % 130.06/18.11 | | | % 130.06/18.11 | | | (12) all_9_9 = e2 & op(e4, e1) = e2 % 130.06/18.11 | | | % 130.06/18.11 | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #154. % 130.06/18.11 | | | % 130.06/18.11 | | Case 2: % 130.06/18.11 | | | % 130.06/18.11 | | | (13) all_9_16 = e2 & op(e4, e0) = e2 % 130.06/18.11 | | | % 130.06/18.11 | | | ALPHA: (13) implies: % 130.06/18.11 | | | (14) op(e4, e0) = e2 % 130.06/18.11 | | | % 130.06/18.11 | | | BETA: splitting (4) gives: % 130.06/18.11 | | | % 130.06/18.11 | | | Case 1: % 130.06/18.11 | | | | % 130.06/18.11 | | | | (15) ~ (op(e4, e0) = e2) % 130.06/18.11 | | | | % 130.06/18.11 | | | | PRED_UNIFY: (14), (15) imply: % 130.06/18.11 | | | | (16) $false % 130.06/18.11 | | | | % 130.06/18.11 | | | | CLOSE: (16) is inconsistent. % 130.06/18.11 | | | | % 130.06/18.11 | | | Case 2: % 130.06/18.11 | | | | % 130.06/18.11 | | | | (17) all_4_20 = e2 % 130.06/18.11 | | | | % 130.06/18.11 | | | | REDUCE: (6), (17) imply: % 130.06/18.11 | | | | (18) $false % 130.06/18.11 | | | | % 130.06/18.11 | | | | CLOSE: (18) is inconsistent. % 130.06/18.11 | | | | % 130.06/18.11 | | | End of split % 130.06/18.11 | | | % 130.06/18.11 | | End of split % 130.06/18.11 | | % 130.06/18.11 | End of split % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #154 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) all_9_9 = e2 & op(e4, e1) = e2 % 130.06/18.11 (2) all_9_9 = e4 % 130.06/18.11 (3) ~ (e4 = e2) % 130.06/18.11 % 130.06/18.11 Begin of proof % 130.06/18.11 | % 130.06/18.11 | ALPHA: (1) implies: % 130.06/18.11 | (4) all_9_9 = e2 % 130.06/18.11 | % 130.06/18.11 | COMBINE_EQS: (2), (4) imply: % 130.06/18.11 | (5) e4 = e2 % 130.06/18.11 | % 130.06/18.11 | SIMP: (5) implies: % 130.06/18.11 | (6) e4 = e2 % 130.06/18.11 | % 130.06/18.11 | REDUCE: (3), (6) imply: % 130.06/18.11 | (7) $false % 130.06/18.11 | % 130.06/18.11 | CLOSE: (7) is inconsistent. % 130.06/18.11 | % 130.06/18.11 End of proof % 130.06/18.11 % 130.06/18.11 Sub-proof #155 shows that the following formulas are inconsistent: % 130.06/18.11 ---------------------------------------------------------------- % 130.06/18.11 (1) op(e1, e3) = e3 % 130.06/18.11 (2) op(e4, e1) = e4 % 130.06/18.11 (3) op(e2, e0) = all_8_96 % 130.06/18.11 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.06/18.11 (5) all_6_9 = all_4_21 % 130.06/18.11 (6) all_6_5 = e1 % 130.06/18.11 (7) ~ (e4 = e0) % 130.06/18.12 (8) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.06/18.12 (9) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.06/18.12 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.06/18.12 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.06/18.12 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.06/18.12 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.06/18.12 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.06/18.12 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = % 130.06/18.12 e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.06/18.12 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.06/18.12 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = % 130.06/18.12 e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.06/18.12 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.06/18.12 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.06/18.12 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.06/18.12 $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ % 130.06/18.12 (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) % 130.06/18.12 = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & % 130.06/18.12 $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ % 130.06/18.12 (all_8_60 = all_8_81) & op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) % 130.06/18.12 = e3 & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & % 130.06/18.12 $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.06/18.12 (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) % 130.06/18.12 = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & % 130.06/18.12 $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ % 130.06/18.12 (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & op(all_8_45, e2) = % 130.06/18.12 all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 130.06/18.12 & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & % 130.06/18.12 ~ (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = % 130.06/18.12 all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) % 130.06/18.12 & $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.06/18.12 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.06/18.12 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.06/18.12 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.06/18.12 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.06/18.12 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.06/18.12 all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = e1 % 130.06/18.12 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) = e1 % 130.06/18.12 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = % 130.06/18.12 all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 % 130.06/18.12 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 % 130.06/18.12 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = % 130.06/18.12 all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 % 130.06/18.12 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) = e1 % 130.06/18.12 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 130.06/18.12 all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 % 130.06/18.12 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = % 130.06/18.12 all_8_30 & op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.06/18.12 all_8_87 & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 % 130.06/18.12 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 % 130.06/18.12 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.06/18.12 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 % 130.06/18.12 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 % 130.06/18.12 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.06/18.12 all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 % 130.06/18.12 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) = e0 % 130.06/18.12 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.06/18.12 all_8_75 & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 % 130.06/18.12 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 % 130.06/18.12 & op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.06/18.12 all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.06/18.12 (10) all_9_20 = e2 % 130.06/18.12 (11) all_6_10 = e3 % 130.06/18.12 (12) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.06/18.12 (13) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.06/18.12 (14) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.06/18.12 (15) ~ (e4 = e2) % 130.06/18.12 (16) all_4_7 = e0 % 130.06/18.12 (17) all_4_20 = e3 % 130.06/18.12 (18) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.06/18.12 (19) e4 = e3 | ~ (op(e2, e4) = e4) % 130.06/18.12 (20) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.06/18.12 (21) all_8_45 = e3 % 130.06/18.12 (22) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 130.06/18.12 (23) op(e4, e3) = e2 % 130.06/18.12 (24) op(e2, e1) = e2 % 130.06/18.12 (25) ~ (all_4_21 = e3) % 130.06/18.12 (26) e4 = e2 | ~ (op(e2, e2) = e2) % 130.06/18.12 (27) op(e3, e2) = e0 % 130.06/18.12 (28) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.06/18.12 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.06/18.12 (all_9_19 = e2 & op(e1, e0) = e2) % 130.06/18.12 (29) all_6_22 = all_4_14 % 130.06/18.12 (30) op(e1, e0) = e0 % 130.06/18.12 (31) op(e1, e4) = e4 % 130.06/18.12 (32) ~ (all_4_14 = e2) % 130.06/18.12 (33) ~ (op(e4, e3) = e4) % 130.06/18.12 (34) op(e4, e2) = e1 % 130.06/18.12 (35) ~ (e2 = e0) % 130.06/18.12 (36) all_9_0 = e0 % 130.06/18.12 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.06/18.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.06/18.12 (38) op(e1, e2) = e2 % 130.06/18.12 (39) op(e2, e3) = all_8_57 % 130.06/18.12 (40) ~ (op(e4, e3) = e3) % 130.06/18.12 (41) op(e2, e0) = e1 % 130.06/18.12 (42) ~ (all_4_22 = e3) % 130.06/18.12 (43) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.06/18.12 (44) op(e3, e1) = e3 % 130.06/18.12 (45) op(e0, e1) = e0 % 130.06/18.12 (46) ~ (e3 = e2) % 130.06/18.12 (47) all_9_14 = e2 % 130.06/18.12 (48) all_9_13 = e3 % 130.06/18.12 (49) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.06/18.12 (50) all_9_12 = e4 % 130.06/18.12 (51) ~ (e4 = e1) % 130.06/18.12 (52) all_9_15 = e1 % 130.06/18.12 (53) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.06/18.12 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.06/18.12 (all_9_22 = e2 & op(e0, e2) = e2) % 130.06/18.12 (54) op(e3, e4) = e1 % 130.06/18.12 (55) ~ (op(e2, e0) = e2) % 130.06/18.12 (56) all_4_11 = e0 % 130.06/18.12 (57) op(e3, e0) = e2 % 130.06/18.12 (58) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.06/18.12 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.06/18.12 (all_9_20 = e2 & op(e0, e4) = e2) % 130.06/18.12 (59) op(e2, e0) = all_4_22 % 130.06/18.12 (60) ~ (op(e0, e4) = e4) % 130.06/18.12 (61) ~ (e4 = e3) % 130.06/18.12 (62) all_4_10 = e4 | ~ (op(e4, e2) = e4) % 130.06/18.12 (63) op(e4, e0) = e3 % 130.06/18.12 (64) op(e2, e3) = e0 % 130.06/18.12 (65) op(e0, all_8_96) = e2 % 130.06/18.12 (66) op(e0, e4) = e2 % 130.06/18.12 (67) all_6_2 = all_4_10 % 130.06/18.12 (68) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.06/18.12 (69) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.06/18.12 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.06/18.12 (all_9_20 = e4 & op(e0, e4) = e4) % 130.06/18.12 (70) ~ (all_4_10 = e4) % 130.06/18.12 (71) ~ (all_4_10 = e2) % 130.06/18.12 (72) all_4_0 = e0 % 130.06/18.12 (73) ~ (e2 = e1) % 130.06/18.12 % 130.06/18.12 Begin of proof % 130.06/18.12 | % 130.06/18.12 | BETA: splitting (13) gives: % 130.06/18.12 | % 130.06/18.12 | Case 1: % 130.06/18.12 | | % 130.06/18.12 | | (74) ~ (op(e2, e3) = e2) % 130.06/18.12 | | % 130.06/18.12 | | BETA: splitting (9) gives: % 130.06/18.12 | | % 130.06/18.12 | | Case 1: % 130.06/18.12 | | | % 130.06/18.12 | | | (75) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) % 130.06/18.12 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 130.06/18.12 | | | & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ % 130.06/18.12 | | | (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 & % 130.06/18.12 | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.06/18.12 | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | (all_8_5 % 130.06/18.12 | | | = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.06/18.12 | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, e1) % 130.06/18.12 | | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 130.06/18.12 | | | & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.06/18.12 | | | (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & % 130.06/18.12 | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.06/18.12 | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | (all_8_9 % 130.06/18.12 | | | = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) % 130.06/18.12 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) % 130.06/18.12 | | | & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ % 130.06/18.12 | | | (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & % 130.06/18.12 | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = % 130.06/18.12 | | | all_8_57 & $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 130.06/18.12 | | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.06/18.12 | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) % 130.06/18.12 | | | = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) % 130.06/18.12 | | | & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.06/18.12 | | | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 130.06/18.12 | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.06/18.12 | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.06/18.12 | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.06/18.12 | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 130.06/18.12 | | | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 130.06/18.12 | | | & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ % 130.06/18.12 | | | (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) % 130.06/18.12 | | | = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.06/18.12 | | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.06/18.12 | | | % 130.06/18.12 | | | BETA: splitting (75) gives: % 130.06/18.12 | | | % 130.06/18.12 | | | Case 1: % 130.06/18.12 | | | | % 130.06/18.12 | | | | (76) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.06/18.12 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.06/18.12 | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = % 130.06/18.12 | | | | e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 % 130.06/18.12 | | | | & op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.06/18.12 | | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | % 130.06/18.12 | | | | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.06/18.12 | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.06/18.12 | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.06/18.12 | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = % 130.06/18.12 | | | | e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 % 130.06/18.12 | | | | & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.06/18.12 | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.06/18.12 | | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 130.06/18.12 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.06/18.12 | | | | $i(all_8_42) & $i(all_8_54)) % 130.06/18.12 | | | | % 130.06/18.12 | | | | BETA: splitting (76) gives: % 130.06/18.12 | | | | % 130.06/18.12 | | | | Case 1: % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | (77) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.06/18.12 | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.06/18.12 | | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = % 130.06/18.12 | | | | | e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, e4) = % 130.06/18.12 | | | | | all_8_2 & op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & % 130.06/18.12 | | | | | op(e2, e4) = all_8_45 & $i(all_8_2) & $i(all_8_45) & % 130.06/18.12 | | | | | $i(all_8_66)) % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | BETA: splitting (77) gives: % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | Case 1: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | (78) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) % 130.06/18.12 | | | | | | & op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & % 130.06/18.12 | | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) % 130.06/18.12 | | | | | | & $i(all_8_42) & $i(all_8_54) % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | ALPHA: (78) implies: % 130.06/18.12 | | | | | | (79) op(e3, e4) = all_8_42 % 130.06/18.12 | | | | | | (80) op(e4, e3) = all_8_54 % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (14), (19), % 130.06/18.12 | | | | | | (20), (23), (26), (28), (29), (32), (33), (36), (37), % 130.06/18.12 | | | | | | (39), (40), (41), (43), (45), (47), (48), (50), (51), % 130.06/18.12 | | | | | | (52), (53), (54), (55), (56), (58), (61), (64), (65), % 130.06/18.12 | | | | | | (67), (69), (71), (72), (74), (79), (80) are inconsistent % 130.06/18.12 | | | | | | by sub-proof #159. % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | Case 2: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | (81) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) % 130.06/18.12 | | | | | | & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.06/18.12 | | | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) % 130.06/18.12 | | | | | | & $i(all_8_45) & $i(all_8_66) % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | ALPHA: (81) implies: % 130.06/18.12 | | | | | | (82) op(e4, e2) = all_8_66 % 130.06/18.12 | | | | | | (83) op(all_8_66, e2) = e4 % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | BETA: splitting (62) gives: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | Case 1: % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | (84) ~ (op(e4, e2) = e4) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | GROUND_INST: instantiating (37) with e0, e2, e1, e0, simplifying % 130.06/18.12 | | | | | | | with (45) gives: % 130.06/18.12 | | | | | | | (85) e2 = e0 | ~ (op(e0, e1) = e2) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | GROUND_INST: instantiating (37) with e1, all_8_96, e0, e2, % 130.06/18.12 | | | | | | | simplifying with (3), (41) gives: % 130.06/18.12 | | | | | | | (86) all_8_96 = e1 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | GROUND_INST: instantiating (37) with e0, all_8_57, e3, e2, % 130.06/18.12 | | | | | | | simplifying with (39), (64) gives: % 130.06/18.12 | | | | | | | (87) all_8_57 = e0 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | GROUND_INST: instantiating (37) with e1, all_8_66, e2, e4, % 130.06/18.12 | | | | | | | simplifying with (34), (82) gives: % 130.06/18.12 | | | | | | | (88) all_8_66 = e1 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | PRED_UNIFY: (3), (55) imply: % 130.06/18.12 | | | | | | | (89) ~ (all_8_96 = e2) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | PRED_UNIFY: (39), (74) imply: % 130.06/18.12 | | | | | | | (90) ~ (all_8_57 = e2) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | PRED_UNIFY: (83), (84) imply: % 130.06/18.12 | | | | | | | (91) ~ (all_8_66 = e4) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | REDUCE: (87), (90) imply: % 130.06/18.12 | | | | | | | (92) ~ (e2 = e0) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15), (19), % 130.06/18.12 | | | | | | | (20), (26), (28), (29), (32), (35), (36), (37), (43), % 130.06/18.12 | | | | | | | (46), (47), (48), (50), (52), (53), (54), (56), (58), % 130.06/18.12 | | | | | | | (61), (65), (67), (69), (71), (72), (85), (86), (88), % 130.06/18.12 | | | | | | | (89), (91) are inconsistent by sub-proof #162. % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | Case 2: % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | (93) op(e4, e2) = e4 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | REF_CLOSE: (49), (67), (70), (93) are inconsistent by sub-proof % 130.06/18.12 | | | | | | | #298. % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | End of split % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | End of split % 130.06/18.12 | | | | | % 130.06/18.12 | | | | Case 2: % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | (94) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.06/18.12 | | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.06/18.12 | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.06/18.12 | | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = % 130.06/18.12 | | | | | e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = % 130.06/18.12 | | | | | all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & % 130.06/18.12 | | | | | op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) & % 130.06/18.12 | | | | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.06/18.12 | | | | | (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, % 130.06/18.12 | | | | | e3) = all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = % 130.06/18.12 | | | | | all_8_42 & $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | BETA: splitting (94) gives: % 130.06/18.12 | | | | | % 130.06/18.12 | | | | | Case 1: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | (95) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) % 130.06/18.12 | | | | | | & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & % 130.06/18.12 | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) % 130.06/18.12 | | | | | | & $i(all_8_48) & $i(all_8_78) % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | ALPHA: (95) implies: % 130.06/18.12 | | | | | | (96) ~ (all_8_48 = all_8_78) % 130.06/18.12 | | | | | | (97) op(e1, e4) = all_8_48 % 130.06/18.12 | | | | | | (98) op(e4, e1) = all_8_78 % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | REF_CLOSE: (2), (31), (37), (96), (97), (98) are inconsistent by % 130.06/18.12 | | | | | | sub-proof #189. % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | Case 2: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | (99) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) % 130.06/18.12 | | | | | | & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & % 130.06/18.12 | | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.06/18.12 | | | | | | $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 % 130.06/18.12 | | | | | | & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.06/18.12 | | | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & % 130.06/18.12 | | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.06/18.12 | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | BETA: splitting (99) gives: % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | | Case 1: % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | (100) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 130.06/18.12 | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, % 130.06/18.12 | | | | | | | e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.06/18.12 | | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | ALPHA: (100) implies: % 130.06/18.12 | | | | | | | (101) ~ (all_8_51 = all_8_90) % 130.06/18.12 | | | | | | | (102) op(e0, e4) = all_8_51 % 130.06/18.12 | | | | | | | (103) op(e4, e0) = all_8_90 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (14), (15), % 130.06/18.12 | | | | | | | (17), (19), (20), (22), (26), (28), (29), (32), (36), % 130.06/18.12 | | | | | | | (37), (39), (41), (43), (45), (47), (48), (50), (51), % 130.06/18.12 | | | | | | | (52), (53), (54), (55), (56), (58), (60), (61), (63), % 130.06/18.12 | | | | | | | (64), (65), (66), (67), (69), (71), (72), (74), (101), % 130.06/18.12 | | | | | | | (102), (103) are inconsistent by sub-proof #158. % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | Case 2: % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | (104) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 130.06/18.12 | | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.06/18.12 | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.06/18.12 | | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54) % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | ALPHA: (104) implies: % 130.06/18.12 | | | | | | | (105) op(e3, e4) = all_8_42 % 130.06/18.12 | | | | | | | (106) op(e4, e3) = all_8_54 % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (14), (19), % 130.06/18.12 | | | | | | | (20), (23), (26), (28), (29), (32), (33), (36), (37), % 130.06/18.12 | | | | | | | (39), (40), (41), (43), (45), (47), (48), (50), (51), % 130.06/18.12 | | | | | | | (52), (53), (54), (55), (56), (58), (61), (64), (65), % 130.06/18.12 | | | | | | | (67), (69), (71), (72), (74), (105), (106) are % 130.06/18.12 | | | | | | | inconsistent by sub-proof #159. % 130.06/18.12 | | | | | | | % 130.06/18.12 | | | | | | End of split % 130.06/18.12 | | | | | | % 130.06/18.12 | | | | | End of split % 130.06/18.12 | | | | | % 130.06/18.12 | | | | End of split % 130.06/18.12 | | | | % 130.06/18.12 | | | Case 2: % 130.06/18.12 | | | | % 130.06/18.12 | | | | (107) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) % 130.06/18.12 | | | | & op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & % 130.06/18.12 | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) % 130.06/18.12 | | | | & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.06/18.12 | | | | (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) % 130.06/18.12 | | | | = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 130.06/18.12 | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) & % 130.06/18.12 | | | | $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.06/18.12 | | | | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 130.06/18.12 | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.06/18.12 | | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.06/18.12 | | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) % 130.06/18.12 | | | | & op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & % 130.06/18.12 | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 130.06/18.12 | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ % 130.06/18.12 | | | | (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) % 130.06/18.12 | | | | = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & % 130.06/18.12 | | | | op(e2, e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & % 130.06/18.12 | | | | $i(all_8_69)) % 130.06/18.12 | | | | % 130.06/18.12 | | | | REF_CLOSE: (1), (5), (18), (21), (25), (27), (37), (42), (44), (54), % 130.06/18.12 | | | | (57), (59), (64), (73), (107) are inconsistent by sub-proof % 130.06/18.12 | | | | #182. % 130.06/18.12 | | | | % 130.06/18.12 | | | End of split % 130.06/18.12 | | | % 130.06/18.12 | | Case 2: % 130.06/18.12 | | | % 130.32/18.12 | | | (108) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.32/18.12 | | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, % 130.32/18.12 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & % 130.32/18.12 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = % 130.32/18.12 | | | e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 % 130.32/18.12 | | | & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.32/18.12 | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.32/18.12 | | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.32/18.12 | | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, % 130.32/18.12 | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & % 130.32/18.12 | | | $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = % 130.32/18.12 | | | e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & % 130.32/18.12 | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, % 130.32/18.12 | | | e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) % 130.32/18.12 | | | | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 130.32/18.12 | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, % 130.32/18.12 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.32/18.12 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = % 130.32/18.12 | | | e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 % 130.32/18.12 | | | & op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.32/18.12 | | | all_8_87 & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 130.32/18.12 | | | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 130.32/18.12 | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & op(e4, % 130.32/18.12 | | | e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & % 130.32/18.12 | | | $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = % 130.32/18.12 | | | e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 & % 130.32/18.12 | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.32/18.12 | | | e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) % 130.32/18.12 | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 130.32/18.12 | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, % 130.32/18.12 | | | e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & % 130.32/18.12 | | | $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = % 130.32/18.12 | | | e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & % 130.32/18.12 | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, % 130.32/18.12 | | | e1) = all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.32/18.12 | | | % 130.32/18.12 | | | BETA: splitting (108) gives: % 130.32/18.12 | | | % 130.32/18.12 | | | Case 1: % 130.32/18.12 | | | | % 130.32/18.13 | | | | (109) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) % 130.32/18.13 | | | | & op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & % 130.32/18.13 | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) % 130.32/18.13 | | | | & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.32/18.13 | | | | (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) % 130.32/18.13 | | | | = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 130.32/18.13 | | | | op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) & % 130.32/18.13 | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ % 130.32/18.13 | | | | (all_8_48 = all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, % 130.32/18.13 | | | | e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = % 130.32/18.13 | | | | all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.32/18.13 | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) % 130.32/18.13 | | | | & op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & % 130.32/18.13 | | | | op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 130.32/18.13 | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ % 130.32/18.13 | | | | (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) % 130.32/18.13 | | | | = e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & % 130.32/18.13 | | | | op(e1, e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & % 130.32/18.13 | | | | $i(all_8_84)) % 130.32/18.13 | | | | % 130.32/18.13 | | | | BETA: splitting (109) gives: % 130.32/18.13 | | | | % 130.32/18.13 | | | | Case 1: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | (110) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = % 130.32/18.13 | | | | | all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.32/18.13 | | | | | e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 % 130.32/18.13 | | | | | & $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = % 130.32/18.13 | | | | | e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 130.32/18.13 | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & % 130.32/18.13 | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.32/18.13 | | | | | $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | BETA: splitting (110) gives: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | Case 1: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (111) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = % 130.32/18.13 | | | | | | all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.32/18.13 | | | | | | e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 % 130.32/18.13 | | | | | | & $i(all_8_20) & $i(all_8_72) & $i(all_8_84) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | ALPHA: (111) implies: % 130.32/18.13 | | | | | | (112) ~ (all_8_72 = all_8_84) % 130.32/18.13 | | | | | | (113) op(e1, e2) = all_8_72 % 130.32/18.13 | | | | | | (114) op(e2, e1) = all_8_84 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | REF_CLOSE: (24), (37), (38), (112), (113), (114) are inconsistent by % 130.32/18.13 | | | | | | sub-proof #181. % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | Case 2: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (115) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = % 130.32/18.13 | | | | | | all_8_96) & op(all_8_96, e2) = all_8_22 & op(all_8_96, % 130.32/18.13 | | | | | | e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.32/18.13 | | | | | | & $i(all_8_22) & $i(all_8_75) & $i(all_8_96) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | ALPHA: (115) implies: % 130.32/18.13 | | | | | | (116) op(all_8_96, e0) = e2 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | GROUND_INST: instantiating (37) with e0, e2, e1, e0, simplifying % 130.32/18.13 | | | | | | with (45) gives: % 130.32/18.13 | | | | | | (117) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | GROUND_INST: instantiating (37) with e1, all_8_96, e0, e2, % 130.32/18.13 | | | | | | simplifying with (3), (41) gives: % 130.32/18.13 | | | | | | (118) all_8_96 = e1 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | GROUND_INST: instantiating (37) with e0, all_8_57, e3, e2, % 130.32/18.13 | | | | | | simplifying with (39), (64) gives: % 130.32/18.13 | | | | | | (119) all_8_57 = e0 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | PRED_UNIFY: (55), (116) imply: % 130.32/18.13 | | | | | | (120) ~ (all_8_96 = e2) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15), (19), % 130.32/18.13 | | | | | | (20), (26), (28), (29), (32), (36), (37), (39), (43), % 130.32/18.13 | | | | | | (46), (47), (48), (50), (51), (52), (53), (54), (56), % 130.32/18.13 | | | | | | (58), (61), (65), (67), (69), (71), (72), (74), (117), % 130.32/18.13 | | | | | | (118), (119), (120) are inconsistent by sub-proof #157. % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | End of split % 130.32/18.13 | | | | | % 130.32/18.13 | | | | Case 2: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | (121) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = % 130.32/18.13 | | | | | all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, e1) = % 130.32/18.13 | | | | | all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 130.32/18.13 | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = % 130.32/18.13 | | | | | e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.32/18.13 | | | | | op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & % 130.32/18.13 | | | | | op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & % 130.32/18.13 | | | | | $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = % 130.32/18.13 | | | | | e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & % 130.32/18.13 | | | | | op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.32/18.13 | | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.32/18.13 | | | | | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | REF_CLOSE: (1), (2), (24), (31), (37), (38), (44), (121) are % 130.32/18.13 | | | | | inconsistent by sub-proof #178. % 130.32/18.13 | | | | | % 130.32/18.13 | | | | End of split % 130.32/18.13 | | | | % 130.32/18.13 | | | Case 2: % 130.32/18.13 | | | | % 130.32/18.13 | | | | (122) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.32/18.13 | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.32/18.13 | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.32/18.13 | | | | & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.32/18.13 | | | | (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) % 130.32/18.13 | | | | = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & % 130.32/18.13 | | | | op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & % 130.32/18.13 | | | | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ % 130.32/18.13 | | | | (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, % 130.32/18.13 | | | | e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.32/18.13 | | | | all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.32/18.13 | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 130.32/18.13 | | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & % 130.32/18.13 | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 130.32/18.13 | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 & ~ % 130.32/18.13 | | | | (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) % 130.32/18.13 | | | | = e0 & op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & % 130.32/18.13 | | | | op(e0, e1) = all_8_87 & $i(all_8_38) & $i(all_8_87) & % 130.32/18.13 | | | | $i(all_8_99)) % 130.32/18.13 | | | | % 130.32/18.13 | | | | BETA: splitting (122) gives: % 130.32/18.13 | | | | % 130.32/18.13 | | | | Case 1: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | (123) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = % 130.32/18.13 | | | | | all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.32/18.13 | | | | | e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.32/18.13 | | | | | & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = % 130.32/18.13 | | | | | e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 130.32/18.13 | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & % 130.32/18.13 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.32/18.13 | | | | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | BETA: splitting (123) gives: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | Case 1: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (124) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = % 130.32/18.13 | | | | | | all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.32/18.13 | | | | | | e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.32/18.13 | | | | | | & $i(all_8_30) & $i(all_8_87) & $i(all_8_99) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | ALPHA: (124) implies: % 130.32/18.13 | | | | | | (125) ~ (all_8_87 = all_8_99) % 130.32/18.13 | | | | | | (126) op(e0, e1) = all_8_87 % 130.32/18.13 | | | | | | (127) op(e1, e0) = all_8_99 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | REF_CLOSE: (30), (37), (45), (125), (126), (127) are inconsistent by % 130.32/18.13 | | | | | | sub-proof #177. % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | Case 2: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (128) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = % 130.32/18.13 | | | | | | all_8_90) & op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 130.32/18.13 | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.32/18.13 | | | | | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | ALPHA: (128) implies: % 130.32/18.13 | | | | | | (129) ~ (all_8_51 = all_8_90) % 130.32/18.13 | | | | | | (130) op(e0, e4) = all_8_51 % 130.32/18.13 | | | | | | (131) op(e4, e0) = all_8_90 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (14), (15), % 130.32/18.13 | | | | | | (17), (19), (20), (22), (26), (28), (29), (32), (36), % 130.32/18.13 | | | | | | (37), (39), (41), (43), (45), (47), (48), (50), (51), % 130.32/18.13 | | | | | | (52), (53), (54), (55), (56), (58), (60), (61), (63), % 130.32/18.13 | | | | | | (64), (65), (66), (67), (69), (71), (72), (74), (129), % 130.32/18.13 | | | | | | (130), (131) are inconsistent by sub-proof #158. % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | End of split % 130.32/18.13 | | | | | % 130.32/18.13 | | | | Case 2: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | (132) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = % 130.32/18.13 | | | | | all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 130.32/18.13 | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.32/18.13 | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = % 130.32/18.13 | | | | | e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.32/18.13 | | | | | op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & % 130.32/18.13 | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.32/18.13 | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = % 130.32/18.13 | | | | | e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.32/18.13 | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.32/18.13 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.32/18.13 | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | BETA: splitting (132) gives: % 130.32/18.13 | | | | | % 130.32/18.13 | | | | | Case 1: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (133) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = % 130.32/18.13 | | | | | | all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 130.32/18.13 | | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.32/18.13 | | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | ALPHA: (133) implies: % 130.32/18.13 | | | | | | (134) op(e3, e0) = all_8_93 % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | BETA: splitting (68) gives: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | Case 1: % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | (135) ~ (op(e3, e0) = e3) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e0, e2, e1, e0, simplifying % 130.32/18.13 | | | | | | | with (45) gives: % 130.32/18.13 | | | | | | | (136) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e1, all_8_96, e0, e2, % 130.32/18.13 | | | | | | | simplifying with (3), (41) gives: % 130.32/18.13 | | | | | | | (137) all_8_96 = e1 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e0, all_8_57, e3, e2, % 130.32/18.13 | | | | | | | simplifying with (39), (64) gives: % 130.32/18.13 | | | | | | | (138) all_8_57 = e0 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e2, all_8_93, e0, e3, % 130.32/18.13 | | | | | | | simplifying with (57), (134) gives: % 130.32/18.13 | | | | | | | (139) all_8_93 = e2 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | PRED_UNIFY: (3), (55) imply: % 130.32/18.13 | | | | | | | (140) ~ (all_8_96 = e2) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | PRED_UNIFY: (39), (74) imply: % 130.32/18.13 | | | | | | | (141) ~ (all_8_57 = e2) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | PRED_UNIFY: (134), (135) imply: % 130.32/18.13 | | | | | | | (142) ~ (all_8_93 = e3) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | REDUCE: (138), (141) imply: % 130.32/18.13 | | | | | | | (143) ~ (e2 = e0) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15), (19), % 130.32/18.13 | | | | | | | (20), (26), (28), (29), (32), (35), (36), (37), (43), % 130.32/18.13 | | | | | | | (47), (48), (50), (51), (52), (53), (54), (56), (58), % 130.32/18.13 | | | | | | | (61), (65), (67), (69), (71), (72), (136), (137), % 130.32/18.13 | | | | | | | (139), (140), (142) are inconsistent by sub-proof #156. % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | Case 2: % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | (144) op(e3, e0) = e3 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | REF_CLOSE: (5), (18), (25), (144) are inconsistent by sub-proof % 130.32/18.13 | | | | | | | #228. % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | End of split % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | Case 2: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | (145) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.32/18.13 | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.32/18.13 | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.32/18.13 | | | | | | & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 % 130.32/18.13 | | | | | | = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.32/18.13 | | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.32/18.13 | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.32/18.13 | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | BETA: splitting (145) gives: % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | | Case 1: % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | (146) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.32/18.13 | | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.32/18.13 | | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.32/18.13 | | | | | | | & $i(all_8_36) & $i(all_8_75) & $i(all_8_96) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e0, e2, e1, e0, simplifying % 130.32/18.13 | | | | | | | with (45) gives: % 130.32/18.13 | | | | | | | (147) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e1, all_8_96, e0, e2, % 130.32/18.13 | | | | | | | simplifying with (3), (41) gives: % 130.32/18.13 | | | | | | | (148) all_8_96 = e1 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | GROUND_INST: instantiating (37) with e0, all_8_57, e3, e2, % 130.32/18.13 | | | | | | | simplifying with (39), (64) gives: % 130.32/18.13 | | | | | | | (149) all_8_57 = e0 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | PRED_UNIFY: (3), (55) imply: % 130.32/18.13 | | | | | | | (150) ~ (all_8_96 = e2) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15), (19), % 130.32/18.13 | | | | | | | (20), (26), (28), (29), (32), (36), (37), (39), (43), % 130.32/18.13 | | | | | | | (46), (47), (48), (50), (51), (52), (53), (54), (56), % 130.32/18.13 | | | | | | | (58), (61), (65), (67), (69), (71), (72), (74), (147), % 130.32/18.13 | | | | | | | (148), (149), (150) are inconsistent by sub-proof #157. % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | Case 2: % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | (151) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.32/18.13 | | | | | | | all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 130.32/18.13 | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.32/18.13 | | | | | | | & $i(all_8_38) & $i(all_8_87) & $i(all_8_99) % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | ALPHA: (151) implies: % 130.32/18.13 | | | | | | | (152) ~ (all_8_87 = all_8_99) % 130.32/18.13 | | | | | | | (153) op(e0, e1) = all_8_87 % 130.32/18.13 | | | | | | | (154) op(e1, e0) = all_8_99 % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | | REF_CLOSE: (30), (37), (45), (152), (153), (154) are inconsistent % 130.32/18.13 | | | | | | | by sub-proof #177. % 130.32/18.13 | | | | | | | % 130.32/18.13 | | | | | | End of split % 130.32/18.13 | | | | | | % 130.32/18.13 | | | | | End of split % 130.32/18.13 | | | | | % 130.32/18.13 | | | | End of split % 130.32/18.13 | | | | % 130.32/18.13 | | | End of split % 130.32/18.13 | | | % 130.32/18.13 | | End of split % 130.32/18.13 | | % 130.32/18.13 | Case 2: % 130.32/18.13 | | % 130.32/18.13 | | (155) all_4_7 = e2 % 130.32/18.13 | | % 130.32/18.13 | | COMBINE_EQS: (16), (155) imply: % 130.32/18.13 | | (156) e2 = e0 % 130.32/18.13 | | % 130.32/18.13 | | COMBINE_EQS: (47), (156) imply: % 130.32/18.13 | | (157) all_9_14 = e0 % 130.32/18.13 | | % 130.32/18.13 | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15), (19), (20), % 130.32/18.13 | | (26), (28), (29), (32), (35), (36), (37), (43), (46), (48), (50), % 130.32/18.13 | | (51), (52), (53), (54), (56), (58), (61), (67), (69), (71), (72), % 130.32/18.13 | | (73), (157) are inconsistent by sub-proof #244. % 130.32/18.13 | | % 130.32/18.13 | End of split % 130.32/18.13 | % 130.32/18.13 End of proof % 130.32/18.13 % 130.32/18.13 Sub-proof #156 shows that the following formulas are inconsistent: % 130.32/18.13 ---------------------------------------------------------------- % 130.32/18.13 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.13 (2) all_6_5 = e1 % 130.32/18.13 (3) ~ (e4 = e0) % 130.32/18.13 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.13 (5) all_9_20 = e2 % 130.32/18.13 (6) all_6_10 = e3 % 130.32/18.13 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.13 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.13 (9) ~ (e4 = e2) % 130.32/18.13 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.13 (11) all_8_96 = e1 % 130.32/18.13 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.13 (13) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.13 (14) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.13 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.13 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.13 (15) all_6_22 = all_4_14 % 130.32/18.13 (16) ~ (all_4_14 = e2) % 130.32/18.13 (17) ~ (e2 = e0) % 130.32/18.13 (18) ~ (all_8_93 = e3) % 130.32/18.13 (19) all_9_0 = e0 % 130.32/18.13 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.13 (21) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.13 (22) all_9_14 = e2 % 130.32/18.13 (23) all_9_13 = e3 % 130.32/18.13 (24) all_9_12 = e4 % 130.32/18.13 (25) ~ (e4 = e1) % 130.32/18.13 (26) all_9_15 = e1 % 130.32/18.13 (27) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.13 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.13 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.13 (28) op(e3, e4) = e1 % 130.32/18.13 (29) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.13 (30) all_4_11 = e0 % 130.32/18.13 (31) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.13 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.13 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.13 (32) ~ (e4 = e3) % 130.32/18.13 (33) op(e0, all_8_96) = e2 % 130.32/18.13 (34) all_6_2 = all_4_10 % 130.32/18.13 (35) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.13 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.13 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.13 (36) ~ (all_4_10 = e2) % 130.32/18.13 (37) all_4_0 = e0 % 130.32/18.13 (38) all_8_93 = e2 % 130.32/18.13 (39) ~ (all_8_96 = e2) % 130.32/18.13 % 130.32/18.13 Begin of proof % 130.32/18.13 | % 130.32/18.13 | REDUCE: (18), (38) imply: % 130.32/18.13 | (40) ~ (e3 = e2) % 130.32/18.13 | % 130.32/18.13 | SIMP: (40) implies: % 130.32/18.13 | (41) ~ (e3 = e2) % 130.32/18.13 | % 130.32/18.13 | REDUCE: (11), (39) imply: % 130.32/18.13 | (42) ~ (e2 = e1) % 130.32/18.13 | % 130.32/18.13 | SIMP: (42) implies: % 130.32/18.13 | (43) ~ (e2 = e1) % 130.32/18.13 | % 130.32/18.13 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.32/18.13 | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), % 130.32/18.13 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.32/18.13 | (36), (37), (41), (43) are inconsistent by sub-proof #163. % 130.32/18.13 | % 130.32/18.13 End of proof % 130.32/18.13 % 130.32/18.13 Sub-proof #157 shows that the following formulas are inconsistent: % 130.32/18.13 ---------------------------------------------------------------- % 130.32/18.13 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.13 (2) all_6_5 = e1 % 130.32/18.13 (3) ~ (e4 = e0) % 130.32/18.13 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.13 (5) all_9_20 = e2 % 130.32/18.13 (6) all_6_10 = e3 % 130.32/18.13 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.13 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.13 (9) ~ (e4 = e2) % 130.32/18.13 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.13 (11) all_8_96 = e1 % 130.32/18.13 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.13 (13) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.13 (14) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.13 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.13 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.13 (15) all_6_22 = all_4_14 % 130.32/18.13 (16) ~ (all_4_14 = e2) % 130.32/18.13 (17) all_9_0 = e0 % 130.32/18.13 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.13 (19) op(e2, e3) = all_8_57 % 130.32/18.13 (20) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.13 (21) ~ (e3 = e2) % 130.32/18.13 (22) all_9_14 = e2 % 130.32/18.13 (23) all_9_13 = e3 % 130.32/18.13 (24) all_9_12 = e4 % 130.32/18.13 (25) ~ (e4 = e1) % 130.32/18.13 (26) all_9_15 = e1 % 130.32/18.13 (27) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.13 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.13 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.13 (28) op(e3, e4) = e1 % 130.32/18.13 (29) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.13 (30) all_4_11 = e0 % 130.32/18.13 (31) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.13 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.13 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.13 (32) ~ (e4 = e3) % 130.32/18.13 (33) op(e0, all_8_96) = e2 % 130.32/18.13 (34) ~ (op(e2, e3) = e2) % 130.32/18.13 (35) all_6_2 = all_4_10 % 130.32/18.13 (36) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.13 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.13 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.13 (37) all_8_57 = e0 % 130.32/18.13 (38) ~ (all_4_10 = e2) % 130.32/18.13 (39) all_4_0 = e0 % 130.32/18.13 (40) ~ (all_8_96 = e2) % 130.32/18.13 % 130.32/18.13 Begin of proof % 130.32/18.13 | % 130.32/18.13 | PRED_UNIFY: (19), (34) imply: % 130.32/18.13 | (41) ~ (all_8_57 = e2) % 130.32/18.13 | % 130.32/18.13 | REDUCE: (37), (41) imply: % 130.32/18.13 | (42) ~ (e2 = e0) % 130.32/18.13 | % 130.32/18.13 | SIMP: (42) implies: % 130.32/18.13 | (43) ~ (e2 = e0) % 130.32/18.13 | % 130.32/18.13 | REDUCE: (11), (40) imply: % 130.32/18.13 | (44) ~ (e2 = e1) % 130.32/18.13 | % 130.32/18.13 | SIMP: (44) implies: % 130.32/18.13 | (45) ~ (e2 = e1) % 130.32/18.13 | % 130.32/18.13 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.32/18.13 | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 130.32/18.13 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 130.32/18.13 | (38), (39), (43), (45) are inconsistent by sub-proof #163. % 130.32/18.13 | % 130.32/18.13 End of proof % 130.32/18.13 % 130.32/18.13 Sub-proof #158 shows that the following formulas are inconsistent: % 130.32/18.13 ---------------------------------------------------------------- % 130.32/18.13 (1) op(e2, e0) = all_8_96 % 130.32/18.13 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.13 (3) all_6_5 = e1 % 130.32/18.13 (4) ~ (e4 = e0) % 130.32/18.14 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.14 (6) all_9_20 = e2 % 130.32/18.14 (7) all_6_10 = e3 % 130.32/18.14 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.14 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.14 (10) ~ (e4 = e2) % 130.32/18.14 (11) all_4_20 = e3 % 130.32/18.14 (12) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.14 (13) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.14 (14) all_4_20 = e4 | ~ (op(e4, e0) = e4) % 130.32/18.14 (15) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.14 (16) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.14 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.14 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.14 (17) all_6_22 = all_4_14 % 130.32/18.14 (18) ~ (all_4_14 = e2) % 130.32/18.14 (19) all_9_0 = e0 % 130.32/18.14 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.14 (21) op(e2, e3) = all_8_57 % 130.32/18.14 (22) op(e2, e0) = e1 % 130.32/18.14 (23) op(e0, e4) = all_8_51 % 130.32/18.14 (24) op(e4, e0) = all_8_90 % 130.32/18.14 (25) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.14 (26) op(e0, e1) = e0 % 130.32/18.14 (27) all_9_14 = e2 % 130.32/18.14 (28) all_9_13 = e3 % 130.32/18.14 (29) all_9_12 = e4 % 130.32/18.14 (30) ~ (e4 = e1) % 130.32/18.14 (31) all_9_15 = e1 % 130.32/18.14 (32) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.14 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.14 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.14 (33) op(e3, e4) = e1 % 130.32/18.14 (34) ~ (op(e2, e0) = e2) % 130.32/18.14 (35) all_4_11 = e0 % 130.32/18.14 (36) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.14 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.14 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.14 (37) ~ (op(e0, e4) = e4) % 130.32/18.14 (38) ~ (e4 = e3) % 130.32/18.14 (39) op(e4, e0) = e3 % 130.32/18.14 (40) op(e2, e3) = e0 % 130.32/18.14 (41) op(e0, all_8_96) = e2 % 130.32/18.14 (42) ~ (op(e2, e3) = e2) % 130.32/18.14 (43) op(e0, e4) = e2 % 130.32/18.14 (44) all_6_2 = all_4_10 % 130.32/18.14 (45) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.14 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.14 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.14 (46) ~ (all_4_10 = e2) % 130.32/18.14 (47) all_4_0 = e0 % 130.32/18.14 (48) ~ (all_8_51 = all_8_90) % 130.32/18.14 % 130.32/18.14 Begin of proof % 130.32/18.14 | % 130.32/18.14 | BETA: splitting (14) gives: % 130.32/18.14 | % 130.32/18.14 | Case 1: % 130.32/18.14 | | % 130.32/18.14 | | (49) ~ (op(e4, e0) = e4) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e2, all_8_51, e4, e0, simplifying with % 130.32/18.14 | | (23), (43) gives: % 130.32/18.14 | | (50) all_8_51 = e2 % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (23), (37) imply: % 130.32/18.14 | | (51) ~ (all_8_51 = e4) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e0, e2, e1, e0, simplifying with (26) % 130.32/18.14 | | gives: % 130.32/18.14 | | (52) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e1, all_8_96, e0, e2, simplifying with % 130.32/18.14 | | (1), (22) gives: % 130.32/18.14 | | (53) all_8_96 = e1 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e0, all_8_57, e3, e2, simplifying with % 130.32/18.14 | | (21), (40) gives: % 130.32/18.14 | | (54) all_8_57 = e0 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e3, all_8_90, e0, e4, simplifying with % 130.32/18.14 | | (24), (39) gives: % 130.32/18.14 | | (55) all_8_90 = e3 % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (1), (34) imply: % 130.32/18.14 | | (56) ~ (all_8_96 = e2) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (21), (42) imply: % 130.32/18.14 | | (57) ~ (all_8_57 = e2) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (24), (49) imply: % 130.32/18.14 | | (58) ~ (all_8_90 = e4) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (48), (50), (55) imply: % 130.32/18.14 | | (59) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (59) implies: % 130.32/18.14 | | (60) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (50), (51) imply: % 130.32/18.14 | | (61) ~ (e4 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (54), (57) imply: % 130.32/18.14 | | (62) ~ (e2 = e0) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (62) implies: % 130.32/18.14 | | (63) ~ (e2 = e0) % 130.32/18.14 | | % 130.32/18.14 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (15), % 130.32/18.14 | | (16), (17), (18), (19), (20), (25), (27), (28), (29), (30), (31), % 130.32/18.14 | | (32), (33), (35), (36), (41), (44), (45), (46), (47), (52), (53), % 130.32/18.14 | | (55), (56), (58), (60), (63) are inconsistent by sub-proof #161. % 130.32/18.14 | | % 130.32/18.14 | Case 2: % 130.32/18.14 | | % 130.32/18.14 | | (64) all_4_20 = e4 % 130.32/18.14 | | % 130.32/18.14 | | COMBINE_EQS: (11), (64) imply: % 130.32/18.14 | | (65) e4 = e3 % 130.32/18.14 | | % 130.32/18.14 | | COMBINE_EQS: (29), (65) imply: % 130.32/18.14 | | (66) all_9_12 = e3 % 130.32/18.14 | | % 130.32/18.14 | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (12), (30), (38), (45), (47), (66) % 130.32/18.14 | | are inconsistent by sub-proof #303. % 130.32/18.14 | | % 130.32/18.14 | End of split % 130.32/18.14 | % 130.32/18.14 End of proof % 130.32/18.14 % 130.32/18.14 Sub-proof #159 shows that the following formulas are inconsistent: % 130.32/18.14 ---------------------------------------------------------------- % 130.32/18.14 (1) op(e2, e0) = all_8_96 % 130.32/18.14 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.14 (3) all_6_5 = e1 % 130.32/18.14 (4) ~ (e4 = e0) % 130.32/18.14 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.14 (6) all_9_20 = e2 % 130.32/18.14 (7) all_6_10 = e3 % 130.32/18.14 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.14 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.14 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.14 (11) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.14 (12) op(e4, e3) = e2 % 130.32/18.14 (13) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.14 (14) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.14 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.14 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.14 (15) all_6_22 = all_4_14 % 130.32/18.14 (16) op(e4, e3) = all_8_54 % 130.32/18.14 (17) ~ (all_4_14 = e2) % 130.32/18.14 (18) ~ (op(e4, e3) = e4) % 130.32/18.14 (19) all_9_0 = e0 % 130.32/18.14 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.14 (21) op(e2, e3) = all_8_57 % 130.32/18.14 (22) ~ (op(e4, e3) = e3) % 130.32/18.14 (23) op(e2, e0) = e1 % 130.32/18.14 (24) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.14 (25) op(e0, e1) = e0 % 130.32/18.14 (26) all_9_14 = e2 % 130.32/18.14 (27) all_9_13 = e3 % 130.32/18.14 (28) all_9_12 = e4 % 130.32/18.14 (29) ~ (e4 = e1) % 130.32/18.14 (30) all_9_15 = e1 % 130.32/18.14 (31) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.14 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.14 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.14 (32) op(e3, e4) = e1 % 130.32/18.14 (33) ~ (op(e2, e0) = e2) % 130.32/18.14 (34) all_4_11 = e0 % 130.32/18.14 (35) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.14 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.14 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.14 (36) ~ (e4 = e3) % 130.32/18.14 (37) op(e2, e3) = e0 % 130.32/18.14 (38) op(e0, all_8_96) = e2 % 130.32/18.14 (39) ~ (op(e2, e3) = e2) % 130.32/18.14 (40) all_6_2 = all_4_10 % 130.32/18.14 (41) op(e3, e4) = all_8_42 % 130.32/18.14 (42) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.14 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.14 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.14 (43) ~ (all_4_10 = e2) % 130.32/18.14 (44) all_4_0 = e0 % 130.32/18.14 % 130.32/18.14 Begin of proof % 130.32/18.14 | % 130.32/18.14 | BETA: splitting (8) gives: % 130.32/18.14 | % 130.32/18.14 | Case 1: % 130.32/18.14 | | % 130.32/18.14 | | (45) ~ (op(e3, e4) = e4) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e0, e2, e1, e0, simplifying with (25) % 130.32/18.14 | | gives: % 130.32/18.14 | | (46) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e1, all_8_96, e0, e2, simplifying with % 130.32/18.14 | | (1), (23) gives: % 130.32/18.14 | | (47) all_8_96 = e1 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e0, all_8_57, e3, e2, simplifying with % 130.32/18.14 | | (21), (37) gives: % 130.32/18.14 | | (48) all_8_57 = e0 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e1, all_8_42, e4, e3, simplifying with % 130.32/18.14 | | (32), (41) gives: % 130.32/18.14 | | (49) all_8_42 = e1 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e2, all_8_54, e3, e4, simplifying with % 130.32/18.14 | | (12), (16) gives: % 130.32/18.14 | | (50) all_8_54 = e2 % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (16), (18) imply: % 130.32/18.14 | | (51) ~ (all_8_54 = e4) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (16), (22) imply: % 130.32/18.14 | | (52) ~ (all_8_54 = e3) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (1), (33) imply: % 130.32/18.14 | | (53) ~ (all_8_96 = e2) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (21), (39) imply: % 130.32/18.14 | | (54) ~ (all_8_57 = e2) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (41), (45) imply: % 130.32/18.14 | | (55) ~ (all_8_42 = e4) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (49), (55) imply: % 130.32/18.14 | | (56) ~ (e4 = e1) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (50), (51) imply: % 130.32/18.14 | | (57) ~ (e4 = e2) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (57) implies: % 130.32/18.14 | | (58) ~ (e4 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (50), (52) imply: % 130.32/18.14 | | (59) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (59) implies: % 130.32/18.14 | | (60) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (48), (54) imply: % 130.32/18.14 | | (61) ~ (e2 = e0) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (61) implies: % 130.32/18.14 | | (62) ~ (e2 = e0) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (47), (53) imply: % 130.32/18.14 | | (63) ~ (e2 = e1) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (63) implies: % 130.32/18.14 | | (64) ~ (e2 = e1) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (38), (47) imply: % 130.32/18.14 | | (65) op(e0, e1) = e2 % 130.32/18.14 | | % 130.32/18.14 | | BETA: splitting (46) gives: % 130.32/18.14 | | % 130.32/18.14 | | Case 1: % 130.32/18.14 | | | % 130.32/18.14 | | | (66) ~ (op(e0, e1) = e2) % 130.32/18.14 | | | % 130.32/18.14 | | | PRED_UNIFY: (65), (66) imply: % 130.32/18.14 | | | (67) $false % 130.32/18.14 | | | % 130.32/18.14 | | | CLOSE: (67) is inconsistent. % 130.32/18.14 | | | % 130.32/18.14 | | Case 2: % 130.32/18.14 | | | % 130.32/18.14 | | | (68) e2 = e0 % 130.32/18.14 | | | % 130.32/18.14 | | | COMBINE_EQS: (26), (68) imply: % 130.32/18.14 | | | (69) all_9_14 = e0 % 130.32/18.14 | | | % 130.32/18.14 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 130.32/18.14 | | | (15), (17), (19), (20), (24), (27), (28), (29), (30), (31), % 130.32/18.14 | | | (32), (34), (35), (36), (40), (42), (43), (44), (58), (60), % 130.32/18.14 | | | (62), (64), (69) are inconsistent by sub-proof #244. % 130.32/18.14 | | | % 130.32/18.14 | | End of split % 130.32/18.14 | | % 130.32/18.14 | Case 2: % 130.32/18.14 | | % 130.32/18.14 | | (70) op(e3, e4) = e4 % 130.32/18.14 | | % 130.32/18.14 | | REF_CLOSE: (3), (8), (29), (70) are inconsistent by sub-proof #316. % 130.32/18.14 | | % 130.32/18.14 | End of split % 130.32/18.14 | % 130.32/18.14 End of proof % 130.32/18.14 % 130.32/18.14 Sub-proof #160 shows that the following formulas are inconsistent: % 130.32/18.14 ---------------------------------------------------------------- % 130.32/18.14 (1) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 130.32/18.14 (2) op(e2, e0) = all_8_96 % 130.32/18.14 (3) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.14 (4) all_6_5 = e1 % 130.32/18.14 (5) ~ (e4 = e0) % 130.32/18.14 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.14 (7) all_9_20 = e2 % 130.32/18.14 (8) all_6_10 = e3 % 130.32/18.14 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.14 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.14 (11) ~ (e4 = e2) % 130.32/18.14 (12) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.14 (13) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.14 (14) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.14 (15) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.14 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.14 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.14 (16) all_6_22 = all_4_14 % 130.32/18.14 (17) ~ (all_4_14 = e2) % 130.32/18.14 (18) ~ (e2 = e0) % 130.32/18.14 (19) all_9_0 = e0 % 130.32/18.14 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.14 (21) op(e2, e0) = e1 % 130.32/18.14 (22) op(e0, e4) = all_8_51 % 130.32/18.14 (23) op(e4, e0) = all_8_90 % 130.32/18.14 (24) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.14 (25) op(e0, e1) = e0 % 130.32/18.14 (26) all_9_14 = e2 % 130.32/18.14 (27) all_9_13 = e3 % 130.32/18.14 (28) all_9_12 = e4 % 130.32/18.14 (29) ~ (e4 = e1) % 130.32/18.14 (30) all_9_15 = e1 % 130.32/18.14 (31) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.14 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.14 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.14 (32) op(e3, e4) = e1 % 130.32/18.14 (33) ~ (op(e2, e0) = e2) % 130.32/18.14 (34) all_4_11 = e0 % 130.32/18.14 (35) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.14 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.14 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.14 (36) ~ (op(e0, e4) = e4) % 130.32/18.14 (37) ~ (e4 = e3) % 130.32/18.14 (38) op(e4, e0) = e3 % 130.32/18.14 (39) op(e0, all_8_96) = e2 % 130.32/18.14 (40) all_6_4 = e3 % 130.32/18.14 (41) op(e0, e4) = e2 % 130.32/18.14 (42) all_6_2 = all_4_10 % 130.32/18.14 (43) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.14 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.14 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.14 (44) ~ (all_4_10 = e2) % 130.32/18.14 (45) all_4_0 = e0 % 130.32/18.14 (46) ~ (all_8_51 = all_8_90) % 130.32/18.14 % 130.32/18.14 Begin of proof % 130.32/18.14 | % 130.32/18.14 | BETA: splitting (1) gives: % 130.32/18.14 | % 130.32/18.14 | Case 1: % 130.32/18.14 | | % 130.32/18.14 | | (47) ~ (op(e4, e0) = e4) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e2, all_8_51, e4, e0, simplifying with % 130.32/18.14 | | (22), (41) gives: % 130.32/18.14 | | (48) all_8_51 = e2 % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (22), (36) imply: % 130.32/18.14 | | (49) ~ (all_8_51 = e4) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e0, e2, e1, e0, simplifying with (25) % 130.32/18.14 | | gives: % 130.32/18.14 | | (50) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e1, all_8_96, e0, e2, simplifying with % 130.32/18.14 | | (2), (21) gives: % 130.32/18.14 | | (51) all_8_96 = e1 % 130.32/18.14 | | % 130.32/18.14 | | GROUND_INST: instantiating (20) with e3, all_8_90, e0, e4, simplifying with % 130.32/18.14 | | (23), (38) gives: % 130.32/18.14 | | (52) all_8_90 = e3 % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (2), (33) imply: % 130.32/18.14 | | (53) ~ (all_8_96 = e2) % 130.32/18.14 | | % 130.32/18.14 | | PRED_UNIFY: (23), (47) imply: % 130.32/18.14 | | (54) ~ (all_8_90 = e4) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (46), (48), (52) imply: % 130.32/18.14 | | (55) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | SIMP: (55) implies: % 130.32/18.14 | | (56) ~ (e3 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REDUCE: (48), (49) imply: % 130.32/18.14 | | (57) ~ (e4 = e2) % 130.32/18.14 | | % 130.32/18.14 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 130.32/18.14 | | (15), (16), (17), (18), (19), (20), (24), (26), (27), (28), (29), % 130.32/18.14 | | (30), (31), (32), (34), (35), (39), (42), (43), (44), (45), (50), % 130.32/18.14 | | (51), (52), (53), (54), (56) are inconsistent by sub-proof #161. % 130.32/18.14 | | % 130.32/18.14 | Case 2: % 130.32/18.14 | | % 130.32/18.14 | | (58) all_6_4 = e4 % 130.32/18.14 | | % 130.32/18.14 | | COMBINE_EQS: (40), (58) imply: % 130.32/18.14 | | (59) e4 = e3 % 130.32/18.14 | | % 130.32/18.14 | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (12), (28), (29), (37), (43), % 130.32/18.14 | | (45), (59) are inconsistent by sub-proof #217. % 130.32/18.14 | | % 130.32/18.14 | End of split % 130.32/18.14 | % 130.32/18.14 End of proof % 130.32/18.14 % 130.32/18.14 Sub-proof #161 shows that the following formulas are inconsistent: % 130.32/18.14 ---------------------------------------------------------------- % 130.32/18.14 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.14 (2) all_6_5 = e1 % 130.32/18.14 (3) ~ (e4 = e0) % 130.32/18.14 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.14 (5) all_9_20 = e2 % 130.32/18.14 (6) all_6_10 = e3 % 130.32/18.14 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.14 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.14 (9) ~ (e4 = e2) % 130.32/18.14 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.14 (11) all_8_96 = e1 % 130.32/18.14 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.14 (13) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.14 (14) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.14 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.14 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.14 (15) all_6_22 = all_4_14 % 130.32/18.14 (16) all_8_90 = e3 % 130.32/18.14 (17) ~ (all_4_14 = e2) % 130.32/18.14 (18) ~ (e2 = e0) % 130.32/18.14 (19) all_9_0 = e0 % 130.32/18.14 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.14 (21) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.14 (22) ~ (e3 = e2) % 130.32/18.14 (23) all_9_14 = e2 % 130.32/18.14 (24) ~ (all_8_90 = e4) % 130.32/18.14 (25) all_9_13 = e3 % 130.32/18.14 (26) all_9_12 = e4 % 130.32/18.14 (27) ~ (e4 = e1) % 130.32/18.14 (28) all_9_15 = e1 % 130.32/18.14 (29) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.14 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.14 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.14 (30) op(e3, e4) = e1 % 130.32/18.14 (31) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.14 (32) all_4_11 = e0 % 130.32/18.14 (33) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.14 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.14 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.14 (34) op(e0, all_8_96) = e2 % 130.32/18.14 (35) all_6_2 = all_4_10 % 130.32/18.14 (36) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.14 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.14 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.14 (37) ~ (all_4_10 = e2) % 130.32/18.14 (38) all_4_0 = e0 % 130.32/18.14 (39) ~ (all_8_96 = e2) % 130.32/18.14 % 130.32/18.14 Begin of proof % 130.32/18.14 | % 130.32/18.14 | REDUCE: (16), (24) imply: % 130.32/18.14 | (40) ~ (e4 = e3) % 130.32/18.14 | % 130.32/18.14 | SIMP: (40) implies: % 130.32/18.14 | (41) ~ (e4 = e3) % 130.32/18.14 | % 130.32/18.14 | REDUCE: (11), (39) imply: % 130.32/18.14 | (42) ~ (e2 = e1) % 130.32/18.14 | % 130.32/18.14 | SIMP: (42) implies: % 130.32/18.14 | (43) ~ (e2 = e1) % 130.32/18.14 | % 130.32/18.14 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.32/18.14 | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (25), % 130.32/18.14 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.32/18.14 | (37), (38), (41), (43) are inconsistent by sub-proof #163. % 130.32/18.14 | % 130.32/18.14 End of proof % 130.32/18.15 % 130.32/18.15 Sub-proof #162 shows that the following formulas are inconsistent: % 130.32/18.15 ---------------------------------------------------------------- % 130.32/18.15 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.15 (2) all_6_5 = e1 % 130.32/18.15 (3) ~ (e4 = e0) % 130.32/18.15 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.15 (5) all_9_20 = e2 % 130.32/18.15 (6) all_6_10 = e3 % 130.32/18.15 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.15 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.15 (9) ~ (e4 = e2) % 130.32/18.15 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.15 (11) all_8_96 = e1 % 130.32/18.15 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.15 (13) ~ (all_8_66 = e4) % 130.32/18.15 (14) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.15 (15) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.15 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.15 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.15 (16) all_6_22 = all_4_14 % 130.32/18.15 (17) ~ (all_4_14 = e2) % 130.32/18.15 (18) ~ (e2 = e0) % 130.32/18.15 (19) all_9_0 = e0 % 130.32/18.15 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.15 (21) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.15 (22) all_8_66 = e1 % 130.32/18.15 (23) ~ (e3 = e2) % 130.32/18.15 (24) all_9_14 = e2 % 130.32/18.15 (25) all_9_13 = e3 % 130.32/18.15 (26) all_9_12 = e4 % 130.32/18.15 (27) all_9_15 = e1 % 130.32/18.15 (28) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.15 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.15 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.15 (29) op(e3, e4) = e1 % 130.32/18.15 (30) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.15 (31) all_4_11 = e0 % 130.32/18.15 (32) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.15 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.15 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.15 (33) ~ (e4 = e3) % 130.32/18.15 (34) op(e0, all_8_96) = e2 % 130.32/18.15 (35) all_6_2 = all_4_10 % 130.32/18.15 (36) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.15 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.15 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.15 (37) ~ (all_4_10 = e2) % 130.32/18.15 (38) all_4_0 = e0 % 130.32/18.15 (39) ~ (all_8_96 = e2) % 130.32/18.15 % 130.32/18.15 Begin of proof % 130.32/18.15 | % 130.32/18.15 | REDUCE: (13), (22) imply: % 130.32/18.15 | (40) ~ (e4 = e1) % 130.32/18.15 | % 130.32/18.15 | SIMP: (40) implies: % 130.32/18.15 | (41) ~ (e4 = e1) % 130.32/18.15 | % 130.32/18.15 | REDUCE: (11), (39) imply: % 130.32/18.15 | (42) ~ (e2 = e1) % 130.32/18.15 | % 130.32/18.15 | SIMP: (42) implies: % 130.32/18.15 | (43) ~ (e2 = e1) % 130.32/18.15 | % 130.32/18.15 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.32/18.15 | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 130.32/18.15 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.32/18.15 | (37), (38), (41), (43) are inconsistent by sub-proof #163. % 130.32/18.15 | % 130.32/18.15 End of proof % 130.32/18.15 % 130.32/18.15 Sub-proof #163 shows that the following formulas are inconsistent: % 130.32/18.15 ---------------------------------------------------------------- % 130.32/18.15 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.15 (2) all_6_5 = e1 % 130.32/18.15 (3) ~ (e4 = e0) % 130.32/18.15 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.15 (5) all_9_20 = e2 % 130.32/18.15 (6) all_6_10 = e3 % 130.32/18.15 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.15 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.15 (9) ~ (e4 = e2) % 130.32/18.15 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.15 (11) all_8_96 = e1 % 130.32/18.15 (12) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.15 (13) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.15 (14) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.15 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.15 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.15 (15) all_6_22 = all_4_14 % 130.32/18.15 (16) ~ (all_4_14 = e2) % 130.32/18.15 (17) ~ (e2 = e0) % 130.32/18.15 (18) all_9_0 = e0 % 130.32/18.15 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.15 (20) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.15 (21) ~ (e3 = e2) % 130.32/18.15 (22) all_9_14 = e2 % 130.32/18.15 (23) all_9_13 = e3 % 130.32/18.15 (24) all_9_12 = e4 % 130.32/18.15 (25) ~ (e4 = e1) % 130.32/18.15 (26) all_9_15 = e1 % 130.32/18.15 (27) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.15 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.15 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.15 (28) op(e3, e4) = e1 % 130.32/18.15 (29) e2 = e0 | ~ (op(e0, e1) = e2) % 130.32/18.15 (30) all_4_11 = e0 % 130.32/18.15 (31) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.15 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.15 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.15 (32) ~ (e4 = e3) % 130.32/18.15 (33) op(e0, all_8_96) = e2 % 130.32/18.15 (34) all_6_2 = all_4_10 % 130.32/18.15 (35) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.15 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.15 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.15 (36) ~ (all_4_10 = e2) % 130.32/18.15 (37) all_4_0 = e0 % 130.32/18.15 (38) ~ (e2 = e1) % 130.32/18.15 % 130.32/18.15 Begin of proof % 130.32/18.15 | % 130.32/18.15 | REDUCE: (11), (33) imply: % 130.32/18.15 | (39) op(e0, e1) = e2 % 130.32/18.15 | % 130.32/18.15 | BETA: splitting (29) gives: % 130.32/18.15 | % 130.32/18.15 | Case 1: % 130.32/18.15 | | % 130.32/18.15 | | (40) ~ (op(e0, e1) = e2) % 130.32/18.15 | | % 130.32/18.15 | | PRED_UNIFY: (39), (40) imply: % 130.32/18.15 | | (41) $false % 130.32/18.15 | | % 130.32/18.15 | | CLOSE: (41) is inconsistent. % 130.32/18.15 | | % 130.32/18.15 | Case 2: % 130.32/18.15 | | % 130.32/18.15 | | (42) e2 = e0 % 130.32/18.15 | | % 130.32/18.15 | | COMBINE_EQS: (22), (42) imply: % 130.32/18.15 | | (43) all_9_14 = e0 % 130.32/18.15 | | % 130.32/18.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), % 130.32/18.15 | | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), % 130.32/18.15 | | (26), (27), (28), (30), (31), (32), (34), (35), (36), (37), (38), % 130.32/18.15 | | (43) are inconsistent by sub-proof #244. % 130.32/18.15 | | % 130.32/18.15 | End of split % 130.32/18.15 | % 130.32/18.15 End of proof % 130.32/18.15 % 130.32/18.15 Sub-proof #164 shows that the following formulas are inconsistent: % 130.32/18.15 ---------------------------------------------------------------- % 130.32/18.15 (1) op(e1, e3) = e3 % 130.32/18.15 (2) all_9_8 = e4 % 130.32/18.15 (3) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.15 (4) op(e4, e1) = e4 % 130.32/18.15 (5) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.32/18.15 (6) all_6_9 = all_4_21 % 130.32/18.15 (7) op(e0, all_8_90) = e4 % 130.32/18.15 (8) all_6_5 = e1 % 130.32/18.15 (9) ~ (e4 = e0) % 130.32/18.15 (10) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.32/18.15 (11) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.32/18.15 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.32/18.15 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.32/18.15 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.32/18.15 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.32/18.15 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.32/18.15 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.32/18.15 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.32/18.15 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.32/18.15 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.32/18.15 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.32/18.15 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.32/18.15 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.32/18.15 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.32/18.15 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.32/18.15 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.32/18.15 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.32/18.15 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.32/18.15 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.32/18.15 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.32/18.15 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.32/18.15 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.32/18.15 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.32/18.15 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.32/18.15 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.32/18.15 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.32/18.15 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.32/18.15 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.32/18.15 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.32/18.15 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.32/18.15 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.32/18.15 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.32/18.15 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.32/18.15 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.32/18.15 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.32/18.15 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.32/18.15 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.32/18.15 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.32/18.15 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.32/18.15 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.32/18.15 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.32/18.15 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.32/18.15 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.32/18.15 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.32/18.15 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.32/18.15 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.32/18.15 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.32/18.15 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.32/18.15 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.32/18.15 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.32/18.15 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.32/18.15 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.32/18.15 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.32/18.15 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.32/18.15 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.32/18.15 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.32/18.15 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.32/18.15 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.32/18.15 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.32/18.15 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.32/18.15 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.32/18.15 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.32/18.15 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.32/18.15 $i(all_8_87) & $i(all_8_99)) % 130.32/18.15 (12) all_9_20 = e2 % 130.32/18.15 (13) all_6_10 = e3 % 130.32/18.15 (14) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.32/18.15 (15) ~ (all_4_3 = all_4_4) % 130.32/18.15 (16) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.32/18.15 (17) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.32/18.15 (18) ~ (e4 = e2) % 130.32/18.15 (19) all_4_7 = e0 % 130.32/18.15 (20) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.32/18.15 (21) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.32/18.15 (22) e4 = e3 | ~ (op(e2, e4) = e4) % 130.32/18.15 (23) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.32/18.15 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.32/18.15 (all_9_16 = e2 & op(e4, e0) = e2) % 130.32/18.15 (24) e4 = e1 | ~ (op(e3, e4) = e4) % 130.32/18.15 (25) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.32/18.15 (26) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.32/18.15 (27) all_8_45 = e3 % 130.32/18.15 (28) op(e4, e3) = e2 % 130.32/18.15 (29) op(e2, e1) = e2 % 130.32/18.15 (30) ~ (all_4_21 = e3) % 130.32/18.15 (31) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.32/18.15 (32) ~ (all_4_3 = e3) % 130.32/18.15 (33) all_6_20 = all_4_4 % 130.32/18.15 (34) e4 = e2 | ~ (op(e2, e2) = e2) % 130.32/18.15 (35) all_9_11 = e2 % 130.32/18.15 (36) ~ (op(e0, e3) = e3) % 130.32/18.15 (37) ~ (e3 = e0) % 130.32/18.15 (38) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.32/18.15 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.32/18.15 (all_9_24 = e4 & op(e0, e0) = e4) % 130.32/18.15 (39) op(e3, e2) = e0 % 130.32/18.15 (40) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.32/18.15 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.32/18.15 (all_9_19 = e2 & op(e1, e0) = e2) % 130.32/18.15 (41) all_9_16 = e3 % 130.32/18.15 (42) all_6_22 = all_4_14 % 130.32/18.15 (43) all_9_17 = e2 % 130.32/18.15 (44) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.32/18.15 (45) op(e1, e0) = e0 % 130.32/18.15 (46) op(e1, e4) = e4 % 130.32/18.15 (47) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.32/18.15 = e0 % 130.32/18.15 (48) ~ (all_4_14 = e2) % 130.32/18.15 (49) ~ (op(e4, e3) = e4) % 130.32/18.15 (50) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.32/18.15 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.32/18.15 (all_9_18 = e1 & op(e2, e0) = e1) % 130.32/18.15 (51) op(e4, e2) = e1 % 130.32/18.15 (52) ~ (e2 = e0) % 130.32/18.15 (53) all_9_0 = e0 % 130.32/18.15 (54) ~ (all_4_22 = e2) % 130.32/18.15 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.32/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.32/18.15 (56) ~ (all_4_4 = e3) % 130.32/18.15 (57) op(e1, e2) = e2 % 130.32/18.15 (58) ~ (op(e4, e3) = e3) % 130.32/18.15 (59) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.32/18.15 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.32/18.15 (all_9_24 = e2 & op(e0, e0) = e2) % 130.32/18.15 (60) op(e2, e0) = e1 % 130.32/18.15 (61) ~ (all_4_22 = e3) % 130.32/18.15 (62) op(e4, e0) = all_8_90 % 130.32/18.15 (63) op(e0, e3) = e1 % 130.32/18.15 (64) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.32/18.15 (65) all_9_6 = e3 % 130.32/18.15 (66) ~ (e1 = e0) % 130.32/18.15 (67) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.32/18.15 (68) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.32/18.15 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.32/18.15 (all_9_20 = e3 & op(e0, e4) = e3) % 130.32/18.15 (69) op(e3, e1) = e3 % 130.32/18.15 (70) op(e0, e1) = e0 % 130.32/18.15 (71) ~ (e3 = e2) % 130.32/18.15 (72) all_9_14 = e2 % 130.32/18.15 (73) all_9_13 = e3 % 130.32/18.15 (74) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.32/18.15 (75) op(e0, e3) = all_8_63 % 130.32/18.15 (76) all_9_12 = e4 % 130.32/18.15 (77) op(e0, e4) = all_4_4 % 130.32/18.15 (78) ~ (e4 = e1) % 130.32/18.15 (79) ~ (all_4_3 = e0) % 130.32/18.15 (80) all_9_15 = e1 % 130.32/18.15 (81) op(e0, e2) = e3 % 130.32/18.15 (82) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.32/18.15 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.32/18.15 (all_9_22 = e2 & op(e0, e2) = e2) % 130.32/18.15 (83) ~ (e3 = e1) % 130.32/18.15 (84) op(e3, e4) = e1 % 130.32/18.15 (85) all_9_9 = e4 % 130.32/18.15 (86) op(e1, e4) = all_4_3 % 130.32/18.15 (87) all_4_11 = e0 % 130.32/18.15 (88) op(e3, e0) = e2 % 130.32/18.15 (89) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.32/18.15 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.32/18.15 (all_9_20 = e2 & op(e0, e4) = e2) % 130.32/18.15 (90) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.32/18.15 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.32/18.15 (all_9_16 = e3 & op(e4, e0) = e3) % 130.32/18.15 (91) all_9_24 = e4 % 130.32/18.15 (92) op(e2, e0) = all_4_22 % 130.32/18.15 (93) all_9_19 = e0 % 130.32/18.15 (94) ~ (op(e0, e4) = e4) % 130.32/18.15 (95) ~ (e4 = e3) % 130.32/18.15 (96) op(e4, e0) = e3 % 130.32/18.15 (97) ~ (all_4_4 = e0) % 130.32/18.15 (98) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.32/18.15 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.32/18.15 (all_9_16 = e1 & op(e4, e0) = e1) % 130.32/18.15 (99) op(e2, e3) = e0 % 130.32/18.15 (100) ~ (all_4_3 = e1) % 130.32/18.15 (101) op(e0, e4) = e2 % 130.32/18.15 (102) all_6_2 = all_4_10 % 130.32/18.15 (103) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.32/18.15 (104) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.32/18.15 (105) op(e2, e4) = e3 % 130.32/18.15 (106) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.32/18.15 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.32/18.15 (all_9_20 = e4 & op(e0, e4) = e4) % 130.32/18.15 (107) ~ (all_4_10 = e4) % 130.32/18.15 (108) ~ (op(e2, e3) = e3) % 130.32/18.15 (109) all_9_2 = e1 % 130.32/18.15 (110) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.32/18.15 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.32/18.15 (all_9_20 = e1 & op(e0, e4) = e1) % 130.32/18.15 (111) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.32/18.15 all_6_15 = e0 % 130.32/18.15 (112) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.32/18.15 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.32/18.15 (all_9_24 = e3 & op(e0, e0) = e3) % 130.32/18.15 (113) ~ (all_4_4 = e1) % 130.32/18.15 (114) ~ (all_4_10 = e2) % 130.32/18.15 (115) all_4_0 = e0 % 130.32/18.15 (116) ~ (e2 = e1) % 130.32/18.15 (117) all_6_15 = all_4_3 % 130.32/18.15 (118) all_9_7 = e0 % 130.32/18.15 (119) op(e4, e4) = e0 % 130.32/18.15 % 130.32/18.15 Begin of proof % 130.32/18.15 | % 130.32/18.15 | BETA: splitting (11) gives: % 130.32/18.15 | % 130.32/18.15 | Case 1: % 130.32/18.15 | | % 130.32/18.15 | | (120) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.32/18.15 | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.32/18.15 | | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.32/18.15 | | $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 % 130.32/18.15 | | = all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 130.32/18.15 | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) % 130.32/18.15 | | & $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 130.32/18.15 | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & % 130.32/18.15 | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = % 130.32/18.15 | | all_8_48 & $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | (all_8_7 % 130.32/18.15 | | = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 130.32/18.15 | | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = % 130.32/18.15 | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) & % 130.32/18.15 | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 % 130.32/18.15 | | = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.32/18.15 | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.32/18.15 | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ % 130.32/18.15 | | (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = % 130.32/18.15 | | all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & op(e2, % 130.32/18.15 | | e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 130.32/18.15 | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.32/18.15 | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) % 130.32/18.15 | | = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) % 130.32/18.15 | | & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.32/18.15 | | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 130.32/18.15 | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.32/18.15 | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.32/18.15 | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.32/18.15 | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 130.32/18.15 | | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 130.32/18.15 | | & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ % 130.32/18.15 | | (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) % 130.32/18.15 | | = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.32/18.15 | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.32/18.15 | | % 130.32/18.15 | | BETA: splitting (120) gives: % 130.32/18.15 | | % 130.32/18.15 | | Case 1: % 130.32/18.15 | | | % 130.32/18.15 | | | (121) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.32/18.15 | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) % 130.32/18.15 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 130.32/18.15 | | | & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ % 130.32/18.15 | | | (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 & % 130.32/18.15 | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.32/18.15 | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | % 130.32/18.15 | | | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.32/18.15 | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, e1) % 130.32/18.15 | | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 130.32/18.15 | | | & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.32/18.15 | | | (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & % 130.32/18.15 | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.32/18.15 | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.32/18.15 | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.32/18.15 | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) % 130.32/18.15 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) % 130.32/18.15 | | | & $i(all_8_54)) % 130.32/18.15 | | | % 130.32/18.15 | | | BETA: splitting (121) gives: % 130.32/18.15 | | | % 130.32/18.15 | | | Case 1: % 130.32/18.15 | | | | % 130.32/18.15 | | | | (122) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.32/18.15 | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.32/18.15 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.32/18.15 | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = % 130.32/18.15 | | | | e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 % 130.32/18.15 | | | | & op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) % 130.32/18.15 | | | | = all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) % 130.32/18.15 | | | | % 130.32/18.15 | | | | BETA: splitting (122) gives: % 130.32/18.15 | | | | % 130.32/18.15 | | | | Case 1: % 130.32/18.15 | | | | | % 130.32/18.16 | | | | | (123) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.32/18.16 | | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.32/18.16 | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.32/18.16 | | | | | $i(all_8_42) & $i(all_8_54) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | ALPHA: (123) implies: % 130.32/18.16 | | | | | (124) op(e4, e3) = all_8_54 % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 130.32/18.16 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 130.32/18.16 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), % 130.32/18.16 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41), % 130.32/18.16 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 130.32/18.16 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), % 130.32/18.16 | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), % 130.32/18.16 | | | | | (72), (73), (74), (76), (77), (78), (79), (80), (81), (82), % 130.32/18.16 | | | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), % 130.32/18.16 | | | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), % 130.32/18.16 | | | | | (102), (103), (104), (105), (106), (107), (108), (109), % 130.32/18.16 | | | | | (110), (111), (112), (113), (114), (115), (116), (117), % 130.32/18.16 | | | | | (118), (119), (124) are inconsistent by sub-proof #170. % 130.32/18.16 | | | | | % 130.32/18.16 | | | | Case 2: % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | (125) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 130.32/18.16 | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & op(e4, % 130.32/18.16 | | | | | e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.32/18.16 | | | | | $i(all_8_45) & $i(all_8_66) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | ALPHA: (125) implies: % 130.32/18.16 | | | | | (126) ~ (all_8_45 = all_8_66) % 130.32/18.16 | | | | | (127) op(e2, e4) = all_8_45 % 130.32/18.16 | | | | | (128) op(e4, e2) = all_8_66 % 130.32/18.16 | | | | | (129) op(all_8_66, e2) = e4 % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | REDUCE: (27), (126) imply: % 130.32/18.16 | | | | | (130) ~ (all_8_66 = e3) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | SIMP: (130) implies: % 130.32/18.16 | | | | | (131) ~ (all_8_66 = e3) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.32/18.16 | | | | | (17), (18), (21), (22), (25), (26), (31), (32), (33), (34), % 130.32/18.16 | | | | | (35), (37), (38), (40), (41), (42), (44), (47), (48), (50), % 130.32/18.16 | | | | | (51), (52), (53), (54), (55), (56), (59), (62), (63), (64), % 130.32/18.16 | | | | | (65), (66), (68), (71), (72), (73), (74), (76), (77), (79), % 130.32/18.16 | | | | | (80), (82), (84), (86), (87), (89), (91), (93), (94), (96), % 130.32/18.16 | | | | | (97), (100), (102), (103), (105), (106), (107), (109), % 130.32/18.16 | | | | | (110), (111), (113), (114), (115), (117), (118), (119), % 130.32/18.16 | | | | | (128), (129), (131) are inconsistent by sub-proof #169. % 130.32/18.16 | | | | | % 130.32/18.16 | | | | End of split % 130.32/18.16 | | | | % 130.32/18.16 | | | Case 2: % 130.32/18.16 | | | | % 130.32/18.16 | | | | (132) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.32/18.16 | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.32/18.16 | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.32/18.16 | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = % 130.32/18.16 | | | | e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 % 130.32/18.16 | | | | & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) % 130.32/18.16 | | | | = all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.32/18.16 | | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.32/18.16 | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 130.32/18.16 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.32/18.16 | | | | $i(all_8_42) & $i(all_8_54)) % 130.32/18.16 | | | | % 130.32/18.16 | | | | BETA: splitting (132) gives: % 130.32/18.16 | | | | % 130.32/18.16 | | | | Case 1: % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | (133) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.32/18.16 | | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.32/18.16 | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.32/18.16 | | | | | $i(all_8_48) & $i(all_8_78) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | ALPHA: (133) implies: % 130.32/18.16 | | | | | (134) ~ (all_8_48 = all_8_78) % 130.32/18.16 | | | | | (135) op(e1, e4) = all_8_48 % 130.32/18.16 | | | | | (136) op(e4, e1) = all_8_78 % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | REF_CLOSE: (4), (46), (55), (134), (135), (136) are inconsistent by % 130.32/18.16 | | | | | sub-proof #189. % 130.32/18.16 | | | | | % 130.32/18.16 | | | | Case 2: % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | (137) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) % 130.32/18.16 | | | | | & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & % 130.32/18.16 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) % 130.32/18.16 | | | | | & $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ % 130.32/18.16 | | | | | (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, % 130.32/18.16 | | | | | e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) = % 130.32/18.16 | | | | | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.32/18.16 | | | | | $i(all_8_42) & $i(all_8_54)) % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | BETA: splitting (137) gives: % 130.32/18.16 | | | | | % 130.32/18.16 | | | | | Case 1: % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | (138) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) % 130.32/18.16 | | | | | | & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & % 130.32/18.16 | | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) % 130.32/18.16 | | | | | | & $i(all_8_51) & $i(all_8_90) % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | ALPHA: (138) implies: % 130.32/18.16 | | | | | | (139) ~ (all_8_51 = all_8_90) % 130.32/18.16 | | | | | | (140) op(e0, e4) = all_8_51 % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.32/18.16 | | | | | | (17), (21), (22), (25), (26), (31), (32), (33), (34), % 130.32/18.16 | | | | | | (35), (36), (37), (38), (40), (41), (42), (44), (47), % 130.32/18.16 | | | | | | (48), (50), (52), (53), (54), (55), (56), (59), (62), % 130.32/18.16 | | | | | | (63), (64), (65), (66), (68), (72), (73), (75), (76), % 130.32/18.16 | | | | | | (77), (78), (79), (80), (82), (84), (86), (87), (89), % 130.32/18.16 | | | | | | (91), (93), (94), (96), (97), (100), (101), (102), (103), % 130.32/18.16 | | | | | | (105), (106), (109), (110), (111), (113), (114), (115), % 130.32/18.16 | | | | | | (116), (117), (118), (119), (139), (140) are inconsistent % 130.32/18.16 | | | | | | by sub-proof #167. % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | Case 2: % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | (141) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) % 130.32/18.16 | | | | | | & op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & % 130.32/18.16 | | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.32/18.16 | | | | | | & $i(all_8_42) & $i(all_8_54) % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | ALPHA: (141) implies: % 130.32/18.16 | | | | | | (142) op(e4, e3) = all_8_54 % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 130.32/18.16 | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), % 130.32/18.16 | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29), % 130.32/18.16 | | | | | | (30), (31), (32), (33), (34), (35), (36), (37), (38), % 130.32/18.16 | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47), % 130.32/18.16 | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.32/18.16 | | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), % 130.32/18.16 | | | | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), % 130.32/18.16 | | | | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), % 130.32/18.16 | | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), % 130.32/18.16 | | | | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), % 130.32/18.16 | | | | | | (103), (104), (105), (106), (107), (108), (109), (110), % 130.32/18.16 | | | | | | (111), (112), (113), (114), (115), (116), (117), (118), % 130.32/18.16 | | | | | | (119), (142) are inconsistent by sub-proof #170. % 130.32/18.16 | | | | | | % 130.32/18.16 | | | | | End of split % 130.32/18.16 | | | | | % 130.32/18.16 | | | | End of split % 130.32/18.16 | | | | % 130.32/18.16 | | | End of split % 130.32/18.16 | | | % 130.32/18.16 | | Case 2: % 130.32/18.16 | | | % 130.32/18.16 | | | (143) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.32/18.16 | | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, % 130.32/18.16 | | | e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & % 130.32/18.16 | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = % 130.32/18.16 | | | e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = all_8_12 % 130.32/18.16 | | | & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 130.32/18.16 | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | % 130.32/18.16 | | | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.32/18.16 | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, % 130.32/18.16 | | | e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & % 130.32/18.16 | | | $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = % 130.32/18.16 | | | e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & % 130.32/18.16 | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = all_8_66 & op(e2, % 130.32/18.16 | | | e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) % 130.32/18.16 | | | | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 130.32/18.16 | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & op(e3, % 130.32/18.16 | | | e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.32/18.16 | | | $i(all_8_57) & $i(all_8_69)) % 130.32/18.16 | | | % 130.32/18.16 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.32/18.16 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.32/18.16 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.32/18.16 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), % 130.32/18.16 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), % 130.32/18.16 | | | (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), % 130.32/18.16 | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), % 130.32/18.16 | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), % 130.32/18.16 | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), % 130.32/18.16 | | | (96), (97), (98), (99), (100), (101), (102), (103), (104), % 130.32/18.16 | | | (105), (106), (107), (108), (109), (110), (111), (112), (113), % 130.32/18.16 | | | (114), (115), (116), (117), (118), (119), (143) are % 130.32/18.16 | | | inconsistent by sub-proof #172. % 130.32/18.16 | | | % 130.32/18.16 | | End of split % 130.32/18.16 | | % 130.32/18.16 | Case 2: % 130.32/18.16 | | % 130.46/18.16 | | (144) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.16 | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) % 130.46/18.16 | | = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) % 130.46/18.16 | | & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = e0) & ~ % 130.46/18.16 | | (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 & % 130.46/18.16 | | op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.46/18.16 | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.46/18.16 | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.46/18.16 | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) % 130.46/18.16 | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) % 130.46/18.16 | | & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ % 130.46/18.16 | | (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & op(all_8_60, e1) % 130.46/18.16 | | = all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & % 130.46/18.16 | | $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ % 130.46/18.16 | | (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) = % 130.46/18.16 | | e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, % 130.46/18.16 | | e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) | % 130.46/18.16 | | (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & % 130.46/18.16 | | op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & op(e1, e0) % 130.46/18.16 | | = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) & $i(all_8_87) % 130.46/18.16 | | & $i(all_8_99)) | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ % 130.46/18.16 | | (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & op(all_8_51, e0) % 130.46/18.16 | | = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.46/18.16 | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 & ~ % 130.46/18.16 | | (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) = % 130.46/18.16 | | e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.16 | | e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.16 | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.16 | | op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) % 130.46/18.16 | | = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) % 130.46/18.16 | | & $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ % 130.46/18.16 | | (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) % 130.46/18.16 | | = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.16 | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.16 | | % 130.46/18.16 | | BETA: splitting (144) gives: % 130.46/18.16 | | % 130.46/18.16 | | Case 1: % 130.46/18.16 | | | % 130.46/18.16 | | | (145) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.16 | | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, % 130.46/18.16 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & % 130.46/18.16 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = % 130.46/18.16 | | | e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 % 130.46/18.16 | | | & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.46/18.16 | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.46/18.16 | | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.46/18.16 | | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, % 130.46/18.16 | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & % 130.46/18.16 | | | $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = % 130.46/18.16 | | | e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & % 130.46/18.16 | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, % 130.46/18.16 | | | e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) % 130.46/18.16 | | | | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 130.46/18.16 | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, % 130.46/18.16 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.16 | | | $i(all_8_72) & $i(all_8_84)) % 130.46/18.16 | | | % 130.46/18.16 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13), (14), % 130.46/18.16 | | | (15), (17), (18), (21), (22), (25), (26), (29), (31), (32), % 130.46/18.16 | | | (33), (34), (35), (37), (38), (40), (41), (42), (44), (46), % 130.46/18.16 | | | (47), (48), (50), (52), (53), (54), (55), (56), (57), (59), % 130.46/18.16 | | | (60), (62), (63), (64), (65), (66), (68), (69), (71), (72), % 130.46/18.16 | | | (73), (76), (77), (78), (79), (80), (81), (82), (84), (86), % 130.46/18.16 | | | (87), (89), (91), (93), (94), (96), (97), (100), (102), (103), % 130.46/18.16 | | | (105), (106), (109), (110), (111), (113), (114), (115), (117), % 130.46/18.16 | | | (118), (119), (145) are inconsistent by sub-proof #165. % 130.46/18.16 | | | % 130.46/18.16 | | Case 2: % 130.46/18.16 | | | % 130.46/18.16 | | | (146) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & % 130.46/18.16 | | | op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & op(e1, % 130.46/18.16 | | | e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) & % 130.46/18.16 | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ (all_8_32 = % 130.46/18.16 | | | e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.16 | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, % 130.46/18.16 | | | e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) % 130.46/18.16 | | | | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.16 | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & op(e3, % 130.46/18.16 | | | e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 130.46/18.16 | | | $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = % 130.46/18.16 | | | e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) = e0 & % 130.46/18.16 | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & op(e0, % 130.46/18.16 | | | e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) % 130.46/18.16 | | | | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 130.46/18.16 | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & op(e1, % 130.46/18.16 | | | e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.16 | | | $i(all_8_87) & $i(all_8_99)) % 130.46/18.16 | | | % 130.46/18.16 | | | BETA: splitting (146) gives: % 130.46/18.16 | | | % 130.46/18.16 | | | Case 1: % 130.46/18.16 | | | | % 130.46/18.16 | | | | (147) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.46/18.16 | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.46/18.16 | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.46/18.16 | | | | & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.16 | | | | (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) % 130.46/18.16 | | | | = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & % 130.46/18.16 | | | | op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & % 130.46/18.16 | | | | $i(all_8_90)) % 130.46/18.16 | | | | % 130.46/18.16 | | | | BETA: splitting (147) gives: % 130.46/18.16 | | | | % 130.46/18.16 | | | | Case 1: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | (148) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.46/18.16 | | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.46/18.16 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.46/18.16 | | | | | & $i(all_8_87) & $i(all_8_99) % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | ALPHA: (148) implies: % 130.46/18.16 | | | | | (149) ~ (all_8_87 = all_8_99) % 130.46/18.16 | | | | | (150) op(e0, e1) = all_8_87 % 130.46/18.16 | | | | | (151) op(e1, e0) = all_8_99 % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | REF_CLOSE: (45), (55), (70), (149), (150), (151) are inconsistent by % 130.46/18.16 | | | | | sub-proof #177. % 130.46/18.16 | | | | | % 130.46/18.16 | | | | Case 2: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | (152) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) % 130.46/18.16 | | | | | & op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & % 130.46/18.16 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) % 130.46/18.16 | | | | | & $i(all_8_51) & $i(all_8_90) % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | ALPHA: (152) implies: % 130.46/18.16 | | | | | (153) ~ (all_8_51 = all_8_90) % 130.46/18.16 | | | | | (154) op(e0, e4) = all_8_51 % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.16 | | | | | (17), (21), (22), (25), (26), (31), (32), (33), (34), (35), % 130.46/18.16 | | | | | (36), (37), (38), (40), (41), (42), (44), (47), (48), (50), % 130.46/18.16 | | | | | (52), (53), (54), (55), (56), (59), (62), (63), (64), (65), % 130.46/18.16 | | | | | (66), (68), (72), (73), (75), (76), (77), (78), (79), (80), % 130.46/18.16 | | | | | (82), (84), (86), (87), (89), (91), (93), (94), (96), (97), % 130.46/18.16 | | | | | (100), (101), (102), (103), (105), (106), (109), (110), % 130.46/18.16 | | | | | (111), (113), (114), (115), (116), (117), (118), (119), % 130.46/18.16 | | | | | (153), (154) are inconsistent by sub-proof #167. % 130.46/18.16 | | | | | % 130.46/18.16 | | | | End of split % 130.46/18.16 | | | | % 130.46/18.16 | | | Case 2: % 130.46/18.16 | | | | % 130.46/18.16 | | | | (155) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.16 | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & % 130.46/18.16 | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 130.46/18.16 | | | | & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ % 130.46/18.16 | | | | (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) % 130.46/18.16 | | | | = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & % 130.46/18.16 | | | | op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.16 | | | | $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ % 130.46/18.16 | | | | (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, % 130.46/18.16 | | | | e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.46/18.16 | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.16 | | | | % 130.46/18.16 | | | | BETA: splitting (155) gives: % 130.46/18.16 | | | | % 130.46/18.16 | | | | Case 1: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | (156) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.16 | | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & % 130.46/18.16 | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 130.46/18.16 | | | | | & $i(all_8_63) & $i(all_8_93) % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | ALPHA: (156) implies: % 130.46/18.16 | | | | | (157) ~ (all_8_63 = all_8_93) % 130.46/18.16 | | | | | (158) op(e3, e0) = all_8_93 % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | BETA: splitting (104) gives: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | Case 1: % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | (159) ~ (op(e3, e0) = e3) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | GROUND_INST: instantiating (55) with e1, all_8_63, e3, e0, % 130.46/18.16 | | | | | | simplifying with (63), (75) gives: % 130.46/18.16 | | | | | | (160) all_8_63 = e1 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | PRED_UNIFY: (36), (75) imply: % 130.46/18.16 | | | | | | (161) ~ (all_8_63 = e3) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | GROUND_INST: instantiating (55) with e1, e4, e3, e0, simplifying % 130.46/18.16 | | | | | | with (63) gives: % 130.46/18.16 | | | | | | (162) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | PRED_UNIFY: (7), (94) imply: % 130.46/18.16 | | | | | | (163) ~ (all_8_90 = e4) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | GROUND_INST: instantiating (55) with e2, all_8_93, e0, e3, % 130.46/18.16 | | | | | | simplifying with (88), (158) gives: % 130.46/18.16 | | | | | | (164) all_8_93 = e2 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | GROUND_INST: instantiating (55) with e3, all_8_90, e0, e4, % 130.46/18.16 | | | | | | simplifying with (62), (96) gives: % 130.46/18.16 | | | | | | (165) all_8_90 = e3 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | PRED_UNIFY: (158), (159) imply: % 130.46/18.16 | | | | | | (166) ~ (all_8_93 = e3) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.16 | | | | | | (17), (18), (21), (22), (25), (26), (31), (32), (33), % 130.46/18.16 | | | | | | (34), (35), (37), (38), (40), (41), (42), (44), (47), % 130.46/18.16 | | | | | | (48), (50), (52), (53), (54), (55), (56), (59), (64), % 130.46/18.16 | | | | | | (65), (66), (68), (72), (73), (76), (77), (78), (79), % 130.46/18.16 | | | | | | (80), (82), (84), (86), (87), (89), (91), (93), (97), % 130.46/18.16 | | | | | | (100), (102), (103), (105), (106), (109), (110), (111), % 130.46/18.16 | | | | | | (113), (114), (115), (117), (118), (119), (157), (160), % 130.46/18.16 | | | | | | (161), (162), (163), (164), (165), (166) are inconsistent % 130.46/18.16 | | | | | | by sub-proof #176. % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | Case 2: % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | (167) op(e3, e0) = e3 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | REF_CLOSE: (6), (20), (30), (167) are inconsistent by sub-proof % 130.46/18.16 | | | | | | #228. % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | End of split % 130.46/18.16 | | | | | % 130.46/18.16 | | | | Case 2: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | (168) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.46/18.16 | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.46/18.16 | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.46/18.16 | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = % 130.46/18.16 | | | | | e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.46/18.16 | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.16 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.16 | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | BETA: splitting (168) gives: % 130.46/18.16 | | | | | % 130.46/18.16 | | | | | Case 1: % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | (169) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.46/18.16 | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.46/18.16 | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.46/18.16 | | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | ALPHA: (169) implies: % 130.46/18.16 | | | | | | (170) ~ (all_8_75 = all_8_96) % 130.46/18.16 | | | | | | (171) op(e0, e2) = all_8_75 % 130.46/18.16 | | | | | | (172) op(e2, e0) = all_8_96 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.16 | | | | | | (17), (18), (21), (22), (25), (26), (31), (32), (33), % 130.46/18.16 | | | | | | (34), (35), (37), (38), (40), (41), (42), (44), (47), % 130.46/18.16 | | | | | | (48), (50), (52), (53), (54), (55), (56), (59), (60), % 130.46/18.16 | | | | | | (62), (63), (64), (65), (66), (68), (71), (72), (73), % 130.46/18.16 | | | | | | (76), (77), (78), (79), (80), (81), (82), (84), (86), % 130.46/18.16 | | | | | | (87), (89), (91), (93), (94), (96), (97), (100), (102), % 130.46/18.16 | | | | | | (103), (105), (106), (109), (110), (111), (113), (114), % 130.46/18.16 | | | | | | (115), (117), (118), (119), (170), (171), (172) are % 130.46/18.16 | | | | | | inconsistent by sub-proof #166. % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | Case 2: % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | (173) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.16 | | | | | | all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 130.46/18.16 | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.16 | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99) % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | ALPHA: (173) implies: % 130.46/18.16 | | | | | | (174) ~ (all_8_87 = all_8_99) % 130.46/18.16 | | | | | | (175) op(e0, e1) = all_8_87 % 130.46/18.16 | | | | | | (176) op(e1, e0) = all_8_99 % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | | REF_CLOSE: (45), (55), (70), (174), (175), (176) are inconsistent by % 130.46/18.16 | | | | | | sub-proof #177. % 130.46/18.16 | | | | | | % 130.46/18.16 | | | | | End of split % 130.46/18.16 | | | | | % 130.46/18.16 | | | | End of split % 130.46/18.16 | | | | % 130.46/18.16 | | | End of split % 130.46/18.16 | | | % 130.46/18.16 | | End of split % 130.46/18.16 | | % 130.46/18.16 | End of split % 130.46/18.16 | % 130.46/18.16 End of proof % 130.46/18.16 % 130.46/18.16 Sub-proof #165 shows that the following formulas are inconsistent: % 130.46/18.16 ---------------------------------------------------------------- % 130.46/18.16 (1) op(e1, e3) = e3 % 130.46/18.16 (2) all_9_8 = e4 % 130.46/18.16 (3) op(e4, e1) = e4 % 130.46/18.16 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.16 (5) op(e0, all_8_90) = e4 % 130.46/18.16 (6) all_6_5 = e1 % 130.46/18.16 (7) ~ (e4 = e0) % 130.46/18.16 (8) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.16 (9) all_9_20 = e2 % 130.46/18.16 (10) all_6_10 = e3 % 130.46/18.16 (11) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.16 (12) ~ (all_4_3 = all_4_4) % 130.46/18.16 (13) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.16 (14) ~ (e4 = e2) % 130.46/18.16 (15) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.16 (16) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.16 (17) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.16 (18) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.16 (19) op(e2, e1) = e2 % 130.46/18.16 (20) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.16 (21) ~ (all_4_3 = e3) % 130.46/18.16 (22) all_6_20 = all_4_4 % 130.46/18.16 (23) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.16 (24) all_9_11 = e2 % 130.46/18.16 (25) ~ (e3 = e0) % 130.46/18.16 (26) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.16 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.16 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.16 (27) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.16 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.16 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.16 (28) all_9_16 = e3 % 130.46/18.16 (29) all_6_22 = all_4_14 % 130.46/18.16 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.16 (31) op(e1, e4) = e4 % 130.46/18.16 (32) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.16 = e0 % 130.46/18.16 (33) ~ (all_4_14 = e2) % 130.46/18.17 (34) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.17 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.17 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.17 (35) ~ (e2 = e0) % 130.46/18.17 (36) all_9_0 = e0 % 130.46/18.17 (37) ~ (all_4_22 = e2) % 130.46/18.17 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.17 (39) ~ (all_4_4 = e3) % 130.46/18.17 (40) op(e1, e2) = e2 % 130.46/18.17 (41) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.17 op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) = % 130.46/18.17 all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) & % 130.46/18.17 $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = % 130.46/18.17 all_8_96) & op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & % 130.46/18.17 op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_22) & % 130.46/18.17 $i(all_8_75) & $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = e4) & % 130.46/18.17 ~ (all_8_48 = all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, e1) = % 130.46/18.17 all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 130.46/18.17 $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ % 130.46/18.17 (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & % 130.46/18.17 op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = % 130.46/18.17 all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = % 130.46/18.17 e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) % 130.46/18.17 = e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, % 130.46/18.17 e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.46/18.17 (42) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.17 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.17 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.17 (43) op(e2, e0) = e1 % 130.46/18.17 (44) op(e4, e0) = all_8_90 % 130.46/18.17 (45) op(e0, e3) = e1 % 130.46/18.17 (46) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.17 (47) all_9_6 = e3 % 130.46/18.17 (48) ~ (e1 = e0) % 130.46/18.17 (49) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.17 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.17 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.17 (50) op(e3, e1) = e3 % 130.46/18.17 (51) ~ (e3 = e2) % 130.46/18.17 (52) all_9_14 = e2 % 130.46/18.17 (53) all_9_13 = e3 % 130.46/18.17 (54) all_9_12 = e4 % 130.46/18.17 (55) op(e0, e4) = all_4_4 % 130.46/18.17 (56) ~ (e4 = e1) % 130.46/18.17 (57) ~ (all_4_3 = e0) % 130.46/18.17 (58) all_9_15 = e1 % 130.46/18.17 (59) op(e0, e2) = e3 % 130.46/18.17 (60) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.17 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.17 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.17 (61) op(e3, e4) = e1 % 130.46/18.17 (62) op(e1, e4) = all_4_3 % 130.46/18.17 (63) all_4_11 = e0 % 130.46/18.17 (64) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.17 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.17 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.17 (65) all_9_24 = e4 % 130.46/18.17 (66) all_9_19 = e0 % 130.46/18.17 (67) ~ (op(e0, e4) = e4) % 130.46/18.17 (68) op(e4, e0) = e3 % 130.46/18.17 (69) ~ (all_4_4 = e0) % 130.46/18.17 (70) ~ (all_4_3 = e1) % 130.46/18.17 (71) all_6_2 = all_4_10 % 130.46/18.17 (72) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.17 (73) op(e2, e4) = e3 % 130.46/18.17 (74) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.17 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.17 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.17 (75) all_9_2 = e1 % 130.46/18.17 (76) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.17 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.17 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.17 (77) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.17 = e0 % 130.46/18.17 (78) ~ (all_4_4 = e1) % 130.46/18.17 (79) ~ (all_4_10 = e2) % 130.46/18.17 (80) all_4_0 = e0 % 130.46/18.17 (81) all_6_15 = all_4_3 % 130.46/18.17 (82) all_9_7 = e0 % 130.46/18.17 (83) op(e4, e4) = e0 % 130.46/18.17 % 130.46/18.17 Begin of proof % 130.46/18.17 | % 130.46/18.17 | BETA: splitting (41) gives: % 130.46/18.17 | % 130.46/18.17 | Case 1: % 130.46/18.17 | | % 130.46/18.17 | | (84) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.17 | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) = % 130.46/18.17 | | all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) & % 130.46/18.17 | | $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 % 130.46/18.17 | | = all_8_96) & op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = % 130.46/18.17 | | e2 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_22) % 130.46/18.17 | | & $i(all_8_75) & $i(all_8_96)) % 130.46/18.17 | | % 130.46/18.17 | | BETA: splitting (84) gives: % 130.46/18.17 | | % 130.46/18.17 | | Case 1: % 130.46/18.17 | | | % 130.46/18.17 | | | (85) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.17 | | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) = % 130.46/18.17 | | | all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) & % 130.46/18.17 | | | $i(all_8_84) % 130.46/18.17 | | | % 130.46/18.17 | | | ALPHA: (85) implies: % 130.46/18.17 | | | (86) ~ (all_8_72 = all_8_84) % 130.46/18.17 | | | (87) op(e1, e2) = all_8_72 % 130.46/18.17 | | | (88) op(e2, e1) = all_8_84 % 130.46/18.17 | | | % 130.46/18.17 | | | REF_CLOSE: (19), (38), (40), (86), (87), (88) are inconsistent by % 130.46/18.17 | | | sub-proof #181. % 130.46/18.17 | | | % 130.46/18.17 | | Case 2: % 130.46/18.17 | | | % 130.46/18.17 | | | (89) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 130.46/18.17 | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = % 130.46/18.17 | | | all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) & % 130.46/18.17 | | | $i(all_8_96) % 130.46/18.17 | | | % 130.46/18.17 | | | ALPHA: (89) implies: % 130.46/18.17 | | | (90) ~ (all_8_75 = all_8_96) % 130.46/18.17 | | | (91) op(e0, e2) = all_8_75 % 130.46/18.17 | | | (92) op(e2, e0) = all_8_96 % 130.46/18.17 | | | % 130.46/18.17 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.46/18.17 | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 130.46/18.17 | | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), % 130.46/18.17 | | | (36), (37), (38), (39), (42), (43), (44), (45), (46), (47), % 130.46/18.17 | | | (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), % 130.46/18.17 | | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 130.46/18.17 | | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 130.46/18.17 | | | (79), (80), (81), (82), (83), (90), (91), (92) are inconsistent % 130.46/18.17 | | | by sub-proof #166. % 130.46/18.17 | | | % 130.46/18.17 | | End of split % 130.46/18.17 | | % 130.46/18.17 | Case 2: % 130.46/18.17 | | % 130.46/18.17 | | (93) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.46/18.17 | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 130.46/18.17 | | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & % 130.46/18.17 | | $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 % 130.46/18.17 | | = all_8_81) & op(all_8_60, e3) = e1 & op(all_8_60, e1) = % 130.46/18.17 | | all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & % 130.46/18.17 | | $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ % 130.46/18.17 | | (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) = e1 % 130.46/18.17 | | & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) % 130.46/18.17 | | = all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.46/18.17 | | % 130.46/18.17 | | REF_CLOSE: (1), (3), (19), (31), (38), (40), (50), (93) are inconsistent by % 130.46/18.17 | | sub-proof #178. % 130.46/18.17 | | % 130.46/18.17 | End of split % 130.46/18.17 | % 130.46/18.17 End of proof % 130.46/18.17 % 130.46/18.17 Sub-proof #166 shows that the following formulas are inconsistent: % 130.46/18.17 ---------------------------------------------------------------- % 130.46/18.17 (1) all_9_8 = e4 % 130.46/18.17 (2) op(e2, e0) = all_8_96 % 130.46/18.17 (3) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.17 (4) op(e0, all_8_90) = e4 % 130.46/18.17 (5) all_6_5 = e1 % 130.46/18.17 (6) ~ (e4 = e0) % 130.46/18.17 (7) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.17 (8) all_9_20 = e2 % 130.46/18.17 (9) all_6_10 = e3 % 130.46/18.17 (10) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.17 (11) ~ (all_4_3 = all_4_4) % 130.46/18.17 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.17 (13) ~ (e4 = e2) % 130.46/18.17 (14) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.17 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.17 (16) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.17 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.17 (18) op(e0, e2) = all_8_75 % 130.46/18.17 (19) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.17 (20) ~ (all_4_3 = e3) % 130.46/18.17 (21) all_6_20 = all_4_4 % 130.46/18.17 (22) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.17 (23) all_9_11 = e2 % 130.46/18.17 (24) ~ (e3 = e0) % 130.46/18.17 (25) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.17 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.17 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.17 (26) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.17 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.17 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.17 (27) all_9_16 = e3 % 130.46/18.17 (28) all_6_22 = all_4_14 % 130.46/18.17 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.17 (30) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.17 = e0 % 130.46/18.17 (31) ~ (all_4_14 = e2) % 130.46/18.17 (32) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.17 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.17 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.17 (33) ~ (e2 = e0) % 130.46/18.17 (34) all_9_0 = e0 % 130.46/18.17 (35) ~ (all_4_22 = e2) % 130.46/18.17 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.17 (37) ~ (all_4_4 = e3) % 130.46/18.17 (38) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.17 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.17 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.17 (39) op(e2, e0) = e1 % 130.46/18.17 (40) op(e4, e0) = all_8_90 % 130.46/18.17 (41) op(e0, e3) = e1 % 130.46/18.17 (42) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.17 (43) all_9_6 = e3 % 130.46/18.17 (44) ~ (e1 = e0) % 130.46/18.17 (45) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.17 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.17 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.17 (46) ~ (e3 = e2) % 130.46/18.17 (47) all_9_14 = e2 % 130.46/18.17 (48) all_9_13 = e3 % 130.46/18.17 (49) all_9_12 = e4 % 130.46/18.17 (50) op(e0, e4) = all_4_4 % 130.46/18.17 (51) ~ (e4 = e1) % 130.46/18.17 (52) ~ (all_4_3 = e0) % 130.46/18.17 (53) all_9_15 = e1 % 130.46/18.17 (54) op(e0, e2) = e3 % 130.46/18.17 (55) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.17 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.17 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.17 (56) op(e3, e4) = e1 % 130.46/18.17 (57) op(e1, e4) = all_4_3 % 130.46/18.17 (58) all_4_11 = e0 % 130.46/18.17 (59) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.17 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.17 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.17 (60) all_9_24 = e4 % 130.46/18.17 (61) all_9_19 = e0 % 130.46/18.17 (62) ~ (op(e0, e4) = e4) % 130.46/18.17 (63) op(e4, e0) = e3 % 130.46/18.17 (64) ~ (all_4_4 = e0) % 130.46/18.17 (65) ~ (all_4_3 = e1) % 130.46/18.17 (66) ~ (all_8_75 = all_8_96) % 130.46/18.17 (67) all_6_2 = all_4_10 % 130.46/18.17 (68) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.17 (69) op(e2, e4) = e3 % 130.46/18.17 (70) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.17 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.17 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.17 (71) all_9_2 = e1 % 130.46/18.17 (72) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.17 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.17 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.17 (73) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.17 = e0 % 130.46/18.17 (74) ~ (all_4_4 = e1) % 130.46/18.17 (75) ~ (all_4_10 = e2) % 130.46/18.17 (76) all_4_0 = e0 % 130.46/18.17 (77) all_6_15 = all_4_3 % 130.46/18.17 (78) all_9_7 = e0 % 130.46/18.17 (79) op(e4, e4) = e0 % 130.46/18.17 % 130.46/18.17 Begin of proof % 130.46/18.17 | % 130.46/18.17 | BETA: splitting (14) gives: % 130.46/18.17 | % 130.46/18.17 | Case 1: % 130.46/18.17 | | % 130.46/18.17 | | (80) ~ (op(e2, e0) = e2) % 130.46/18.17 | | % 130.46/18.17 | | GROUND_INST: instantiating (36) with e3, all_8_75, e2, e0, simplifying with % 130.46/18.17 | | (18), (54) gives: % 130.46/18.17 | | (81) all_8_75 = e3 % 130.46/18.17 | | % 130.46/18.17 | | GROUND_INST: instantiating (36) with e1, e4, e3, e0, simplifying with (41) % 130.46/18.17 | | gives: % 130.46/18.17 | | (82) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.17 | | % 130.46/18.17 | | PRED_UNIFY: (4), (62) imply: % 130.46/18.17 | | (83) ~ (all_8_90 = e4) % 130.46/18.17 | | % 130.46/18.17 | | GROUND_INST: instantiating (36) with e1, all_8_96, e0, e2, simplifying with % 130.46/18.17 | | (2), (39) gives: % 130.46/18.17 | | (84) all_8_96 = e1 % 130.46/18.17 | | % 130.46/18.17 | | GROUND_INST: instantiating (36) with e3, all_8_90, e0, e4, simplifying with % 130.46/18.17 | | (40), (63) gives: % 130.46/18.17 | | (85) all_8_90 = e3 % 130.46/18.17 | | % 130.46/18.17 | | PRED_UNIFY: (2), (80) imply: % 130.46/18.17 | | (86) ~ (all_8_96 = e2) % 130.46/18.17 | | % 130.46/18.17 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.46/18.17 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 130.46/18.17 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.46/18.17 | | (37), (38), (42), (43), (44), (45), (46), (47), (48), (49), (50), % 130.46/18.17 | | (51), (52), (53), (55), (56), (57), (58), (59), (60), (61), (64), % 130.46/18.17 | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), % 130.46/18.17 | | (76), (77), (78), (79), (81), (82), (83), (84), (85), (86) are % 130.46/18.17 | | inconsistent by sub-proof #180. % 130.46/18.17 | | % 130.46/18.17 | Case 2: % 130.46/18.17 | | % 130.46/18.17 | | (87) op(e2, e0) = e2 % 130.46/18.17 | | % 130.46/18.17 | | REF_CLOSE: (14), (35), (87) are inconsistent by sub-proof #214. % 130.46/18.17 | | % 130.46/18.17 | End of split % 130.46/18.17 | % 130.46/18.17 End of proof % 130.46/18.17 % 130.46/18.17 Sub-proof #167 shows that the following formulas are inconsistent: % 130.46/18.17 ---------------------------------------------------------------- % 130.46/18.17 (1) all_9_8 = e4 % 130.46/18.17 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.17 (3) op(e0, all_8_90) = e4 % 130.46/18.17 (4) all_6_5 = e1 % 130.46/18.17 (5) ~ (e4 = e0) % 130.46/18.17 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.17 (7) all_9_20 = e2 % 130.46/18.17 (8) all_6_10 = e3 % 130.46/18.17 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.17 (10) ~ (all_4_3 = all_4_4) % 130.46/18.17 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.17 (12) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.17 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.17 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.17 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.17 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.17 (17) ~ (all_4_3 = e3) % 130.46/18.17 (18) all_6_20 = all_4_4 % 130.46/18.17 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.17 (20) all_9_11 = e2 % 130.46/18.17 (21) ~ (op(e0, e3) = e3) % 130.46/18.17 (22) ~ (e3 = e0) % 130.46/18.17 (23) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.17 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.17 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.17 (24) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.17 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.17 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.17 (25) all_9_16 = e3 % 130.46/18.17 (26) all_6_22 = all_4_14 % 130.46/18.17 (27) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.17 (28) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.17 = e0 % 130.46/18.17 (29) ~ (all_4_14 = e2) % 130.46/18.17 (30) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.17 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.17 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.17 (31) ~ (e2 = e0) % 130.46/18.17 (32) all_9_0 = e0 % 130.46/18.17 (33) ~ (all_4_22 = e2) % 130.46/18.17 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.17 (35) ~ (all_4_4 = e3) % 130.46/18.17 (36) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.17 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.17 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.17 (37) op(e0, e4) = all_8_51 % 130.46/18.17 (38) op(e4, e0) = all_8_90 % 130.46/18.17 (39) op(e0, e3) = e1 % 130.46/18.17 (40) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.17 (41) all_9_6 = e3 % 130.46/18.17 (42) ~ (e1 = e0) % 130.46/18.17 (43) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.17 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.17 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.17 (44) all_9_14 = e2 % 130.46/18.17 (45) all_9_13 = e3 % 130.46/18.17 (46) op(e0, e3) = all_8_63 % 130.46/18.17 (47) all_9_12 = e4 % 130.46/18.17 (48) op(e0, e4) = all_4_4 % 130.46/18.17 (49) ~ (e4 = e1) % 130.46/18.17 (50) ~ (all_4_3 = e0) % 130.46/18.17 (51) all_9_15 = e1 % 130.46/18.17 (52) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.17 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.17 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.17 (53) op(e3, e4) = e1 % 130.46/18.17 (54) op(e1, e4) = all_4_3 % 130.46/18.17 (55) all_4_11 = e0 % 130.46/18.17 (56) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.17 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.17 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.17 (57) all_9_24 = e4 % 130.46/18.17 (58) all_9_19 = e0 % 130.46/18.17 (59) ~ (op(e0, e4) = e4) % 130.46/18.17 (60) op(e4, e0) = e3 % 130.46/18.17 (61) ~ (all_4_4 = e0) % 130.46/18.17 (62) ~ (all_4_3 = e1) % 130.46/18.17 (63) op(e0, e4) = e2 % 130.46/18.17 (64) all_6_2 = all_4_10 % 130.46/18.17 (65) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.17 (66) op(e2, e4) = e3 % 130.46/18.17 (67) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.17 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.17 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.17 (68) all_9_2 = e1 % 130.46/18.17 (69) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.17 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.17 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.17 (70) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.17 = e0 % 130.46/18.17 (71) ~ (all_4_4 = e1) % 130.46/18.17 (72) ~ (all_4_10 = e2) % 130.46/18.17 (73) all_4_0 = e0 % 130.46/18.17 (74) ~ (all_8_51 = all_8_90) % 130.46/18.17 (75) ~ (e2 = e1) % 130.46/18.17 (76) all_6_15 = all_4_3 % 130.46/18.17 (77) all_9_7 = e0 % 130.46/18.17 (78) op(e4, e4) = e0 % 130.46/18.17 % 130.46/18.17 Begin of proof % 130.46/18.17 | % 130.46/18.17 | GROUND_INST: instantiating (34) with e1, all_8_63, e3, e0, simplifying with % 130.46/18.17 | (39), (46) gives: % 130.46/18.17 | (79) all_8_63 = e1 % 130.46/18.17 | % 130.46/18.17 | PRED_UNIFY: (21), (46) imply: % 130.46/18.17 | (80) ~ (all_8_63 = e3) % 130.46/18.17 | % 130.46/18.17 | GROUND_INST: instantiating (34) with e2, all_8_51, e4, e0, simplifying with % 130.46/18.17 | (37), (63) gives: % 130.46/18.18 | (81) all_8_51 = e2 % 130.46/18.18 | % 130.46/18.18 | PRED_UNIFY: (37), (59) imply: % 130.46/18.18 | (82) ~ (all_8_51 = e4) % 130.46/18.18 | % 130.46/18.18 | GROUND_INST: instantiating (34) with e1, e4, e3, e0, simplifying with (39) % 130.46/18.18 | gives: % 130.46/18.18 | (83) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.18 | % 130.46/18.18 | PRED_UNIFY: (3), (59) imply: % 130.46/18.18 | (84) ~ (all_8_90 = e4) % 130.46/18.18 | % 130.46/18.18 | GROUND_INST: instantiating (34) with e3, all_8_90, e0, e4, simplifying with % 130.46/18.18 | (38), (60) gives: % 130.46/18.18 | (85) all_8_90 = e3 % 130.46/18.18 | % 130.46/18.18 | REDUCE: (74), (81), (85) imply: % 130.46/18.18 | (86) ~ (e3 = e2) % 130.46/18.18 | % 130.46/18.18 | SIMP: (86) implies: % 130.46/18.18 | (87) ~ (e3 = e2) % 130.46/18.18 | % 130.46/18.18 | REDUCE: (81), (82) imply: % 130.46/18.18 | (88) ~ (e4 = e2) % 130.46/18.18 | % 130.46/18.18 | SIMP: (88) implies: % 130.46/18.18 | (89) ~ (e4 = e2) % 130.46/18.18 | % 130.46/18.18 | REDUCE: (79), (80) imply: % 130.46/18.18 | (90) ~ (e3 = e1) % 130.46/18.18 | % 130.46/18.18 | SIMP: (90) implies: % 130.46/18.18 | (91) ~ (e3 = e1) % 130.46/18.18 | % 130.46/18.18 | REDUCE: (84), (85) imply: % 130.46/18.18 | (92) ~ (e4 = e3) % 130.46/18.18 | % 130.46/18.18 | SIMP: (92) implies: % 130.46/18.18 | (93) ~ (e4 = e3) % 130.46/18.18 | % 130.46/18.18 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.18 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 130.46/18.18 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.46/18.18 | (36), (40), (41), (42), (43), (44), (45), (47), (48), (49), (50), % 130.46/18.18 | (51), (52), (53), (54), (55), (56), (57), (58), (61), (62), (64), % 130.46/18.18 | (65), (66), (67), (68), (69), (70), (71), (72), (73), (75), (76), % 130.46/18.18 | (77), (78), (83), (85), (87), (89), (91), (93) are inconsistent by % 130.46/18.18 | sub-proof #194. % 130.46/18.18 | % 130.46/18.18 End of proof % 130.46/18.18 % 130.46/18.18 Sub-proof #168 shows that the following formulas are inconsistent: % 130.46/18.18 ---------------------------------------------------------------- % 130.46/18.18 (1) all_9_8 = e4 % 130.46/18.18 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.18 (3) op(e0, all_8_90) = e4 % 130.46/18.18 (4) all_6_5 = e1 % 130.46/18.18 (5) ~ (e4 = e0) % 130.46/18.18 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.18 (7) all_9_20 = e2 % 130.46/18.18 (8) all_6_10 = e3 % 130.46/18.18 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.18 (10) ~ (all_4_3 = all_4_4) % 130.46/18.18 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.18 (12) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.18 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.18 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.18 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.18 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.18 (17) ~ (all_4_3 = e3) % 130.46/18.18 (18) all_6_20 = all_4_4 % 130.46/18.18 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.18 (20) all_9_11 = e2 % 130.46/18.18 (21) ~ (e3 = e0) % 130.46/18.18 (22) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.18 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.18 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.18 (23) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.18 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.18 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.18 (24) all_9_16 = e3 % 130.46/18.18 (25) all_6_22 = all_4_14 % 130.46/18.18 (26) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.18 (27) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.18 = e0 % 130.46/18.18 (28) ~ (all_4_14 = e2) % 130.46/18.18 (29) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.18 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.18 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.18 (30) ~ (e2 = e0) % 130.46/18.18 (31) all_9_0 = e0 % 130.46/18.18 (32) ~ (all_4_22 = e2) % 130.46/18.18 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.18 (34) ~ (all_4_4 = e3) % 130.46/18.18 (35) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.18 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.18 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.18 (36) op(e0, e4) = all_8_51 % 130.46/18.18 (37) op(e4, e0) = all_8_90 % 130.46/18.18 (38) op(e0, e3) = e1 % 130.46/18.18 (39) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.18 (40) all_9_6 = e3 % 130.46/18.18 (41) ~ (e1 = e0) % 130.46/18.18 (42) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.18 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.18 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.18 (43) all_9_14 = e2 % 130.46/18.18 (44) all_9_13 = e3 % 130.46/18.18 (45) all_9_12 = e4 % 130.46/18.18 (46) op(e0, e4) = all_4_4 % 130.46/18.18 (47) ~ (e4 = e1) % 130.46/18.18 (48) ~ (all_4_3 = e0) % 130.46/18.18 (49) all_9_15 = e1 % 130.46/18.18 (50) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.18 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.18 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.18 (51) ~ (e3 = e1) % 130.46/18.18 (52) op(e3, e4) = e1 % 130.46/18.18 (53) op(e1, e4) = all_4_3 % 130.46/18.18 (54) all_4_11 = e0 % 130.46/18.18 (55) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.18 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.18 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.18 (56) all_9_24 = e4 % 130.46/18.18 (57) all_9_19 = e0 % 130.46/18.18 (58) ~ (op(e0, e4) = e4) % 130.46/18.18 (59) op(e4, e0) = e3 % 130.46/18.18 (60) ~ (all_4_4 = e0) % 130.46/18.18 (61) ~ (all_4_3 = e1) % 130.46/18.18 (62) op(e0, e4) = e2 % 130.46/18.18 (63) all_6_2 = all_4_10 % 130.46/18.18 (64) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.18 (65) op(e2, e4) = e3 % 130.46/18.18 (66) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.18 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.18 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.18 (67) all_9_2 = e1 % 130.46/18.18 (68) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.18 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.18 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.18 (69) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.18 = e0 % 130.46/18.18 (70) ~ (all_4_4 = e1) % 130.46/18.18 (71) ~ (all_4_10 = e2) % 130.46/18.18 (72) all_4_0 = e0 % 130.46/18.18 (73) ~ (all_8_51 = all_8_90) % 130.46/18.18 (74) ~ (e2 = e1) % 130.46/18.18 (75) all_6_15 = all_4_3 % 130.46/18.18 (76) all_9_7 = e0 % 130.46/18.18 (77) op(e4, e4) = e0 % 130.46/18.18 % 130.46/18.18 Begin of proof % 130.46/18.18 | % 130.46/18.18 | GROUND_INST: instantiating (33) with e2, all_8_51, e4, e0, simplifying with % 130.46/18.18 | (36), (62) gives: % 130.46/18.18 | (78) all_8_51 = e2 % 130.46/18.18 | % 130.46/18.18 | PRED_UNIFY: (36), (58) imply: % 130.46/18.18 | (79) ~ (all_8_51 = e4) % 130.46/18.18 | % 130.46/18.18 | GROUND_INST: instantiating (33) with e1, e4, e3, e0, simplifying with (38) % 130.46/18.18 | gives: % 130.46/18.18 | (80) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.18 | % 130.46/18.18 | PRED_UNIFY: (3), (58) imply: % 130.46/18.18 | (81) ~ (all_8_90 = e4) % 130.46/18.18 | % 130.46/18.18 | GROUND_INST: instantiating (33) with e3, all_8_90, e0, e4, simplifying with % 130.46/18.18 | (37), (59) gives: % 130.46/18.18 | (82) all_8_90 = e3 % 130.46/18.18 | % 130.46/18.18 | REDUCE: (73), (78), (82) imply: % 130.46/18.18 | (83) ~ (e3 = e2) % 130.46/18.18 | % 130.46/18.18 | SIMP: (83) implies: % 130.46/18.18 | (84) ~ (e3 = e2) % 130.46/18.18 | % 130.46/18.18 | REDUCE: (78), (79) imply: % 130.46/18.18 | (85) ~ (e4 = e2) % 130.46/18.18 | % 130.46/18.18 | SIMP: (85) implies: % 130.46/18.18 | (86) ~ (e4 = e2) % 130.46/18.18 | % 130.46/18.18 | REDUCE: (81), (82) imply: % 130.46/18.18 | (87) ~ (e4 = e3) % 130.46/18.18 | % 130.46/18.18 | SIMP: (87) implies: % 130.46/18.18 | (88) ~ (e4 = e3) % 130.46/18.18 | % 130.46/18.18 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.18 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.18 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.46/18.18 | (35), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 130.46/18.18 | (49), (50), (51), (52), (53), (54), (55), (56), (57), (60), (61), % 130.46/18.18 | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (74), % 130.46/18.18 | (75), (76), (77), (80), (82), (84), (86), (88) are inconsistent by % 130.46/18.18 | sub-proof #194. % 130.46/18.18 | % 130.46/18.18 End of proof % 130.46/18.18 % 130.46/18.18 Sub-proof #169 shows that the following formulas are inconsistent: % 130.46/18.18 ---------------------------------------------------------------- % 130.46/18.18 (1) all_9_8 = e4 % 130.46/18.18 (2) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.18 (3) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.18 (4) op(e0, all_8_90) = e4 % 130.46/18.18 (5) all_6_5 = e1 % 130.46/18.18 (6) ~ (e4 = e0) % 130.46/18.18 (7) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.18 (8) all_9_20 = e2 % 130.46/18.18 (9) all_6_10 = e3 % 130.46/18.18 (10) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.18 (11) ~ (all_4_3 = all_4_4) % 130.46/18.18 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.18 (13) ~ (e4 = e2) % 130.46/18.18 (14) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.18 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.18 (16) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.18 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.18 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.18 (19) ~ (all_4_3 = e3) % 130.46/18.18 (20) all_6_20 = all_4_4 % 130.46/18.18 (21) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.18 (22) all_9_11 = e2 % 130.46/18.18 (23) ~ (e3 = e0) % 130.46/18.18 (24) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.18 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.18 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.18 (25) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.18 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.18 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.18 (26) all_9_16 = e3 % 130.46/18.18 (27) all_6_22 = all_4_14 % 130.46/18.18 (28) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.18 (29) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.18 = e0 % 130.46/18.18 (30) ~ (all_4_14 = e2) % 130.46/18.18 (31) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.18 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.18 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.18 (32) op(e4, e2) = e1 % 130.46/18.18 (33) ~ (e2 = e0) % 130.46/18.18 (34) all_9_0 = e0 % 130.46/18.18 (35) ~ (all_4_22 = e2) % 130.46/18.18 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.18 (37) ~ (all_4_4 = e3) % 130.46/18.18 (38) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.18 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.18 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.18 (39) op(e4, e0) = all_8_90 % 130.46/18.18 (40) op(e0, e3) = e1 % 130.46/18.18 (41) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.18 (42) all_9_6 = e3 % 130.46/18.18 (43) ~ (e1 = e0) % 130.46/18.18 (44) ~ (all_8_66 = e3) % 130.46/18.18 (45) op(e4, e2) = all_8_66 % 130.46/18.18 (46) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.18 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.18 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.18 (47) ~ (e3 = e2) % 130.46/18.18 (48) all_9_14 = e2 % 130.46/18.18 (49) all_9_13 = e3 % 130.46/18.18 (50) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.18 (51) all_9_12 = e4 % 130.46/18.18 (52) op(e0, e4) = all_4_4 % 130.46/18.18 (53) ~ (all_4_3 = e0) % 130.46/18.18 (54) all_9_15 = e1 % 130.46/18.18 (55) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.18 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.18 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.18 (56) op(e3, e4) = e1 % 130.46/18.18 (57) op(e1, e4) = all_4_3 % 130.46/18.18 (58) all_4_11 = e0 % 130.46/18.18 (59) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.18 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.18 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.18 (60) all_9_24 = e4 % 130.46/18.18 (61) op(all_8_66, e2) = e4 % 130.46/18.18 (62) all_9_19 = e0 % 130.46/18.18 (63) ~ (op(e0, e4) = e4) % 130.46/18.18 (64) op(e4, e0) = e3 % 130.46/18.18 (65) ~ (all_4_4 = e0) % 130.46/18.18 (66) ~ (all_4_3 = e1) % 130.46/18.18 (67) all_6_2 = all_4_10 % 130.46/18.18 (68) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.18 (69) op(e2, e4) = e3 % 130.46/18.18 (70) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.18 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.18 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.18 (71) ~ (all_4_10 = e4) % 130.46/18.18 (72) all_9_2 = e1 % 130.46/18.18 (73) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.18 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.18 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.18 (74) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.18 = e0 % 130.46/18.18 (75) ~ (all_4_4 = e1) % 130.46/18.18 (76) ~ (all_4_10 = e2) % 130.46/18.18 (77) all_4_0 = e0 % 130.46/18.18 (78) all_6_15 = all_4_3 % 130.46/18.18 (79) all_9_7 = e0 % 130.46/18.18 (80) op(e4, e4) = e0 % 130.46/18.18 % 130.46/18.18 Begin of proof % 130.46/18.18 | % 130.46/18.18 | BETA: splitting (50) gives: % 130.46/18.18 | % 130.46/18.18 | Case 1: % 130.46/18.18 | | % 130.46/18.18 | | (81) ~ (op(e4, e2) = e4) % 130.46/18.18 | | % 130.46/18.18 | | BETA: splitting (2) gives: % 130.46/18.18 | | % 130.46/18.18 | | Case 1: % 130.46/18.18 | | | % 130.46/18.18 | | | (82) ~ (op(e4, e2) = e2) % 130.46/18.18 | | | % 130.46/18.18 | | | GROUND_INST: instantiating (36) with e1, e4, e3, e0, simplifying with (40) % 130.46/18.18 | | | gives: % 130.46/18.18 | | | (83) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.18 | | | % 130.46/18.18 | | | PRED_UNIFY: (4), (63) imply: % 130.46/18.18 | | | (84) ~ (all_8_90 = e4) % 130.46/18.18 | | | % 130.46/18.18 | | | GROUND_INST: instantiating (36) with e3, all_8_90, e0, e4, simplifying % 130.46/18.18 | | | with (39), (64) gives: % 130.46/18.18 | | | (85) all_8_90 = e3 % 130.46/18.18 | | | % 130.46/18.18 | | | GROUND_INST: instantiating (36) with e1, all_8_66, e2, e4, simplifying % 130.46/18.18 | | | with (32), (45) gives: % 130.46/18.18 | | | (86) all_8_66 = e1 % 130.46/18.18 | | | % 130.46/18.18 | | | PRED_UNIFY: (45), (82) imply: % 130.46/18.18 | | | (87) ~ (all_8_66 = e2) % 130.46/18.18 | | | % 130.46/18.18 | | | PRED_UNIFY: (61), (81) imply: % 130.46/18.18 | | | (88) ~ (all_8_66 = e4) % 130.46/18.18 | | | % 130.46/18.18 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.46/18.18 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.18 | | | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), % 130.46/18.18 | | | (35), (36), (37), (38), (41), (42), (43), (44), (46), (47), % 130.46/18.18 | | | (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), % 130.46/18.18 | | | (59), (60), (62), (65), (66), (67), (68), (69), (70), (72), % 130.46/18.18 | | | (73), (74), (75), (76), (77), (78), (79), (80), (83), (84), % 130.46/18.18 | | | (85), (86), (87), (88) are inconsistent by sub-proof #190. % 130.46/18.18 | | | % 130.46/18.18 | | Case 2: % 130.46/18.18 | | | % 130.46/18.18 | | | (89) op(e4, e2) = e2 % 130.46/18.18 | | | % 130.46/18.18 | | | REF_CLOSE: (41), (67), (76), (89) are inconsistent by sub-proof #261. % 130.46/18.18 | | | % 130.46/18.18 | | End of split % 130.46/18.18 | | % 130.46/18.18 | Case 2: % 130.46/18.18 | | % 130.46/18.18 | | (90) op(e4, e2) = e4 % 130.46/18.18 | | % 130.46/18.18 | | REF_CLOSE: (50), (67), (71), (90) are inconsistent by sub-proof #298. % 130.46/18.18 | | % 130.46/18.18 | End of split % 130.46/18.18 | % 130.46/18.18 End of proof % 130.46/18.18 % 130.46/18.18 Sub-proof #170 shows that the following formulas are inconsistent: % 130.46/18.18 ---------------------------------------------------------------- % 130.46/18.18 (1) op(e1, e3) = e3 % 130.46/18.18 (2) all_9_8 = e4 % 130.46/18.18 (3) all_4_10 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.18 (4) op(e4, e1) = e4 % 130.46/18.18 (5) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.18 (6) all_6_9 = all_4_21 % 130.46/18.18 (7) op(e0, all_8_90) = e4 % 130.46/18.18 (8) all_6_5 = e1 % 130.46/18.18 (9) ~ (e4 = e0) % 130.46/18.18 (10) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.18 (11) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.18 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.18 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.18 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.46/18.18 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.18 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.18 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.46/18.18 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.46/18.18 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.18 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.18 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.46/18.18 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.46/18.18 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.46/18.18 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.18 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.18 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.46/18.18 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.46/18.18 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.18 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.46/18.18 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.46/18.18 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.46/18.18 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.46/18.18 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.46/18.18 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.18 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.18 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.18 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.18 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.18 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.18 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.18 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.18 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.46/18.18 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.46/18.18 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.46/18.18 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.18 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.46/18.18 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.46/18.18 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.46/18.18 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.46/18.18 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.46/18.18 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.46/18.18 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.46/18.18 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.46/18.18 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.18 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.46/18.18 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.46/18.18 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.18 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.46/18.18 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.46/18.18 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.18 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.18 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.18 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.18 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.46/18.18 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.46/18.18 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.18 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.18 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.18 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.46/18.18 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.18 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.18 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.18 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.18 $i(all_8_87) & $i(all_8_99)) % 130.46/18.18 (12) all_9_20 = e2 % 130.46/18.18 (13) all_6_10 = e3 % 130.46/18.18 (14) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.18 (15) ~ (all_4_3 = all_4_4) % 130.46/18.18 (16) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.46/18.18 (17) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.18 (18) ~ (e4 = e2) % 130.46/18.18 (19) all_4_7 = e0 % 130.46/18.18 (20) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.18 (21) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.18 (22) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.18 (23) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.46/18.18 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.46/18.18 (all_9_16 = e2 & op(e4, e0) = e2) % 130.46/18.18 (24) e4 = e1 | ~ (op(e3, e4) = e4) % 130.46/18.18 (25) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.19 (26) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.19 (27) all_8_45 = e3 % 130.46/18.19 (28) op(e4, e3) = e2 % 130.46/18.19 (29) op(e2, e1) = e2 % 130.46/18.19 (30) ~ (all_4_21 = e3) % 130.46/18.19 (31) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.19 (32) ~ (all_4_3 = e3) % 130.46/18.19 (33) all_6_20 = all_4_4 % 130.46/18.19 (34) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.19 (35) all_9_11 = e2 % 130.46/18.19 (36) ~ (op(e0, e3) = e3) % 130.46/18.19 (37) ~ (e3 = e0) % 130.46/18.19 (38) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.19 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.19 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.19 (39) op(e3, e2) = e0 % 130.46/18.19 (40) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.19 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.19 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.19 (41) all_9_16 = e3 % 130.46/18.19 (42) all_6_22 = all_4_14 % 130.46/18.19 (43) all_9_17 = e2 % 130.46/18.19 (44) op(e4, e3) = all_8_54 % 130.46/18.19 (45) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.19 (46) op(e1, e0) = e0 % 130.46/18.19 (47) op(e1, e4) = e4 % 130.46/18.19 (48) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.19 = e0 % 130.46/18.19 (49) ~ (all_4_14 = e2) % 130.46/18.19 (50) ~ (op(e4, e3) = e4) % 130.46/18.19 (51) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.19 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.19 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.19 (52) op(e4, e2) = e1 % 130.46/18.19 (53) ~ (e2 = e0) % 130.46/18.19 (54) all_9_0 = e0 % 130.46/18.19 (55) ~ (all_4_22 = e2) % 130.46/18.19 (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.19 (57) ~ (all_4_4 = e3) % 130.46/18.19 (58) op(e1, e2) = e2 % 130.46/18.19 (59) ~ (op(e4, e3) = e3) % 130.46/18.19 (60) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.19 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.19 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.19 (61) op(e2, e0) = e1 % 130.46/18.19 (62) ~ (all_4_22 = e3) % 130.46/18.19 (63) op(e4, e0) = all_8_90 % 130.46/18.19 (64) op(e0, e3) = e1 % 130.46/18.19 (65) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.19 (66) all_9_6 = e3 % 130.46/18.19 (67) ~ (e1 = e0) % 130.46/18.19 (68) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.46/18.19 (69) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.19 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.19 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.19 (70) op(e3, e1) = e3 % 130.46/18.19 (71) op(e0, e1) = e0 % 130.46/18.19 (72) ~ (e3 = e2) % 130.46/18.19 (73) all_9_14 = e2 % 130.46/18.19 (74) all_9_13 = e3 % 130.46/18.19 (75) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.19 (76) all_9_12 = e4 % 130.46/18.19 (77) op(e0, e4) = all_4_4 % 130.46/18.19 (78) ~ (e4 = e1) % 130.46/18.19 (79) ~ (all_4_3 = e0) % 130.46/18.19 (80) all_9_15 = e1 % 130.46/18.19 (81) op(e0, e2) = e3 % 130.46/18.19 (82) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.19 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.19 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.19 (83) ~ (e3 = e1) % 130.46/18.19 (84) op(e3, e4) = e1 % 130.46/18.19 (85) all_9_9 = e4 % 130.46/18.19 (86) op(e1, e4) = all_4_3 % 130.46/18.19 (87) all_4_11 = e0 % 130.46/18.19 (88) op(e3, e0) = e2 % 130.46/18.19 (89) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.19 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.19 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.19 (90) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.46/18.19 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.46/18.19 (all_9_16 = e3 & op(e4, e0) = e3) % 130.46/18.19 (91) all_9_24 = e4 % 130.46/18.19 (92) op(e2, e0) = all_4_22 % 130.46/18.19 (93) all_9_19 = e0 % 130.46/18.19 (94) ~ (op(e0, e4) = e4) % 130.46/18.19 (95) ~ (e4 = e3) % 130.46/18.19 (96) op(e4, e0) = e3 % 130.46/18.19 (97) ~ (all_4_4 = e0) % 130.46/18.19 (98) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.46/18.19 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.46/18.19 (all_9_16 = e1 & op(e4, e0) = e1) % 130.46/18.19 (99) op(e2, e3) = e0 % 130.46/18.19 (100) ~ (all_4_3 = e1) % 130.46/18.19 (101) op(e0, e4) = e2 % 130.46/18.19 (102) all_6_2 = all_4_10 % 130.46/18.19 (103) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.19 (104) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.19 (105) op(e2, e4) = e3 % 130.46/18.19 (106) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.19 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.19 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.19 (107) ~ (all_4_10 = e4) % 130.46/18.19 (108) ~ (op(e2, e3) = e3) % 130.46/18.19 (109) all_9_2 = e1 % 130.46/18.19 (110) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.19 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.19 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.19 (111) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.46/18.19 all_6_15 = e0 % 130.46/18.19 (112) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.46/18.19 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.46/18.19 (all_9_24 = e3 & op(e0, e0) = e3) % 130.46/18.19 (113) ~ (all_4_4 = e1) % 130.46/18.19 (114) ~ (all_4_10 = e2) % 130.46/18.19 (115) all_4_0 = e0 % 130.46/18.19 (116) ~ (e2 = e1) % 130.46/18.19 (117) all_6_15 = all_4_3 % 130.46/18.19 (118) all_9_7 = e0 % 130.46/18.19 (119) op(e4, e4) = e0 % 130.46/18.19 % 130.46/18.19 Begin of proof % 130.46/18.19 | % 130.46/18.19 | BETA: splitting (11) gives: % 130.46/18.19 | % 130.46/18.19 | Case 1: % 130.46/18.19 | | % 130.46/18.19 | | (120) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.19 | | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.19 | | $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 % 130.46/18.19 | | = all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = % 130.46/18.19 | | e4 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) % 130.46/18.19 | | & $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = % 130.46/18.19 | | e1) & ~ (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & % 130.46/18.19 | | op(all_8_78, e1) = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = % 130.46/18.19 | | all_8_48 & $i(all_8_4) & $i(all_8_48) & $i(all_8_78)) | (all_8_7 % 130.46/18.19 | | = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & % 130.46/18.19 | | op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = % 130.46/18.19 | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & $i(all_8_51) & % 130.46/18.19 | | $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 % 130.46/18.19 | | = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.19 | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.46/18.19 | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ % 130.46/18.19 | | (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = % 130.46/18.19 | | all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & op(e2, % 130.46/18.19 | | e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 130.46/18.19 | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.46/18.19 | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) % 130.46/18.19 | | = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) % 130.46/18.19 | | & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.46/18.19 | | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 130.46/18.19 | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.46/18.19 | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.19 | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.19 | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 130.46/18.19 | | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 130.46/18.19 | | & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ % 130.46/18.19 | | (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) % 130.46/18.19 | | = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.19 | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.46/18.19 | | % 130.46/18.19 | | BETA: splitting (120) gives: % 130.46/18.19 | | % 130.46/18.19 | | Case 1: % 130.46/18.19 | | | % 130.46/18.19 | | | (121) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) % 130.46/18.19 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 130.46/18.19 | | | & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ % 130.46/18.19 | | | (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 & % 130.46/18.19 | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.46/18.19 | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | % 130.46/18.19 | | | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.46/18.19 | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, e1) % 130.46/18.19 | | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 130.46/18.19 | | | & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.19 | | | (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & % 130.46/18.19 | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.19 | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.46/18.19 | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) % 130.46/18.19 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) % 130.46/18.19 | | | & $i(all_8_54)) % 130.46/18.19 | | | % 130.46/18.19 | | | BETA: splitting (121) gives: % 130.46/18.19 | | | % 130.46/18.19 | | | Case 1: % 130.46/18.19 | | | | % 130.46/18.19 | | | | (122) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.46/18.19 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.46/18.19 | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = % 130.46/18.19 | | | | e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 % 130.46/18.19 | | | | & op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) % 130.46/18.19 | | | | = all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) % 130.46/18.19 | | | | % 130.46/18.19 | | | | BETA: splitting (122) gives: % 130.46/18.19 | | | | % 130.46/18.19 | | | | Case 1: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | (123) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.46/18.19 | | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.46/18.19 | | | | | $i(all_8_42) & $i(all_8_54) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | ALPHA: (123) implies: % 130.46/18.19 | | | | | (124) ~ (all_8_42 = all_8_54) % 130.46/18.19 | | | | | (125) op(e3, e4) = all_8_42 % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.19 | | | | | (17), (18), (20), (21), (22), (23), (24), (25), (26), (28), % 130.46/18.19 | | | | | (30), (31), (32), (33), (34), (35), (37), (38), (40), (41), % 130.46/18.19 | | | | | (42), (43), (44), (45), (48), (49), (50), (51), (53), (54), % 130.46/18.19 | | | | | (55), (56), (57), (59), (60), (62), (63), (64), (65), (66), % 130.46/18.19 | | | | | (67), (68), (69), (72), (73), (74), (76), (77), (78), (79), % 130.46/18.19 | | | | | (80), (82), (83), (84), (85), (86), (87), (89), (90), (91), % 130.46/18.19 | | | | | (92), (93), (94), (95), (96), (97), (98), (100), (102), % 130.46/18.19 | | | | | (103), (105), (106), (109), (110), (111), (112), (113), % 130.46/18.19 | | | | | (114), (115), (116), (117), (118), (119), (124), (125) are % 130.46/18.19 | | | | | inconsistent by sub-proof #191. % 130.46/18.19 | | | | | % 130.46/18.19 | | | | Case 2: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | (126) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & % 130.46/18.19 | | | | | op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & op(e4, % 130.46/18.19 | | | | | e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.19 | | | | | $i(all_8_45) & $i(all_8_66) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | ALPHA: (126) implies: % 130.46/18.19 | | | | | (127) ~ (all_8_45 = all_8_66) % 130.46/18.19 | | | | | (128) op(e2, e4) = all_8_45 % 130.46/18.19 | | | | | (129) op(e4, e2) = all_8_66 % 130.46/18.19 | | | | | (130) op(all_8_66, e2) = e4 % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | REDUCE: (27), (127) imply: % 130.46/18.19 | | | | | (131) ~ (all_8_66 = e3) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | SIMP: (131) implies: % 130.46/18.19 | | | | | (132) ~ (all_8_66 = e3) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | BETA: splitting (75) gives: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | Case 1: % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | (133) ~ (op(e4, e2) = e4) % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | BETA: splitting (3) gives: % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | Case 1: % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | (134) ~ (op(e4, e2) = e2) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | GROUND_INST: instantiating (56) with e1, e4, e3, e0, simplifying % 130.46/18.19 | | | | | | | with (64) gives: % 130.46/18.19 | | | | | | | (135) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | PRED_UNIFY: (7), (94) imply: % 130.46/18.19 | | | | | | | (136) ~ (all_8_90 = e4) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | GROUND_INST: instantiating (56) with e3, all_8_90, e0, e4, % 130.46/18.19 | | | | | | | simplifying with (63), (96) gives: % 130.46/18.19 | | | | | | | (137) all_8_90 = e3 % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | GROUND_INST: instantiating (56) with e1, all_8_66, e2, e4, % 130.46/18.19 | | | | | | | simplifying with (52), (129) gives: % 130.46/18.19 | | | | | | | (138) all_8_66 = e1 % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | GROUND_INST: instantiating (56) with e2, all_8_54, e3, e4, % 130.46/18.19 | | | | | | | simplifying with (28), (44) gives: % 130.46/18.19 | | | | | | | (139) all_8_54 = e2 % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | PRED_UNIFY: (44), (50) imply: % 130.46/18.19 | | | | | | | (140) ~ (all_8_54 = e4) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | PRED_UNIFY: (44), (59) imply: % 130.46/18.19 | | | | | | | (141) ~ (all_8_54 = e3) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | PRED_UNIFY: (129), (134) imply: % 130.46/18.19 | | | | | | | (142) ~ (all_8_66 = e2) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | PRED_UNIFY: (130), (133) imply: % 130.46/18.19 | | | | | | | (143) ~ (all_8_66 = e4) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | REDUCE: (139), (140) imply: % 130.46/18.19 | | | | | | | (144) ~ (e4 = e2) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | REDUCE: (139), (141) imply: % 130.46/18.19 | | | | | | | (145) ~ (e3 = e2) % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.19 | | | | | | | (17), (18), (21), (22), (25), (26), (31), (32), (33), % 130.46/18.19 | | | | | | | (34), (35), (37), (38), (40), (41), (42), (45), (48), % 130.46/18.19 | | | | | | | (49), (51), (53), (54), (55), (56), (57), (60), (65), % 130.46/18.19 | | | | | | | (66), (67), (69), (72), (73), (74), (76), (77), (79), % 130.46/18.19 | | | | | | | (80), (82), (84), (86), (87), (89), (91), (93), (97), % 130.46/18.19 | | | | | | | (100), (102), (103), (105), (106), (109), (110), (111), % 130.46/18.19 | | | | | | | (113), (114), (115), (117), (118), (119), (132), (135), % 130.46/18.19 | | | | | | | (136), (137), (138), (142), (143) are inconsistent by % 130.46/18.19 | | | | | | | sub-proof #190. % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | Case 2: % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | (146) op(e4, e2) = e2 % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | | REF_CLOSE: (65), (102), (114), (146) are inconsistent by sub-proof % 130.46/18.19 | | | | | | | #261. % 130.46/18.19 | | | | | | | % 130.46/18.19 | | | | | | End of split % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | Case 2: % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | (147) op(e4, e2) = e4 % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | REF_CLOSE: (75), (102), (107), (147) are inconsistent by sub-proof % 130.46/18.19 | | | | | | #298. % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | End of split % 130.46/18.19 | | | | | % 130.46/18.19 | | | | End of split % 130.46/18.19 | | | | % 130.46/18.19 | | | Case 2: % 130.46/18.19 | | | | % 130.46/18.19 | | | | (148) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.46/18.19 | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.46/18.19 | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.19 | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = % 130.46/18.19 | | | | e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 % 130.46/18.19 | | | | & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) % 130.46/18.19 | | | | = all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.46/18.19 | | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.46/18.19 | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 130.46/18.19 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.46/18.19 | | | | $i(all_8_42) & $i(all_8_54)) % 130.46/18.19 | | | | % 130.46/18.19 | | | | BETA: splitting (148) gives: % 130.46/18.19 | | | | % 130.46/18.19 | | | | Case 1: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | (149) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.46/18.19 | | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.46/18.19 | | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.19 | | | | | $i(all_8_48) & $i(all_8_78) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | ALPHA: (149) implies: % 130.46/18.19 | | | | | (150) ~ (all_8_48 = all_8_78) % 130.46/18.19 | | | | | (151) op(e1, e4) = all_8_48 % 130.46/18.19 | | | | | (152) op(e4, e1) = all_8_78 % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | REF_CLOSE: (4), (47), (56), (150), (151), (152) are inconsistent by % 130.46/18.19 | | | | | sub-proof #189. % 130.46/18.19 | | | | | % 130.46/18.19 | | | | Case 2: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | (153) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) % 130.46/18.19 | | | | | & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & % 130.46/18.19 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) % 130.46/18.19 | | | | | & $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ % 130.46/18.19 | | | | | (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, % 130.46/18.19 | | | | | e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) = % 130.46/18.19 | | | | | all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.46/18.19 | | | | | $i(all_8_42) & $i(all_8_54)) % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | BETA: splitting (153) gives: % 130.46/18.19 | | | | | % 130.46/18.19 | | | | | Case 1: % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | (154) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = all_8_90) % 130.46/18.19 | | | | | | & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) = e4 & % 130.46/18.19 | | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) % 130.46/18.19 | | | | | | & $i(all_8_51) & $i(all_8_90) % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.19 | | | | | | (17), (21), (22), (25), (26), (28), (31), (32), (33), % 130.46/18.19 | | | | | | (34), (35), (37), (38), (40), (41), (42), (44), (45), % 130.46/18.19 | | | | | | (48), (49), (50), (51), (53), (54), (55), (56), (57), % 130.46/18.19 | | | | | | (59), (60), (63), (64), (65), (66), (67), (69), (73), % 130.46/18.19 | | | | | | (74), (76), (77), (78), (79), (80), (82), (83), (84), % 130.46/18.19 | | | | | | (86), (87), (89), (91), (93), (94), (96), (97), (100), % 130.46/18.19 | | | | | | (102), (103), (105), (106), (109), (110), (111), (113), % 130.46/18.19 | | | | | | (114), (115), (116), (117), (118), (119) are inconsistent % 130.46/18.19 | | | | | | by sub-proof #188. % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | Case 2: % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | (155) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) % 130.46/18.19 | | | | | | & op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & % 130.46/18.19 | | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.19 | | | | | | & $i(all_8_42) & $i(all_8_54) % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | ALPHA: (155) implies: % 130.46/18.19 | | | | | | (156) ~ (all_8_42 = all_8_54) % 130.46/18.19 | | | | | | (157) op(e3, e4) = all_8_42 % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 130.46/18.19 | | | | | | (15), (17), (18), (20), (21), (22), (23), (24), (25), % 130.46/18.19 | | | | | | (26), (28), (30), (31), (32), (33), (34), (35), (37), % 130.46/18.19 | | | | | | (38), (40), (41), (42), (43), (44), (45), (48), (49), % 130.46/18.19 | | | | | | (50), (51), (53), (54), (55), (56), (57), (59), (60), % 130.46/18.19 | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (72), % 130.46/18.19 | | | | | | (73), (74), (76), (77), (78), (79), (80), (82), (83), % 130.46/18.19 | | | | | | (84), (85), (86), (87), (89), (90), (91), (92), (93), % 130.46/18.19 | | | | | | (94), (95), (96), (97), (98), (100), (102), (103), (105), % 130.46/18.19 | | | | | | (106), (109), (110), (111), (112), (113), (114), (115), % 130.46/18.19 | | | | | | (116), (117), (118), (119), (156), (157) are inconsistent % 130.46/18.19 | | | | | | by sub-proof #191. % 130.46/18.19 | | | | | | % 130.46/18.19 | | | | | End of split % 130.46/18.19 | | | | | % 130.46/18.19 | | | | End of split % 130.46/18.19 | | | | % 130.46/18.19 | | | End of split % 130.46/18.19 | | | % 130.46/18.19 | | Case 2: % 130.46/18.19 | | | % 130.46/18.19 | | | (158) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.46/18.19 | | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, % 130.46/18.19 | | | e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & % 130.46/18.19 | | | $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = % 130.46/18.19 | | | e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = all_8_12 % 130.46/18.19 | | | & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 130.46/18.19 | | | all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | % 130.46/18.19 | | | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.46/18.19 | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, % 130.46/18.19 | | | e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & % 130.46/18.19 | | | $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = % 130.46/18.19 | | | e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & % 130.46/18.19 | | | op(all_8_45, e2) = all_8_16 & op(e4, e2) = all_8_66 & op(e2, % 130.46/18.19 | | | e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) % 130.46/18.19 | | | | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) % 130.46/18.19 | | | & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & op(e3, % 130.46/18.19 | | | e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.19 | | | $i(all_8_57) & $i(all_8_69)) % 130.46/18.19 | | | % 130.46/18.19 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.46/18.19 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.19 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.46/18.19 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (45), % 130.46/18.19 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 130.46/18.19 | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65), % 130.46/18.19 | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), % 130.46/18.19 | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), % 130.46/18.19 | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), % 130.46/18.19 | | | (96), (97), (98), (99), (100), (101), (102), (103), (104), % 130.46/18.19 | | | (105), (106), (107), (108), (109), (110), (111), (112), (113), % 130.46/18.19 | | | (114), (115), (116), (117), (118), (119), (158) are % 130.46/18.19 | | | inconsistent by sub-proof #172. % 130.46/18.19 | | | % 130.46/18.19 | | End of split % 130.46/18.19 | | % 130.46/18.19 | Case 2: % 130.46/18.19 | | % 130.46/18.19 | | (159) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.19 | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, e1) % 130.46/18.19 | | = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & $i(all_8_72) % 130.46/18.19 | | & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = e0) & ~ % 130.46/18.19 | | (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 & % 130.46/18.19 | | op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.46/18.19 | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.46/18.19 | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.46/18.19 | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) % 130.46/18.19 | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) % 130.46/18.19 | | & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ % 130.46/18.19 | | (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & op(all_8_60, e1) % 130.46/18.19 | | = all_8_26 & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & % 130.46/18.19 | | $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ % 130.46/18.19 | | (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) = % 130.46/18.19 | | e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, % 130.46/18.19 | | e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) | % 130.46/18.19 | | (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & % 130.46/18.19 | | op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & op(e1, e0) % 130.46/18.19 | | = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) & $i(all_8_87) % 130.46/18.19 | | & $i(all_8_99)) | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ % 130.46/18.19 | | (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & op(all_8_51, e0) % 130.46/18.19 | | = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.46/18.19 | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 & ~ % 130.46/18.19 | | (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) = % 130.46/18.19 | | e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.19 | | e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.19 | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.19 | | op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) % 130.46/18.19 | | = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) % 130.46/18.19 | | & $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ % 130.46/18.19 | | (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) % 130.46/18.19 | | = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.19 | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.19 | | % 130.46/18.19 | | BETA: splitting (159) gives: % 130.46/18.19 | | % 130.46/18.19 | | Case 1: % 130.46/18.19 | | | % 130.46/18.20 | | | (160) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.46/18.20 | | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, % 130.46/18.20 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & % 130.46/18.20 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = % 130.46/18.20 | | | e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 % 130.46/18.20 | | | & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.46/18.20 | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.46/18.20 | | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.46/18.20 | | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, % 130.46/18.20 | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & % 130.46/18.20 | | | $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = % 130.46/18.20 | | | e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & % 130.46/18.20 | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, % 130.46/18.20 | | | e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) % 130.46/18.20 | | | | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 130.46/18.20 | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, % 130.46/18.20 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.20 | | | $i(all_8_72) & $i(all_8_84)) % 130.46/18.20 | | | % 130.46/18.20 | | | BETA: splitting (160) gives: % 130.46/18.20 | | | % 130.46/18.20 | | | Case 1: % 130.46/18.20 | | | | % 130.46/18.20 | | | | (161) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) % 130.46/18.20 | | | | & op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & % 130.46/18.20 | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) % 130.46/18.20 | | | | & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.20 | | | | (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) % 130.46/18.20 | | | | = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 130.46/18.20 | | | | op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) & % 130.46/18.20 | | | | $i(all_8_96)) % 130.46/18.20 | | | | % 130.46/18.20 | | | | BETA: splitting (161) gives: % 130.46/18.20 | | | | % 130.46/18.20 | | | | Case 1: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (162) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) % 130.46/18.20 | | | | | & op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & % 130.46/18.20 | | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) % 130.46/18.20 | | | | | & $i(all_8_72) & $i(all_8_84) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | ALPHA: (162) implies: % 130.46/18.20 | | | | | (163) ~ (all_8_72 = all_8_84) % 130.46/18.20 | | | | | (164) op(e1, e2) = all_8_72 % 130.46/18.20 | | | | | (165) op(e2, e1) = all_8_84 % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | REF_CLOSE: (29), (56), (58), (163), (164), (165) are inconsistent by % 130.46/18.20 | | | | | sub-proof #181. % 130.46/18.20 | | | | | % 130.46/18.20 | | | | Case 2: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (166) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) % 130.46/18.20 | | | | | & op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & % 130.46/18.20 | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_22) % 130.46/18.20 | | | | | & $i(all_8_75) & $i(all_8_96) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | ALPHA: (166) implies: % 130.46/18.20 | | | | | (167) ~ (all_8_75 = all_8_96) % 130.46/18.20 | | | | | (168) op(e0, e2) = all_8_75 % 130.46/18.20 | | | | | (169) op(e2, e0) = all_8_96 % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.20 | | | | | (17), (21), (22), (25), (26), (28), (31), (32), (33), (34), % 130.46/18.20 | | | | | (35), (37), (38), (40), (41), (42), (44), (45), (48), (49), % 130.46/18.20 | | | | | (50), (51), (53), (54), (55), (56), (57), (59), (60), (61), % 130.46/18.20 | | | | | (63), (64), (65), (66), (67), (69), (73), (74), (76), (77), % 130.46/18.20 | | | | | (78), (79), (80), (81), (82), (84), (86), (87), (89), (91), % 130.46/18.20 | | | | | (93), (94), (96), (97), (100), (102), (103), (105), (106), % 130.46/18.20 | | | | | (109), (110), (111), (113), (114), (115), (117), (118), % 130.46/18.20 | | | | | (119), (167), (168), (169) are inconsistent by sub-proof % 130.46/18.20 | | | | | #171. % 130.46/18.20 | | | | | % 130.46/18.20 | | | | End of split % 130.46/18.20 | | | | % 130.46/18.20 | | | Case 2: % 130.46/18.20 | | | | % 130.46/18.20 | | | | (170) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) % 130.46/18.20 | | | | & op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & % 130.46/18.20 | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) % 130.46/18.20 | | | | & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ % 130.46/18.20 | | | | (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) % 130.46/18.20 | | | | = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & % 130.46/18.20 | | | | op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.20 | | | | $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ % 130.46/18.20 | | | | (all_8_72 = all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, % 130.46/18.20 | | | | e1) = all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = % 130.46/18.20 | | | | all_8_72 & $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.46/18.20 | | | | % 130.46/18.20 | | | | REF_CLOSE: (1), (4), (29), (47), (56), (58), (70), (170) are % 130.46/18.20 | | | | inconsistent by sub-proof #178. % 130.46/18.20 | | | | % 130.46/18.20 | | | End of split % 130.46/18.20 | | | % 130.46/18.20 | | Case 2: % 130.46/18.20 | | | % 130.46/18.20 | | | (171) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) & % 130.46/18.20 | | | op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & op(e1, % 130.46/18.20 | | | e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) & % 130.46/18.20 | | | $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ (all_8_32 = % 130.46/18.20 | | | e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.20 | | | op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, % 130.46/18.20 | | | e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) % 130.46/18.20 | | | | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.20 | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & op(e3, % 130.46/18.20 | | | e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) & % 130.46/18.20 | | | $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ (all_8_36 = % 130.46/18.20 | | | e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) = e0 & % 130.46/18.20 | | | op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & op(e0, % 130.46/18.20 | | | e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) % 130.46/18.20 | | | | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) % 130.46/18.20 | | | & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & op(e1, % 130.46/18.20 | | | e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.20 | | | $i(all_8_87) & $i(all_8_99)) % 130.46/18.20 | | | % 130.46/18.20 | | | BETA: splitting (171) gives: % 130.46/18.20 | | | % 130.46/18.20 | | | Case 1: % 130.46/18.20 | | | | % 130.46/18.20 | | | | (172) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.46/18.20 | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.46/18.20 | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.46/18.20 | | | | & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.20 | | | | (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) % 130.46/18.20 | | | | = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & % 130.46/18.20 | | | | op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & % 130.46/18.20 | | | | $i(all_8_90)) % 130.46/18.20 | | | | % 130.46/18.20 | | | | BETA: splitting (172) gives: % 130.46/18.20 | | | | % 130.46/18.20 | | | | Case 1: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (173) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.46/18.20 | | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.46/18.20 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.46/18.20 | | | | | & $i(all_8_87) & $i(all_8_99) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | ALPHA: (173) implies: % 130.46/18.20 | | | | | (174) ~ (all_8_87 = all_8_99) % 130.46/18.20 | | | | | (175) op(e0, e1) = all_8_87 % 130.46/18.20 | | | | | (176) op(e1, e0) = all_8_99 % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | REF_CLOSE: (46), (56), (71), (174), (175), (176) are inconsistent by % 130.46/18.20 | | | | | sub-proof #177. % 130.46/18.20 | | | | | % 130.46/18.20 | | | | Case 2: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (177) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) % 130.46/18.20 | | | | | & op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & % 130.46/18.20 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) % 130.46/18.20 | | | | | & $i(all_8_51) & $i(all_8_90) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.20 | | | | | (17), (21), (22), (25), (26), (28), (31), (32), (33), (34), % 130.46/18.20 | | | | | (35), (37), (38), (40), (41), (42), (44), (45), (48), (49), % 130.46/18.20 | | | | | (50), (51), (53), (54), (55), (56), (57), (59), (60), (63), % 130.46/18.20 | | | | | (64), (65), (66), (67), (69), (73), (74), (76), (77), (78), % 130.46/18.20 | | | | | (79), (80), (82), (83), (84), (86), (87), (89), (91), (93), % 130.46/18.20 | | | | | (94), (96), (97), (100), (102), (103), (105), (106), (109), % 130.46/18.20 | | | | | (110), (111), (113), (114), (115), (116), (117), (118), % 130.46/18.20 | | | | | (119) are inconsistent by sub-proof #188. % 130.46/18.20 | | | | | % 130.46/18.20 | | | | End of split % 130.46/18.20 | | | | % 130.46/18.20 | | | Case 2: % 130.46/18.20 | | | | % 130.46/18.20 | | | | (178) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.20 | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & % 130.46/18.20 | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 130.46/18.20 | | | | & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = e0 & ~ % 130.46/18.20 | | | | (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & op(all_8_75, e2) % 130.46/18.20 | | | | = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = all_8_96 & % 130.46/18.20 | | | | op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.20 | | | | $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ % 130.46/18.20 | | | | (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, % 130.46/18.20 | | | | e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.46/18.20 | | | | all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.20 | | | | % 130.46/18.20 | | | | BETA: splitting (178) gives: % 130.46/18.20 | | | | % 130.46/18.20 | | | | Case 1: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (179) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) % 130.46/18.20 | | | | | & op(all_8_63, e3) = e0 & op(all_8_63, e0) = all_8_34 & % 130.46/18.20 | | | | | op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_34) % 130.46/18.20 | | | | | & $i(all_8_63) & $i(all_8_93) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | ALPHA: (179) implies: % 130.46/18.20 | | | | | (180) ~ (all_8_63 = all_8_93) % 130.46/18.20 | | | | | (181) op(e0, e3) = all_8_63 % 130.46/18.20 | | | | | (182) op(e3, e0) = all_8_93 % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | BETA: splitting (104) gives: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | Case 1: % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | (183) ~ (op(e3, e0) = e3) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | GROUND_INST: instantiating (56) with e1, all_8_63, e3, e0, % 130.46/18.20 | | | | | | simplifying with (64), (181) gives: % 130.46/18.20 | | | | | | (184) all_8_63 = e1 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | PRED_UNIFY: (36), (181) imply: % 130.46/18.20 | | | | | | (185) ~ (all_8_63 = e3) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | GROUND_INST: instantiating (56) with e1, e4, e3, e0, simplifying % 130.46/18.20 | | | | | | with (64) gives: % 130.46/18.20 | | | | | | (186) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | PRED_UNIFY: (7), (94) imply: % 130.46/18.20 | | | | | | (187) ~ (all_8_90 = e4) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | GROUND_INST: instantiating (56) with e2, all_8_93, e0, e3, % 130.46/18.20 | | | | | | simplifying with (88), (182) gives: % 130.46/18.20 | | | | | | (188) all_8_93 = e2 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | GROUND_INST: instantiating (56) with e3, all_8_90, e0, e4, % 130.46/18.20 | | | | | | simplifying with (63), (96) gives: % 130.46/18.20 | | | | | | (189) all_8_90 = e3 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | GROUND_INST: instantiating (56) with e2, all_8_54, e3, e4, % 130.46/18.20 | | | | | | simplifying with (28), (44) gives: % 130.46/18.20 | | | | | | (190) all_8_54 = e2 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | PRED_UNIFY: (44), (50) imply: % 130.46/18.20 | | | | | | (191) ~ (all_8_54 = e4) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | PRED_UNIFY: (182), (183) imply: % 130.46/18.20 | | | | | | (192) ~ (all_8_93 = e3) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | REDUCE: (190), (191) imply: % 130.46/18.20 | | | | | | (193) ~ (e4 = e2) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.20 | | | | | | (17), (18), (21), (22), (25), (26), (31), (32), (33), % 130.46/18.20 | | | | | | (34), (35), (37), (38), (40), (41), (42), (45), (48), % 130.46/18.20 | | | | | | (49), (51), (53), (54), (55), (56), (57), (60), (65), % 130.46/18.20 | | | | | | (66), (67), (69), (73), (74), (76), (77), (78), (79), % 130.46/18.20 | | | | | | (80), (82), (84), (86), (87), (89), (91), (93), (97), % 130.46/18.20 | | | | | | (100), (102), (103), (105), (106), (109), (110), (111), % 130.46/18.20 | | | | | | (113), (114), (115), (117), (118), (119), (180), (184), % 130.46/18.20 | | | | | | (185), (186), (187), (188), (189), (192) are inconsistent % 130.46/18.20 | | | | | | by sub-proof #176. % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | Case 2: % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | (194) op(e3, e0) = e3 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | REF_CLOSE: (6), (20), (30), (194) are inconsistent by sub-proof % 130.46/18.20 | | | | | | #228. % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | End of split % 130.46/18.20 | | | | | % 130.46/18.20 | | | | Case 2: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | (195) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.46/18.20 | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.46/18.20 | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.46/18.20 | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = % 130.46/18.20 | | | | | e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.46/18.20 | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.20 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.20 | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | BETA: splitting (195) gives: % 130.46/18.20 | | | | | % 130.46/18.20 | | | | | Case 1: % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | (196) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.46/18.20 | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.46/18.20 | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.46/18.20 | | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | ALPHA: (196) implies: % 130.46/18.20 | | | | | | (197) ~ (all_8_75 = all_8_96) % 130.46/18.20 | | | | | | (198) op(e0, e2) = all_8_75 % 130.46/18.20 | | | | | | (199) op(e2, e0) = all_8_96 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 130.46/18.20 | | | | | | (17), (21), (22), (25), (26), (28), (31), (32), (33), % 130.46/18.20 | | | | | | (34), (35), (37), (38), (40), (41), (42), (44), (45), % 130.46/18.20 | | | | | | (48), (49), (50), (51), (53), (54), (55), (56), (57), % 130.46/18.20 | | | | | | (59), (60), (61), (63), (64), (65), (66), (67), (69), % 130.46/18.20 | | | | | | (73), (74), (76), (77), (78), (79), (80), (81), (82), % 130.46/18.20 | | | | | | (84), (86), (87), (89), (91), (93), (94), (96), (97), % 130.46/18.20 | | | | | | (100), (102), (103), (105), (106), (109), (110), (111), % 130.46/18.20 | | | | | | (113), (114), (115), (117), (118), (119), (197), (198), % 130.46/18.20 | | | | | | (199) are inconsistent by sub-proof #171. % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | Case 2: % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | (200) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.20 | | | | | | all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 130.46/18.20 | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.20 | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99) % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | ALPHA: (200) implies: % 130.46/18.20 | | | | | | (201) ~ (all_8_87 = all_8_99) % 130.46/18.20 | | | | | | (202) op(e0, e1) = all_8_87 % 130.46/18.20 | | | | | | (203) op(e1, e0) = all_8_99 % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | | REF_CLOSE: (46), (56), (71), (201), (202), (203) are inconsistent by % 130.46/18.20 | | | | | | sub-proof #177. % 130.46/18.20 | | | | | | % 130.46/18.20 | | | | | End of split % 130.46/18.20 | | | | | % 130.46/18.20 | | | | End of split % 130.46/18.20 | | | | % 130.46/18.20 | | | End of split % 130.46/18.20 | | | % 130.46/18.20 | | End of split % 130.46/18.20 | | % 130.46/18.20 | End of split % 130.46/18.20 | % 130.46/18.20 End of proof % 130.46/18.20 % 130.46/18.20 Sub-proof #171 shows that the following formulas are inconsistent: % 130.46/18.20 ---------------------------------------------------------------- % 130.46/18.20 (1) all_9_8 = e4 % 130.46/18.20 (2) op(e2, e0) = all_8_96 % 130.46/18.20 (3) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.20 (4) op(e0, all_8_90) = e4 % 130.46/18.20 (5) all_6_5 = e1 % 130.46/18.20 (6) ~ (e4 = e0) % 130.46/18.20 (7) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.20 (8) all_9_20 = e2 % 130.46/18.20 (9) all_6_10 = e3 % 130.46/18.20 (10) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.20 (11) ~ (all_4_3 = all_4_4) % 130.46/18.20 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.20 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.20 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.20 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.20 (16) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.20 (17) op(e0, e2) = all_8_75 % 130.46/18.20 (18) op(e4, e3) = e2 % 130.46/18.20 (19) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.20 (20) ~ (all_4_3 = e3) % 130.46/18.20 (21) all_6_20 = all_4_4 % 130.46/18.20 (22) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.20 (23) all_9_11 = e2 % 130.46/18.20 (24) ~ (e3 = e0) % 130.46/18.20 (25) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.20 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.20 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.20 (26) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.20 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.20 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.20 (27) all_9_16 = e3 % 130.46/18.20 (28) all_6_22 = all_4_14 % 130.46/18.20 (29) op(e4, e3) = all_8_54 % 130.46/18.20 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.20 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.20 = e0 % 130.46/18.20 (32) ~ (all_4_14 = e2) % 130.46/18.20 (33) ~ (op(e4, e3) = e4) % 130.46/18.20 (34) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.20 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.20 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.20 (35) ~ (e2 = e0) % 130.46/18.20 (36) all_9_0 = e0 % 130.46/18.20 (37) ~ (all_4_22 = e2) % 130.46/18.20 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.20 (39) ~ (all_4_4 = e3) % 130.46/18.20 (40) ~ (op(e4, e3) = e3) % 130.46/18.20 (41) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.20 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.20 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.20 (42) op(e2, e0) = e1 % 130.46/18.20 (43) op(e4, e0) = all_8_90 % 130.46/18.20 (44) op(e0, e3) = e1 % 130.46/18.20 (45) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.20 (46) all_9_6 = e3 % 130.46/18.20 (47) ~ (e1 = e0) % 130.46/18.20 (48) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.20 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.20 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.20 (49) all_9_14 = e2 % 130.46/18.20 (50) all_9_13 = e3 % 130.46/18.20 (51) all_9_12 = e4 % 130.46/18.20 (52) op(e0, e4) = all_4_4 % 130.46/18.20 (53) ~ (e4 = e1) % 130.46/18.20 (54) ~ (all_4_3 = e0) % 130.46/18.20 (55) all_9_15 = e1 % 130.46/18.20 (56) op(e0, e2) = e3 % 130.46/18.20 (57) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.20 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.20 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.20 (58) op(e3, e4) = e1 % 130.46/18.20 (59) op(e1, e4) = all_4_3 % 130.46/18.20 (60) all_4_11 = e0 % 130.46/18.20 (61) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.20 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.20 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.20 (62) all_9_24 = e4 % 130.46/18.20 (63) all_9_19 = e0 % 130.46/18.20 (64) ~ (op(e0, e4) = e4) % 130.46/18.20 (65) op(e4, e0) = e3 % 130.46/18.20 (66) ~ (all_4_4 = e0) % 130.46/18.20 (67) ~ (all_4_3 = e1) % 130.46/18.20 (68) ~ (all_8_75 = all_8_96) % 130.46/18.20 (69) all_6_2 = all_4_10 % 130.46/18.20 (70) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.20 (71) op(e2, e4) = e3 % 130.46/18.20 (72) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.20 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.20 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.20 (73) all_9_2 = e1 % 130.46/18.20 (74) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.20 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.20 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.20 (75) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.46/18.20 = e0 % 130.46/18.20 (76) ~ (all_4_4 = e1) % 130.46/18.20 (77) ~ (all_4_10 = e2) % 130.46/18.20 (78) all_4_0 = e0 % 130.46/18.20 (79) all_6_15 = all_4_3 % 130.46/18.20 (80) all_9_7 = e0 % 130.46/18.20 (81) op(e4, e4) = e0 % 130.46/18.20 % 130.46/18.20 Begin of proof % 130.46/18.20 | % 130.46/18.20 | BETA: splitting (13) gives: % 130.46/18.20 | % 130.46/18.20 | Case 1: % 130.46/18.20 | | % 130.46/18.20 | | (82) ~ (op(e2, e0) = e2) % 130.46/18.20 | | % 130.46/18.20 | | GROUND_INST: instantiating (38) with e3, all_8_75, e2, e0, simplifying with % 130.46/18.20 | | (17), (56) gives: % 130.46/18.20 | | (83) all_8_75 = e3 % 130.46/18.20 | | % 130.46/18.20 | | GROUND_INST: instantiating (38) with e1, e4, e3, e0, simplifying with (44) % 130.46/18.20 | | gives: % 130.46/18.20 | | (84) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.20 | | % 130.46/18.20 | | PRED_UNIFY: (4), (64) imply: % 130.46/18.20 | | (85) ~ (all_8_90 = e4) % 130.46/18.20 | | % 130.46/18.20 | | GROUND_INST: instantiating (38) with e1, all_8_96, e0, e2, simplifying with % 130.46/18.20 | | (2), (42) gives: % 130.46/18.20 | | (86) all_8_96 = e1 % 130.46/18.20 | | % 130.46/18.20 | | GROUND_INST: instantiating (38) with e3, all_8_90, e0, e4, simplifying with % 130.46/18.20 | | (43), (65) gives: % 130.46/18.20 | | (87) all_8_90 = e3 % 130.46/18.20 | | % 130.46/18.20 | | GROUND_INST: instantiating (38) with e2, all_8_54, e3, e4, simplifying with % 130.46/18.20 | | (18), (29) gives: % 130.46/18.20 | | (88) all_8_54 = e2 % 130.46/18.20 | | % 130.46/18.20 | | PRED_UNIFY: (29), (33) imply: % 130.46/18.20 | | (89) ~ (all_8_54 = e4) % 130.46/18.20 | | % 130.46/18.20 | | PRED_UNIFY: (29), (40) imply: % 130.46/18.20 | | (90) ~ (all_8_54 = e3) % 130.46/18.20 | | % 130.46/18.20 | | PRED_UNIFY: (2), (82) imply: % 130.46/18.20 | | (91) ~ (all_8_96 = e2) % 130.46/18.20 | | % 130.46/18.20 | | REDUCE: (88), (89) imply: % 130.46/18.20 | | (92) ~ (e4 = e2) % 130.46/18.20 | | % 130.46/18.20 | | SIMP: (92) implies: % 130.46/18.20 | | (93) ~ (e4 = e2) % 130.46/18.20 | | % 130.46/18.20 | | REDUCE: (88), (90) imply: % 130.46/18.20 | | (94) ~ (e3 = e2) % 130.46/18.20 | | % 130.46/18.20 | | SIMP: (94) implies: % 130.46/18.20 | | (95) ~ (e3 = e2) % 130.46/18.20 | | % 130.46/18.20 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.46/18.20 | | (14), (15), (16), (19), (20), (21), (22), (23), (24), (25), (26), % 130.46/18.20 | | (27), (28), (30), (31), (32), (34), (35), (36), (37), (38), (39), % 130.46/18.20 | | (41), (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), % 130.46/18.20 | | (55), (57), (58), (59), (60), (61), (62), (63), (66), (67), (68), % 130.46/18.20 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 130.46/18.20 | | (80), (81), (83), (84), (85), (86), (87), (91), (93), (95) are % 130.46/18.20 | | inconsistent by sub-proof #180. % 130.46/18.20 | | % 130.46/18.20 | Case 2: % 130.46/18.20 | | % 130.46/18.20 | | (96) op(e2, e0) = e2 % 130.46/18.20 | | % 130.46/18.20 | | REF_CLOSE: (13), (37), (96) are inconsistent by sub-proof #214. % 130.46/18.20 | | % 130.46/18.20 | End of split % 130.46/18.20 | % 130.46/18.20 End of proof % 130.46/18.20 % 130.46/18.20 Sub-proof #172 shows that the following formulas are inconsistent: % 130.46/18.20 ---------------------------------------------------------------- % 130.46/18.20 (1) op(e1, e3) = e3 % 130.46/18.20 (2) all_9_8 = e4 % 130.46/18.20 (3) op(e4, e1) = e4 % 130.46/18.20 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.20 (5) all_6_9 = all_4_21 % 130.46/18.20 (6) op(e0, all_8_90) = e4 % 130.46/18.20 (7) all_6_5 = e1 % 130.46/18.20 (8) ~ (e4 = e0) % 130.46/18.20 (9) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.21 (10) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.21 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.21 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.21 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.46/18.21 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.21 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.21 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.46/18.21 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.46/18.21 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.21 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.21 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.46/18.21 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.46/18.21 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.46/18.21 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.21 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.21 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.46/18.21 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.46/18.21 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.21 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.46/18.21 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.46/18.21 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.46/18.21 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.46/18.21 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.46/18.21 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.21 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.21 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.21 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.21 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.21 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.21 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.21 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.21 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.46/18.21 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.46/18.21 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.46/18.21 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.21 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.46/18.21 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.46/18.21 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.46/18.21 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.46/18.21 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.46/18.21 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.46/18.21 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.46/18.21 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.46/18.21 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.21 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.46/18.21 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.46/18.21 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.21 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.46/18.21 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.46/18.21 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.21 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.21 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.21 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.21 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.46/18.21 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.46/18.21 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.21 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.21 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.21 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.46/18.21 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.21 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.21 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.21 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.21 $i(all_8_87) & $i(all_8_99)) % 130.46/18.21 (11) all_9_20 = e2 % 130.46/18.21 (12) all_6_10 = e3 % 130.46/18.21 (13) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.21 (14) ~ (all_4_3 = all_4_4) % 130.46/18.21 (15) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.46/18.21 (16) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.21 (17) ~ (e4 = e2) % 130.46/18.21 (18) all_4_7 = e0 % 130.46/18.21 (19) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.21 (20) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.21 (21) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.21 (22) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.46/18.21 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.46/18.21 (all_9_16 = e2 & op(e4, e0) = e2) % 130.46/18.21 (23) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.21 (24) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.21 (25) all_8_45 = e3 % 130.46/18.21 (26) op(e4, e3) = e2 % 130.46/18.21 (27) op(e2, e1) = e2 % 130.46/18.21 (28) ~ (all_4_21 = e3) % 130.46/18.21 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.21 (30) ~ (all_4_3 = e3) % 130.46/18.21 (31) all_6_20 = all_4_4 % 130.46/18.21 (32) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.21 (33) all_9_11 = e2 % 130.46/18.21 (34) ~ (op(e0, e3) = e3) % 130.46/18.21 (35) ~ (e3 = e0) % 130.46/18.21 (36) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.21 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.21 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.21 (37) op(e3, e2) = e0 % 130.46/18.21 (38) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.21 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.21 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.21 (39) all_9_16 = e3 % 130.46/18.21 (40) all_6_22 = all_4_14 % 130.46/18.21 (41) all_9_17 = e2 % 130.46/18.21 (42) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.21 (43) op(e1, e0) = e0 % 130.46/18.21 (44) op(e1, e4) = e4 % 130.46/18.21 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.21 = e0 % 130.46/18.21 (46) ~ (all_4_14 = e2) % 130.46/18.21 (47) ~ (op(e4, e3) = e4) % 130.46/18.21 (48) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.21 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.21 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.21 (49) op(e4, e2) = e1 % 130.46/18.21 (50) ~ (e2 = e0) % 130.46/18.21 (51) all_9_0 = e0 % 130.46/18.21 (52) ~ (all_4_22 = e2) % 130.46/18.21 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.21 (54) ~ (all_4_4 = e3) % 130.46/18.21 (55) op(e1, e2) = e2 % 130.46/18.21 (56) ~ (op(e4, e3) = e3) % 130.46/18.21 (57) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.21 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.21 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.21 (58) op(e2, e0) = e1 % 130.46/18.21 (59) ~ (all_4_22 = e3) % 130.46/18.21 (60) op(e4, e0) = all_8_90 % 130.46/18.21 (61) op(e0, e3) = e1 % 130.46/18.21 (62) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.21 (63) all_9_6 = e3 % 130.46/18.21 (64) ~ (e1 = e0) % 130.46/18.21 (65) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.46/18.21 (66) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.21 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.21 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.21 (67) op(e3, e1) = e3 % 130.46/18.21 (68) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.46/18.21 op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.46/18.21 all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.46/18.21 $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = % 130.46/18.21 all_8_81) & op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & % 130.46/18.21 op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & % 130.46/18.21 $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & % 130.46/18.21 ~ (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & op(all_8_93, % 130.46/18.21 e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.46/18.21 $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & ~ % 130.46/18.21 (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & % 130.46/18.21 op(all_8_45, e2) = all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.46/18.21 all_8_45 & $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = % 130.46/18.21 e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) % 130.46/18.21 = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, % 130.46/18.21 e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.46/18.21 (69) op(e0, e1) = e0 % 130.46/18.21 (70) ~ (e3 = e2) % 130.46/18.21 (71) all_9_14 = e2 % 130.46/18.21 (72) all_9_13 = e3 % 130.46/18.21 (73) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.21 (74) all_9_12 = e4 % 130.46/18.21 (75) op(e0, e4) = all_4_4 % 130.46/18.21 (76) ~ (e4 = e1) % 130.46/18.21 (77) ~ (all_4_3 = e0) % 130.46/18.21 (78) all_9_15 = e1 % 130.46/18.21 (79) op(e0, e2) = e3 % 130.46/18.21 (80) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.21 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.21 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.21 (81) ~ (e3 = e1) % 130.46/18.21 (82) op(e3, e4) = e1 % 130.46/18.21 (83) all_9_9 = e4 % 130.46/18.21 (84) op(e1, e4) = all_4_3 % 130.46/18.21 (85) all_4_11 = e0 % 130.46/18.21 (86) op(e3, e0) = e2 % 130.46/18.21 (87) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.21 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.21 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.21 (88) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.46/18.21 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.46/18.21 (all_9_16 = e3 & op(e4, e0) = e3) % 130.46/18.21 (89) all_9_24 = e4 % 130.46/18.21 (90) op(e2, e0) = all_4_22 % 130.46/18.21 (91) all_9_19 = e0 % 130.46/18.21 (92) ~ (op(e0, e4) = e4) % 130.46/18.21 (93) ~ (e4 = e3) % 130.46/18.21 (94) op(e4, e0) = e3 % 130.46/18.21 (95) ~ (all_4_4 = e0) % 130.46/18.21 (96) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.46/18.21 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.46/18.21 (all_9_16 = e1 & op(e4, e0) = e1) % 130.46/18.21 (97) op(e2, e3) = e0 % 130.46/18.21 (98) ~ (all_4_3 = e1) % 130.46/18.21 (99) op(e0, e4) = e2 % 130.46/18.21 (100) all_6_2 = all_4_10 % 130.46/18.21 (101) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.21 (102) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.21 (103) op(e2, e4) = e3 % 130.46/18.21 (104) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.21 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.21 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.21 (105) ~ (all_4_10 = e4) % 130.46/18.21 (106) ~ (op(e2, e3) = e3) % 130.46/18.21 (107) all_9_2 = e1 % 130.46/18.21 (108) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.21 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.21 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.21 (109) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.46/18.21 all_6_15 = e0 % 130.46/18.21 (110) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.46/18.21 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.46/18.21 (all_9_24 = e3 & op(e0, e0) = e3) % 130.46/18.21 (111) ~ (all_4_4 = e1) % 130.46/18.21 (112) ~ (all_4_10 = e2) % 130.46/18.21 (113) all_4_0 = e0 % 130.46/18.21 (114) ~ (e2 = e1) % 130.46/18.21 (115) all_6_15 = all_4_3 % 130.46/18.21 (116) all_9_7 = e0 % 130.46/18.21 (117) op(e4, e4) = e0 % 130.46/18.21 % 130.46/18.21 Begin of proof % 130.46/18.21 | % 130.46/18.21 | BETA: splitting (68) gives: % 130.46/18.21 | % 130.46/18.21 | Case 1: % 130.46/18.21 | | % 130.46/18.21 | | (118) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.46/18.21 | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) % 130.46/18.21 | | = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) % 130.46/18.21 | | & $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ % 130.46/18.21 | | (all_8_60 = all_8_81) & op(all_8_81, e3) = all_8_12 & % 130.46/18.21 | | op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) = % 130.46/18.21 | | all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) % 130.46/18.21 | | % 130.46/18.21 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.21 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.21 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.46/18.21 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 130.46/18.21 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.46/18.21 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 130.46/18.21 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 130.46/18.21 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), % 130.46/18.21 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), % 130.46/18.21 | | (101), (102), (103), (104), (105), (106), (107), (108), (109), % 130.46/18.21 | | (110), (111), (112), (113), (114), (115), (116), (117), (118) are % 130.46/18.21 | | inconsistent by sub-proof #174. % 130.46/18.21 | | % 130.46/18.21 | Case 2: % 130.46/18.21 | | % 130.46/18.21 | | (119) (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.46/18.21 | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) % 130.46/18.21 | | = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) % 130.46/18.21 | | & $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ % 130.46/18.21 | | (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & op(all_8_45, e2) % 130.46/18.21 | | = all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & % 130.46/18.21 | | $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ % 130.46/18.21 | | (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) = % 130.46/18.21 | | e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, % 130.46/18.21 | | e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.46/18.21 | | % 130.46/18.21 | | BETA: splitting (119) gives: % 130.46/18.21 | | % 130.46/18.21 | | Case 1: % 130.46/18.21 | | | % 130.46/18.21 | | | (120) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.46/18.21 | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) % 130.46/18.21 | | | = all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) % 130.46/18.21 | | | & $i(all_8_93) % 130.46/18.21 | | | % 130.46/18.21 | | | REF_CLOSE: (5), (19), (28), (53), (59), (86), (90), (120) are inconsistent % 130.46/18.21 | | | by sub-proof #183. % 130.46/18.21 | | | % 130.46/18.21 | | Case 2: % 130.46/18.21 | | | % 130.46/18.21 | | | (121) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.21 | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, % 130.46/18.21 | | | e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & % 130.46/18.21 | | | $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = % 130.46/18.21 | | | e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & % 130.46/18.21 | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, % 130.46/18.21 | | | e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.46/18.21 | | | % 130.46/18.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.21 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), % 130.46/18.21 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 130.46/18.21 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), % 130.46/18.21 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), % 130.46/18.21 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), % 130.46/18.21 | | | (63), (64), (65), (66), (67), (69), (70), (71), (72), (73), % 130.46/18.21 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), % 130.46/18.21 | | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), % 130.46/18.21 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (103), % 130.46/18.21 | | | (104), (105), (106), (107), (108), (109), (110), (111), (112), % 130.46/18.21 | | | (113), (114), (115), (116), (117), (121) are inconsistent by % 130.46/18.21 | | | sub-proof #173. % 130.46/18.21 | | | % 130.46/18.21 | | End of split % 130.46/18.21 | | % 130.46/18.21 | End of split % 130.46/18.21 | % 130.46/18.21 End of proof % 130.46/18.21 % 130.46/18.21 Sub-proof #173 shows that the following formulas are inconsistent: % 130.46/18.21 ---------------------------------------------------------------- % 130.46/18.21 (1) op(e1, e3) = e3 % 130.46/18.21 (2) all_9_8 = e4 % 130.46/18.21 (3) op(e4, e1) = e4 % 130.46/18.21 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.21 (5) all_6_9 = all_4_21 % 130.46/18.21 (6) op(e0, all_8_90) = e4 % 130.46/18.21 (7) all_6_5 = e1 % 130.46/18.21 (8) ~ (e4 = e0) % 130.46/18.21 (9) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.21 (10) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.21 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.21 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.21 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.46/18.21 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.21 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.21 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.46/18.21 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.46/18.21 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.21 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.21 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.46/18.21 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.46/18.21 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.46/18.21 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.21 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.21 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.46/18.21 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.46/18.21 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.21 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.46/18.21 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.46/18.21 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.46/18.21 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.46/18.21 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.46/18.21 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.21 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.21 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.21 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.21 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.21 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.21 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.21 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.21 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.46/18.21 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.46/18.21 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.46/18.21 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.21 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.46/18.21 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.46/18.21 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.46/18.21 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.46/18.21 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.46/18.21 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.46/18.21 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.46/18.21 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.46/18.21 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.21 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.46/18.21 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.46/18.21 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.21 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.46/18.21 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.46/18.21 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.21 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.21 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.21 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.21 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.46/18.21 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.46/18.21 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.21 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.21 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.21 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.46/18.21 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.21 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.21 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.21 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.21 $i(all_8_87) & $i(all_8_99)) % 130.46/18.21 (11) all_9_20 = e2 % 130.46/18.21 (12) all_6_10 = e3 % 130.46/18.21 (13) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.21 (14) ~ (all_4_3 = all_4_4) % 130.46/18.21 (15) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.46/18.21 (16) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.21 (17) ~ (e4 = e2) % 130.46/18.21 (18) all_4_7 = e0 % 130.46/18.21 (19) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.21 (20) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.21 (21) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.21 (22) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.46/18.21 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.46/18.21 (all_9_16 = e2 & op(e4, e0) = e2) % 130.46/18.21 (23) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.21 (24) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.21 (25) all_8_45 = e3 % 130.46/18.21 (26) op(e4, e3) = e2 % 130.46/18.21 (27) op(e2, e1) = e2 % 130.46/18.21 (28) ~ (all_4_21 = e3) % 130.46/18.21 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.21 (30) ~ (all_4_3 = e3) % 130.46/18.21 (31) all_6_20 = all_4_4 % 130.46/18.21 (32) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.21 (33) all_9_11 = e2 % 130.46/18.21 (34) ~ (op(e0, e3) = e3) % 130.46/18.21 (35) ~ (e3 = e0) % 130.46/18.21 (36) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.21 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.21 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.21 (37) op(e3, e2) = e0 % 130.46/18.21 (38) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.21 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.21 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.21 (39) all_9_16 = e3 % 130.46/18.21 (40) all_6_22 = all_4_14 % 130.46/18.21 (41) all_9_17 = e2 % 130.46/18.21 (42) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.21 (43) op(e1, e0) = e0 % 130.46/18.21 (44) op(e1, e4) = e4 % 130.46/18.21 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.21 = e0 % 130.46/18.21 (46) ~ (all_4_14 = e2) % 130.46/18.21 (47) ~ (op(e4, e3) = e4) % 130.46/18.21 (48) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.21 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.21 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.21 (49) op(e4, e2) = e1 % 130.46/18.21 (50) ~ (e2 = e0) % 130.46/18.21 (51) all_9_0 = e0 % 130.46/18.21 (52) ~ (all_4_22 = e2) % 130.46/18.21 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.21 (54) ~ (all_4_4 = e3) % 130.46/18.21 (55) op(e1, e2) = e2 % 130.46/18.21 (56) ~ (op(e4, e3) = e3) % 130.46/18.21 (57) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.21 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.21 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.21 (58) op(e2, e0) = e1 % 130.46/18.21 (59) ~ (all_4_22 = e3) % 130.46/18.21 (60) op(e4, e0) = all_8_90 % 130.46/18.21 (61) op(e0, e3) = e1 % 130.46/18.21 (62) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.21 (63) all_9_6 = e3 % 130.46/18.21 (64) ~ (e1 = e0) % 130.46/18.21 (65) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.46/18.21 (66) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.21 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.21 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.21 (67) op(e3, e1) = e3 % 130.46/18.21 (68) op(e0, e1) = e0 % 130.46/18.21 (69) ~ (e3 = e2) % 130.46/18.21 (70) all_9_14 = e2 % 130.46/18.21 (71) all_9_13 = e3 % 130.46/18.21 (72) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.21 (73) all_9_12 = e4 % 130.46/18.21 (74) op(e0, e4) = all_4_4 % 130.46/18.21 (75) ~ (e4 = e1) % 130.46/18.22 (76) ~ (all_4_3 = e0) % 130.46/18.22 (77) all_9_15 = e1 % 130.46/18.22 (78) op(e0, e2) = e3 % 130.46/18.22 (79) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.22 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.22 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.22 (80) ~ (e3 = e1) % 130.46/18.22 (81) op(e3, e4) = e1 % 130.46/18.22 (82) all_9_9 = e4 % 130.46/18.22 (83) op(e1, e4) = all_4_3 % 130.46/18.22 (84) all_4_11 = e0 % 130.46/18.22 (85) op(e3, e0) = e2 % 130.46/18.22 (86) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.22 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.22 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.22 (87) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.46/18.22 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.46/18.22 (all_9_16 = e3 & op(e4, e0) = e3) % 130.46/18.22 (88) all_9_24 = e4 % 130.46/18.22 (89) op(e2, e0) = all_4_22 % 130.46/18.22 (90) all_9_19 = e0 % 130.46/18.22 (91) ~ (op(e0, e4) = e4) % 130.46/18.22 (92) ~ (e4 = e3) % 130.46/18.22 (93) op(e4, e0) = e3 % 130.46/18.22 (94) ~ (all_4_4 = e0) % 130.46/18.22 (95) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.46/18.22 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.46/18.22 (all_9_16 = e1 & op(e4, e0) = e1) % 130.46/18.22 (96) op(e2, e3) = e0 % 130.46/18.22 (97) ~ (all_4_3 = e1) % 130.46/18.22 (98) op(e0, e4) = e2 % 130.46/18.22 (99) all_6_2 = all_4_10 % 130.46/18.22 (100) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.22 (101) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.22 (102) op(e2, e4) = e3 % 130.46/18.22 (103) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.22 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.22 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.22 (104) ~ (all_4_10 = e4) % 130.46/18.22 (105) ~ (op(e2, e3) = e3) % 130.46/18.22 (106) all_9_2 = e1 % 130.46/18.22 (107) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.22 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.22 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.22 (108) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.46/18.22 all_6_15 = e0 % 130.46/18.22 (109) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.46/18.22 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.46/18.22 (all_9_24 = e3 & op(e0, e0) = e3) % 130.46/18.22 (110) ~ (all_4_4 = e1) % 130.46/18.22 (111) ~ (all_4_10 = e2) % 130.46/18.22 (112) all_4_0 = e0 % 130.46/18.22 (113) ~ (e2 = e1) % 130.46/18.22 (114) all_6_15 = all_4_3 % 130.46/18.22 (115) all_9_7 = e0 % 130.46/18.22 (116) op(e4, e4) = e0 % 130.46/18.22 (117) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.22 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.22 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.22 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.22 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.22 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.22 $i(all_8_57) & $i(all_8_69)) % 130.46/18.22 % 130.46/18.22 Begin of proof % 130.46/18.22 | % 130.46/18.22 | BETA: splitting (117) gives: % 130.46/18.22 | % 130.46/18.22 | Case 1: % 130.46/18.22 | | % 130.46/18.22 | | (118) all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.22 | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.22 | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.22 | | $i(all_8_66) % 130.46/18.22 | | % 130.46/18.22 | | ALPHA: (118) implies: % 130.46/18.22 | | (119) op(all_8_45, e4) = e2 % 130.46/18.22 | | % 130.46/18.22 | | REDUCE: (25), (119) imply: % 130.46/18.22 | | (120) op(e3, e4) = e2 % 130.46/18.22 | | % 130.46/18.22 | | REF_CLOSE: (53), (81), (113), (120) are inconsistent by sub-proof #313. % 130.46/18.22 | | % 130.46/18.22 | Case 2: % 130.46/18.22 | | % 130.46/18.22 | | (121) all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & % 130.46/18.22 | | op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = % 130.46/18.22 | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & % 130.46/18.22 | | $i(all_8_69) % 130.46/18.22 | | % 130.46/18.22 | | ALPHA: (121) implies: % 130.46/18.22 | | (122) op(e2, e3) = all_8_57 % 130.46/18.22 | | % 130.46/18.22 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.22 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.22 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.46/18.22 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 130.46/18.22 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.46/18.22 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 130.46/18.22 | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 130.46/18.22 | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), % 130.46/18.22 | | (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), % 130.46/18.22 | | (100), (101), (102), (103), (104), (105), (106), (107), (108), % 130.46/18.22 | | (109), (110), (111), (112), (113), (114), (115), (116), (122) are % 130.46/18.22 | | inconsistent by sub-proof #175. % 130.46/18.22 | | % 130.46/18.22 | End of split % 130.46/18.22 | % 130.46/18.22 End of proof % 130.46/18.22 % 130.46/18.22 Sub-proof #174 shows that the following formulas are inconsistent: % 130.46/18.22 ---------------------------------------------------------------- % 130.46/18.22 (1) op(e1, e3) = e3 % 130.46/18.22 (2) all_9_8 = e4 % 130.46/18.22 (3) op(e4, e1) = e4 % 130.46/18.22 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.22 (5) all_6_9 = all_4_21 % 130.46/18.22 (6) op(e0, all_8_90) = e4 % 130.46/18.22 (7) all_6_5 = e1 % 130.46/18.22 (8) ~ (e4 = e0) % 130.46/18.22 (9) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.22 (10) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.22 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.22 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.22 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.46/18.22 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.22 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.22 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.46/18.22 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.46/18.22 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.22 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.22 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.46/18.22 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.46/18.22 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.46/18.22 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.22 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.22 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.46/18.22 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.46/18.22 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.22 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.46/18.22 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.46/18.22 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.46/18.22 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.46/18.22 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.46/18.22 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.22 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.22 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.22 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.22 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.22 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.22 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.22 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.22 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.46/18.22 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.46/18.22 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.46/18.22 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.22 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.46/18.22 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.46/18.22 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.46/18.22 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.46/18.22 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.46/18.22 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.46/18.22 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.46/18.22 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.46/18.22 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.22 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.46/18.22 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.46/18.22 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.22 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.46/18.22 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.46/18.22 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.22 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.22 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.22 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.22 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.46/18.22 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.46/18.22 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.22 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.22 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.22 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.46/18.22 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.22 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.22 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.22 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.22 $i(all_8_87) & $i(all_8_99)) % 130.46/18.22 (11) all_9_20 = e2 % 130.46/18.22 (12) all_6_10 = e3 % 130.46/18.22 (13) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.22 (14) ~ (all_4_3 = all_4_4) % 130.46/18.22 (15) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.46/18.22 (16) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.22 (17) ~ (e4 = e2) % 130.46/18.22 (18) all_4_7 = e0 % 130.46/18.22 (19) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.22 (20) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.22 (21) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.22 (22) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.46/18.22 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.46/18.22 (all_9_16 = e2 & op(e4, e0) = e2) % 130.46/18.22 (23) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.22 (24) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.22 (25) all_8_45 = e3 % 130.46/18.22 (26) op(e4, e3) = e2 % 130.46/18.22 (27) op(e2, e1) = e2 % 130.46/18.22 (28) ~ (all_4_21 = e3) % 130.46/18.22 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.22 (30) ~ (all_4_3 = e3) % 130.46/18.22 (31) all_6_20 = all_4_4 % 130.46/18.22 (32) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.22 (33) all_9_11 = e2 % 130.46/18.22 (34) ~ (op(e0, e3) = e3) % 130.46/18.22 (35) ~ (e3 = e0) % 130.46/18.22 (36) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.22 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.22 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.22 (37) op(e3, e2) = e0 % 130.46/18.22 (38) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.22 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.22 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.22 (39) all_9_16 = e3 % 130.46/18.22 (40) all_6_22 = all_4_14 % 130.46/18.22 (41) all_9_17 = e2 % 130.46/18.22 (42) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.22 (43) op(e1, e0) = e0 % 130.46/18.22 (44) op(e1, e4) = e4 % 130.46/18.22 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.22 = e0 % 130.46/18.22 (46) ~ (all_4_14 = e2) % 130.46/18.22 (47) ~ (op(e4, e3) = e4) % 130.46/18.22 (48) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.22 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.22 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.22 (49) op(e4, e2) = e1 % 130.46/18.22 (50) ~ (e2 = e0) % 130.46/18.22 (51) all_9_0 = e0 % 130.46/18.22 (52) ~ (all_4_22 = e2) % 130.46/18.22 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.22 (54) ~ (all_4_4 = e3) % 130.46/18.22 (55) op(e1, e2) = e2 % 130.46/18.22 (56) ~ (op(e4, e3) = e3) % 130.46/18.22 (57) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.22 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.22 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.22 (58) op(e2, e0) = e1 % 130.46/18.22 (59) ~ (all_4_22 = e3) % 130.46/18.22 (60) op(e4, e0) = all_8_90 % 130.46/18.22 (61) op(e0, e3) = e1 % 130.46/18.22 (62) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.22 (63) all_9_6 = e3 % 130.46/18.22 (64) ~ (e1 = e0) % 130.46/18.22 (65) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.46/18.22 (66) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.22 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.22 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.22 (67) op(e3, e1) = e3 % 130.46/18.22 (68) op(e0, e1) = e0 % 130.46/18.22 (69) ~ (e3 = e2) % 130.46/18.22 (70) all_9_14 = e2 % 130.46/18.22 (71) all_9_13 = e3 % 130.46/18.22 (72) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.22 (73) all_9_12 = e4 % 130.46/18.22 (74) op(e0, e4) = all_4_4 % 130.46/18.22 (75) ~ (e4 = e1) % 130.46/18.22 (76) ~ (all_4_3 = e0) % 130.46/18.22 (77) all_9_15 = e1 % 130.46/18.22 (78) op(e0, e2) = e3 % 130.46/18.22 (79) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.22 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.22 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.22 (80) ~ (e3 = e1) % 130.46/18.22 (81) op(e3, e4) = e1 % 130.46/18.22 (82) all_9_9 = e4 % 130.46/18.22 (83) op(e1, e4) = all_4_3 % 130.46/18.22 (84) all_4_11 = e0 % 130.46/18.22 (85) op(e3, e0) = e2 % 130.46/18.22 (86) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.22 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.22 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.22 (87) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.46/18.22 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.46/18.22 (all_9_16 = e3 & op(e4, e0) = e3) % 130.46/18.22 (88) all_9_24 = e4 % 130.46/18.22 (89) op(e2, e0) = all_4_22 % 130.46/18.22 (90) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.46/18.22 op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.46/18.22 all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.46/18.22 $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = % 130.46/18.22 all_8_81) & op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & % 130.46/18.22 op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & % 130.46/18.22 $i(all_8_60) & $i(all_8_81)) % 130.46/18.22 (91) all_9_19 = e0 % 130.46/18.22 (92) ~ (op(e0, e4) = e4) % 130.46/18.22 (93) ~ (e4 = e3) % 130.46/18.22 (94) op(e4, e0) = e3 % 130.46/18.22 (95) ~ (all_4_4 = e0) % 130.46/18.22 (96) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.46/18.22 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.46/18.22 (all_9_16 = e1 & op(e4, e0) = e1) % 130.46/18.22 (97) op(e2, e3) = e0 % 130.46/18.22 (98) ~ (all_4_3 = e1) % 130.46/18.22 (99) op(e0, e4) = e2 % 130.46/18.22 (100) all_6_2 = all_4_10 % 130.46/18.22 (101) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.22 (102) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.22 (103) op(e2, e4) = e3 % 130.46/18.22 (104) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.22 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.22 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.22 (105) ~ (all_4_10 = e4) % 130.46/18.22 (106) ~ (op(e2, e3) = e3) % 130.46/18.22 (107) all_9_2 = e1 % 130.46/18.22 (108) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.22 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.22 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.22 (109) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.46/18.22 all_6_15 = e0 % 130.46/18.22 (110) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.46/18.22 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.46/18.22 (all_9_24 = e3 & op(e0, e0) = e3) % 130.46/18.22 (111) ~ (all_4_4 = e1) % 130.46/18.22 (112) ~ (all_4_10 = e2) % 130.46/18.22 (113) all_4_0 = e0 % 130.46/18.22 (114) ~ (e2 = e1) % 130.46/18.22 (115) all_6_15 = all_4_3 % 130.46/18.22 (116) all_9_7 = e0 % 130.46/18.22 (117) op(e4, e4) = e0 % 130.46/18.22 % 130.46/18.22 Begin of proof % 130.46/18.22 | % 130.46/18.22 | BETA: splitting (90) gives: % 130.46/18.22 | % 130.46/18.22 | Case 1: % 130.46/18.22 | | % 130.46/18.22 | | (118) all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.46/18.22 | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.46/18.22 | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.46/18.22 | | $i(all_8_69) % 130.46/18.22 | | % 130.46/18.22 | | ALPHA: (118) implies: % 130.46/18.22 | | (119) op(e2, e3) = all_8_57 % 130.46/18.22 | | % 130.46/18.22 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.46/18.22 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.46/18.22 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.46/18.22 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 130.46/18.22 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.46/18.22 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 130.46/18.22 | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 130.46/18.22 | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), % 130.46/18.22 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), % 130.46/18.22 | | (101), (102), (103), (104), (105), (106), (107), (108), (109), % 130.46/18.22 | | (110), (111), (112), (113), (114), (115), (116), (117), (119) are % 130.46/18.22 | | inconsistent by sub-proof #175. % 130.46/18.22 | | % 130.46/18.22 | Case 2: % 130.46/18.22 | | % 130.46/18.22 | | (120) all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.46/18.22 | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = % 130.46/18.22 | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) & % 130.46/18.22 | | $i(all_8_81) % 130.46/18.22 | | % 130.46/18.22 | | ALPHA: (120) implies: % 130.46/18.22 | | (121) ~ (all_8_60 = all_8_81) % 130.46/18.22 | | (122) op(e1, e3) = all_8_60 % 130.46/18.22 | | (123) op(e3, e1) = all_8_81 % 130.46/18.22 | | % 130.46/18.22 | | REF_CLOSE: (1), (53), (67), (121), (122), (123) are inconsistent by % 130.46/18.22 | | sub-proof #184. % 130.46/18.22 | | % 130.46/18.22 | End of split % 130.46/18.22 | % 130.46/18.22 End of proof % 130.46/18.22 % 130.46/18.22 Sub-proof #175 shows that the following formulas are inconsistent: % 130.46/18.22 ---------------------------------------------------------------- % 130.46/18.22 (1) op(e1, e3) = e3 % 130.46/18.22 (2) all_9_8 = e4 % 130.46/18.22 (3) op(e4, e1) = e4 % 130.46/18.22 (4) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.46/18.22 (5) all_6_9 = all_4_21 % 130.46/18.22 (6) op(e0, all_8_90) = e4 % 130.46/18.22 (7) all_6_5 = e1 % 130.46/18.22 (8) ~ (e4 = e0) % 130.46/18.22 (9) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.46/18.22 (10) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.22 op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) = % 130.46/18.22 all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) & % 130.46/18.22 $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = % 130.46/18.22 all_8_66) & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.22 op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.22 $i(all_8_45) & $i(all_8_66)) | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ % 130.46/18.22 (all_8_48 = all_8_78) & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) % 130.46/18.22 = e4 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.22 $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.22 (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, e0) % 130.46/18.22 = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.46/18.22 $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ % 130.46/18.22 (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.46/18.22 all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) % 130.46/18.22 & $i(all_8_42) & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & % 130.46/18.22 ~ (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & op(all_8_69, % 130.46/18.22 e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.46/18.22 $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.46/18.22 (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) = % 130.46/18.22 all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & op(e1, e3) % 130.46/18.22 = all_8_60 & $i(all_8_12) & $i(all_8_60) & $i(all_8_81)) | (all_8_15 = % 130.46/18.22 e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) % 130.46/18.22 = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.22 e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.22 (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.22 op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) = % 130.46/18.22 all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) & % 130.46/18.22 $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = % 130.46/18.22 all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & % 130.46/18.22 op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & % 130.46/18.22 $i(all_8_57) & $i(all_8_69)) | (all_8_21 = e2 & ~ (all_8_20 = e1) & % 130.46/18.22 ~ (all_8_72 = all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.46/18.22 e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.46/18.22 $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.46/18.22 (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = % 130.46/18.22 all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) % 130.46/18.22 = all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | (all_8_25 = % 130.46/18.22 e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & op(all_8_48, e4) % 130.46/18.22 = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, % 130.46/18.22 e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.46/18.22 (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.46/18.22 op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.46/18.22 all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.46/18.22 $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = % 130.46/18.22 all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.46/18.22 op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.46/18.22 $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = e0) & % 130.46/18.22 ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.46/18.22 e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.46/18.22 $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.46/18.22 (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) = e0 & % 130.46/18.22 op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.22 all_8_51 & $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) | (all_8_35 = % 130.46/18.22 e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) % 130.46/18.22 = e0 & op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.46/18.22 e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.22 (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.46/18.22 op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, e0) = % 130.46/18.22 all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & $i(all_8_75) & % 130.46/18.22 $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.46/18.22 all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.46/18.22 op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_38) & % 130.46/18.22 $i(all_8_87) & $i(all_8_99)) % 130.46/18.22 (11) all_9_20 = e2 % 130.46/18.22 (12) all_6_10 = e3 % 130.46/18.22 (13) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.46/18.22 (14) ~ (all_4_3 = all_4_4) % 130.46/18.22 (15) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 130.46/18.22 (16) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.46/18.22 (17) ~ (e4 = e2) % 130.46/18.22 (18) all_4_7 = e0 % 130.46/18.22 (19) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.22 (20) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.46/18.22 (21) e4 = e3 | ~ (op(e2, e4) = e4) % 130.46/18.22 (22) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.46/18.22 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.46/18.22 (all_9_16 = e2 & op(e4, e0) = e2) % 130.46/18.22 (23) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.22 (24) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.46/18.22 (25) all_8_45 = e3 % 130.46/18.22 (26) op(e4, e3) = e2 % 130.46/18.23 (27) op(e2, e1) = e2 % 130.46/18.23 (28) ~ (all_4_21 = e3) % 130.46/18.23 (29) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.46/18.23 (30) ~ (all_4_3 = e3) % 130.46/18.23 (31) all_6_20 = all_4_4 % 130.46/18.23 (32) e4 = e2 | ~ (op(e2, e2) = e2) % 130.46/18.23 (33) all_9_11 = e2 % 130.46/18.23 (34) ~ (op(e0, e3) = e3) % 130.46/18.23 (35) ~ (e3 = e0) % 130.46/18.23 (36) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.46/18.23 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.46/18.23 (all_9_24 = e4 & op(e0, e0) = e4) % 130.46/18.23 (37) op(e3, e2) = e0 % 130.46/18.23 (38) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.46/18.23 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.46/18.23 (all_9_19 = e2 & op(e1, e0) = e2) % 130.46/18.23 (39) all_9_16 = e3 % 130.46/18.23 (40) all_6_22 = all_4_14 % 130.46/18.23 (41) all_9_17 = e2 % 130.46/18.23 (42) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.46/18.23 (43) op(e1, e0) = e0 % 130.46/18.23 (44) op(e1, e4) = e4 % 130.46/18.23 (45) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.46/18.23 = e0 % 130.46/18.23 (46) ~ (all_4_14 = e2) % 130.46/18.23 (47) ~ (op(e4, e3) = e4) % 130.46/18.23 (48) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.46/18.23 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.46/18.23 (all_9_18 = e1 & op(e2, e0) = e1) % 130.46/18.23 (49) op(e4, e2) = e1 % 130.46/18.23 (50) ~ (e2 = e0) % 130.46/18.23 (51) all_9_0 = e0 % 130.46/18.23 (52) ~ (all_4_22 = e2) % 130.46/18.23 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.46/18.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.46/18.23 (54) ~ (all_4_4 = e3) % 130.46/18.23 (55) op(e1, e2) = e2 % 130.46/18.23 (56) op(e2, e3) = all_8_57 % 130.46/18.23 (57) ~ (op(e4, e3) = e3) % 130.46/18.23 (58) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.46/18.23 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.46/18.23 (all_9_24 = e2 & op(e0, e0) = e2) % 130.46/18.23 (59) op(e2, e0) = e1 % 130.46/18.23 (60) ~ (all_4_22 = e3) % 130.46/18.23 (61) op(e4, e0) = all_8_90 % 130.46/18.23 (62) op(e0, e3) = e1 % 130.46/18.23 (63) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.46/18.23 (64) all_9_6 = e3 % 130.46/18.23 (65) ~ (e1 = e0) % 130.46/18.23 (66) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.46/18.23 (67) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.46/18.23 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.46/18.23 (all_9_20 = e3 & op(e0, e4) = e3) % 130.46/18.23 (68) op(e3, e1) = e3 % 130.46/18.23 (69) op(e0, e1) = e0 % 130.46/18.23 (70) ~ (e3 = e2) % 130.46/18.23 (71) all_9_14 = e2 % 130.46/18.23 (72) all_9_13 = e3 % 130.46/18.23 (73) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 130.46/18.23 (74) all_9_12 = e4 % 130.46/18.23 (75) op(e0, e4) = all_4_4 % 130.46/18.23 (76) ~ (e4 = e1) % 130.46/18.23 (77) ~ (all_4_3 = e0) % 130.46/18.23 (78) all_9_15 = e1 % 130.46/18.23 (79) op(e0, e2) = e3 % 130.46/18.23 (80) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.46/18.23 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.46/18.23 (all_9_22 = e2 & op(e0, e2) = e2) % 130.46/18.23 (81) ~ (e3 = e1) % 130.46/18.23 (82) op(e3, e4) = e1 % 130.46/18.23 (83) all_9_9 = e4 % 130.46/18.23 (84) op(e1, e4) = all_4_3 % 130.46/18.23 (85) all_4_11 = e0 % 130.46/18.23 (86) op(e3, e0) = e2 % 130.46/18.23 (87) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.46/18.23 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.46/18.23 (all_9_20 = e2 & op(e0, e4) = e2) % 130.46/18.23 (88) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.46/18.23 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.46/18.23 (all_9_16 = e3 & op(e4, e0) = e3) % 130.46/18.23 (89) all_9_24 = e4 % 130.46/18.23 (90) op(e2, e0) = all_4_22 % 130.46/18.23 (91) all_9_19 = e0 % 130.46/18.23 (92) ~ (op(e0, e4) = e4) % 130.46/18.23 (93) ~ (e4 = e3) % 130.46/18.23 (94) op(e4, e0) = e3 % 130.46/18.23 (95) ~ (all_4_4 = e0) % 130.46/18.23 (96) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.46/18.23 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.46/18.23 (all_9_16 = e1 & op(e4, e0) = e1) % 130.46/18.23 (97) op(e2, e3) = e0 % 130.46/18.23 (98) ~ (all_4_3 = e1) % 130.46/18.23 (99) op(e0, e4) = e2 % 130.46/18.23 (100) all_6_2 = all_4_10 % 130.46/18.23 (101) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.46/18.23 (102) all_4_21 = e3 | ~ (op(e3, e0) = e3) % 130.46/18.23 (103) op(e2, e4) = e3 % 130.46/18.23 (104) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.46/18.23 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.46/18.23 (all_9_20 = e4 & op(e0, e4) = e4) % 130.46/18.23 (105) ~ (all_4_10 = e4) % 130.46/18.23 (106) ~ (op(e2, e3) = e3) % 130.46/18.23 (107) all_9_2 = e1 % 130.46/18.23 (108) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.46/18.23 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.46/18.23 (all_9_20 = e1 & op(e0, e4) = e1) % 130.46/18.23 (109) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 130.46/18.23 all_6_15 = e0 % 130.46/18.23 (110) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.46/18.23 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.46/18.23 (all_9_24 = e3 & op(e0, e0) = e3) % 130.46/18.23 (111) ~ (all_4_4 = e1) % 130.46/18.23 (112) ~ (all_4_10 = e2) % 130.46/18.23 (113) all_4_0 = e0 % 130.46/18.23 (114) ~ (e2 = e1) % 130.46/18.23 (115) all_6_15 = all_4_3 % 130.46/18.23 (116) all_9_7 = e0 % 130.46/18.23 (117) op(e4, e4) = e0 % 130.46/18.23 % 130.46/18.23 Begin of proof % 130.46/18.23 | % 130.46/18.23 | BETA: splitting (15) gives: % 130.46/18.23 | % 130.46/18.23 | Case 1: % 130.46/18.23 | | % 130.46/18.23 | | (118) ~ (op(e2, e3) = e2) % 130.46/18.23 | | % 130.46/18.23 | | BETA: splitting (10) gives: % 130.46/18.23 | | % 130.46/18.23 | | Case 1: % 130.46/18.23 | | | % 130.46/18.23 | | | (119) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.23 | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, e3) % 130.46/18.23 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & $i(all_8_42) % 130.46/18.23 | | | & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = e2) & ~ % 130.46/18.23 | | | (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 & % 130.46/18.23 | | | op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.46/18.23 | | | all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | % 130.46/18.23 | | | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.46/18.23 | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, e1) % 130.46/18.23 | | | = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & $i(all_8_48) % 130.46/18.23 | | | & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ % 130.46/18.23 | | | (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 & % 130.46/18.23 | | | op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.46/18.23 | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.46/18.23 | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.46/18.23 | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, e3) % 130.46/18.23 | | | = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) % 130.46/18.23 | | | & $i(all_8_54)) | (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ % 130.46/18.23 | | | (all_8_57 = all_8_69) & op(all_8_69, e3) = all_8_10 & % 130.46/18.23 | | | op(all_8_69, e2) = e3 & op(e3, e2) = all_8_69 & op(e2, e3) = % 130.46/18.23 | | | all_8_57 & $i(all_8_10) & $i(all_8_57) & $i(all_8_69)) | % 130.46/18.23 | | | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.46/18.23 | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, % 130.46/18.23 | | | e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & % 130.46/18.23 | | | $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = % 130.46/18.23 | | | e0) & ~ (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 % 130.46/18.23 | | | & op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.46/18.23 | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.46/18.23 | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.46/18.23 | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, % 130.46/18.23 | | | e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & % 130.46/18.23 | | | $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = % 130.46/18.23 | | | e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & % 130.46/18.23 | | | op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, % 130.46/18.23 | | | e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.46/18.23 | | | % 130.46/18.23 | | | BETA: splitting (119) gives: % 130.46/18.23 | | | % 130.46/18.23 | | | Case 1: % 130.46/18.23 | | | | % 130.46/18.23 | | | | (120) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) & % 130.46/18.23 | | | | op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & op(e4, % 130.46/18.23 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) & % 130.46/18.23 | | | | $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ (all_8_2 = % 130.46/18.23 | | | | e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, e4) = all_8_2 % 130.46/18.23 | | | | & op(all_8_66, e2) = e4 & op(e4, e2) = all_8_66 & op(e2, e4) % 130.46/18.23 | | | | = all_8_45 & $i(all_8_2) & $i(all_8_45) & $i(all_8_66)) | % 130.46/18.23 | | | | (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) & % 130.46/18.23 | | | | op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & op(e4, % 130.46/18.23 | | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) & % 130.46/18.23 | | | | $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ (all_8_6 = % 130.46/18.23 | | | | e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, e4) = all_8_6 % 130.46/18.23 | | | | & op(all_8_90, e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) % 130.46/18.23 | | | | = all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.46/18.23 | | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = all_8_54) & % 130.46/18.23 | | | | op(all_8_42, e4) = e3 & op(all_8_42, e3) = all_8_8 & op(e4, % 130.46/18.23 | | | | e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_8) & % 130.46/18.23 | | | | $i(all_8_42) & $i(all_8_54)) % 130.46/18.23 | | | | % 130.46/18.23 | | | | BETA: splitting (120) gives: % 130.46/18.23 | | | | % 130.46/18.23 | | | | Case 1: % 130.46/18.23 | | | | | % 130.46/18.23 | | | | | (121) (all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) % 130.46/18.23 | | | | | & op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & % 130.46/18.23 | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) % 130.46/18.23 | | | | | & $i(all_8_42) & $i(all_8_54)) | (all_8_3 = e4 & ~ % 130.46/18.23 | | | | | (all_8_2 = e2) & ~ (all_8_45 = all_8_66) & op(all_8_66, % 130.46/18.23 | | | | | e4) = all_8_2 & op(all_8_66, e2) = e4 & op(e4, e2) = % 130.46/18.23 | | | | | all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) & % 130.46/18.23 | | | | | $i(all_8_45) & $i(all_8_66)) % 130.46/18.23 | | | | | % 130.46/18.23 | | | | | BETA: splitting (121) gives: % 130.46/18.23 | | | | | % 130.46/18.23 | | | | | Case 1: % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | (122) all_8_1 = e4 & ~ (all_8_0 = e3) & ~ (all_8_42 = all_8_54) % 130.46/18.23 | | | | | | & op(all_8_54, e4) = all_8_0 & op(all_8_54, e3) = e4 & % 130.46/18.23 | | | | | | op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & $i(all_8_0) % 130.46/18.23 | | | | | | & $i(all_8_42) & $i(all_8_54) % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | ALPHA: (122) implies: % 130.46/18.23 | | | | | | (123) ~ (all_8_42 = all_8_54) % 130.46/18.23 | | | | | | (124) op(e3, e4) = all_8_42 % 130.46/18.23 | | | | | | (125) op(e4, e3) = all_8_54 % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 130.46/18.23 | | | | | | (14), (16), (17), (19), (20), (21), (22), (23), (24), % 130.46/18.23 | | | | | | (26), (28), (29), (30), (31), (32), (33), (35), (36), % 130.46/18.23 | | | | | | (38), (39), (40), (41), (42), (45), (46), (47), (48), % 130.46/18.23 | | | | | | (50), (51), (52), (53), (54), (56), (57), (58), (60), % 130.46/18.23 | | | | | | (61), (62), (63), (64), (65), (66), (67), (70), (71), % 130.46/18.23 | | | | | | (72), (74), (75), (76), (77), (78), (80), (81), (82), % 130.46/18.23 | | | | | | (83), (84), (85), (87), (88), (89), (90), (91), (92), % 130.46/18.23 | | | | | | (93), (94), (95), (96), (97), (98), (100), (101), (103), % 130.46/18.23 | | | | | | (104), (106), (107), (108), (109), (110), (111), (112), % 130.46/18.23 | | | | | | (113), (114), (115), (116), (117), (118), (123), (124), % 130.46/18.23 | | | | | | (125) are inconsistent by sub-proof #187. % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | Case 2: % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | (126) all_8_3 = e4 & ~ (all_8_2 = e2) & ~ (all_8_45 = all_8_66) % 130.46/18.23 | | | | | | & op(all_8_66, e4) = all_8_2 & op(all_8_66, e2) = e4 & % 130.46/18.23 | | | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_2) % 130.46/18.23 | | | | | | & $i(all_8_45) & $i(all_8_66) % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | ALPHA: (126) implies: % 130.46/18.23 | | | | | | (127) ~ (all_8_45 = all_8_66) % 130.46/18.23 | | | | | | (128) op(e2, e4) = all_8_45 % 130.46/18.23 | | | | | | (129) op(e4, e2) = all_8_66 % 130.46/18.23 | | | | | | (130) op(all_8_66, e2) = e4 % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | REDUCE: (25), (127) imply: % 130.46/18.23 | | | | | | (131) ~ (all_8_66 = e3) % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | SIMP: (131) implies: % 130.46/18.23 | | | | | | (132) ~ (all_8_66 = e3) % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | BETA: splitting (73) gives: % 130.46/18.23 | | | | | | % 130.46/18.23 | | | | | | Case 1: % 130.46/18.23 | | | | | | | % 130.46/18.23 | | | | | | | (133) ~ (op(e4, e2) = e4) % 130.46/18.23 | | | | | | | % 130.46/18.23 | | | | | | | BETA: splitting (63) gives: % 130.46/18.23 | | | | | | | % 130.46/18.23 | | | | | | | Case 1: % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | (134) ~ (op(e4, e2) = e2) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | GROUND_INST: instantiating (53) with e1, e4, e3, e0, simplifying % 130.46/18.23 | | | | | | | | with (62) gives: % 130.46/18.23 | | | | | | | | (135) e4 = e1 | ~ (op(e0, e3) = e4) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | PRED_UNIFY: (6), (92) imply: % 130.46/18.23 | | | | | | | | (136) ~ (all_8_90 = e4) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | GROUND_INST: instantiating (53) with e0, all_8_57, e3, e2, % 130.46/18.23 | | | | | | | | simplifying with (56), (97) gives: % 130.46/18.23 | | | | | | | | (137) all_8_57 = e0 % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_90, e0, e4, % 130.46/18.23 | | | | | | | | simplifying with (61), (94) gives: % 130.46/18.23 | | | | | | | | (138) all_8_90 = e3 % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | GROUND_INST: instantiating (53) with e1, all_8_66, e2, e4, % 130.46/18.23 | | | | | | | | simplifying with (49), (129) gives: % 130.46/18.23 | | | | | | | | (139) all_8_66 = e1 % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | PRED_UNIFY: (56), (118) imply: % 130.46/18.23 | | | | | | | | (140) ~ (all_8_57 = e2) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | PRED_UNIFY: (56), (106) imply: % 130.46/18.23 | | | | | | | | (141) ~ (all_8_57 = e3) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | PRED_UNIFY: (129), (134) imply: % 130.46/18.23 | | | | | | | | (142) ~ (all_8_66 = e2) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | PRED_UNIFY: (130), (133) imply: % 130.46/18.23 | | | | | | | | (143) ~ (all_8_66 = e4) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | REDUCE: (137), (141) imply: % 130.46/18.23 | | | | | | | | (144) ~ (e3 = e0) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | REDUCE: (137), (140) imply: % 130.46/18.23 | | | | | | | | (145) ~ (e2 = e0) % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.46/18.23 | | | | | | | | (16), (17), (20), (21), (23), (24), (29), (30), (31), % 130.46/18.23 | | | | | | | | (32), (33), (35), (36), (38), (39), (40), (42), (45), % 130.46/18.23 | | | | | | | | (46), (48), (50), (51), (52), (53), (54), (58), (63), % 130.46/18.23 | | | | | | | | (64), (65), (67), (70), (71), (72), (74), (75), (77), % 130.46/18.23 | | | | | | | | (78), (80), (82), (84), (85), (87), (89), (91), (95), % 130.46/18.23 | | | | | | | | (98), (100), (101), (103), (104), (107), (108), % 130.46/18.23 | | | | | | | | (109), (111), (112), (113), (115), (116), (117), % 130.46/18.23 | | | | | | | | (132), (135), (136), (138), (139), (142), (143) are % 130.46/18.23 | | | | | | | | inconsistent by sub-proof #190. % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | Case 2: % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | (146) op(e4, e2) = e2 % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | | REF_CLOSE: (63), (100), (112), (146) are inconsistent by % 130.46/18.23 | | | | | | | | sub-proof #261. % 130.46/18.23 | | | | | | | | % 130.46/18.23 | | | | | | | End of split % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | Case 2: % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | (147) op(e4, e2) = e4 % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | REF_CLOSE: (73), (100), (105), (147) are inconsistent by sub-proof % 130.74/18.23 | | | | | | | #298. % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | End of split % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | End of split % 130.74/18.23 | | | | | % 130.74/18.23 | | | | Case 2: % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | (148) (all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) % 130.74/18.23 | | | | | & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & % 130.74/18.23 | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) % 130.74/18.23 | | | | | & $i(all_8_48) & $i(all_8_78)) | (all_8_7 = e4 & ~ % 130.74/18.23 | | | | | (all_8_6 = e0) & ~ (all_8_51 = all_8_90) & op(all_8_90, % 130.74/18.23 | | | | | e4) = all_8_6 & op(all_8_90, e0) = e4 & op(e4, e0) = % 130.74/18.23 | | | | | all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_6) & % 130.74/18.23 | | | | | $i(all_8_51) & $i(all_8_90)) | (all_8_9 = e3 & ~ (all_8_8 % 130.74/18.23 | | | | | = e4) & ~ (all_8_42 = all_8_54) & op(all_8_42, e4) = e3 % 130.74/18.23 | | | | | & op(all_8_42, e3) = all_8_8 & op(e4, e3) = all_8_54 & % 130.74/18.23 | | | | | op(e3, e4) = all_8_42 & $i(all_8_8) & $i(all_8_42) & % 130.74/18.23 | | | | | $i(all_8_54)) % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | BETA: splitting (148) gives: % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | Case 1: % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | (149) all_8_5 = e4 & ~ (all_8_4 = e1) & ~ (all_8_48 = all_8_78) % 130.74/18.23 | | | | | | & op(all_8_78, e4) = all_8_4 & op(all_8_78, e1) = e4 & % 130.74/18.23 | | | | | | op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_4) % 130.74/18.23 | | | | | | & $i(all_8_48) & $i(all_8_78) % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | ALPHA: (149) implies: % 130.74/18.23 | | | | | | (150) ~ (all_8_48 = all_8_78) % 130.74/18.23 | | | | | | (151) op(e1, e4) = all_8_48 % 130.74/18.23 | | | | | | (152) op(e4, e1) = all_8_78 % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | REF_CLOSE: (3), (44), (53), (150), (151), (152) are inconsistent by % 130.74/18.23 | | | | | | sub-proof #189. % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | Case 2: % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | (153) (all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 130.74/18.23 | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, % 130.74/18.23 | | | | | | e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.74/18.23 | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90)) | % 130.74/18.23 | | | | | | (all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 130.74/18.23 | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.74/18.23 | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.74/18.23 | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54)) % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | BETA: splitting (153) gives: % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | Case 1: % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | (154) all_8_7 = e4 & ~ (all_8_6 = e0) & ~ (all_8_51 = % 130.74/18.23 | | | | | | | all_8_90) & op(all_8_90, e4) = all_8_6 & op(all_8_90, % 130.74/18.23 | | | | | | | e0) = e4 & op(e4, e0) = all_8_90 & op(e0, e4) = % 130.74/18.23 | | | | | | | all_8_51 & $i(all_8_6) & $i(all_8_51) & $i(all_8_90) % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | ALPHA: (154) implies: % 130.74/18.23 | | | | | | | (155) ~ (all_8_51 = all_8_90) % 130.74/18.23 | | | | | | | (156) op(e0, e4) = all_8_51 % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.74/18.23 | | | | | | | (16), (20), (21), (23), (24), (29), (30), (31), (32), % 130.74/18.23 | | | | | | | (33), (36), (38), (39), (40), (42), (45), (46), (48), % 130.74/18.23 | | | | | | | (51), (52), (53), (54), (56), (58), (61), (62), (63), % 130.74/18.23 | | | | | | | (64), (65), (67), (71), (72), (74), (75), (76), (77), % 130.74/18.23 | | | | | | | (78), (80), (81), (82), (84), (85), (87), (89), (91), % 130.74/18.23 | | | | | | | (92), (94), (95), (97), (98), (99), (100), (101), % 130.74/18.23 | | | | | | | (103), (104), (106), (107), (108), (109), (111), (112), % 130.74/18.23 | | | | | | | (113), (114), (115), (116), (117), (118), (155), (156) % 130.74/18.23 | | | | | | | are inconsistent by sub-proof #186. % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | Case 2: % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | (157) all_8_9 = e3 & ~ (all_8_8 = e4) & ~ (all_8_42 = % 130.74/18.23 | | | | | | | all_8_54) & op(all_8_42, e4) = e3 & op(all_8_42, e3) = % 130.74/18.23 | | | | | | | all_8_8 & op(e4, e3) = all_8_54 & op(e3, e4) = all_8_42 & % 130.74/18.23 | | | | | | | $i(all_8_8) & $i(all_8_42) & $i(all_8_54) % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | ALPHA: (157) implies: % 130.74/18.23 | | | | | | | (158) ~ (all_8_42 = all_8_54) % 130.74/18.23 | | | | | | | (159) op(e3, e4) = all_8_42 % 130.74/18.23 | | | | | | | (160) op(e4, e3) = all_8_54 % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 130.74/18.23 | | | | | | | (14), (16), (17), (19), (20), (21), (22), (23), (24), % 130.74/18.23 | | | | | | | (26), (28), (29), (30), (31), (32), (33), (35), (36), % 130.74/18.23 | | | | | | | (38), (39), (40), (41), (42), (45), (46), (47), (48), % 130.74/18.23 | | | | | | | (50), (51), (52), (53), (54), (56), (57), (58), (60), % 130.74/18.23 | | | | | | | (61), (62), (63), (64), (65), (66), (67), (70), (71), % 130.74/18.23 | | | | | | | (72), (74), (75), (76), (77), (78), (80), (81), (82), % 130.74/18.23 | | | | | | | (83), (84), (85), (87), (88), (89), (90), (91), (92), % 130.74/18.23 | | | | | | | (93), (94), (95), (96), (97), (98), (100), (101), % 130.74/18.23 | | | | | | | (103), (104), (106), (107), (108), (109), (110), (111), % 130.74/18.23 | | | | | | | (112), (113), (114), (115), (116), (117), (118), (158), % 130.74/18.23 | | | | | | | (159), (160) are inconsistent by sub-proof #187. % 130.74/18.23 | | | | | | | % 130.74/18.23 | | | | | | End of split % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | End of split % 130.74/18.23 | | | | | % 130.74/18.23 | | | | End of split % 130.74/18.23 | | | | % 130.74/18.23 | | | Case 2: % 130.74/18.23 | | | | % 130.74/18.23 | | | | (161) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) % 130.74/18.23 | | | | & op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & % 130.74/18.23 | | | | op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) % 130.74/18.23 | | | | & $i(all_8_57) & $i(all_8_69)) | (all_8_13 = e3 & ~ % 130.74/18.23 | | | | (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & op(all_8_81, e3) % 130.74/18.23 | | | | = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = all_8_81 & % 130.74/18.23 | | | | op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) & % 130.74/18.23 | | | | $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ % 130.74/18.23 | | | | (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & % 130.74/18.23 | | | | op(all_8_93, e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.74/18.23 | | | | all_8_63 & $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | % 130.74/18.23 | | | | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) % 130.74/18.23 | | | | & op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & % 130.74/18.23 | | | | op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) % 130.74/18.23 | | | | & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ % 130.74/18.23 | | | | (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) % 130.74/18.23 | | | | = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & % 130.74/18.23 | | | | op(e2, e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & % 130.74/18.23 | | | | $i(all_8_69)) % 130.74/18.23 | | | | % 130.74/18.23 | | | | REF_CLOSE: (1), (5), (19), (25), (28), (37), (53), (60), (68), (82), % 130.74/18.23 | | | | (86), (90), (97), (114), (161) are inconsistent by sub-proof % 130.74/18.23 | | | | #182. % 130.74/18.23 | | | | % 130.74/18.23 | | | End of split % 130.74/18.23 | | | % 130.74/18.23 | | Case 2: % 130.74/18.23 | | | % 130.74/18.23 | | | (162) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) & % 130.74/18.23 | | | op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & op(e2, % 130.74/18.23 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) & % 130.74/18.23 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ (all_8_22 = % 130.74/18.23 | | | e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) = all_8_22 % 130.74/18.23 | | | & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = % 130.74/18.23 | | | all_8_75 & $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) | % 130.74/18.23 | | | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.74/18.23 | | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, % 130.74/18.23 | | | e1) = all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & % 130.74/18.23 | | | $i(all_8_48) & $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = % 130.74/18.23 | | | e3) & ~ (all_8_60 = all_8_81) & op(all_8_60, e3) = e1 & % 130.74/18.23 | | | op(all_8_60, e1) = all_8_26 & op(e3, e1) = all_8_81 & op(e1, % 130.74/18.23 | | | e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) % 130.74/18.23 | | | | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) % 130.74/18.23 | | | & op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, % 130.74/18.23 | | | e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & % 130.74/18.23 | | | $i(all_8_72) & $i(all_8_84)) | (all_8_31 = e1 & ~ (all_8_30 = % 130.74/18.23 | | | e0) & ~ (all_8_87 = all_8_99) & op(all_8_99, e1) = all_8_30 % 130.74/18.23 | | | & op(all_8_99, e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = % 130.74/18.23 | | | all_8_87 & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | % 130.74/18.23 | | | (all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 130.74/18.23 | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & op(e4, % 130.74/18.23 | | | e0) = all_8_90 & op(e0, e4) = all_8_51 & $i(all_8_32) & % 130.74/18.23 | | | $i(all_8_51) & $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = % 130.74/18.23 | | | e3) & ~ (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 & % 130.74/18.23 | | | op(all_8_63, e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, % 130.74/18.23 | | | e3) = all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) % 130.74/18.23 | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 130.74/18.23 | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & op(e2, % 130.74/18.23 | | | e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) & % 130.74/18.23 | | | $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 & ~ (all_8_38 = % 130.74/18.23 | | | e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) = e0 & % 130.74/18.23 | | | op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & op(e0, % 130.74/18.23 | | | e1) = all_8_87 & $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.74/18.23 | | | % 130.74/18.23 | | | BETA: splitting (162) gives: % 130.74/18.23 | | | % 130.74/18.23 | | | Case 1: % 130.74/18.23 | | | | % 130.74/18.23 | | | | (163) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = all_8_84) % 130.74/18.23 | | | | & op(all_8_84, e2) = all_8_20 & op(all_8_84, e1) = e2 & % 130.74/18.23 | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_20) % 130.74/18.23 | | | | & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = e2 & ~ % 130.74/18.23 | | | | (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & op(all_8_96, e2) % 130.74/18.23 | | | | = all_8_22 & op(all_8_96, e0) = e2 & op(e2, e0) = all_8_96 & % 130.74/18.23 | | | | op(e0, e2) = all_8_75 & $i(all_8_22) & $i(all_8_75) & % 130.74/18.23 | | | | $i(all_8_96)) | (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ % 130.74/18.23 | | | | (all_8_48 = all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, % 130.74/18.23 | | | | e1) = all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = % 130.74/18.23 | | | | all_8_48 & $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | % 130.74/18.23 | | | | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) % 130.74/18.23 | | | | & op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & % 130.74/18.23 | | | | op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) % 130.74/18.23 | | | | & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ % 130.74/18.23 | | | | (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & op(all_8_72, e2) % 130.74/18.23 | | | | = e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = all_8_84 & % 130.74/18.23 | | | | op(e1, e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & % 130.74/18.23 | | | | $i(all_8_84)) % 130.74/18.23 | | | | % 130.74/18.23 | | | | BETA: splitting (163) gives: % 130.74/18.23 | | | | % 130.74/18.23 | | | | Case 1: % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | (164) (all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = % 130.74/18.23 | | | | | all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.74/18.23 | | | | | e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 % 130.74/18.23 | | | | | & $i(all_8_20) & $i(all_8_72) & $i(all_8_84)) | (all_8_23 = % 130.74/18.23 | | | | | e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = all_8_96) & % 130.74/18.23 | | | | | op(all_8_96, e2) = all_8_22 & op(all_8_96, e0) = e2 & % 130.74/18.23 | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.74/18.23 | | | | | $i(all_8_22) & $i(all_8_75) & $i(all_8_96)) % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | BETA: splitting (164) gives: % 130.74/18.23 | | | | | % 130.74/18.23 | | | | | Case 1: % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | (165) all_8_21 = e2 & ~ (all_8_20 = e1) & ~ (all_8_72 = % 130.74/18.23 | | | | | | all_8_84) & op(all_8_84, e2) = all_8_20 & op(all_8_84, % 130.74/18.23 | | | | | | e1) = e2 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 % 130.74/18.23 | | | | | | & $i(all_8_20) & $i(all_8_72) & $i(all_8_84) % 130.74/18.23 | | | | | | % 130.74/18.23 | | | | | | ALPHA: (165) implies: % 130.74/18.24 | | | | | | (166) ~ (all_8_72 = all_8_84) % 130.74/18.24 | | | | | | (167) op(e1, e2) = all_8_72 % 130.74/18.24 | | | | | | (168) op(e2, e1) = all_8_84 % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | REF_CLOSE: (27), (53), (55), (166), (167), (168) are inconsistent by % 130.74/18.24 | | | | | | sub-proof #181. % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | Case 2: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | (169) all_8_23 = e2 & ~ (all_8_22 = e0) & ~ (all_8_75 = % 130.74/18.24 | | | | | | all_8_96) & op(all_8_96, e2) = all_8_22 & op(all_8_96, % 130.74/18.24 | | | | | | e0) = e2 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.74/18.24 | | | | | | & $i(all_8_22) & $i(all_8_75) & $i(all_8_96) % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | ALPHA: (169) implies: % 130.74/18.24 | | | | | | (170) ~ (all_8_75 = all_8_96) % 130.74/18.24 | | | | | | (171) op(e0, e2) = all_8_75 % 130.74/18.24 | | | | | | (172) op(e2, e0) = all_8_96 % 130.74/18.24 | | | | | | (173) op(all_8_96, e0) = e2 % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | BETA: splitting (20) gives: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | Case 1: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (174) ~ (op(e2, e0) = e2) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_75, e2, e0, % 130.74/18.24 | | | | | | | simplifying with (79), (171) gives: % 130.74/18.24 | | | | | | | (175) all_8_75 = e3 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e1, e4, e3, e0, simplifying % 130.74/18.24 | | | | | | | with (62) gives: % 130.74/18.24 | | | | | | | (176) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (6), (92) imply: % 130.74/18.24 | | | | | | | (177) ~ (all_8_90 = e4) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e1, all_8_96, e0, e2, % 130.74/18.24 | | | | | | | simplifying with (59), (172) gives: % 130.74/18.24 | | | | | | | (178) all_8_96 = e1 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e0, all_8_57, e3, e2, % 130.74/18.24 | | | | | | | simplifying with (56), (97) gives: % 130.74/18.24 | | | | | | | (179) all_8_57 = e0 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_90, e0, e4, % 130.74/18.24 | | | | | | | simplifying with (61), (94) gives: % 130.74/18.24 | | | | | | | (180) all_8_90 = e3 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (173), (174) imply: % 130.74/18.24 | | | | | | | (181) ~ (all_8_96 = e2) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.74/18.24 | | | | | | | (16), (17), (20), (21), (23), (24), (29), (30), (31), % 130.74/18.24 | | | | | | | (32), (33), (36), (38), (39), (40), (42), (45), (46), % 130.74/18.24 | | | | | | | (48), (51), (52), (53), (54), (56), (58), (63), (64), % 130.74/18.24 | | | | | | | (65), (67), (70), (71), (72), (74), (75), (76), (77), % 130.74/18.24 | | | | | | | (78), (80), (82), (84), (85), (87), (89), (91), (95), % 130.74/18.24 | | | | | | | (98), (100), (101), (103), (104), (106), (107), (108), % 130.74/18.24 | | | | | | | (109), (111), (112), (113), (115), (116), (117), (118), % 130.74/18.24 | | | | | | | (170), (175), (176), (177), (178), (179), (180), (181) % 130.74/18.24 | | | | | | | are inconsistent by sub-proof #179. % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | Case 2: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (182) op(e2, e0) = e2 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REF_CLOSE: (20), (52), (182) are inconsistent by sub-proof #214. % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | End of split % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | End of split % 130.74/18.24 | | | | | % 130.74/18.24 | | | | Case 2: % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | (183) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = % 130.74/18.24 | | | | | all_8_78) & op(all_8_48, e4) = e1 & op(all_8_48, e1) = % 130.74/18.24 | | | | | all_8_24 & op(e4, e1) = all_8_78 & op(e1, e4) = all_8_48 & % 130.74/18.24 | | | | | $i(all_8_24) & $i(all_8_48) & $i(all_8_78)) | (all_8_27 = % 130.74/18.24 | | | | | e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.74/18.24 | | | | | op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & % 130.74/18.24 | | | | | op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & % 130.74/18.24 | | | | | $i(all_8_26) & $i(all_8_60) & $i(all_8_81)) | (all_8_29 = % 130.74/18.24 | | | | | e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & % 130.74/18.24 | | | | | op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & % 130.74/18.24 | | | | | op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.74/18.24 | | | | | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | REF_CLOSE: (1), (3), (27), (44), (53), (55), (68), (183) are % 130.74/18.24 | | | | | inconsistent by sub-proof #178. % 130.74/18.24 | | | | | % 130.74/18.24 | | | | End of split % 130.74/18.24 | | | | % 130.74/18.24 | | | Case 2: % 130.74/18.24 | | | | % 130.74/18.24 | | | | (184) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = all_8_99) % 130.74/18.24 | | | | & op(all_8_99, e1) = all_8_30 & op(all_8_99, e0) = e1 & % 130.74/18.24 | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & $i(all_8_30) % 130.74/18.24 | | | | & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = e0 & ~ % 130.74/18.24 | | | | (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & op(all_8_51, e4) % 130.74/18.24 | | | | = e0 & op(all_8_51, e0) = all_8_32 & op(e4, e0) = all_8_90 & % 130.74/18.24 | | | | op(e0, e4) = all_8_51 & $i(all_8_32) & $i(all_8_51) & % 130.74/18.24 | | | | $i(all_8_90)) | (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ % 130.74/18.24 | | | | (all_8_63 = all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, % 130.74/18.24 | | | | e0) = all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = % 130.74/18.24 | | | | all_8_63 & $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | % 130.74/18.24 | | | | (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) % 130.74/18.24 | | | | & op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & % 130.74/18.24 | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & $i(all_8_36) % 130.74/18.24 | | | | & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = e0 & ~ % 130.74/18.24 | | | | (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & op(all_8_87, e1) % 130.74/18.24 | | | | = e0 & op(all_8_87, e0) = all_8_38 & op(e1, e0) = all_8_99 & % 130.74/18.24 | | | | op(e0, e1) = all_8_87 & $i(all_8_38) & $i(all_8_87) & % 130.74/18.24 | | | | $i(all_8_99)) % 130.74/18.24 | | | | % 130.74/18.24 | | | | BETA: splitting (184) gives: % 130.74/18.24 | | | | % 130.74/18.24 | | | | Case 1: % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | (185) (all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = % 130.74/18.24 | | | | | all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.74/18.24 | | | | | e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.74/18.24 | | | | | & $i(all_8_30) & $i(all_8_87) & $i(all_8_99)) | (all_8_33 = % 130.74/18.24 | | | | | e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = all_8_90) & % 130.74/18.24 | | | | | op(all_8_51, e4) = e0 & op(all_8_51, e0) = all_8_32 & % 130.74/18.24 | | | | | op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.74/18.24 | | | | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90)) % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | BETA: splitting (185) gives: % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | Case 1: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | (186) all_8_31 = e1 & ~ (all_8_30 = e0) & ~ (all_8_87 = % 130.74/18.24 | | | | | | all_8_99) & op(all_8_99, e1) = all_8_30 & op(all_8_99, % 130.74/18.24 | | | | | | e0) = e1 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.74/18.24 | | | | | | & $i(all_8_30) & $i(all_8_87) & $i(all_8_99) % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | ALPHA: (186) implies: % 130.74/18.24 | | | | | | (187) ~ (all_8_87 = all_8_99) % 130.74/18.24 | | | | | | (188) op(e0, e1) = all_8_87 % 130.74/18.24 | | | | | | (189) op(e1, e0) = all_8_99 % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | REF_CLOSE: (43), (53), (69), (187), (188), (189) are inconsistent by % 130.74/18.24 | | | | | | sub-proof #177. % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | Case 2: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | (190) all_8_33 = e0 & ~ (all_8_32 = e4) & ~ (all_8_51 = % 130.74/18.24 | | | | | | all_8_90) & op(all_8_51, e4) = e0 & op(all_8_51, e0) = % 130.74/18.24 | | | | | | all_8_32 & op(e4, e0) = all_8_90 & op(e0, e4) = all_8_51 & % 130.74/18.24 | | | | | | $i(all_8_32) & $i(all_8_51) & $i(all_8_90) % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | ALPHA: (190) implies: % 130.74/18.24 | | | | | | (191) ~ (all_8_51 = all_8_90) % 130.74/18.24 | | | | | | (192) op(e0, e4) = all_8_51 % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.74/18.24 | | | | | | (16), (20), (21), (23), (24), (29), (30), (31), (32), % 130.74/18.24 | | | | | | (33), (36), (38), (39), (40), (42), (45), (46), (48), % 130.74/18.24 | | | | | | (51), (52), (53), (54), (56), (58), (61), (62), (63), % 130.74/18.24 | | | | | | (64), (65), (67), (71), (72), (74), (75), (76), (77), % 130.74/18.24 | | | | | | (78), (80), (81), (82), (84), (85), (87), (89), (91), % 130.74/18.24 | | | | | | (92), (94), (95), (97), (98), (99), (100), (101), (103), % 130.74/18.24 | | | | | | (104), (106), (107), (108), (109), (111), (112), (113), % 130.74/18.24 | | | | | | (114), (115), (116), (117), (118), (191), (192) are % 130.74/18.24 | | | | | | inconsistent by sub-proof #186. % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | End of split % 130.74/18.24 | | | | | % 130.74/18.24 | | | | Case 2: % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | (193) (all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = % 130.74/18.24 | | | | | all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 130.74/18.24 | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.74/18.24 | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93)) | (all_8_37 = % 130.74/18.24 | | | | | e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = all_8_96) & % 130.74/18.24 | | | | | op(all_8_75, e2) = e0 & op(all_8_75, e0) = all_8_36 & % 130.74/18.24 | | | | | op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 & % 130.74/18.24 | | | | | $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 = % 130.74/18.24 | | | | | e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.74/18.24 | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.74/18.24 | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.74/18.24 | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | BETA: splitting (193) gives: % 130.74/18.24 | | | | | % 130.74/18.24 | | | | | Case 1: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | (194) all_8_35 = e0 & ~ (all_8_34 = e3) & ~ (all_8_63 = % 130.74/18.24 | | | | | | all_8_93) & op(all_8_63, e3) = e0 & op(all_8_63, e0) = % 130.74/18.24 | | | | | | all_8_34 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.74/18.24 | | | | | | $i(all_8_34) & $i(all_8_63) & $i(all_8_93) % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | ALPHA: (194) implies: % 130.74/18.24 | | | | | | (195) ~ (all_8_63 = all_8_93) % 130.74/18.24 | | | | | | (196) op(e0, e3) = all_8_63 % 130.74/18.24 | | | | | | (197) op(e3, e0) = all_8_93 % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | BETA: splitting (102) gives: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | Case 1: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (198) ~ (op(e3, e0) = e3) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e1, all_8_63, e3, e0, % 130.74/18.24 | | | | | | | simplifying with (62), (196) gives: % 130.74/18.24 | | | | | | | (199) all_8_63 = e1 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (34), (196) imply: % 130.74/18.24 | | | | | | | (200) ~ (all_8_63 = e3) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e1, e4, e3, e0, simplifying % 130.74/18.24 | | | | | | | with (62) gives: % 130.74/18.24 | | | | | | | (201) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (6), (92) imply: % 130.74/18.24 | | | | | | | (202) ~ (all_8_90 = e4) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e0, all_8_57, e3, e2, % 130.74/18.24 | | | | | | | simplifying with (56), (97) gives: % 130.74/18.24 | | | | | | | (203) all_8_57 = e0 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e2, all_8_93, e0, e3, % 130.74/18.24 | | | | | | | simplifying with (86), (197) gives: % 130.74/18.24 | | | | | | | (204) all_8_93 = e2 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_90, e0, e4, % 130.74/18.24 | | | | | | | simplifying with (61), (94) gives: % 130.74/18.24 | | | | | | | (205) all_8_90 = e3 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (56), (118) imply: % 130.74/18.24 | | | | | | | (206) ~ (all_8_57 = e2) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (56), (106) imply: % 130.74/18.24 | | | | | | | (207) ~ (all_8_57 = e3) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | PRED_UNIFY: (197), (198) imply: % 130.74/18.24 | | | | | | | (208) ~ (all_8_93 = e3) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REDUCE: (203), (207) imply: % 130.74/18.24 | | | | | | | (209) ~ (e3 = e0) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REDUCE: (203), (206) imply: % 130.74/18.24 | | | | | | | (210) ~ (e2 = e0) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.74/18.24 | | | | | | | (16), (17), (20), (21), (23), (24), (29), (30), (31), % 130.74/18.24 | | | | | | | (32), (33), (35), (36), (38), (39), (40), (42), (45), % 130.74/18.24 | | | | | | | (46), (48), (50), (51), (52), (53), (54), (58), (63), % 130.74/18.24 | | | | | | | (64), (65), (67), (71), (72), (74), (75), (76), (77), % 130.74/18.24 | | | | | | | (78), (80), (82), (84), (85), (87), (89), (91), (95), % 130.74/18.24 | | | | | | | (98), (100), (101), (103), (104), (107), (108), (109), % 130.74/18.24 | | | | | | | (111), (112), (113), (115), (116), (117), (195), (199), % 130.74/18.24 | | | | | | | (200), (201), (202), (204), (205), (208) are % 130.74/18.24 | | | | | | | inconsistent by sub-proof #176. % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | Case 2: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (211) op(e3, e0) = e3 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REF_CLOSE: (5), (19), (28), (211) are inconsistent by sub-proof % 130.74/18.24 | | | | | | | #228. % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | End of split % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | Case 2: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | (212) (all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.74/18.24 | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.74/18.24 | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.74/18.24 | | | | | | & $i(all_8_36) & $i(all_8_75) & $i(all_8_96)) | (all_8_39 % 130.74/18.24 | | | | | | = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = all_8_99) & % 130.74/18.24 | | | | | | op(all_8_87, e1) = e0 & op(all_8_87, e0) = all_8_38 & % 130.74/18.24 | | | | | | op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 & % 130.74/18.24 | | | | | | $i(all_8_38) & $i(all_8_87) & $i(all_8_99)) % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | BETA: splitting (212) gives: % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | | Case 1: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (213) all_8_37 = e0 & ~ (all_8_36 = e2) & ~ (all_8_75 = % 130.74/18.24 | | | | | | | all_8_96) & op(all_8_75, e2) = e0 & op(all_8_75, e0) = % 130.74/18.24 | | | | | | | all_8_36 & op(e2, e0) = all_8_96 & op(e0, e2) = all_8_75 % 130.74/18.24 | | | | | | | & $i(all_8_36) & $i(all_8_75) & $i(all_8_96) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | ALPHA: (213) implies: % 130.74/18.24 | | | | | | | (214) ~ (all_8_75 = all_8_96) % 130.74/18.24 | | | | | | | (215) op(e0, e2) = all_8_75 % 130.74/18.24 | | | | | | | (216) op(e2, e0) = all_8_96 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | BETA: splitting (20) gives: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | Case 1: % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | (217) ~ (op(e2, e0) = e2) % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_75, e2, e0, % 130.74/18.24 | | | | | | | | simplifying with (79), (215) gives: % 130.74/18.24 | | | | | | | | (218) all_8_75 = e3 % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | GROUND_INST: instantiating (53) with e1, e4, e3, e0, simplifying % 130.74/18.24 | | | | | | | | with (62) gives: % 130.74/18.24 | | | | | | | | (219) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | PRED_UNIFY: (6), (92) imply: % 130.74/18.24 | | | | | | | | (220) ~ (all_8_90 = e4) % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | GROUND_INST: instantiating (53) with e1, all_8_96, e0, e2, % 130.74/18.24 | | | | | | | | simplifying with (59), (216) gives: % 130.74/18.24 | | | | | | | | (221) all_8_96 = e1 % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | GROUND_INST: instantiating (53) with e0, all_8_57, e3, e2, % 130.74/18.24 | | | | | | | | simplifying with (56), (97) gives: % 130.74/18.24 | | | | | | | | (222) all_8_57 = e0 % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | GROUND_INST: instantiating (53) with e3, all_8_90, e0, e4, % 130.74/18.24 | | | | | | | | simplifying with (61), (94) gives: % 130.74/18.24 | | | | | | | | (223) all_8_90 = e3 % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | PRED_UNIFY: (216), (217) imply: % 130.74/18.24 | | | | | | | | (224) ~ (all_8_96 = e2) % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 130.74/18.24 | | | | | | | | (16), (17), (20), (21), (23), (24), (29), (30), (31), % 130.74/18.24 | | | | | | | | (32), (33), (36), (38), (39), (40), (42), (45), (46), % 130.74/18.24 | | | | | | | | (48), (51), (52), (53), (54), (56), (58), (63), (64), % 130.74/18.24 | | | | | | | | (65), (67), (70), (71), (72), (74), (75), (76), (77), % 130.74/18.24 | | | | | | | | (78), (80), (82), (84), (85), (87), (89), (91), (95), % 130.74/18.24 | | | | | | | | (98), (100), (101), (103), (104), (106), (107), % 130.74/18.24 | | | | | | | | (108), (109), (111), (112), (113), (115), (116), % 130.74/18.24 | | | | | | | | (117), (118), (214), (218), (219), (220), (221), % 130.74/18.24 | | | | | | | | (222), (223), (224) are inconsistent by sub-proof % 130.74/18.24 | | | | | | | | #179. % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | Case 2: % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | (225) op(e2, e0) = e2 % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | | REF_CLOSE: (20), (52), (225) are inconsistent by sub-proof #214. % 130.74/18.24 | | | | | | | | % 130.74/18.24 | | | | | | | End of split % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | Case 2: % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | (226) all_8_39 = e0 & ~ (all_8_38 = e1) & ~ (all_8_87 = % 130.74/18.24 | | | | | | | all_8_99) & op(all_8_87, e1) = e0 & op(all_8_87, e0) = % 130.74/18.24 | | | | | | | all_8_38 & op(e1, e0) = all_8_99 & op(e0, e1) = all_8_87 % 130.74/18.24 | | | | | | | & $i(all_8_38) & $i(all_8_87) & $i(all_8_99) % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | ALPHA: (226) implies: % 130.74/18.24 | | | | | | | (227) ~ (all_8_87 = all_8_99) % 130.74/18.24 | | | | | | | (228) op(e0, e1) = all_8_87 % 130.74/18.24 | | | | | | | (229) op(e1, e0) = all_8_99 % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | | REF_CLOSE: (43), (53), (69), (227), (228), (229) are inconsistent % 130.74/18.24 | | | | | | | by sub-proof #177. % 130.74/18.24 | | | | | | | % 130.74/18.24 | | | | | | End of split % 130.74/18.24 | | | | | | % 130.74/18.24 | | | | | End of split % 130.74/18.24 | | | | | % 130.74/18.24 | | | | End of split % 130.74/18.24 | | | | % 130.74/18.24 | | | End of split % 130.74/18.24 | | | % 130.74/18.24 | | End of split % 130.74/18.24 | | % 130.74/18.24 | Case 2: % 130.74/18.24 | | % 130.74/18.24 | | (230) all_4_7 = e2 % 130.74/18.24 | | % 130.74/18.24 | | COMBINE_EQS: (18), (230) imply: % 130.74/18.24 | | (231) e2 = e0 % 130.74/18.24 | | % 130.74/18.24 | | COMBINE_EQS: (71), (231) imply: % 130.74/18.24 | | (232) all_9_14 = e0 % 130.74/18.24 | | % 130.74/18.24 | | REF_CLOSE: (4), (7), (8), (9), (11), (12), (13), (16), (17), (21), (24), % 130.74/18.24 | | (32), (38), (40), (46), (50), (51), (53), (63), (70), (72), (74), % 130.74/18.24 | | (76), (78), (80), (82), (85), (87), (93), (100), (104), (112), % 130.74/18.24 | | (113), (114), (232) are inconsistent by sub-proof #244. % 130.74/18.24 | | % 130.74/18.24 | End of split % 130.74/18.24 | % 130.74/18.24 End of proof % 130.74/18.24 % 130.74/18.24 Sub-proof #176 shows that the following formulas are inconsistent: % 130.74/18.24 ---------------------------------------------------------------- % 130.74/18.24 (1) all_9_8 = e4 % 130.74/18.24 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.24 (3) op(e0, all_8_90) = e4 % 130.74/18.24 (4) all_6_5 = e1 % 130.74/18.24 (5) ~ (e4 = e0) % 130.74/18.24 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.24 (7) all_9_20 = e2 % 130.74/18.24 (8) all_6_10 = e3 % 130.74/18.24 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.24 (10) ~ (all_4_3 = all_4_4) % 130.74/18.24 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.24 (12) ~ (e4 = e2) % 130.74/18.24 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.24 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.24 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.24 (16) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.24 (17) all_8_63 = e1 % 130.74/18.24 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.24 (19) ~ (all_4_3 = e3) % 130.74/18.24 (20) all_6_20 = all_4_4 % 130.74/18.24 (21) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.24 (22) all_9_11 = e2 % 130.74/18.24 (23) ~ (e3 = e0) % 130.74/18.24 (24) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.24 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.24 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.24 (25) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.24 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.24 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.24 (26) all_9_16 = e3 % 130.74/18.24 (27) all_6_22 = all_4_14 % 130.74/18.24 (28) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.24 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.24 (30) all_8_90 = e3 % 130.74/18.24 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.24 = e0 % 130.74/18.24 (32) ~ (all_4_14 = e2) % 130.74/18.24 (33) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.24 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.24 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.24 (34) ~ (e2 = e0) % 130.74/18.24 (35) ~ (all_8_93 = e3) % 130.74/18.24 (36) all_9_0 = e0 % 130.74/18.24 (37) ~ (all_4_22 = e2) % 130.74/18.24 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.24 (39) ~ (all_4_4 = e3) % 130.74/18.24 (40) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.24 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.24 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.24 (41) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.24 (42) all_9_6 = e3 % 130.74/18.24 (43) ~ (e1 = e0) % 130.74/18.24 (44) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.24 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.24 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.24 (45) all_9_14 = e2 % 130.74/18.24 (46) ~ (all_8_90 = e4) % 130.74/18.24 (47) all_9_13 = e3 % 130.74/18.24 (48) all_9_12 = e4 % 130.74/18.24 (49) op(e0, e4) = all_4_4 % 130.74/18.24 (50) ~ (e4 = e1) % 130.74/18.24 (51) ~ (all_4_3 = e0) % 130.74/18.24 (52) ~ (all_8_63 = e3) % 130.74/18.24 (53) all_9_15 = e1 % 130.74/18.24 (54) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.24 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.24 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.24 (55) op(e3, e4) = e1 % 130.74/18.24 (56) op(e1, e4) = all_4_3 % 130.74/18.24 (57) all_4_11 = e0 % 130.74/18.24 (58) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.24 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.24 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.24 (59) all_9_24 = e4 % 130.74/18.24 (60) all_9_19 = e0 % 130.74/18.24 (61) ~ (all_4_4 = e0) % 130.74/18.24 (62) ~ (all_4_3 = e1) % 130.74/18.24 (63) all_6_2 = all_4_10 % 130.74/18.24 (64) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.24 (65) op(e2, e4) = e3 % 130.74/18.24 (66) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.24 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.24 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.24 (67) all_9_2 = e1 % 130.74/18.24 (68) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.24 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.24 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.24 (69) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.24 = e0 % 130.74/18.24 (70) ~ (all_4_4 = e1) % 130.74/18.24 (71) ~ (all_4_10 = e2) % 130.74/18.24 (72) all_4_0 = e0 % 130.74/18.24 (73) all_6_15 = all_4_3 % 130.74/18.24 (74) all_9_7 = e0 % 130.74/18.24 (75) op(e4, e4) = e0 % 130.74/18.24 (76) ~ (all_8_63 = all_8_93) % 130.74/18.24 (77) all_8_93 = e2 % 130.74/18.24 % 130.74/18.24 Begin of proof % 130.74/18.24 | % 130.74/18.24 | REDUCE: (17), (76), (77) imply: % 130.74/18.24 | (78) ~ (e2 = e1) % 130.74/18.24 | % 130.74/18.24 | SIMP: (78) implies: % 130.74/18.24 | (79) ~ (e2 = e1) % 130.74/18.24 | % 130.74/18.24 | REDUCE: (17), (52) imply: % 130.74/18.24 | (80) ~ (e3 = e1) % 130.74/18.24 | % 130.74/18.24 | SIMP: (80) implies: % 130.74/18.24 | (81) ~ (e3 = e1) % 130.74/18.24 | % 130.74/18.24 | REDUCE: (30), (46) imply: % 130.74/18.24 | (82) ~ (e4 = e3) % 130.74/18.24 | % 130.74/18.24 | SIMP: (82) implies: % 130.74/18.24 | (83) ~ (e4 = e3) % 130.74/18.24 | % 130.74/18.24 | REDUCE: (35), (77) imply: % 130.74/18.24 | (84) ~ (e3 = e2) % 130.74/18.24 | % 130.74/18.24 | SIMP: (84) implies: % 130.74/18.24 | (85) ~ (e3 = e2) % 130.74/18.24 | % 130.74/18.24 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.74/18.24 | (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), % 130.74/18.24 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), % 130.74/18.24 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48), % 130.74/18.24 | (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60), % 130.74/18.24 | (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), % 130.74/18.24 | (72), (73), (74), (75), (79), (81), (83), (85) are inconsistent by % 130.74/18.24 | sub-proof #194. % 130.74/18.24 | % 130.74/18.24 End of proof % 130.74/18.24 % 130.74/18.24 Sub-proof #177 shows that the following formulas are inconsistent: % 130.74/18.24 ---------------------------------------------------------------- % 130.74/18.24 (1) op(e1, e0) = e0 % 130.74/18.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.24 (3) op(e0, e1) = e0 % 130.74/18.24 (4) ~ (all_8_87 = all_8_99) % 130.74/18.24 (5) op(e0, e1) = all_8_87 % 130.74/18.24 (6) op(e1, e0) = all_8_99 % 130.74/18.24 % 130.74/18.24 Begin of proof % 130.74/18.24 | % 130.74/18.24 | GROUND_INST: instantiating (2) with e0, all_8_87, e1, e0, simplifying with % 130.74/18.24 | (3), (5) gives: % 130.74/18.24 | (7) all_8_87 = e0 % 130.74/18.24 | % 130.74/18.24 | GROUND_INST: instantiating (2) with e0, all_8_99, e0, e1, simplifying with % 130.74/18.24 | (1), (6) gives: % 130.74/18.24 | (8) all_8_99 = e0 % 130.74/18.24 | % 130.74/18.24 | REDUCE: (4), (7), (8) imply: % 130.74/18.24 | (9) $false % 130.74/18.24 | % 130.74/18.24 | CLOSE: (9) is inconsistent. % 130.74/18.24 | % 130.74/18.24 End of proof % 130.74/18.24 % 130.74/18.24 Sub-proof #178 shows that the following formulas are inconsistent: % 130.74/18.24 ---------------------------------------------------------------- % 130.74/18.24 (1) op(e1, e3) = e3 % 130.74/18.24 (2) op(e4, e1) = e4 % 130.74/18.24 (3) (all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.74/18.24 op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 130.74/18.24 all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & % 130.74/18.24 $i(all_8_78)) | (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = % 130.74/18.24 all_8_81) & op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & % 130.74/18.24 op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & % 130.74/18.24 $i(all_8_60) & $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ % 130.74/18.24 (all_8_72 = all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 130.74/18.24 all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) % 130.74/18.24 & $i(all_8_72) & $i(all_8_84)) % 130.74/18.24 (4) op(e2, e1) = e2 % 130.74/18.24 (5) op(e1, e4) = e4 % 130.74/18.25 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.25 (7) op(e1, e2) = e2 % 130.74/18.25 (8) op(e3, e1) = e3 % 130.74/18.25 % 130.74/18.25 Begin of proof % 130.74/18.25 | % 130.74/18.25 | BETA: splitting (3) gives: % 130.74/18.25 | % 130.74/18.25 | Case 1: % 130.74/18.25 | | % 130.74/18.25 | | (9) all_8_25 = e1 & ~ (all_8_24 = e4) & ~ (all_8_48 = all_8_78) & % 130.74/18.25 | | op(all_8_48, e4) = e1 & op(all_8_48, e1) = all_8_24 & op(e4, e1) = % 130.74/18.25 | | all_8_78 & op(e1, e4) = all_8_48 & $i(all_8_24) & $i(all_8_48) & % 130.74/18.25 | | $i(all_8_78) % 130.74/18.25 | | % 130.74/18.25 | | ALPHA: (9) implies: % 130.74/18.25 | | (10) ~ (all_8_48 = all_8_78) % 130.74/18.25 | | (11) op(e1, e4) = all_8_48 % 130.74/18.25 | | (12) op(e4, e1) = all_8_78 % 130.74/18.25 | | % 130.74/18.25 | | REF_CLOSE: (2), (5), (6), (10), (11), (12) are inconsistent by sub-proof % 130.74/18.25 | | #189. % 130.74/18.25 | | % 130.74/18.25 | Case 2: % 130.74/18.25 | | % 130.74/18.25 | | (13) (all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.74/18.25 | | op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.74/18.25 | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.74/18.25 | | $i(all_8_81)) | (all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 % 130.74/18.25 | | = all_8_84) & op(all_8_72, e2) = e1 & op(all_8_72, e1) = % 130.74/18.25 | | all_8_28 & op(e2, e1) = all_8_84 & op(e1, e2) = all_8_72 & % 130.74/18.25 | | $i(all_8_28) & $i(all_8_72) & $i(all_8_84)) % 130.74/18.25 | | % 130.74/18.25 | | BETA: splitting (13) gives: % 130.74/18.25 | | % 130.74/18.25 | | Case 1: % 130.74/18.25 | | | % 130.74/18.25 | | | (14) all_8_27 = e1 & ~ (all_8_26 = e3) & ~ (all_8_60 = all_8_81) & % 130.74/18.25 | | | op(all_8_60, e3) = e1 & op(all_8_60, e1) = all_8_26 & op(e3, e1) = % 130.74/18.25 | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_26) & $i(all_8_60) & % 130.74/18.25 | | | $i(all_8_81) % 130.74/18.25 | | | % 130.74/18.25 | | | ALPHA: (14) implies: % 130.74/18.25 | | | (15) ~ (all_8_60 = all_8_81) % 130.74/18.25 | | | (16) op(e1, e3) = all_8_60 % 130.74/18.25 | | | (17) op(e3, e1) = all_8_81 % 130.74/18.25 | | | % 130.74/18.25 | | | REF_CLOSE: (1), (6), (8), (15), (16), (17) are inconsistent by sub-proof % 130.74/18.25 | | | #184. % 130.74/18.25 | | | % 130.74/18.25 | | Case 2: % 130.74/18.25 | | | % 130.74/18.25 | | | (18) all_8_29 = e1 & ~ (all_8_28 = e2) & ~ (all_8_72 = all_8_84) & % 130.74/18.25 | | | op(all_8_72, e2) = e1 & op(all_8_72, e1) = all_8_28 & op(e2, e1) = % 130.74/18.25 | | | all_8_84 & op(e1, e2) = all_8_72 & $i(all_8_28) & $i(all_8_72) & % 130.74/18.25 | | | $i(all_8_84) % 130.74/18.25 | | | % 130.74/18.25 | | | ALPHA: (18) implies: % 130.74/18.25 | | | (19) ~ (all_8_72 = all_8_84) % 130.74/18.25 | | | (20) op(e1, e2) = all_8_72 % 130.74/18.25 | | | (21) op(e2, e1) = all_8_84 % 130.74/18.25 | | | % 130.74/18.25 | | | REF_CLOSE: (4), (6), (7), (19), (20), (21) are inconsistent by sub-proof % 130.74/18.25 | | | #181. % 130.74/18.25 | | | % 130.74/18.25 | | End of split % 130.74/18.25 | | % 130.74/18.25 | End of split % 130.74/18.25 | % 130.74/18.25 End of proof % 130.74/18.25 % 130.74/18.25 Sub-proof #179 shows that the following formulas are inconsistent: % 130.74/18.25 ---------------------------------------------------------------- % 130.74/18.25 (1) all_9_8 = e4 % 130.74/18.25 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.25 (3) op(e0, all_8_90) = e4 % 130.74/18.25 (4) all_6_5 = e1 % 130.74/18.25 (5) ~ (e4 = e0) % 130.74/18.25 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.25 (7) all_9_20 = e2 % 130.74/18.25 (8) all_6_10 = e3 % 130.74/18.25 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.25 (10) ~ (all_4_3 = all_4_4) % 130.74/18.25 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.25 (12) ~ (e4 = e2) % 130.74/18.25 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.25 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.25 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.25 (16) all_8_96 = e1 % 130.74/18.25 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.25 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.25 (19) all_8_75 = e3 % 130.74/18.25 (20) ~ (all_4_3 = e3) % 130.74/18.25 (21) all_6_20 = all_4_4 % 130.74/18.25 (22) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.25 (23) all_9_11 = e2 % 130.74/18.25 (24) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.25 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.25 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.25 (25) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.25 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.25 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.25 (26) all_9_16 = e3 % 130.74/18.25 (27) all_6_22 = all_4_14 % 130.74/18.25 (28) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.25 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.25 (30) all_8_90 = e3 % 130.74/18.25 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.25 = e0 % 130.74/18.25 (32) ~ (all_4_14 = e2) % 130.74/18.25 (33) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.25 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.25 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.25 (34) all_9_0 = e0 % 130.74/18.25 (35) ~ (all_4_22 = e2) % 130.74/18.25 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.25 (37) ~ (all_4_4 = e3) % 130.74/18.25 (38) op(e2, e3) = all_8_57 % 130.74/18.25 (39) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.25 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.25 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.25 (40) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.25 (41) all_9_6 = e3 % 130.74/18.25 (42) ~ (e1 = e0) % 130.74/18.25 (43) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.25 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.25 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.25 (44) ~ (e3 = e2) % 130.74/18.25 (45) all_9_14 = e2 % 130.74/18.25 (46) ~ (all_8_90 = e4) % 130.74/18.25 (47) all_9_13 = e3 % 130.74/18.25 (48) all_9_12 = e4 % 130.74/18.25 (49) op(e0, e4) = all_4_4 % 130.74/18.25 (50) ~ (e4 = e1) % 130.74/18.25 (51) ~ (all_4_3 = e0) % 130.74/18.25 (52) all_9_15 = e1 % 130.74/18.25 (53) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.25 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.25 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.25 (54) op(e3, e4) = e1 % 130.74/18.25 (55) op(e1, e4) = all_4_3 % 130.74/18.25 (56) all_4_11 = e0 % 130.74/18.25 (57) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.25 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.25 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.25 (58) all_9_24 = e4 % 130.74/18.25 (59) all_9_19 = e0 % 130.74/18.25 (60) ~ (all_4_4 = e0) % 130.74/18.25 (61) ~ (all_4_3 = e1) % 130.74/18.25 (62) ~ (op(e2, e3) = e2) % 130.74/18.25 (63) ~ (all_8_75 = all_8_96) % 130.74/18.25 (64) all_6_2 = all_4_10 % 130.74/18.25 (65) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.25 (66) op(e2, e4) = e3 % 130.74/18.25 (67) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.25 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.25 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.25 (68) ~ (op(e2, e3) = e3) % 130.74/18.25 (69) all_9_2 = e1 % 130.74/18.25 (70) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.25 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.25 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.25 (71) all_8_57 = e0 % 130.74/18.25 (72) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.25 = e0 % 130.74/18.25 (73) ~ (all_4_4 = e1) % 130.74/18.25 (74) ~ (all_4_10 = e2) % 130.74/18.25 (75) all_4_0 = e0 % 130.74/18.25 (76) all_6_15 = all_4_3 % 130.74/18.25 (77) all_9_7 = e0 % 130.74/18.25 (78) op(e4, e4) = e0 % 130.74/18.25 (79) ~ (all_8_96 = e2) % 130.74/18.25 % 130.74/18.25 Begin of proof % 130.74/18.25 | % 130.74/18.25 | PRED_UNIFY: (38), (62) imply: % 130.74/18.25 | (80) ~ (all_8_57 = e2) % 130.74/18.25 | % 130.74/18.25 | PRED_UNIFY: (38), (68) imply: % 130.74/18.25 | (81) ~ (all_8_57 = e3) % 130.74/18.25 | % 130.74/18.25 | REDUCE: (71), (81) imply: % 130.74/18.25 | (82) ~ (e3 = e0) % 130.74/18.25 | % 130.74/18.25 | SIMP: (82) implies: % 130.74/18.25 | (83) ~ (e3 = e0) % 130.74/18.25 | % 130.74/18.25 | REDUCE: (71), (80) imply: % 130.74/18.25 | (84) ~ (e2 = e0) % 130.74/18.25 | % 130.74/18.25 | SIMP: (84) implies: % 130.74/18.25 | (85) ~ (e2 = e0) % 130.74/18.25 | % 130.74/18.25 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.74/18.25 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.74/18.25 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 130.74/18.25 | (35), (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), % 130.74/18.25 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 130.74/18.25 | (58), (59), (60), (61), (63), (64), (65), (66), (67), (69), (70), % 130.74/18.25 | (72), (73), (74), (75), (76), (77), (78), (79), (83), (85) are % 130.74/18.25 | inconsistent by sub-proof #180. % 130.74/18.25 | % 130.74/18.25 End of proof % 130.74/18.25 % 130.74/18.25 Sub-proof #180 shows that the following formulas are inconsistent: % 130.74/18.25 ---------------------------------------------------------------- % 130.74/18.25 (1) all_9_8 = e4 % 130.74/18.25 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.25 (3) op(e0, all_8_90) = e4 % 130.74/18.25 (4) all_6_5 = e1 % 130.74/18.25 (5) ~ (e4 = e0) % 130.74/18.25 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.25 (7) all_9_20 = e2 % 130.74/18.25 (8) all_6_10 = e3 % 130.74/18.25 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.25 (10) ~ (all_4_3 = all_4_4) % 130.74/18.25 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.25 (12) ~ (e4 = e2) % 130.74/18.25 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.25 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.25 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.25 (16) all_8_96 = e1 % 130.74/18.25 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.25 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.25 (19) all_8_75 = e3 % 130.74/18.25 (20) ~ (all_4_3 = e3) % 130.74/18.25 (21) all_6_20 = all_4_4 % 130.74/18.25 (22) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.25 (23) all_9_11 = e2 % 130.74/18.25 (24) ~ (e3 = e0) % 130.74/18.25 (25) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.25 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.25 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.25 (26) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.25 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.25 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.25 (27) all_9_16 = e3 % 130.74/18.25 (28) all_6_22 = all_4_14 % 130.74/18.25 (29) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.25 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.25 (31) all_8_90 = e3 % 130.74/18.25 (32) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.25 = e0 % 130.74/18.25 (33) ~ (all_4_14 = e2) % 130.74/18.25 (34) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.25 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.25 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.25 (35) ~ (e2 = e0) % 130.74/18.25 (36) all_9_0 = e0 % 130.74/18.25 (37) ~ (all_4_22 = e2) % 130.74/18.25 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.25 (39) ~ (all_4_4 = e3) % 130.74/18.25 (40) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.25 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.25 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.25 (41) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.25 (42) all_9_6 = e3 % 130.74/18.25 (43) ~ (e1 = e0) % 130.74/18.25 (44) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.25 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.25 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.25 (45) ~ (e3 = e2) % 130.74/18.25 (46) all_9_14 = e2 % 130.74/18.25 (47) ~ (all_8_90 = e4) % 130.74/18.25 (48) all_9_13 = e3 % 130.74/18.25 (49) all_9_12 = e4 % 130.74/18.25 (50) op(e0, e4) = all_4_4 % 130.74/18.25 (51) ~ (e4 = e1) % 130.74/18.25 (52) ~ (all_4_3 = e0) % 130.74/18.25 (53) all_9_15 = e1 % 130.74/18.25 (54) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.25 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.25 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.25 (55) op(e3, e4) = e1 % 130.74/18.25 (56) op(e1, e4) = all_4_3 % 130.74/18.25 (57) all_4_11 = e0 % 130.74/18.25 (58) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.25 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.25 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.25 (59) all_9_24 = e4 % 130.74/18.25 (60) all_9_19 = e0 % 130.74/18.25 (61) ~ (all_4_4 = e0) % 130.74/18.25 (62) ~ (all_4_3 = e1) % 130.74/18.25 (63) ~ (all_8_75 = all_8_96) % 130.74/18.25 (64) all_6_2 = all_4_10 % 130.74/18.25 (65) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.25 (66) op(e2, e4) = e3 % 130.74/18.25 (67) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.25 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.25 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.25 (68) all_9_2 = e1 % 130.74/18.25 (69) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.25 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.25 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.25 (70) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.25 = e0 % 130.74/18.25 (71) ~ (all_4_4 = e1) % 130.74/18.25 (72) ~ (all_4_10 = e2) % 130.74/18.25 (73) all_4_0 = e0 % 130.74/18.25 (74) all_6_15 = all_4_3 % 130.74/18.25 (75) all_9_7 = e0 % 130.74/18.25 (76) op(e4, e4) = e0 % 130.74/18.25 (77) ~ (all_8_96 = e2) % 130.74/18.25 % 130.74/18.25 Begin of proof % 130.74/18.25 | % 130.74/18.25 | REDUCE: (16), (19), (63) imply: % 130.74/18.25 | (78) ~ (e3 = e1) % 130.74/18.25 | % 130.74/18.25 | REDUCE: (31), (47) imply: % 130.74/18.25 | (79) ~ (e4 = e3) % 130.74/18.25 | % 130.74/18.25 | SIMP: (79) implies: % 130.74/18.25 | (80) ~ (e4 = e3) % 130.74/18.25 | % 130.74/18.25 | REDUCE: (16), (77) imply: % 130.74/18.25 | (81) ~ (e2 = e1) % 130.74/18.25 | % 130.74/18.25 | SIMP: (81) implies: % 130.74/18.25 | (82) ~ (e2 = e1) % 130.74/18.25 | % 130.74/18.25 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.74/18.25 | (13), (14), (15), (17), (18), (20), (21), (22), (23), (24), (25), % 130.74/18.25 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.74/18.25 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48), % 130.74/18.25 | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), % 130.74/18.25 | (60), (61), (62), (64), (65), (66), (67), (68), (69), (70), (71), % 130.74/18.25 | (72), (73), (74), (75), (76), (78), (80), (82) are inconsistent by % 130.74/18.25 | sub-proof #194. % 130.74/18.25 | % 130.74/18.25 End of proof % 130.74/18.25 % 130.74/18.25 Sub-proof #181 shows that the following formulas are inconsistent: % 130.74/18.25 ---------------------------------------------------------------- % 130.74/18.25 (1) op(e1, e2) = all_8_72 % 130.74/18.25 (2) op(e2, e1) = e2 % 130.74/18.25 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.25 (4) op(e1, e2) = e2 % 130.74/18.25 (5) ~ (all_8_72 = all_8_84) % 130.74/18.25 (6) op(e2, e1) = all_8_84 % 130.74/18.25 % 130.74/18.25 Begin of proof % 130.74/18.25 | % 130.74/18.25 | GROUND_INST: instantiating (3) with e2, all_8_72, e2, e1, simplifying with % 130.74/18.25 | (1), (4) gives: % 130.74/18.25 | (7) all_8_72 = e2 % 130.74/18.25 | % 130.74/18.25 | GROUND_INST: instantiating (3) with e2, all_8_84, e1, e2, simplifying with % 130.74/18.25 | (2), (6) gives: % 130.74/18.25 | (8) all_8_84 = e2 % 130.74/18.25 | % 130.74/18.25 | REDUCE: (5), (7), (8) imply: % 130.74/18.25 | (9) $false % 130.74/18.25 | % 130.74/18.25 | CLOSE: (9) is inconsistent. % 130.74/18.25 | % 130.74/18.25 End of proof % 130.74/18.25 % 130.74/18.25 Sub-proof #182 shows that the following formulas are inconsistent: % 130.74/18.25 ---------------------------------------------------------------- % 130.74/18.25 (1) op(e1, e3) = e3 % 130.74/18.25 (2) all_6_9 = all_4_21 % 130.74/18.25 (3) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.74/18.25 (4) all_8_45 = e3 % 130.74/18.25 (5) ~ (all_4_21 = e3) % 130.74/18.25 (6) op(e3, e2) = e0 % 130.74/18.25 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.25 (8) ~ (all_4_22 = e3) % 130.74/18.25 (9) op(e3, e1) = e3 % 130.74/18.25 (10) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.74/18.25 op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.74/18.25 all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.74/18.25 $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = % 130.74/18.25 all_8_81) & op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & % 130.74/18.25 op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & % 130.74/18.25 $i(all_8_60) & $i(all_8_81)) | (all_8_15 = e3 & ~ (all_8_14 = e0) & % 130.74/18.25 ~ (all_8_63 = all_8_93) & op(all_8_93, e3) = all_8_14 & op(all_8_93, % 130.74/18.25 e0) = e3 & op(e3, e0) = all_8_93 & op(e0, e3) = all_8_63 & % 130.74/18.25 $i(all_8_14) & $i(all_8_63) & $i(all_8_93)) | (all_8_17 = e2 & ~ % 130.74/18.25 (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & op(all_8_45, e4) = e2 & % 130.74/18.25 op(all_8_45, e2) = all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = % 130.74/18.25 all_8_45 & $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = % 130.74/18.25 e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) % 130.74/18.25 = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, % 130.74/18.25 e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.74/18.25 (11) op(e3, e4) = e1 % 130.74/18.25 (12) op(e3, e0) = e2 % 130.74/18.25 (13) op(e2, e0) = all_4_22 % 130.74/18.25 (14) op(e2, e3) = e0 % 130.74/18.25 (15) ~ (e2 = e1) % 130.74/18.25 % 130.74/18.25 Begin of proof % 130.74/18.25 | % 130.74/18.25 | BETA: splitting (10) gives: % 130.74/18.25 | % 130.74/18.25 | Case 1: % 130.74/18.25 | | % 130.74/18.25 | | (16) (all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.74/18.25 | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.74/18.25 | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.74/18.25 | | $i(all_8_69)) | (all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 % 130.74/18.25 | | = all_8_81) & op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = % 130.74/18.25 | | e3 & op(e3, e1) = all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) % 130.74/18.25 | | & $i(all_8_60) & $i(all_8_81)) % 130.74/18.25 | | % 130.74/18.25 | | BETA: splitting (16) gives: % 130.74/18.25 | | % 130.74/18.25 | | Case 1: % 130.74/18.25 | | | % 130.74/18.25 | | | (17) all_8_11 = e3 & ~ (all_8_10 = e2) & ~ (all_8_57 = all_8_69) & % 130.74/18.25 | | | op(all_8_69, e3) = all_8_10 & op(all_8_69, e2) = e3 & op(e3, e2) = % 130.74/18.25 | | | all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_10) & $i(all_8_57) & % 130.74/18.25 | | | $i(all_8_69) % 130.74/18.25 | | | % 130.74/18.25 | | | ALPHA: (17) implies: % 130.74/18.25 | | | (18) ~ (all_8_57 = all_8_69) % 130.74/18.25 | | | (19) op(e2, e3) = all_8_57 % 130.74/18.25 | | | (20) op(e3, e2) = all_8_69 % 130.74/18.25 | | | % 130.74/18.25 | | | REF_CLOSE: (6), (7), (14), (18), (19), (20) are inconsistent by sub-proof % 130.74/18.25 | | | #185. % 130.74/18.25 | | | % 130.74/18.25 | | Case 2: % 130.74/18.25 | | | % 130.74/18.25 | | | (21) all_8_13 = e3 & ~ (all_8_12 = e1) & ~ (all_8_60 = all_8_81) & % 130.74/18.25 | | | op(all_8_81, e3) = all_8_12 & op(all_8_81, e1) = e3 & op(e3, e1) = % 130.74/18.25 | | | all_8_81 & op(e1, e3) = all_8_60 & $i(all_8_12) & $i(all_8_60) & % 130.74/18.25 | | | $i(all_8_81) % 130.74/18.25 | | | % 130.74/18.25 | | | ALPHA: (21) implies: % 130.74/18.25 | | | (22) ~ (all_8_60 = all_8_81) % 130.74/18.25 | | | (23) op(e1, e3) = all_8_60 % 130.74/18.25 | | | (24) op(e3, e1) = all_8_81 % 130.74/18.25 | | | % 130.74/18.25 | | | REF_CLOSE: (1), (7), (9), (22), (23), (24) are inconsistent by sub-proof % 130.74/18.25 | | | #184. % 130.74/18.25 | | | % 130.74/18.25 | | End of split % 130.74/18.25 | | % 130.74/18.25 | Case 2: % 130.74/18.25 | | % 130.74/18.25 | | (25) (all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.74/18.25 | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = % 130.74/18.25 | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & % 130.74/18.25 | | $i(all_8_93)) | (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 % 130.74/18.25 | | = all_8_66) & op(all_8_45, e4) = e2 & op(all_8_45, e2) = % 130.74/18.25 | | all_8_16 & op(e4, e2) = all_8_66 & op(e2, e4) = all_8_45 & % 130.74/18.25 | | $i(all_8_16) & $i(all_8_45) & $i(all_8_66)) | (all_8_19 = e2 & ~ % 130.74/18.25 | | (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 % 130.74/18.25 | | & op(all_8_57, e2) = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) % 130.74/18.25 | | = all_8_57 & $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.74/18.25 | | % 130.74/18.25 | | BETA: splitting (25) gives: % 130.74/18.25 | | % 130.74/18.25 | | Case 1: % 130.74/18.25 | | | % 130.74/18.25 | | | (26) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.74/18.25 | | | op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = % 130.74/18.25 | | | all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & % 130.74/18.25 | | | $i(all_8_93) % 130.74/18.25 | | | % 130.74/18.25 | | | REF_CLOSE: (2), (3), (5), (7), (8), (12), (13), (26) are inconsistent by % 130.74/18.25 | | | sub-proof #183. % 130.74/18.25 | | | % 130.74/18.25 | | Case 2: % 130.74/18.25 | | | % 130.74/18.25 | | | (27) (all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.74/18.25 | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 130.74/18.25 | | | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 130.74/18.25 | | | & $i(all_8_66)) | (all_8_19 = e2 & ~ (all_8_18 = e3) & ~ % 130.74/18.25 | | | (all_8_57 = all_8_69) & op(all_8_57, e3) = e2 & op(all_8_57, e2) % 130.74/18.25 | | | = all_8_18 & op(e3, e2) = all_8_69 & op(e2, e3) = all_8_57 & % 130.74/18.25 | | | $i(all_8_18) & $i(all_8_57) & $i(all_8_69)) % 130.74/18.25 | | | % 130.74/18.25 | | | BETA: splitting (27) gives: % 130.74/18.25 | | | % 130.74/18.25 | | | Case 1: % 130.74/18.25 | | | | % 130.74/18.25 | | | | (28) all_8_17 = e2 & ~ (all_8_16 = e4) & ~ (all_8_45 = all_8_66) & % 130.74/18.25 | | | | op(all_8_45, e4) = e2 & op(all_8_45, e2) = all_8_16 & op(e4, e2) % 130.74/18.25 | | | | = all_8_66 & op(e2, e4) = all_8_45 & $i(all_8_16) & $i(all_8_45) % 130.74/18.25 | | | | & $i(all_8_66) % 130.74/18.25 | | | | % 130.74/18.25 | | | | ALPHA: (28) implies: % 130.74/18.25 | | | | (29) op(all_8_45, e4) = e2 % 130.74/18.25 | | | | % 130.74/18.25 | | | | REDUCE: (4), (29) imply: % 130.74/18.25 | | | | (30) op(e3, e4) = e2 % 130.74/18.25 | | | | % 130.74/18.25 | | | | REF_CLOSE: (7), (11), (15), (30) are inconsistent by sub-proof #313. % 130.74/18.25 | | | | % 130.74/18.25 | | | Case 2: % 130.74/18.25 | | | | % 130.74/18.25 | | | | (31) all_8_19 = e2 & ~ (all_8_18 = e3) & ~ (all_8_57 = all_8_69) & % 130.74/18.25 | | | | op(all_8_57, e3) = e2 & op(all_8_57, e2) = all_8_18 & op(e3, e2) % 130.74/18.25 | | | | = all_8_69 & op(e2, e3) = all_8_57 & $i(all_8_18) & $i(all_8_57) % 130.74/18.25 | | | | & $i(all_8_69) % 130.74/18.25 | | | | % 130.74/18.25 | | | | ALPHA: (31) implies: % 130.74/18.26 | | | | (32) ~ (all_8_57 = all_8_69) % 130.74/18.26 | | | | (33) op(e2, e3) = all_8_57 % 130.74/18.26 | | | | (34) op(e3, e2) = all_8_69 % 130.74/18.26 | | | | % 130.74/18.26 | | | | REF_CLOSE: (6), (7), (14), (32), (33), (34) are inconsistent by % 130.74/18.26 | | | | sub-proof #185. % 130.74/18.26 | | | | % 130.74/18.26 | | | End of split % 130.74/18.26 | | | % 130.74/18.26 | | End of split % 130.74/18.26 | | % 130.74/18.26 | End of split % 130.74/18.26 | % 130.74/18.26 End of proof % 130.74/18.26 % 130.74/18.26 Sub-proof #183 shows that the following formulas are inconsistent: % 130.74/18.26 ---------------------------------------------------------------- % 130.74/18.26 (1) all_6_9 = all_4_21 % 130.74/18.26 (2) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.74/18.26 (3) ~ (all_4_21 = e3) % 130.74/18.26 (4) all_8_15 = e3 & ~ (all_8_14 = e0) & ~ (all_8_63 = all_8_93) & % 130.74/18.26 op(all_8_93, e3) = all_8_14 & op(all_8_93, e0) = e3 & op(e3, e0) = % 130.74/18.26 all_8_93 & op(e0, e3) = all_8_63 & $i(all_8_14) & $i(all_8_63) & % 130.74/18.26 $i(all_8_93) % 130.74/18.26 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.26 (6) ~ (all_4_22 = e3) % 130.74/18.26 (7) op(e3, e0) = e2 % 130.74/18.26 (8) op(e2, e0) = all_4_22 % 130.74/18.26 % 130.74/18.26 Begin of proof % 130.74/18.26 | % 130.74/18.26 | ALPHA: (4) implies: % 130.74/18.26 | (9) op(e3, e0) = all_8_93 % 130.74/18.26 | (10) op(all_8_93, e0) = e3 % 130.74/18.26 | % 130.74/18.26 | BETA: splitting (2) gives: % 130.74/18.26 | % 130.74/18.26 | Case 1: % 130.74/18.26 | | % 130.74/18.26 | | % 130.74/18.26 | | GROUND_INST: instantiating (5) with e2, all_8_93, e0, e3, simplifying with % 130.74/18.26 | | (7), (9) gives: % 130.74/18.26 | | (11) all_8_93 = e2 % 130.74/18.26 | | % 130.74/18.26 | | REDUCE: (10), (11) imply: % 130.74/18.26 | | (12) op(e2, e0) = e3 % 130.74/18.26 | | % 130.74/18.26 | | REF_CLOSE: (5), (6), (8), (12) are inconsistent by sub-proof #226. % 130.74/18.26 | | % 130.74/18.26 | Case 2: % 130.74/18.26 | | % 130.74/18.26 | | (13) op(e3, e0) = e3 % 130.74/18.26 | | % 130.74/18.26 | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #228. % 130.74/18.26 | | % 130.74/18.26 | End of split % 130.74/18.26 | % 130.74/18.26 End of proof % 130.74/18.26 % 130.74/18.26 Sub-proof #184 shows that the following formulas are inconsistent: % 130.74/18.26 ---------------------------------------------------------------- % 130.74/18.26 (1) op(e1, e3) = e3 % 130.74/18.26 (2) ~ (all_8_60 = all_8_81) % 130.74/18.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.26 (4) op(e3, e1) = e3 % 130.74/18.26 (5) op(e1, e3) = all_8_60 % 130.74/18.26 (6) op(e3, e1) = all_8_81 % 130.74/18.26 % 130.74/18.26 Begin of proof % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (3) with e3, all_8_60, e3, e1, simplifying with % 130.74/18.26 | (1), (5) gives: % 130.74/18.26 | (7) all_8_60 = e3 % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (3) with e3, all_8_81, e1, e3, simplifying with % 130.74/18.26 | (4), (6) gives: % 130.74/18.26 | (8) all_8_81 = e3 % 130.74/18.26 | % 130.74/18.26 | REDUCE: (2), (7), (8) imply: % 130.74/18.26 | (9) $false % 130.74/18.26 | % 130.74/18.26 | CLOSE: (9) is inconsistent. % 130.74/18.26 | % 130.74/18.26 End of proof % 130.74/18.26 % 130.74/18.26 Sub-proof #185 shows that the following formulas are inconsistent: % 130.74/18.26 ---------------------------------------------------------------- % 130.74/18.26 (1) ~ (all_8_57 = all_8_69) % 130.74/18.26 (2) op(e3, e2) = e0 % 130.74/18.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.26 (4) op(e2, e3) = all_8_57 % 130.74/18.26 (5) op(e2, e3) = e0 % 130.74/18.26 (6) op(e3, e2) = all_8_69 % 130.74/18.26 % 130.74/18.26 Begin of proof % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (3) with e0, all_8_57, e3, e2, simplifying with % 130.74/18.26 | (4), (5) gives: % 130.74/18.26 | (7) all_8_57 = e0 % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (3) with e0, all_8_69, e2, e3, simplifying with % 130.74/18.26 | (2), (6) gives: % 130.74/18.26 | (8) all_8_69 = e0 % 130.74/18.26 | % 130.74/18.26 | REDUCE: (1), (7), (8) imply: % 130.74/18.26 | (9) $false % 130.74/18.26 | % 130.74/18.26 | CLOSE: (9) is inconsistent. % 130.74/18.26 | % 130.74/18.26 End of proof % 130.74/18.26 % 130.74/18.26 Sub-proof #186 shows that the following formulas are inconsistent: % 130.74/18.26 ---------------------------------------------------------------- % 130.74/18.26 (1) all_9_8 = e4 % 130.74/18.26 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.26 (3) op(e0, all_8_90) = e4 % 130.74/18.26 (4) all_6_5 = e1 % 130.74/18.26 (5) ~ (e4 = e0) % 130.74/18.26 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.26 (7) all_9_20 = e2 % 130.74/18.26 (8) all_6_10 = e3 % 130.74/18.26 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.26 (10) ~ (all_4_3 = all_4_4) % 130.74/18.26 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.26 (12) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.26 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.26 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.26 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.26 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.26 (17) ~ (all_4_3 = e3) % 130.74/18.26 (18) all_6_20 = all_4_4 % 130.74/18.26 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.26 (20) all_9_11 = e2 % 130.74/18.26 (21) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.26 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.26 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.26 (22) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.26 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.26 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.26 (23) all_9_16 = e3 % 130.74/18.26 (24) all_6_22 = all_4_14 % 130.74/18.26 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.26 (26) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.26 = e0 % 130.74/18.26 (27) ~ (all_4_14 = e2) % 130.74/18.26 (28) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.26 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.26 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.26 (29) all_9_0 = e0 % 130.74/18.26 (30) ~ (all_4_22 = e2) % 130.74/18.26 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.26 (32) ~ (all_4_4 = e3) % 130.74/18.26 (33) op(e2, e3) = all_8_57 % 130.74/18.26 (34) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.26 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.26 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.26 (35) op(e0, e4) = all_8_51 % 130.74/18.26 (36) op(e4, e0) = all_8_90 % 130.74/18.26 (37) op(e0, e3) = e1 % 130.74/18.26 (38) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.26 (39) all_9_6 = e3 % 130.74/18.26 (40) ~ (e1 = e0) % 130.74/18.26 (41) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.26 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.26 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.26 (42) all_9_14 = e2 % 130.74/18.26 (43) all_9_13 = e3 % 130.74/18.26 (44) all_9_12 = e4 % 130.74/18.26 (45) op(e0, e4) = all_4_4 % 130.74/18.26 (46) ~ (e4 = e1) % 130.74/18.26 (47) ~ (all_4_3 = e0) % 130.74/18.26 (48) all_9_15 = e1 % 130.74/18.26 (49) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.26 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.26 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.26 (50) ~ (e3 = e1) % 130.74/18.26 (51) op(e3, e4) = e1 % 130.74/18.26 (52) op(e1, e4) = all_4_3 % 130.74/18.26 (53) all_4_11 = e0 % 130.74/18.26 (54) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.26 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.26 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.26 (55) all_9_24 = e4 % 130.74/18.26 (56) all_9_19 = e0 % 130.74/18.26 (57) ~ (op(e0, e4) = e4) % 130.74/18.26 (58) op(e4, e0) = e3 % 130.74/18.26 (59) ~ (all_4_4 = e0) % 130.74/18.26 (60) op(e2, e3) = e0 % 130.74/18.26 (61) ~ (all_4_3 = e1) % 130.74/18.26 (62) ~ (op(e2, e3) = e2) % 130.74/18.26 (63) op(e0, e4) = e2 % 130.74/18.26 (64) all_6_2 = all_4_10 % 130.74/18.26 (65) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.26 (66) op(e2, e4) = e3 % 130.74/18.26 (67) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.26 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.26 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.26 (68) ~ (op(e2, e3) = e3) % 130.74/18.26 (69) all_9_2 = e1 % 130.74/18.26 (70) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.26 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.26 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.26 (71) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.26 = e0 % 130.74/18.26 (72) ~ (all_4_4 = e1) % 130.74/18.26 (73) ~ (all_4_10 = e2) % 130.74/18.26 (74) all_4_0 = e0 % 130.74/18.26 (75) ~ (all_8_51 = all_8_90) % 130.74/18.26 (76) ~ (e2 = e1) % 130.74/18.26 (77) all_6_15 = all_4_3 % 130.74/18.26 (78) all_9_7 = e0 % 130.74/18.26 (79) op(e4, e4) = e0 % 130.74/18.26 % 130.74/18.26 Begin of proof % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (31) with e2, all_8_51, e4, e0, simplifying with % 130.74/18.26 | (35), (63) gives: % 130.74/18.26 | (80) all_8_51 = e2 % 130.74/18.26 | % 130.74/18.26 | PRED_UNIFY: (35), (57) imply: % 130.74/18.26 | (81) ~ (all_8_51 = e4) % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (31) with e1, e4, e3, e0, simplifying with (37) % 130.74/18.26 | gives: % 130.74/18.26 | (82) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.26 | % 130.74/18.26 | PRED_UNIFY: (3), (57) imply: % 130.74/18.26 | (83) ~ (all_8_90 = e4) % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (31) with e0, all_8_57, e3, e2, simplifying with % 130.74/18.26 | (33), (60) gives: % 130.74/18.26 | (84) all_8_57 = e0 % 130.74/18.26 | % 130.74/18.26 | GROUND_INST: instantiating (31) with e3, all_8_90, e0, e4, simplifying with % 130.74/18.26 | (36), (58) gives: % 130.74/18.26 | (85) all_8_90 = e3 % 130.74/18.26 | % 130.74/18.26 | PRED_UNIFY: (33), (62) imply: % 130.74/18.26 | (86) ~ (all_8_57 = e2) % 130.74/18.26 | % 130.74/18.26 | PRED_UNIFY: (33), (68) imply: % 130.74/18.26 | (87) ~ (all_8_57 = e3) % 130.74/18.26 | % 130.74/18.26 | REDUCE: (75), (80), (85) imply: % 130.74/18.26 | (88) ~ (e3 = e2) % 130.74/18.26 | % 130.74/18.26 | SIMP: (88) implies: % 130.74/18.26 | (89) ~ (e3 = e2) % 130.74/18.26 | % 130.74/18.26 | REDUCE: (80), (81) imply: % 130.74/18.26 | (90) ~ (e4 = e2) % 130.74/18.26 | % 130.74/18.26 | SIMP: (90) implies: % 130.74/18.26 | (91) ~ (e4 = e2) % 130.74/18.26 | % 130.74/18.26 | REDUCE: (84), (87) imply: % 130.74/18.26 | (92) ~ (e3 = e0) % 130.74/18.26 | % 130.74/18.26 | SIMP: (92) implies: % 130.74/18.26 | (93) ~ (e3 = e0) % 130.74/18.26 | % 130.74/18.26 | REDUCE: (84), (86) imply: % 130.74/18.26 | (94) ~ (e2 = e0) % 130.74/18.26 | % 130.74/18.26 | SIMP: (94) implies: % 130.74/18.26 | (95) ~ (e2 = e0) % 130.74/18.26 | % 130.74/18.26 | REDUCE: (83), (85) imply: % 130.74/18.26 | (96) ~ (e4 = e3) % 130.74/18.26 | % 130.74/18.26 | SIMP: (96) implies: % 130.74/18.26 | (97) ~ (e4 = e3) % 130.74/18.26 | % 130.74/18.26 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.74/18.26 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 130.74/18.26 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (38), % 130.74/18.26 | (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), % 130.74/18.26 | (50), (51), (52), (53), (54), (55), (56), (59), (61), (64), (65), % 130.74/18.26 | (66), (67), (69), (70), (71), (72), (73), (74), (76), (77), (78), % 130.74/18.26 | (79), (82), (85), (89), (91), (93), (95), (97) are inconsistent by % 130.74/18.26 | sub-proof #194. % 130.74/18.26 | % 130.74/18.26 End of proof % 130.74/18.26 % 130.74/18.26 Sub-proof #187 shows that the following formulas are inconsistent: % 130.74/18.26 ---------------------------------------------------------------- % 130.74/18.26 (1) all_9_8 = e4 % 130.74/18.26 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.26 (3) all_6_9 = all_4_21 % 130.74/18.26 (4) ~ (all_8_42 = all_8_54) % 130.74/18.26 (5) op(e0, all_8_90) = e4 % 130.74/18.26 (6) all_6_5 = e1 % 130.74/18.26 (7) ~ (e4 = e0) % 130.74/18.26 (8) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.26 (9) all_9_20 = e2 % 130.74/18.26 (10) all_6_10 = e3 % 130.74/18.26 (11) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.26 (12) ~ (all_4_3 = all_4_4) % 130.74/18.26 (13) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.26 (14) ~ (e4 = e2) % 130.74/18.26 (15) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.74/18.26 (16) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.26 (17) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.26 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.74/18.26 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.74/18.26 (all_9_16 = e2 & op(e4, e0) = e2) % 130.74/18.26 (19) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.26 (20) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.26 (21) op(e4, e3) = e2 % 130.74/18.26 (22) ~ (all_4_21 = e3) % 130.74/18.26 (23) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.26 (24) ~ (all_4_3 = e3) % 130.74/18.26 (25) all_6_20 = all_4_4 % 130.74/18.26 (26) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.26 (27) all_9_11 = e2 % 130.74/18.26 (28) ~ (e3 = e0) % 130.74/18.26 (29) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.26 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.26 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.26 (30) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.26 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.26 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.26 (31) all_9_16 = e3 % 130.74/18.26 (32) all_6_22 = all_4_14 % 130.74/18.26 (33) all_9_17 = e2 % 130.74/18.26 (34) op(e4, e3) = all_8_54 % 130.74/18.26 (35) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.26 (36) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.26 = e0 % 130.74/18.26 (37) ~ (all_4_14 = e2) % 130.74/18.26 (38) ~ (op(e4, e3) = e4) % 130.74/18.26 (39) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.26 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.26 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.26 (40) ~ (e2 = e0) % 130.74/18.26 (41) all_9_0 = e0 % 130.74/18.26 (42) ~ (all_4_22 = e2) % 130.74/18.26 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.26 (44) ~ (all_4_4 = e3) % 130.74/18.26 (45) op(e2, e3) = all_8_57 % 130.74/18.26 (46) ~ (op(e4, e3) = e3) % 130.74/18.26 (47) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.26 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.26 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.26 (48) ~ (all_4_22 = e3) % 130.74/18.26 (49) op(e4, e0) = all_8_90 % 130.74/18.26 (50) op(e0, e3) = e1 % 130.74/18.26 (51) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.26 (52) all_9_6 = e3 % 130.74/18.26 (53) ~ (e1 = e0) % 130.74/18.26 (54) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.74/18.26 (55) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.26 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.26 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.26 (56) ~ (e3 = e2) % 130.74/18.26 (57) all_9_14 = e2 % 130.74/18.26 (58) all_9_13 = e3 % 130.74/18.26 (59) all_9_12 = e4 % 130.74/18.26 (60) op(e0, e4) = all_4_4 % 130.74/18.26 (61) ~ (e4 = e1) % 130.74/18.26 (62) ~ (all_4_3 = e0) % 130.74/18.26 (63) all_9_15 = e1 % 130.74/18.26 (64) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.26 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.26 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.26 (65) ~ (e3 = e1) % 130.74/18.26 (66) op(e3, e4) = e1 % 130.74/18.26 (67) all_9_9 = e4 % 130.74/18.26 (68) op(e1, e4) = all_4_3 % 130.74/18.26 (69) all_4_11 = e0 % 130.74/18.26 (70) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.26 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.26 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.26 (71) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.74/18.26 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.74/18.26 (all_9_16 = e3 & op(e4, e0) = e3) % 130.74/18.26 (72) all_9_24 = e4 % 130.74/18.26 (73) op(e2, e0) = all_4_22 % 130.74/18.26 (74) all_9_19 = e0 % 130.74/18.26 (75) ~ (op(e0, e4) = e4) % 130.74/18.26 (76) ~ (e4 = e3) % 130.74/18.26 (77) op(e4, e0) = e3 % 130.74/18.26 (78) ~ (all_4_4 = e0) % 130.74/18.26 (79) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.74/18.26 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.74/18.26 (all_9_16 = e1 & op(e4, e0) = e1) % 130.74/18.26 (80) op(e2, e3) = e0 % 130.74/18.26 (81) ~ (all_4_3 = e1) % 130.74/18.26 (82) ~ (op(e2, e3) = e2) % 130.74/18.26 (83) all_6_2 = all_4_10 % 130.74/18.26 (84) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.26 (85) op(e3, e4) = all_8_42 % 130.74/18.26 (86) op(e2, e4) = e3 % 130.74/18.26 (87) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.26 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.26 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.26 (88) ~ (op(e2, e3) = e3) % 130.74/18.26 (89) all_9_2 = e1 % 130.74/18.26 (90) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.26 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.26 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.26 (91) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.26 = e0 % 130.74/18.26 (92) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.74/18.26 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.74/18.26 (all_9_24 = e3 & op(e0, e0) = e3) % 130.74/18.26 (93) ~ (all_4_4 = e1) % 130.74/18.26 (94) ~ (all_4_10 = e2) % 130.74/18.26 (95) all_4_0 = e0 % 130.74/18.26 (96) ~ (e2 = e1) % 130.74/18.26 (97) all_6_15 = all_4_3 % 130.74/18.26 (98) all_9_7 = e0 % 130.74/18.26 (99) op(e4, e4) = e0 % 130.74/18.26 % 130.74/18.26 Begin of proof % 130.74/18.26 | % 130.74/18.26 | BETA: splitting (54) gives: % 130.74/18.26 | % 130.74/18.26 | Case 1: % 130.74/18.26 | | % 130.74/18.26 | | (100) ~ (op(e3, e4) = e3) % 130.74/18.26 | | % 130.74/18.26 | | BETA: splitting (11) gives: % 130.74/18.26 | | % 130.74/18.26 | | Case 1: % 130.74/18.26 | | | % 130.74/18.26 | | | (101) ~ (op(e3, e4) = e4) % 130.74/18.26 | | | % 130.74/18.26 | | | GROUND_INST: instantiating (43) with e1, e4, e3, e0, simplifying with (50) % 130.74/18.26 | | | gives: % 130.74/18.26 | | | (102) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (5), (75) imply: % 130.74/18.26 | | | (103) ~ (all_8_90 = e4) % 130.74/18.26 | | | % 130.74/18.26 | | | GROUND_INST: instantiating (43) with e0, all_8_57, e3, e2, simplifying % 130.74/18.26 | | | with (45), (80) gives: % 130.74/18.26 | | | (104) all_8_57 = e0 % 130.74/18.26 | | | % 130.74/18.26 | | | GROUND_INST: instantiating (43) with e1, all_8_42, e4, e3, simplifying % 130.74/18.26 | | | with (66), (85) gives: % 130.74/18.26 | | | (105) all_8_42 = e1 % 130.74/18.26 | | | % 130.74/18.26 | | | GROUND_INST: instantiating (43) with e3, all_8_90, e0, e4, simplifying % 130.74/18.26 | | | with (49), (77) gives: % 130.74/18.26 | | | (106) all_8_90 = e3 % 130.74/18.26 | | | % 130.74/18.26 | | | GROUND_INST: instantiating (43) with e2, all_8_54, e3, e4, simplifying % 130.74/18.26 | | | with (21), (34) gives: % 130.74/18.26 | | | (107) all_8_54 = e2 % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (34), (38) imply: % 130.74/18.26 | | | (108) ~ (all_8_54 = e4) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (34), (46) imply: % 130.74/18.26 | | | (109) ~ (all_8_54 = e3) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (45), (82) imply: % 130.74/18.26 | | | (110) ~ (all_8_57 = e2) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (45), (88) imply: % 130.74/18.26 | | | (111) ~ (all_8_57 = e3) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (85), (100) imply: % 130.74/18.26 | | | (112) ~ (all_8_42 = e3) % 130.74/18.26 | | | % 130.74/18.26 | | | PRED_UNIFY: (85), (101) imply: % 130.74/18.26 | | | (113) ~ (all_8_42 = e4) % 130.74/18.26 | | | % 130.74/18.26 | | | REDUCE: (4), (105), (107) imply: % 130.74/18.26 | | | (114) ~ (e2 = e1) % 130.74/18.26 | | | % 130.74/18.26 | | | REDUCE: (105), (113) imply: % 130.74/18.26 | | | (115) ~ (e4 = e1) % 130.74/18.26 | | | % 130.74/18.26 | | | REDUCE: (105), (112) imply: % 130.74/18.26 | | | (116) ~ (e3 = e1) % 130.74/18.26 | | | % 130.74/18.26 | | | REDUCE: (107), (108) imply: % 130.74/18.26 | | | (117) ~ (e4 = e2) % 130.74/18.26 | | | % 130.74/18.26 | | | REDUCE: (107), (109) imply: % 130.74/18.26 | | | (118) ~ (e3 = e2) % 130.74/18.26 | | | % 130.74/18.27 | | | REDUCE: (104), (111) imply: % 130.74/18.27 | | | (119) ~ (e3 = e0) % 130.74/18.27 | | | % 130.74/18.27 | | | REDUCE: (104), (110) imply: % 130.74/18.27 | | | (120) ~ (e2 = e0) % 130.74/18.27 | | | % 130.74/18.27 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.74/18.27 | | | (14), (16), (17), (19), (20), (23), (24), (25), (26), (27), % 130.74/18.27 | | | (28), (29), (30), (31), (32), (35), (36), (37), (39), (40), % 130.74/18.27 | | | (41), (42), (43), (44), (47), (51), (52), (53), (55), (56), % 130.74/18.27 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (68), % 130.74/18.27 | | | (69), (70), (72), (74), (78), (81), (83), (84), (85), (86), % 130.74/18.27 | | | (87), (89), (90), (91), (93), (94), (95), (96), (97), (98), % 130.74/18.27 | | | (99), (102), (103), (105), (106) are inconsistent by sub-proof % 130.74/18.27 | | | #193. % 130.74/18.27 | | | % 130.74/18.27 | | Case 2: % 130.74/18.27 | | | % 130.74/18.27 | | | (121) op(e3, e4) = e4 % 130.74/18.27 | | | % 130.74/18.27 | | | REF_CLOSE: (6), (11), (61), (121) are inconsistent by sub-proof #316. % 130.74/18.27 | | | % 130.74/18.27 | | End of split % 130.74/18.27 | | % 130.74/18.27 | Case 2: % 130.74/18.27 | | % 130.74/18.27 | | (122) all_6_5 = e3 % 130.74/18.27 | | % 130.74/18.27 | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 130.74/18.27 | | (17), (18), (19), (22), (23), (24), (25), (27), (28), (29), (31), % 130.74/18.27 | | (33), (35), (36), (39), (40), (41), (43), (44), (46), (48), (51), % 130.74/18.27 | | (52), (53), (55), (56), (59), (60), (61), (62), (65), (66), (67), % 130.74/18.27 | | (68), (70), (71), (73), (74), (76), (78), (79), (81), (83), (84), % 130.74/18.27 | | (86), (87), (89), (90), (91), (92), (93), (94), (95), (96), (97), % 130.74/18.27 | | (98), (99), (122) are inconsistent by sub-proof #192. % 130.74/18.27 | | % 130.74/18.27 | End of split % 130.74/18.27 | % 130.74/18.27 End of proof % 130.74/18.27 % 130.74/18.27 Sub-proof #188 shows that the following formulas are inconsistent: % 130.74/18.27 ---------------------------------------------------------------- % 130.74/18.27 (1) all_9_8 = e4 % 130.74/18.27 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.74/18.27 (3) op(e0, all_8_90) = e4 % 130.74/18.27 (4) all_6_5 = e1 % 130.74/18.27 (5) ~ (e4 = e0) % 130.74/18.27 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.74/18.27 (7) all_9_20 = e2 % 130.74/18.27 (8) all_6_10 = e3 % 130.74/18.27 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.74/18.27 (10) ~ (all_4_3 = all_4_4) % 130.74/18.27 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.74/18.27 (12) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.74/18.27 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.74/18.27 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.27 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.74/18.27 (16) op(e4, e3) = e2 % 130.74/18.27 (17) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.74/18.27 (18) ~ (all_4_3 = e3) % 130.74/18.27 (19) all_6_20 = all_4_4 % 130.74/18.27 (20) e4 = e2 | ~ (op(e2, e2) = e2) % 130.74/18.27 (21) all_9_11 = e2 % 130.74/18.27 (22) ~ (e3 = e0) % 130.74/18.27 (23) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.74/18.27 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.74/18.27 (all_9_24 = e4 & op(e0, e0) = e4) % 130.74/18.27 (24) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.74/18.27 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.74/18.27 (all_9_19 = e2 & op(e1, e0) = e2) % 130.74/18.27 (25) all_9_16 = e3 % 130.74/18.27 (26) all_6_22 = all_4_14 % 130.74/18.27 (27) op(e4, e3) = all_8_54 % 130.74/18.27 (28) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.74/18.27 (29) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.74/18.27 = e0 % 130.74/18.27 (30) ~ (all_4_14 = e2) % 130.74/18.27 (31) ~ (op(e4, e3) = e4) % 130.74/18.27 (32) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.74/18.27 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.74/18.27 (all_9_18 = e1 & op(e2, e0) = e1) % 130.74/18.27 (33) ~ (e2 = e0) % 130.74/18.27 (34) all_9_0 = e0 % 130.74/18.27 (35) ~ (all_4_22 = e2) % 130.74/18.27 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.74/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.74/18.27 (37) ~ (all_4_4 = e3) % 130.74/18.27 (38) ~ (op(e4, e3) = e3) % 130.74/18.27 (39) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.74/18.27 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.74/18.27 (all_9_24 = e2 & op(e0, e0) = e2) % 130.74/18.27 (40) op(e4, e0) = all_8_90 % 130.74/18.27 (41) op(e0, e3) = e1 % 130.74/18.27 (42) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.74/18.27 (43) all_9_6 = e3 % 130.74/18.27 (44) ~ (e1 = e0) % 130.74/18.27 (45) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.74/18.27 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.74/18.27 (all_9_20 = e3 & op(e0, e4) = e3) % 130.74/18.27 (46) all_9_14 = e2 % 130.74/18.27 (47) all_9_13 = e3 % 130.74/18.27 (48) all_9_12 = e4 % 130.74/18.27 (49) op(e0, e4) = all_4_4 % 130.74/18.27 (50) ~ (e4 = e1) % 130.74/18.27 (51) ~ (all_4_3 = e0) % 130.74/18.27 (52) all_9_15 = e1 % 130.74/18.27 (53) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.74/18.27 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.74/18.27 (all_9_22 = e2 & op(e0, e2) = e2) % 130.74/18.27 (54) ~ (e3 = e1) % 130.74/18.27 (55) op(e3, e4) = e1 % 130.74/18.27 (56) op(e1, e4) = all_4_3 % 130.74/18.27 (57) all_4_11 = e0 % 130.74/18.27 (58) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.74/18.27 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.74/18.27 (all_9_20 = e2 & op(e0, e4) = e2) % 130.74/18.27 (59) all_9_24 = e4 % 130.74/18.27 (60) all_9_19 = e0 % 130.74/18.27 (61) ~ (op(e0, e4) = e4) % 130.74/18.27 (62) op(e4, e0) = e3 % 130.74/18.27 (63) ~ (all_4_4 = e0) % 130.74/18.27 (64) ~ (all_4_3 = e1) % 130.74/18.27 (65) all_6_2 = all_4_10 % 130.74/18.27 (66) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.74/18.27 (67) op(e2, e4) = e3 % 130.74/18.27 (68) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.74/18.27 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.74/18.27 (all_9_20 = e4 & op(e0, e4) = e4) % 130.74/18.27 (69) all_9_2 = e1 % 130.74/18.27 (70) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.74/18.27 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.74/18.27 (all_9_20 = e1 & op(e0, e4) = e1) % 130.74/18.27 (71) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.74/18.27 = e0 % 130.74/18.27 (72) ~ (all_4_4 = e1) % 130.74/18.27 (73) ~ (all_4_10 = e2) % 130.74/18.27 (74) all_4_0 = e0 % 130.74/18.27 (75) ~ (e2 = e1) % 130.74/18.27 (76) all_6_15 = all_4_3 % 130.74/18.27 (77) all_9_7 = e0 % 130.74/18.27 (78) op(e4, e4) = e0 % 130.74/18.27 % 130.74/18.27 Begin of proof % 130.74/18.27 | % 130.74/18.27 | GROUND_INST: instantiating (36) with e1, e4, e3, e0, simplifying with (41) % 130.74/18.27 | gives: % 130.74/18.27 | (79) e4 = e1 | ~ (op(e0, e3) = e4) % 130.74/18.27 | % 130.74/18.27 | PRED_UNIFY: (3), (61) imply: % 130.74/18.27 | (80) ~ (all_8_90 = e4) % 130.74/18.27 | % 130.74/18.27 | GROUND_INST: instantiating (36) with e3, all_8_90, e0, e4, simplifying with % 130.74/18.27 | (40), (62) gives: % 130.74/18.27 | (81) all_8_90 = e3 % 130.74/18.27 | % 130.74/18.27 | GROUND_INST: instantiating (36) with e2, all_8_54, e3, e4, simplifying with % 130.74/18.27 | (16), (27) gives: % 130.74/18.27 | (82) all_8_54 = e2 % 130.74/18.27 | % 130.74/18.27 | PRED_UNIFY: (27), (31) imply: % 130.74/18.27 | (83) ~ (all_8_54 = e4) % 130.74/18.27 | % 130.74/18.27 | PRED_UNIFY: (27), (38) imply: % 130.74/18.27 | (84) ~ (all_8_54 = e3) % 130.74/18.27 | % 130.74/18.27 | REDUCE: (82), (83) imply: % 130.74/18.27 | (85) ~ (e4 = e2) % 130.74/18.27 | % 130.74/18.27 | SIMP: (85) implies: % 130.74/18.27 | (86) ~ (e4 = e2) % 130.74/18.27 | % 130.74/18.27 | REDUCE: (82), (84) imply: % 130.74/18.27 | (87) ~ (e3 = e2) % 130.74/18.27 | % 130.74/18.27 | SIMP: (87) implies: % 130.74/18.27 | (88) ~ (e3 = e2) % 130.74/18.27 | % 130.74/18.27 | REDUCE: (80), (81) imply: % 130.74/18.27 | (89) ~ (e4 = e3) % 130.74/18.27 | % 130.74/18.27 | SIMP: (89) implies: % 130.74/18.27 | (90) ~ (e4 = e3) % 130.74/18.27 | % 130.74/18.27 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.74/18.27 | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), % 130.74/18.27 | (25), (26), (28), (29), (30), (32), (33), (34), (35), (36), (37), % 130.74/18.27 | (39), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 130.74/18.27 | (52), (53), (54), (55), (56), (57), (58), (59), (60), (63), (64), % 130.74/18.27 | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), % 130.74/18.27 | (76), (77), (78), (79), (81), (86), (88), (90) are inconsistent by % 130.74/18.27 | sub-proof #194. % 130.74/18.27 | % 130.74/18.27 End of proof % 130.74/18.27 % 130.74/18.27 Sub-proof #189 shows that the following formulas are inconsistent: % 130.74/18.27 ---------------------------------------------------------------- % 130.74/18.27 (1) op(e4, e1) = e4 % 130.74/18.27 (2) op(e4, e1) = all_8_78 % 130.74/18.27 (3) op(e1, e4) = e4 % 130.86/18.27 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.27 (5) ~ (all_8_48 = all_8_78) % 130.86/18.27 (6) op(e1, e4) = all_8_48 % 130.86/18.27 % 130.86/18.27 Begin of proof % 130.86/18.27 | % 130.86/18.27 | GROUND_INST: instantiating (4) with e4, all_8_48, e4, e1, simplifying with % 130.86/18.27 | (3), (6) gives: % 130.86/18.27 | (7) all_8_48 = e4 % 130.86/18.27 | % 130.86/18.27 | GROUND_INST: instantiating (4) with e4, all_8_78, e1, e4, simplifying with % 130.86/18.27 | (1), (2) gives: % 130.86/18.27 | (8) all_8_78 = e4 % 130.86/18.27 | % 130.86/18.27 | REDUCE: (5), (7), (8) imply: % 130.86/18.27 | (9) $false % 130.86/18.27 | % 130.86/18.27 | CLOSE: (9) is inconsistent. % 130.86/18.27 | % 130.86/18.27 End of proof % 130.86/18.27 % 130.86/18.27 Sub-proof #190 shows that the following formulas are inconsistent: % 130.86/18.27 ---------------------------------------------------------------- % 130.86/18.27 (1) all_9_8 = e4 % 130.86/18.27 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.27 (3) op(e0, all_8_90) = e4 % 130.86/18.27 (4) all_6_5 = e1 % 130.86/18.27 (5) ~ (e4 = e0) % 130.86/18.27 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.27 (7) all_9_20 = e2 % 130.86/18.27 (8) all_6_10 = e3 % 130.86/18.27 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.27 (10) ~ (all_4_3 = all_4_4) % 130.86/18.27 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.27 (12) ~ (e4 = e2) % 130.86/18.27 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.27 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.27 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.27 (16) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.27 (17) ~ (all_8_66 = e4) % 130.86/18.27 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.27 (19) ~ (all_4_3 = e3) % 130.86/18.27 (20) all_6_20 = all_4_4 % 130.86/18.27 (21) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.27 (22) all_9_11 = e2 % 130.86/18.27 (23) ~ (e3 = e0) % 130.86/18.27 (24) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.27 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.27 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.27 (25) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.27 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.27 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.27 (26) all_9_16 = e3 % 130.86/18.27 (27) all_6_22 = all_4_14 % 130.86/18.27 (28) e4 = e1 | ~ (op(e0, e3) = e4) % 130.86/18.27 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.27 (30) all_8_90 = e3 % 130.86/18.27 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.27 = e0 % 130.86/18.27 (32) ~ (all_4_14 = e2) % 130.86/18.27 (33) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.27 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.27 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.27 (34) ~ (e2 = e0) % 130.86/18.27 (35) all_9_0 = e0 % 130.86/18.27 (36) ~ (all_4_22 = e2) % 130.86/18.27 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.27 (38) ~ (all_4_4 = e3) % 130.86/18.27 (39) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.27 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.27 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.27 (40) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.27 (41) all_9_6 = e3 % 130.86/18.27 (42) ~ (e1 = e0) % 130.86/18.27 (43) ~ (all_8_66 = e3) % 130.86/18.27 (44) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.27 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.27 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.27 (45) all_8_66 = e1 % 130.86/18.27 (46) ~ (all_8_66 = e2) % 130.86/18.27 (47) ~ (e3 = e2) % 130.86/18.27 (48) all_9_14 = e2 % 130.86/18.27 (49) ~ (all_8_90 = e4) % 130.86/18.27 (50) all_9_13 = e3 % 130.86/18.27 (51) all_9_12 = e4 % 130.86/18.27 (52) op(e0, e4) = all_4_4 % 130.86/18.27 (53) ~ (all_4_3 = e0) % 130.86/18.27 (54) all_9_15 = e1 % 130.86/18.27 (55) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.27 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.27 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.27 (56) op(e3, e4) = e1 % 130.86/18.27 (57) op(e1, e4) = all_4_3 % 130.86/18.27 (58) all_4_11 = e0 % 130.86/18.27 (59) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.27 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.27 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.27 (60) all_9_24 = e4 % 130.86/18.27 (61) all_9_19 = e0 % 130.86/18.27 (62) ~ (all_4_4 = e0) % 130.86/18.27 (63) ~ (all_4_3 = e1) % 130.86/18.27 (64) all_6_2 = all_4_10 % 130.86/18.27 (65) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.27 (66) op(e2, e4) = e3 % 130.86/18.27 (67) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.27 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.27 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.27 (68) all_9_2 = e1 % 130.86/18.27 (69) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.27 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.27 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.27 (70) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.27 = e0 % 130.86/18.27 (71) ~ (all_4_4 = e1) % 130.86/18.27 (72) ~ (all_4_10 = e2) % 130.86/18.27 (73) all_4_0 = e0 % 130.86/18.27 (74) all_6_15 = all_4_3 % 130.86/18.27 (75) all_9_7 = e0 % 130.86/18.27 (76) op(e4, e4) = e0 % 130.86/18.27 % 130.86/18.27 Begin of proof % 130.86/18.27 | % 130.86/18.27 | REDUCE: (17), (45) imply: % 130.86/18.27 | (77) ~ (e4 = e1) % 130.86/18.27 | % 130.86/18.27 | SIMP: (77) implies: % 130.86/18.27 | (78) ~ (e4 = e1) % 130.86/18.27 | % 130.86/18.27 | REDUCE: (43), (45) imply: % 130.86/18.27 | (79) ~ (e3 = e1) % 130.86/18.27 | % 130.86/18.27 | SIMP: (79) implies: % 130.86/18.27 | (80) ~ (e3 = e1) % 130.86/18.27 | % 130.86/18.27 | REDUCE: (45), (46) imply: % 130.86/18.27 | (81) ~ (e2 = e1) % 130.86/18.27 | % 130.86/18.27 | SIMP: (81) implies: % 130.86/18.27 | (82) ~ (e2 = e1) % 130.86/18.27 | % 130.86/18.27 | REDUCE: (30), (49) imply: % 130.86/18.27 | (83) ~ (e4 = e3) % 130.86/18.27 | % 130.86/18.27 | SIMP: (83) implies: % 130.86/18.27 | (84) ~ (e4 = e3) % 130.86/18.27 | % 130.86/18.27 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.27 | (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), % 130.86/18.27 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.86/18.27 | (36), (37), (38), (39), (40), (41), (42), (44), (47), (48), (50), % 130.86/18.27 | (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), % 130.86/18.27 | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), % 130.86/18.27 | (73), (74), (75), (76), (78), (80), (82), (84) are inconsistent by % 130.86/18.27 | sub-proof #194. % 130.86/18.27 | % 130.86/18.27 End of proof % 130.86/18.27 % 130.86/18.27 Sub-proof #191 shows that the following formulas are inconsistent: % 130.86/18.27 ---------------------------------------------------------------- % 130.86/18.27 (1) all_9_8 = e4 % 130.86/18.27 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.27 (3) all_6_9 = all_4_21 % 130.86/18.27 (4) ~ (all_8_42 = all_8_54) % 130.86/18.27 (5) op(e0, all_8_90) = e4 % 130.86/18.27 (6) all_6_5 = e1 % 130.86/18.27 (7) ~ (e4 = e0) % 130.86/18.27 (8) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.27 (9) all_9_20 = e2 % 130.86/18.27 (10) all_6_10 = e3 % 130.86/18.27 (11) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.27 (12) ~ (all_4_3 = all_4_4) % 130.86/18.27 (13) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.27 (14) ~ (e4 = e2) % 130.86/18.27 (15) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.27 (16) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.27 (17) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.27 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.27 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.27 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.27 (19) e4 = e1 | ~ (op(e3, e4) = e4) % 130.86/18.27 (20) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.27 (21) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.27 (22) op(e4, e3) = e2 % 130.86/18.27 (23) ~ (all_4_21 = e3) % 130.86/18.27 (24) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.27 (25) ~ (all_4_3 = e3) % 130.86/18.27 (26) all_6_20 = all_4_4 % 130.86/18.27 (27) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.27 (28) all_9_11 = e2 % 130.86/18.27 (29) ~ (e3 = e0) % 130.86/18.27 (30) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.27 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.27 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.27 (31) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.27 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.27 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.27 (32) all_9_16 = e3 % 130.86/18.27 (33) all_6_22 = all_4_14 % 130.86/18.27 (34) all_9_17 = e2 % 130.86/18.27 (35) op(e4, e3) = all_8_54 % 130.86/18.27 (36) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.27 (37) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.27 = e0 % 130.86/18.27 (38) ~ (all_4_14 = e2) % 130.86/18.27 (39) ~ (op(e4, e3) = e4) % 130.86/18.27 (40) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.27 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.27 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.27 (41) ~ (e2 = e0) % 130.86/18.27 (42) all_9_0 = e0 % 130.86/18.27 (43) ~ (all_4_22 = e2) % 130.86/18.27 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.27 (45) ~ (all_4_4 = e3) % 130.86/18.27 (46) ~ (op(e4, e3) = e3) % 130.86/18.27 (47) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.27 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.27 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.27 (48) ~ (all_4_22 = e3) % 130.86/18.27 (49) op(e4, e0) = all_8_90 % 130.86/18.27 (50) op(e0, e3) = e1 % 130.86/18.27 (51) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.27 (52) all_9_6 = e3 % 130.86/18.27 (53) ~ (e1 = e0) % 130.86/18.27 (54) all_6_5 = e3 | ~ (op(e3, e4) = e3) % 130.86/18.27 (55) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.27 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.27 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.27 (56) ~ (e3 = e2) % 130.86/18.27 (57) all_9_14 = e2 % 130.86/18.27 (58) all_9_13 = e3 % 130.86/18.27 (59) all_9_12 = e4 % 130.86/18.27 (60) op(e0, e4) = all_4_4 % 130.86/18.27 (61) ~ (e4 = e1) % 130.86/18.27 (62) ~ (all_4_3 = e0) % 130.86/18.27 (63) all_9_15 = e1 % 130.86/18.27 (64) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.27 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.27 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.27 (65) ~ (e3 = e1) % 130.86/18.27 (66) op(e3, e4) = e1 % 130.86/18.27 (67) all_9_9 = e4 % 130.86/18.27 (68) op(e1, e4) = all_4_3 % 130.86/18.27 (69) all_4_11 = e0 % 130.86/18.27 (70) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.27 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.27 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.28 (71) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.28 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.28 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.28 (72) all_9_24 = e4 % 130.86/18.28 (73) op(e2, e0) = all_4_22 % 130.86/18.28 (74) all_9_19 = e0 % 130.86/18.28 (75) ~ (op(e0, e4) = e4) % 130.86/18.28 (76) ~ (e4 = e3) % 130.86/18.28 (77) op(e4, e0) = e3 % 130.86/18.28 (78) ~ (all_4_4 = e0) % 130.86/18.28 (79) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.28 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.28 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.28 (80) ~ (all_4_3 = e1) % 130.86/18.28 (81) all_6_2 = all_4_10 % 130.86/18.28 (82) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.28 (83) op(e3, e4) = all_8_42 % 130.86/18.28 (84) op(e2, e4) = e3 % 130.86/18.28 (85) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.28 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.28 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.28 (86) all_9_2 = e1 % 130.86/18.28 (87) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.28 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.28 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.28 (88) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.28 = e0 % 130.86/18.28 (89) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.28 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.28 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.28 (90) ~ (all_4_4 = e1) % 130.86/18.28 (91) ~ (all_4_10 = e2) % 130.86/18.28 (92) all_4_0 = e0 % 130.86/18.28 (93) ~ (e2 = e1) % 130.86/18.28 (94) all_6_15 = all_4_3 % 130.86/18.28 (95) all_9_7 = e0 % 130.86/18.28 (96) op(e4, e4) = e0 % 130.86/18.28 % 130.86/18.28 Begin of proof % 130.86/18.28 | % 130.86/18.28 | BETA: splitting (54) gives: % 130.86/18.28 | % 130.86/18.28 | Case 1: % 130.86/18.28 | | % 130.86/18.28 | | (97) ~ (op(e3, e4) = e3) % 130.86/18.28 | | % 130.86/18.28 | | BETA: splitting (19) gives: % 130.86/18.28 | | % 130.86/18.28 | | Case 1: % 130.86/18.28 | | | % 130.86/18.28 | | | (98) ~ (op(e3, e4) = e4) % 130.86/18.28 | | | % 130.86/18.28 | | | GROUND_INST: instantiating (44) with e1, e4, e3, e0, simplifying with (50) % 130.86/18.28 | | | gives: % 130.86/18.28 | | | (99) e4 = e1 | ~ (op(e0, e3) = e4) % 130.86/18.28 | | | % 130.86/18.28 | | | PRED_UNIFY: (5), (75) imply: % 130.86/18.28 | | | (100) ~ (all_8_90 = e4) % 130.86/18.28 | | | % 130.86/18.28 | | | GROUND_INST: instantiating (44) with e1, all_8_42, e4, e3, simplifying % 130.86/18.28 | | | with (66), (83) gives: % 130.86/18.28 | | | (101) all_8_42 = e1 % 130.86/18.28 | | | % 130.86/18.28 | | | GROUND_INST: instantiating (44) with e3, all_8_90, e0, e4, simplifying % 130.86/18.28 | | | with (49), (77) gives: % 130.86/18.28 | | | (102) all_8_90 = e3 % 130.86/18.28 | | | % 130.86/18.28 | | | GROUND_INST: instantiating (44) with e2, all_8_54, e3, e4, simplifying % 130.86/18.28 | | | with (22), (35) gives: % 130.86/18.28 | | | (103) all_8_54 = e2 % 130.86/18.28 | | | % 130.86/18.28 | | | PRED_UNIFY: (35), (39) imply: % 130.86/18.28 | | | (104) ~ (all_8_54 = e4) % 130.86/18.28 | | | % 130.86/18.28 | | | PRED_UNIFY: (35), (46) imply: % 130.86/18.28 | | | (105) ~ (all_8_54 = e3) % 130.86/18.28 | | | % 130.86/18.28 | | | PRED_UNIFY: (83), (97) imply: % 130.86/18.28 | | | (106) ~ (all_8_42 = e3) % 130.86/18.28 | | | % 130.86/18.28 | | | PRED_UNIFY: (83), (98) imply: % 130.86/18.28 | | | (107) ~ (all_8_42 = e4) % 130.86/18.28 | | | % 130.86/18.28 | | | REDUCE: (4), (101), (103) imply: % 130.86/18.28 | | | (108) ~ (e2 = e1) % 130.86/18.28 | | | % 130.86/18.28 | | | REDUCE: (101), (107) imply: % 130.86/18.28 | | | (109) ~ (e4 = e1) % 130.86/18.28 | | | % 130.86/18.28 | | | REDUCE: (101), (106) imply: % 130.86/18.28 | | | (110) ~ (e3 = e1) % 130.86/18.28 | | | % 130.86/18.28 | | | REDUCE: (103), (104) imply: % 130.86/18.28 | | | (111) ~ (e4 = e2) % 130.86/18.28 | | | % 130.86/18.28 | | | REDUCE: (103), (105) imply: % 130.86/18.28 | | | (112) ~ (e3 = e2) % 130.86/18.28 | | | % 130.86/18.28 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.86/18.28 | | | (14), (16), (17), (20), (21), (24), (25), (26), (27), (28), % 130.86/18.28 | | | (29), (30), (31), (32), (33), (36), (37), (38), (40), (41), % 130.86/18.28 | | | (42), (43), (44), (45), (47), (51), (52), (53), (55), (56), % 130.86/18.28 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (68), % 130.86/18.28 | | | (69), (70), (72), (74), (78), (80), (81), (82), (83), (84), % 130.86/18.28 | | | (85), (86), (87), (88), (90), (91), (92), (93), (94), (95), % 130.86/18.28 | | | (96), (99), (100), (101), (102) are inconsistent by sub-proof % 130.86/18.28 | | | #193. % 130.86/18.28 | | | % 130.86/18.28 | | Case 2: % 130.86/18.28 | | | % 130.86/18.28 | | | (113) op(e3, e4) = e4 % 130.86/18.28 | | | % 130.86/18.28 | | | REF_CLOSE: (6), (11), (61), (113) are inconsistent by sub-proof #316. % 130.86/18.28 | | | % 130.86/18.28 | | End of split % 130.86/18.28 | | % 130.86/18.28 | Case 2: % 130.86/18.28 | | % 130.86/18.28 | | (114) all_6_5 = e3 % 130.86/18.28 | | % 130.86/18.28 | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 130.86/18.28 | | (17), (18), (20), (23), (24), (25), (26), (28), (29), (30), (32), % 130.86/18.28 | | (34), (36), (37), (40), (41), (42), (44), (45), (46), (48), (51), % 130.86/18.28 | | (52), (53), (55), (56), (59), (60), (61), (62), (65), (66), (67), % 130.86/18.28 | | (68), (70), (71), (73), (74), (76), (78), (79), (80), (81), (82), % 130.86/18.28 | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), % 130.86/18.28 | | (95), (96), (114) are inconsistent by sub-proof #192. % 130.86/18.28 | | % 130.86/18.28 | End of split % 130.86/18.28 | % 130.86/18.28 End of proof % 130.86/18.28 % 130.86/18.28 Sub-proof #192 shows that the following formulas are inconsistent: % 130.86/18.28 ---------------------------------------------------------------- % 130.86/18.28 (1) all_9_8 = e4 % 130.86/18.28 (2) all_6_9 = all_4_21 % 130.86/18.28 (3) all_6_5 = e1 % 130.86/18.28 (4) ~ (e4 = e0) % 130.86/18.28 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.28 (6) all_9_20 = e2 % 130.86/18.28 (7) all_6_10 = e3 % 130.86/18.28 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.28 (9) ~ (all_4_3 = all_4_4) % 130.86/18.28 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.28 (11) ~ (e4 = e2) % 130.86/18.28 (12) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.28 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.28 (14) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.28 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.28 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.28 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (16) ~ (all_4_21 = e3) % 130.86/18.28 (17) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.28 (18) ~ (all_4_3 = e3) % 130.86/18.28 (19) all_6_20 = all_4_4 % 130.86/18.28 (20) all_9_11 = e2 % 130.86/18.28 (21) ~ (e3 = e0) % 130.86/18.28 (22) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.28 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.28 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.28 (23) all_9_16 = e3 % 130.86/18.28 (24) all_9_17 = e2 % 130.86/18.28 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (26) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.28 = e0 % 130.86/18.28 (27) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.28 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.28 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.28 (28) ~ (e2 = e0) % 130.86/18.28 (29) all_9_0 = e0 % 130.86/18.28 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.28 (31) ~ (all_4_4 = e3) % 130.86/18.28 (32) ~ (op(e4, e3) = e3) % 130.86/18.28 (33) ~ (all_4_22 = e3) % 130.86/18.28 (34) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.28 (35) all_9_6 = e3 % 130.86/18.28 (36) ~ (e1 = e0) % 130.86/18.28 (37) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.28 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.28 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.28 (38) ~ (e3 = e2) % 130.86/18.28 (39) all_9_12 = e4 % 130.86/18.28 (40) op(e0, e4) = all_4_4 % 130.86/18.28 (41) ~ (e4 = e1) % 130.86/18.28 (42) ~ (all_4_3 = e0) % 130.86/18.28 (43) ~ (e3 = e1) % 130.86/18.28 (44) op(e3, e4) = e1 % 130.86/18.28 (45) all_9_9 = e4 % 130.86/18.28 (46) op(e1, e4) = all_4_3 % 130.86/18.28 (47) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.28 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.28 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.28 (48) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.28 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.28 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.28 (49) op(e2, e0) = all_4_22 % 130.86/18.28 (50) all_9_19 = e0 % 130.86/18.28 (51) ~ (e4 = e3) % 130.86/18.28 (52) ~ (all_4_4 = e0) % 130.86/18.28 (53) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.28 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.28 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.28 (54) ~ (all_4_3 = e1) % 130.86/18.28 (55) all_6_2 = all_4_10 % 130.86/18.28 (56) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.28 (57) op(e2, e4) = e3 % 130.86/18.28 (58) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.28 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.28 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.28 (59) all_9_2 = e1 % 130.86/18.28 (60) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.28 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.28 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.28 (61) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.28 = e0 % 130.86/18.28 (62) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.28 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.28 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.28 (63) all_6_5 = e3 % 130.86/18.28 (64) ~ (all_4_4 = e1) % 130.86/18.28 (65) ~ (all_4_10 = e2) % 130.86/18.28 (66) all_4_0 = e0 % 130.86/18.28 (67) ~ (e2 = e1) % 130.86/18.28 (68) all_6_15 = all_4_3 % 130.86/18.28 (69) all_9_7 = e0 % 130.86/18.28 (70) op(e4, e4) = e0 % 130.86/18.28 % 130.86/18.28 Begin of proof % 130.86/18.28 | % 130.86/18.28 | COMBINE_EQS: (3), (63) imply: % 130.86/18.28 | (71) e3 = e1 % 130.86/18.28 | % 130.86/18.28 | SIMP: (71) implies: % 130.86/18.28 | (72) e3 = e1 % 130.86/18.28 | % 130.86/18.28 | COMBINE_EQS: (23), (72) imply: % 130.86/18.28 | (73) all_9_16 = e1 % 130.86/18.28 | % 130.86/18.28 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.28 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), % 130.86/18.28 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.86/18.28 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 130.86/18.28 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 130.86/18.28 | (58), (59), (60), (61), (62), (64), (65), (66), (67), (68), (69), % 130.86/18.28 | (70), (73) are inconsistent by sub-proof #215. % 130.86/18.28 | % 130.86/18.28 End of proof % 130.86/18.28 % 130.86/18.28 Sub-proof #193 shows that the following formulas are inconsistent: % 130.86/18.28 ---------------------------------------------------------------- % 130.86/18.28 (1) all_9_8 = e4 % 130.86/18.28 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.28 (3) op(e0, all_8_90) = e4 % 130.86/18.28 (4) all_6_5 = e1 % 130.86/18.28 (5) ~ (e4 = e0) % 130.86/18.28 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.28 (7) all_9_20 = e2 % 130.86/18.28 (8) all_6_10 = e3 % 130.86/18.28 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.28 (10) ~ (all_4_3 = all_4_4) % 130.86/18.28 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.28 (12) ~ (e4 = e2) % 130.86/18.28 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.28 (14) all_8_42 = e1 % 130.86/18.28 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.28 (16) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.28 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.28 (19) ~ (all_4_3 = e3) % 130.86/18.28 (20) all_6_20 = all_4_4 % 130.86/18.28 (21) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.28 (22) all_9_11 = e2 % 130.86/18.28 (23) ~ (e3 = e0) % 130.86/18.28 (24) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.28 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.28 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.28 (25) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.28 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.28 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.28 (26) all_9_16 = e3 % 130.86/18.28 (27) all_6_22 = all_4_14 % 130.86/18.28 (28) e4 = e1 | ~ (op(e0, e3) = e4) % 130.86/18.28 (29) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (30) all_8_90 = e3 % 130.86/18.28 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.28 = e0 % 130.86/18.28 (32) ~ (all_4_14 = e2) % 130.86/18.28 (33) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.28 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.28 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.28 (34) ~ (e2 = e0) % 130.86/18.28 (35) all_9_0 = e0 % 130.86/18.28 (36) ~ (all_4_22 = e2) % 130.86/18.28 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.28 (38) ~ (all_4_4 = e3) % 130.86/18.28 (39) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.28 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.28 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.28 (40) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.28 (41) all_9_6 = e3 % 130.86/18.28 (42) ~ (e1 = e0) % 130.86/18.28 (43) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.28 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.28 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.28 (44) ~ (e3 = e2) % 130.86/18.28 (45) all_9_14 = e2 % 130.86/18.28 (46) ~ (all_8_90 = e4) % 130.86/18.28 (47) all_9_13 = e3 % 130.86/18.28 (48) all_9_12 = e4 % 130.86/18.28 (49) op(e0, e4) = all_4_4 % 130.86/18.28 (50) ~ (e4 = e1) % 130.86/18.28 (51) ~ (all_4_3 = e0) % 130.86/18.28 (52) all_9_15 = e1 % 130.86/18.28 (53) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.28 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.28 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.28 (54) ~ (e3 = e1) % 130.86/18.28 (55) op(e1, e4) = all_4_3 % 130.86/18.28 (56) all_4_11 = e0 % 130.86/18.28 (57) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.28 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.28 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.28 (58) all_9_24 = e4 % 130.86/18.28 (59) all_9_19 = e0 % 130.86/18.28 (60) ~ (all_4_4 = e0) % 130.86/18.28 (61) ~ (all_4_3 = e1) % 130.86/18.28 (62) all_6_2 = all_4_10 % 130.86/18.28 (63) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.28 (64) op(e3, e4) = all_8_42 % 130.86/18.28 (65) op(e2, e4) = e3 % 130.86/18.28 (66) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.28 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.28 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.28 (67) all_9_2 = e1 % 130.86/18.28 (68) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.28 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.28 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.28 (69) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.28 = e0 % 130.86/18.28 (70) ~ (all_4_4 = e1) % 130.86/18.28 (71) ~ (all_4_10 = e2) % 130.86/18.28 (72) all_4_0 = e0 % 130.86/18.28 (73) ~ (e2 = e1) % 130.86/18.28 (74) all_6_15 = all_4_3 % 130.86/18.28 (75) all_9_7 = e0 % 130.86/18.28 (76) op(e4, e4) = e0 % 130.86/18.28 % 130.86/18.28 Begin of proof % 130.86/18.28 | % 130.86/18.28 | REDUCE: (30), (46) imply: % 130.86/18.28 | (77) ~ (e4 = e3) % 130.86/18.28 | % 130.86/18.28 | SIMP: (77) implies: % 130.86/18.28 | (78) ~ (e4 = e3) % 130.86/18.28 | % 130.86/18.28 | REDUCE: (14), (64) imply: % 130.86/18.28 | (79) op(e3, e4) = e1 % 130.86/18.28 | % 130.86/18.28 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.28 | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 130.86/18.28 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.86/18.28 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), % 130.86/18.28 | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), % 130.86/18.28 | (59), (60), (61), (62), (63), (65), (66), (67), (68), (69), (70), % 130.86/18.28 | (71), (72), (73), (74), (75), (76), (78), (79) are inconsistent by % 130.86/18.28 | sub-proof #194. % 130.86/18.28 | % 130.86/18.28 End of proof % 130.86/18.28 % 130.86/18.28 Sub-proof #194 shows that the following formulas are inconsistent: % 130.86/18.28 ---------------------------------------------------------------- % 130.86/18.28 (1) all_9_8 = e4 % 130.86/18.28 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.28 (3) op(e0, all_8_90) = e4 % 130.86/18.28 (4) all_6_5 = e1 % 130.86/18.28 (5) ~ (e4 = e0) % 130.86/18.28 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.28 (7) all_9_20 = e2 % 130.86/18.28 (8) all_6_10 = e3 % 130.86/18.28 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.28 (10) ~ (all_4_3 = all_4_4) % 130.86/18.28 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.28 (12) ~ (e4 = e2) % 130.86/18.28 (13) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.28 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.28 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (16) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.28 (17) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.28 (18) ~ (all_4_3 = e3) % 130.86/18.28 (19) all_6_20 = all_4_4 % 130.86/18.28 (20) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.28 (21) all_9_11 = e2 % 130.86/18.28 (22) ~ (e3 = e0) % 130.86/18.28 (23) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.28 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.28 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.28 (24) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.28 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.28 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.28 (25) all_9_16 = e3 % 130.86/18.28 (26) all_6_22 = all_4_14 % 130.86/18.28 (27) e4 = e1 | ~ (op(e0, e3) = e4) % 130.86/18.28 (28) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.28 (29) all_8_90 = e3 % 130.86/18.28 (30) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.28 = e0 % 130.86/18.28 (31) ~ (all_4_14 = e2) % 130.86/18.28 (32) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.28 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.28 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.28 (33) ~ (e2 = e0) % 130.86/18.28 (34) all_9_0 = e0 % 130.86/18.28 (35) ~ (all_4_22 = e2) % 130.86/18.28 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.28 (37) ~ (all_4_4 = e3) % 130.86/18.28 (38) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.28 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.28 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.28 (39) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.28 (40) all_9_6 = e3 % 130.86/18.28 (41) ~ (e1 = e0) % 130.86/18.28 (42) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.28 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.28 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.28 (43) ~ (e3 = e2) % 130.86/18.28 (44) all_9_14 = e2 % 130.86/18.28 (45) all_9_13 = e3 % 130.86/18.28 (46) all_9_12 = e4 % 130.86/18.28 (47) op(e0, e4) = all_4_4 % 130.86/18.28 (48) ~ (e4 = e1) % 130.86/18.28 (49) ~ (all_4_3 = e0) % 130.86/18.28 (50) all_9_15 = e1 % 130.86/18.28 (51) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.28 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.28 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.28 (52) ~ (e3 = e1) % 130.86/18.28 (53) op(e3, e4) = e1 % 130.86/18.28 (54) op(e1, e4) = all_4_3 % 130.86/18.28 (55) all_4_11 = e0 % 130.86/18.28 (56) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.28 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.28 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.28 (57) all_9_24 = e4 % 130.86/18.28 (58) all_9_19 = e0 % 130.86/18.28 (59) ~ (e4 = e3) % 130.86/18.28 (60) ~ (all_4_4 = e0) % 130.86/18.28 (61) ~ (all_4_3 = e1) % 130.86/18.28 (62) all_6_2 = all_4_10 % 130.86/18.28 (63) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.28 (64) op(e2, e4) = e3 % 130.86/18.28 (65) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.28 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.28 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.28 (66) all_9_2 = e1 % 130.86/18.28 (67) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.28 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.28 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.28 (68) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.29 = e0 % 130.86/18.29 (69) ~ (all_4_4 = e1) % 130.86/18.29 (70) ~ (all_4_10 = e2) % 130.86/18.29 (71) all_4_0 = e0 % 130.86/18.29 (72) ~ (e2 = e1) % 130.86/18.29 (73) all_6_15 = all_4_3 % 130.86/18.29 (74) all_9_7 = e0 % 130.86/18.29 (75) op(e4, e4) = e0 % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | REDUCE: (3), (29) imply: % 130.86/18.29 | (76) op(e0, e3) = e4 % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (27) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (77) ~ (op(e0, e3) = e4) % 130.86/18.29 | | % 130.86/18.29 | | PRED_UNIFY: (76), (77) imply: % 130.86/18.29 | | (78) $false % 130.86/18.29 | | % 130.86/18.29 | | CLOSE: (78) is inconsistent. % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (79) e4 = e1 % 130.86/18.29 | | % 130.86/18.29 | | COMBINE_EQS: (57), (79) imply: % 130.86/18.29 | | (80) all_9_24 = e1 % 130.86/18.29 | | % 130.86/18.29 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.86/18.29 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 130.86/18.29 | | (25), (26), (28), (30), (31), (32), (33), (34), (35), (36), (37), % 130.86/18.29 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 130.86/18.29 | | (49), (50), (51), (52), (53), (54), (55), (56), (58), (59), (60), % 130.86/18.29 | | (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), % 130.86/18.29 | | (72), (73), (74), (75), (80) are inconsistent by sub-proof #207. % 130.86/18.29 | | % 130.86/18.29 | End of split % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #195 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_9_16 = e4 & op(e4, e0) = e4 % 130.86/18.29 (2) all_6_4 = e4 | ~ (op(e4, e0) = e4) % 130.86/18.29 (3) all_6_4 = all_4_20 % 130.86/18.29 (4) ~ (all_4_20 = e4) % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | ALPHA: (1) implies: % 130.86/18.29 | (5) op(e4, e0) = e4 % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (2) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (6) ~ (op(e4, e0) = e4) % 130.86/18.29 | | % 130.86/18.29 | | PRED_UNIFY: (5), (6) imply: % 130.86/18.29 | | (7) $false % 130.86/18.29 | | % 130.86/18.29 | | CLOSE: (7) is inconsistent. % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (8) all_6_4 = e4 % 130.86/18.29 | | % 130.86/18.29 | | COMBINE_EQS: (3), (8) imply: % 130.86/18.29 | | (9) all_4_20 = e4 % 130.86/18.29 | | % 130.86/18.29 | | SIMP: (9) implies: % 130.86/18.29 | | (10) all_4_20 = e4 % 130.86/18.29 | | % 130.86/18.29 | | REDUCE: (4), (10) imply: % 130.86/18.29 | | (11) $false % 130.86/18.29 | | % 130.86/18.29 | | CLOSE: (11) is inconsistent. % 130.86/18.29 | | % 130.86/18.29 | End of split % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #196 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_9_10 = e3 % 130.86/18.29 (2) all_9_10 = e2 % 130.86/18.29 (3) ~ (e3 = e2) % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | COMBINE_EQS: (1), (2) imply: % 130.86/18.29 | (4) e3 = e2 % 130.86/18.29 | % 130.86/18.29 | SIMP: (4) implies: % 130.86/18.29 | (5) e3 = e2 % 130.86/18.29 | % 130.86/18.29 | REDUCE: (3), (5) imply: % 130.86/18.29 | (6) $false % 130.86/18.29 | % 130.86/18.29 | CLOSE: (6) is inconsistent. % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #197 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_9_23 = e3 & op(e0, e1) = e3 % 130.86/18.29 (2) all_9_23 = e0 % 130.86/18.29 (3) ~ (e3 = e0) % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | ALPHA: (1) implies: % 130.86/18.29 | (4) all_9_23 = e3 % 130.86/18.29 | % 130.86/18.29 | COMBINE_EQS: (2), (4) imply: % 130.86/18.29 | (5) e3 = e0 % 130.86/18.29 | % 130.86/18.29 | REDUCE: (3), (5) imply: % 130.86/18.29 | (6) $false % 130.86/18.29 | % 130.86/18.29 | CLOSE: (6) is inconsistent. % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #198 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) ~ (e4 = e0) % 130.86/18.29 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.29 (3) all_6_10 = e3 % 130.86/18.29 (4) ~ (all_4_3 = all_4_4) % 130.86/18.29 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.29 (6) ~ (e4 = e2) % 130.86/18.29 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.29 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.29 (9) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.29 (10) ~ (all_4_3 = e3) % 130.86/18.29 (11) all_6_20 = all_4_4 % 130.86/18.29 (12) ~ (e3 = e0) % 130.86/18.29 (13) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.29 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.29 = e0 % 130.86/18.29 (15) ~ (e2 = e0) % 130.86/18.29 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.29 (17) ~ (all_4_4 = e3) % 130.86/18.29 (18) all_9_23 = e0 % 130.86/18.29 (19) ~ (e1 = e0) % 130.86/18.29 (20) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.29 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.29 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.29 (21) ~ (e3 = e2) % 130.86/18.29 (22) op(e0, e4) = all_4_4 % 130.86/18.29 (23) ~ (e4 = e1) % 130.86/18.29 (24) ~ (all_4_3 = e0) % 130.86/18.29 (25) ~ (e3 = e1) % 130.86/18.29 (26) op(e1, e4) = all_4_3 % 130.86/18.29 (27) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.29 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.29 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.29 (28) ~ (e4 = e3) % 130.86/18.29 (29) all_9_23 = e1 & op(e0, e1) = e1 % 130.86/18.29 (30) ~ (all_4_4 = e0) % 130.86/18.29 (31) ~ (all_4_3 = e1) % 130.86/18.29 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.29 (33) op(e2, e4) = e3 % 130.86/18.29 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.29 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.29 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 (35) all_9_2 = e1 % 130.86/18.29 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.29 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.29 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.29 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.29 = e0 % 130.86/18.29 (38) ~ (all_4_4 = e1) % 130.86/18.29 (39) all_4_0 = e0 % 130.86/18.29 (40) ~ (e2 = e1) % 130.86/18.29 (41) all_6_15 = all_4_3 % 130.86/18.29 (42) op(e4, e4) = e0 % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | ALPHA: (29) implies: % 130.86/18.29 | (43) all_9_23 = e1 % 130.86/18.29 | % 130.86/18.29 | COMBINE_EQS: (18), (43) imply: % 130.86/18.29 | (44) e1 = e0 % 130.86/18.29 | % 130.86/18.29 | COMBINE_EQS: (35), (44) imply: % 130.86/18.29 | (45) all_9_2 = e0 % 130.86/18.29 | % 130.86/18.29 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.29 | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), % 130.86/18.29 | (25), (26), (27), (28), (30), (31), (32), (33), (34), (36), (37), % 130.86/18.29 | (38), (39), (40), (41), (42), (45) are inconsistent by sub-proof % 130.86/18.29 | #265. % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #199 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_9_8 = e4 % 130.86/18.29 (2) all_6_9 = all_4_21 % 130.86/18.29 (3) all_6_5 = e1 % 130.86/18.29 (4) ~ (e4 = e0) % 130.86/18.29 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.29 (6) all_9_20 = e2 % 130.86/18.29 (7) all_6_10 = e3 % 130.86/18.29 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.29 (9) ~ (all_4_3 = all_4_4) % 130.86/18.29 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.29 (11) ~ (e4 = e2) % 130.86/18.29 (12) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.29 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.29 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.29 (15) ~ (all_4_21 = e3) % 130.86/18.29 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.29 (17) ~ (all_4_3 = e3) % 130.86/18.29 (18) all_6_20 = all_4_4 % 130.86/18.29 (19) all_9_11 = e2 % 130.86/18.29 (20) ~ (e3 = e0) % 130.86/18.29 (21) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.29 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.29 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.29 (22) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.29 (23) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.29 = e0 % 130.86/18.29 (24) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.29 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.29 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.29 (25) all_9_17 = e1 % 130.86/18.29 (26) ~ (e2 = e0) % 130.86/18.29 (27) all_9_0 = e0 % 130.86/18.29 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.29 (29) ~ (all_4_4 = e3) % 130.86/18.29 (30) ~ (all_4_22 = e3) % 130.86/18.29 (31) all_9_6 = e3 % 130.86/18.29 (32) ~ (e1 = e0) % 130.86/18.29 (33) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.29 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.29 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.29 (34) ~ (e3 = e2) % 130.86/18.29 (35) all_9_12 = e4 % 130.86/18.29 (36) op(e0, e4) = all_4_4 % 130.86/18.29 (37) ~ (e4 = e1) % 130.86/18.29 (38) ~ (all_4_3 = e0) % 130.86/18.29 (39) ~ (e3 = e1) % 130.86/18.29 (40) op(e3, e4) = e1 % 130.86/18.29 (41) all_9_24 = e2 % 130.86/18.29 (42) op(e1, e4) = all_4_3 % 130.86/18.29 (43) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.29 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.29 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.29 (44) op(e2, e0) = all_4_22 % 130.86/18.29 (45) all_9_19 = e0 % 130.86/18.29 (46) ~ (e4 = e3) % 130.86/18.29 (47) ~ (all_4_4 = e0) % 130.86/18.29 (48) ~ (all_4_3 = e1) % 130.86/18.29 (49) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.29 (50) op(e2, e4) = e3 % 130.86/18.29 (51) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.29 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.29 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 (52) all_9_2 = e1 % 130.86/18.29 (53) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.29 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.29 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.29 (54) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.29 = e0 % 130.86/18.29 (55) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.29 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.29 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.29 (56) ~ (all_4_4 = e1) % 130.86/18.29 (57) all_4_0 = e0 % 130.86/18.29 (58) ~ (e2 = e1) % 130.86/18.29 (59) all_6_15 = all_4_3 % 130.86/18.29 (60) all_9_7 = e0 % 130.86/18.29 (61) op(e4, e4) = e0 % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (55) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (62) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = % 130.86/18.29 | | e3) % 130.86/18.29 | | % 130.86/18.29 | | BETA: splitting (62) gives: % 130.86/18.29 | | % 130.86/18.29 | | Case 1: % 130.86/18.29 | | | % 130.86/18.29 | | | (63) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | ALPHA: (63) implies: % 130.86/18.29 | | | (64) all_9_16 = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | BETA: splitting (21) gives: % 130.86/18.29 | | | % 130.86/18.29 | | | Case 1: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (65) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) % 130.86/18.29 | | | | = e4) % 130.86/18.29 | | | | % 130.86/18.29 | | | | BETA: splitting (65) gives: % 130.86/18.29 | | | | % 130.86/18.29 | | | | Case 1: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (66) all_9_16 = e4 & op(e4, e0) = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | ALPHA: (66) implies: % 130.86/18.29 | | | | | (67) all_9_16 = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | COMBINE_EQS: (64), (67) imply: % 130.86/18.29 | | | | | (68) e4 = e3 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | COMBINE_EQS: (35), (68) imply: % 130.86/18.29 | | | | | (69) all_9_12 = e3 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | REF_CLOSE: (3), (4), (6), (8), (10), (11), (13), (37), (46), (51), % 130.86/18.29 | | | | | (57), (69) are inconsistent by sub-proof #303. % 130.86/18.29 | | | | | % 130.86/18.29 | | | | Case 2: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (70) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | ALPHA: (70) implies: % 130.86/18.29 | | | | | (71) all_9_17 = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | COMBINE_EQS: (25), (71) imply: % 130.86/18.29 | | | | | (72) e4 = e1 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | SIMP: (72) implies: % 130.86/18.29 | | | | | (73) e4 = e1 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | REDUCE: (37), (73) imply: % 130.86/18.29 | | | | | (74) $false % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | CLOSE: (74) is inconsistent. % 130.86/18.29 | | | | | % 130.86/18.29 | | | | End of split % 130.86/18.29 | | | | % 130.86/18.29 | | | Case 2: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (75) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) % 130.86/18.29 | | | | = e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.29 | | | | % 130.86/18.29 | | | | BETA: splitting (75) gives: % 130.86/18.29 | | | | % 130.86/18.29 | | | | Case 1: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (76) all_9_18 = e4 & op(e2, e0) = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | ALPHA: (76) implies: % 130.86/18.29 | | | | | (77) all_9_18 = e4 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 130.86/18.29 | | | | | (14), (16), (17), (18), (19), (20), (22), (23), (24), (26), % 130.86/18.29 | | | | | (27), (28), (29), (31), (32), (33), (34), (36), (37), (38), % 130.86/18.29 | | | | | (39), (40), (42), (43), (46), (47), (48), (49), (50), (51), % 130.86/18.29 | | | | | (52), (53), (54), (56), (57), (58), (59), (60), (61), (77) % 130.86/18.29 | | | | | are inconsistent by sub-proof #221. % 130.86/18.29 | | | | | % 130.86/18.29 | | | | Case 2: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (78) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, % 130.86/18.29 | | | | | e0) = e4) % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | BETA: splitting (78) gives: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | Case 1: % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | (79) all_9_19 = e4 & op(e1, e0) = e4 % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | REF_CLOSE: (4), (45), (79) are inconsistent by sub-proof #220. % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | Case 2: % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | (80) all_9_24 = e4 & op(e0, e0) = e4 % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | ALPHA: (80) implies: % 130.86/18.29 | | | | | | (81) all_9_24 = e4 % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | COMBINE_EQS: (41), (81) imply: % 130.86/18.29 | | | | | | (82) e4 = e2 % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | REDUCE: (11), (82) imply: % 130.86/18.29 | | | | | | (83) $false % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | | CLOSE: (83) is inconsistent. % 130.86/18.29 | | | | | | % 130.86/18.29 | | | | | End of split % 130.86/18.29 | | | | | % 130.86/18.29 | | | | End of split % 130.86/18.29 | | | | % 130.86/18.29 | | | End of split % 130.86/18.29 | | | % 130.86/18.29 | | Case 2: % 130.86/18.29 | | | % 130.86/18.29 | | | (84) all_9_17 = e3 & op(e3, e0) = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | ALPHA: (84) implies: % 130.86/18.29 | | | (85) op(e3, e0) = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | REF_CLOSE: (2), (12), (15), (85) are inconsistent by sub-proof #228. % 130.86/18.29 | | | % 130.86/18.29 | | End of split % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (86) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = % 130.86/18.29 | | e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.29 | | % 130.86/18.29 | | BETA: splitting (86) gives: % 130.86/18.29 | | % 130.86/18.29 | | Case 1: % 130.86/18.29 | | | % 130.86/18.29 | | | (87) all_9_18 = e3 & op(e2, e0) = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | ALPHA: (87) implies: % 130.86/18.29 | | | (88) op(e2, e0) = e3 % 130.86/18.29 | | | % 130.86/18.29 | | | REF_CLOSE: (28), (30), (44), (88) are inconsistent by sub-proof #226. % 130.86/18.29 | | | % 130.86/18.29 | | Case 2: % 130.86/18.29 | | | % 130.86/18.29 | | | (89) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = % 130.86/18.29 | | | e3) % 130.86/18.29 | | | % 130.86/18.29 | | | BETA: splitting (89) gives: % 130.86/18.29 | | | % 130.86/18.29 | | | Case 1: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (90) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REF_CLOSE: (20), (45), (90) are inconsistent by sub-proof #206. % 130.86/18.29 | | | | % 130.86/18.29 | | | Case 2: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (91) all_9_24 = e3 & op(e0, e0) = e3 % 130.86/18.29 | | | | % 130.86/18.29 | | | | ALPHA: (91) implies: % 130.86/18.29 | | | | (92) all_9_24 = e3 % 130.86/18.29 | | | | % 130.86/18.29 | | | | COMBINE_EQS: (41), (92) imply: % 130.86/18.29 | | | | (93) e3 = e2 % 130.86/18.29 | | | | % 130.86/18.29 | | | | SIMP: (93) implies: % 130.86/18.29 | | | | (94) e3 = e2 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REDUCE: (34), (94) imply: % 130.86/18.29 | | | | (95) $false % 130.86/18.29 | | | | % 130.86/18.29 | | | | CLOSE: (95) is inconsistent. % 130.86/18.29 | | | | % 130.86/18.29 | | | End of split % 130.86/18.29 | | | % 130.86/18.29 | | End of split % 130.86/18.29 | | % 130.86/18.29 | End of split % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #200 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) (all_9_20 = e3 & op(e0, e4) = e3) | (all_9_21 = e3 & op(e0, e3) = e3) % 130.86/18.29 (2) all_6_5 = e1 % 130.86/18.29 (3) ~ (e4 = e0) % 130.86/18.29 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.29 (5) all_6_10 = e3 % 130.86/18.29 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.29 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.29 (8) ~ (e4 = e2) % 130.86/18.29 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.29 (10) ~ (op(e0, e3) = e3) % 130.86/18.29 (11) ~ (e2 = e0) % 130.86/18.29 (12) all_9_0 = e0 % 130.86/18.29 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.29 (14) ~ (e3 = e2) % 130.86/18.29 (15) ~ (e4 = e1) % 130.86/18.29 (16) op(e3, e4) = e1 % 130.86/18.29 (17) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.29 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.29 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.29 (18) ~ (e4 = e3) % 130.86/18.29 (19) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.29 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.29 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 (20) all_4_0 = e0 % 130.86/18.29 (21) ~ (e2 = e1) % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (1) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (22) all_9_20 = e3 & op(e0, e4) = e3 % 130.86/18.29 | | % 130.86/18.29 | | ALPHA: (22) implies: % 130.86/18.29 | | (23) all_9_20 = e3 % 130.86/18.29 | | % 130.86/18.29 | | BETA: splitting (17) gives: % 130.86/18.29 | | % 130.86/18.29 | | Case 1: % 130.86/18.29 | | | % 130.86/18.29 | | | (24) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = % 130.86/18.29 | | | e2) % 130.86/18.29 | | | % 130.86/18.29 | | | REF_CLOSE: (11), (12), (13), (16), (21), (24) are inconsistent by % 130.86/18.29 | | | sub-proof #312. % 130.86/18.29 | | | % 130.86/18.29 | | Case 2: % 130.86/18.29 | | | % 130.86/18.29 | | | (25) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = % 130.86/18.29 | | | e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.29 | | | % 130.86/18.29 | | | BETA: splitting (25) gives: % 130.86/18.29 | | | % 130.86/18.29 | | | Case 1: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (26) all_9_6 = e2 & op(e2, e4) = e2 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REF_CLOSE: (4), (5), (14), (26) are inconsistent by sub-proof #311. % 130.86/18.29 | | | | % 130.86/18.29 | | | Case 2: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (27) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 130.86/18.29 | | | | = e2) % 130.86/18.29 | | | | % 130.86/18.29 | | | | BETA: splitting (27) gives: % 130.86/18.29 | | | | % 130.86/18.29 | | | | Case 1: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (28) all_9_12 = e2 & op(e1, e4) = e2 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | ALPHA: (28) implies: % 130.86/18.29 | | | | | (29) all_9_12 = e2 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (15), (18), (19), (20), (23), % 130.86/18.29 | | | | | (29) are inconsistent by sub-proof #202. % 130.86/18.29 | | | | | % 130.86/18.29 | | | | Case 2: % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | (30) all_9_20 = e2 & op(e0, e4) = e2 % 130.86/18.29 | | | | | % 130.86/18.29 | | | | | REF_CLOSE: (14), (23), (30) are inconsistent by sub-proof #270. % 130.86/18.29 | | | | | % 130.86/18.29 | | | | End of split % 130.86/18.29 | | | | % 130.86/18.29 | | | End of split % 130.86/18.29 | | | % 130.86/18.29 | | End of split % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (31) all_9_21 = e3 & op(e0, e3) = e3 % 130.86/18.29 | | % 130.86/18.29 | | REF_CLOSE: (10), (31) are inconsistent by sub-proof #201. % 130.86/18.29 | | % 130.86/18.29 | End of split % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #201 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_9_21 = e3 & op(e0, e3) = e3 % 130.86/18.29 (2) ~ (op(e0, e3) = e3) % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | ALPHA: (1) implies: % 130.86/18.29 | (3) op(e0, e3) = e3 % 130.86/18.29 | % 130.86/18.29 | PRED_UNIFY: (2), (3) imply: % 130.86/18.29 | (4) $false % 130.86/18.29 | % 130.86/18.29 | CLOSE: (4) is inconsistent. % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #202 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_6_5 = e1 % 130.86/18.29 (2) ~ (e4 = e0) % 130.86/18.29 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.29 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.29 (5) ~ (e4 = e2) % 130.86/18.29 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.29 (7) all_9_12 = e2 % 130.86/18.29 (8) ~ (e4 = e1) % 130.86/18.29 (9) ~ (e4 = e3) % 130.86/18.29 (10) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.29 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.29 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 (11) all_9_20 = e3 % 130.86/18.29 (12) all_4_0 = e0 % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (10) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 130.86/18.29 | | % 130.86/18.29 | | REF_CLOSE: (1), (2), (3), (4), (8), (12), (13) are inconsistent by sub-proof % 130.86/18.29 | | #315. % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (14) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 130.86/18.29 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 | | % 130.86/18.29 | | BETA: splitting (14) gives: % 130.86/18.29 | | % 130.86/18.29 | | Case 1: % 130.86/18.29 | | | % 130.86/18.29 | | | (15) all_9_6 = e4 & op(e2, e4) = e4 % 130.86/18.29 | | | % 130.86/18.29 | | | ALPHA: (15) implies: % 130.86/18.29 | | | (16) op(e2, e4) = e4 % 130.86/18.29 | | | % 130.86/18.29 | | | REF_CLOSE: (6), (9), (16) are inconsistent by sub-proof #320. % 130.86/18.29 | | | % 130.86/18.29 | | Case 2: % 130.86/18.29 | | | % 130.86/18.29 | | | (17) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 130.86/18.29 | | | e4) % 130.86/18.29 | | | % 130.86/18.29 | | | BETA: splitting (17) gives: % 130.86/18.29 | | | % 130.86/18.29 | | | Case 1: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (18) all_9_12 = e4 & op(e1, e4) = e4 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #273. % 130.86/18.29 | | | | % 130.86/18.29 | | | Case 2: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (19) all_9_20 = e4 & op(e0, e4) = e4 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REF_CLOSE: (9), (11), (19) are inconsistent by sub-proof #272. % 130.86/18.29 | | | | % 130.86/18.29 | | | End of split % 130.86/18.29 | | | % 130.86/18.29 | | End of split % 130.86/18.29 | | % 130.86/18.29 | End of split % 130.86/18.29 | % 130.86/18.29 End of proof % 130.86/18.29 % 130.86/18.29 Sub-proof #203 shows that the following formulas are inconsistent: % 130.86/18.29 ---------------------------------------------------------------- % 130.86/18.29 (1) all_6_5 = e1 % 130.86/18.29 (2) ~ (e4 = e0) % 130.86/18.29 (3) all_9_20 = e2 % 130.86/18.29 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.29 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.29 (6) ~ (e4 = e2) % 130.86/18.29 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.29 (8) all_9_17 = e2 % 130.86/18.29 (9) all_9_10 = e3 % 130.86/18.29 (10) all_9_3 = e2 % 130.86/18.29 (11) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) | % 130.86/18.29 (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) | % 130.86/18.29 (all_9_17 = e4 & op(e3, e0) = e4) % 130.86/18.29 (12) all_9_12 = e4 % 130.86/18.29 (13) ~ (e4 = e1) % 130.86/18.29 (14) all_9_5 = e0 % 130.86/18.29 (15) ~ (e4 = e3) % 130.86/18.29 (16) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.29 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.29 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.29 (17) all_4_0 = e0 % 130.86/18.29 % 130.86/18.29 Begin of proof % 130.86/18.29 | % 130.86/18.29 | BETA: splitting (11) gives: % 130.86/18.29 | % 130.86/18.29 | Case 1: % 130.86/18.29 | | % 130.86/18.29 | | (18) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) % 130.86/18.29 | | % 130.86/18.29 | | REF_CLOSE: (1), (4), (6), (10), (13), (18) are inconsistent by sub-proof % 130.86/18.29 | | #232. % 130.86/18.29 | | % 130.86/18.29 | Case 2: % 130.86/18.29 | | % 130.86/18.29 | | (19) (all_9_5 = e4 & op(e3, e2) = e4) | (all_9_10 = e4 & op(e3, e1) = e4) % 130.86/18.29 | | | (all_9_17 = e4 & op(e3, e0) = e4) % 130.86/18.29 | | % 130.86/18.29 | | BETA: splitting (19) gives: % 130.86/18.29 | | % 130.86/18.29 | | Case 1: % 130.86/18.29 | | | % 130.86/18.29 | | | (20) all_9_5 = e4 & op(e3, e2) = e4 % 130.86/18.29 | | | % 130.86/18.29 | | | REF_CLOSE: (2), (14), (20) are inconsistent by sub-proof #231. % 130.86/18.29 | | | % 130.86/18.29 | | Case 2: % 130.86/18.29 | | | % 130.86/18.29 | | | (21) (all_9_10 = e4 & op(e3, e1) = e4) | (all_9_17 = e4 & op(e3, e0) = % 130.86/18.29 | | | e4) % 130.86/18.29 | | | % 130.86/18.29 | | | BETA: splitting (21) gives: % 130.86/18.29 | | | % 130.86/18.29 | | | Case 1: % 130.86/18.29 | | | | % 130.86/18.29 | | | | (22) all_9_10 = e4 & op(e3, e1) = e4 % 130.86/18.29 | | | | % 130.86/18.29 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (15), % 130.86/18.29 | | | | (16), (17), (22) are inconsistent by sub-proof #230. % 130.86/18.29 | | | | % 130.86/18.29 | | | Case 2: % 130.86/18.30 | | | | % 130.86/18.30 | | | | (23) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.30 | | | | % 130.86/18.30 | | | | ALPHA: (23) implies: % 130.86/18.30 | | | | (24) all_9_17 = e4 % 130.86/18.30 | | | | % 130.86/18.30 | | | | REF_CLOSE: (6), (8), (24) are inconsistent by sub-proof #210. % 130.86/18.30 | | | | % 130.86/18.30 | | | End of split % 130.86/18.30 | | | % 130.86/18.30 | | End of split % 130.86/18.30 | | % 130.86/18.30 | End of split % 130.86/18.30 | % 130.86/18.30 End of proof % 130.86/18.30 % 130.86/18.30 Sub-proof #204 shows that the following formulas are inconsistent: % 130.86/18.30 ---------------------------------------------------------------- % 130.86/18.30 (1) all_9_8 = e4 % 130.86/18.30 (2) all_6_9 = all_4_21 % 130.86/18.30 (3) all_6_5 = e1 % 130.86/18.30 (4) ~ (e4 = e0) % 130.86/18.30 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.30 (6) all_9_20 = e2 % 130.86/18.30 (7) all_6_10 = e3 % 130.86/18.30 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.30 (9) ~ (all_4_3 = all_4_4) % 130.86/18.30 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.30 (11) ~ (e4 = e2) % 130.86/18.30 (12) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.30 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.30 (14) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.30 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.30 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.30 (15) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (16) ~ (all_4_21 = e3) % 130.86/18.30 (17) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.30 (18) ~ (all_4_3 = e3) % 130.86/18.30 (19) all_6_20 = all_4_4 % 130.86/18.30 (20) all_9_4 = e3 % 130.86/18.30 (21) all_9_11 = e2 % 130.86/18.30 (22) ~ (e3 = e0) % 130.86/18.30 (23) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.30 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.30 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.30 (24) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (25) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.30 = e0 % 130.86/18.30 (26) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.30 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.30 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.30 (27) all_9_17 = e1 % 130.86/18.30 (28) ~ (e2 = e0) % 130.86/18.30 (29) all_9_0 = e0 % 130.86/18.30 (30) all_9_16 = e2 % 130.86/18.30 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.30 (32) ~ (all_4_4 = e3) % 130.86/18.30 (33) ~ (op(e4, e3) = e3) % 130.86/18.30 (34) ~ (all_4_22 = e3) % 130.86/18.30 (35) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.30 (36) all_9_6 = e3 % 130.86/18.30 (37) ~ (e1 = e0) % 130.86/18.30 (38) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.30 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.30 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.30 (39) ~ (e3 = e2) % 130.86/18.30 (40) all_9_12 = e4 % 130.86/18.30 (41) op(e0, e4) = all_4_4 % 130.86/18.30 (42) ~ (e4 = e1) % 130.86/18.30 (43) ~ (all_4_3 = e0) % 130.86/18.30 (44) ~ (e3 = e1) % 130.86/18.30 (45) op(e3, e4) = e1 % 130.86/18.30 (46) all_9_9 = e4 % 130.86/18.30 (47) op(e1, e4) = all_4_3 % 130.86/18.30 (48) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.30 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.30 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.30 (49) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.30 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.30 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.30 (50) op(e2, e0) = all_4_22 % 130.86/18.30 (51) all_9_19 = e0 % 130.86/18.30 (52) ~ (e4 = e3) % 130.86/18.30 (53) ~ (all_4_4 = e0) % 130.86/18.30 (54) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.30 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.30 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.30 (55) ~ (all_4_3 = e1) % 130.86/18.30 (56) all_6_2 = all_4_10 % 130.86/18.30 (57) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.30 (58) op(e2, e4) = e3 % 130.86/18.30 (59) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.30 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.30 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.30 (60) all_9_2 = e1 % 130.86/18.30 (61) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.30 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.30 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.30 (62) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.30 = e0 % 130.86/18.30 (63) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.30 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.30 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.30 (64) ~ (all_4_4 = e1) % 130.86/18.30 (65) ~ (all_4_10 = e2) % 130.86/18.30 (66) all_4_0 = e0 % 130.86/18.30 (67) ~ (e2 = e1) % 130.86/18.30 (68) all_6_15 = all_4_3 % 130.86/18.30 (69) all_9_7 = e0 % 130.86/18.30 (70) op(e4, e4) = e0 % 130.86/18.30 % 130.86/18.30 Begin of proof % 130.86/18.30 | % 130.86/18.30 | BETA: splitting (23) gives: % 130.86/18.30 | % 130.86/18.30 | Case 1: % 130.86/18.30 | | % 130.86/18.30 | | (71) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = % 130.86/18.30 | | e4) % 130.86/18.30 | | % 130.86/18.30 | | BETA: splitting (71) gives: % 130.86/18.30 | | % 130.86/18.30 | | Case 1: % 130.86/18.30 | | | % 130.86/18.30 | | | (72) all_9_16 = e4 & op(e4, e0) = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (72) implies: % 130.86/18.30 | | | (73) all_9_16 = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | COMBINE_EQS: (30), (73) imply: % 130.86/18.30 | | | (74) e4 = e2 % 130.86/18.30 | | | % 130.86/18.30 | | | SIMP: (74) implies: % 130.86/18.30 | | | (75) e4 = e2 % 130.86/18.30 | | | % 130.86/18.30 | | | REDUCE: (11), (75) imply: % 130.86/18.30 | | | (76) $false % 130.86/18.30 | | | % 130.86/18.30 | | | CLOSE: (76) is inconsistent. % 130.86/18.30 | | | % 130.86/18.30 | | Case 2: % 130.86/18.30 | | | % 130.86/18.30 | | | (77) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (77) implies: % 130.86/18.30 | | | (78) all_9_17 = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | COMBINE_EQS: (27), (78) imply: % 130.86/18.30 | | | (79) e4 = e1 % 130.86/18.30 | | | % 130.86/18.30 | | | REDUCE: (42), (79) imply: % 130.86/18.30 | | | (80) $false % 130.86/18.30 | | | % 130.86/18.30 | | | CLOSE: (80) is inconsistent. % 130.86/18.30 | | | % 130.86/18.30 | | End of split % 130.86/18.30 | | % 130.86/18.30 | Case 2: % 130.86/18.30 | | % 130.86/18.30 | | (81) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = % 130.86/18.30 | | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.30 | | % 130.86/18.30 | | BETA: splitting (81) gives: % 130.86/18.30 | | % 130.86/18.30 | | Case 1: % 130.86/18.30 | | | % 130.86/18.30 | | | (82) all_9_18 = e4 & op(e2, e0) = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (82) implies: % 130.86/18.30 | | | (83) all_9_18 = e4 % 130.86/18.30 | | | % 130.86/18.30 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15), % 130.86/18.30 | | | (17), (18), (19), (21), (22), (24), (25), (26), (28), (29), % 130.86/18.30 | | | (31), (32), (36), (37), (38), (39), (41), (42), (43), (44), % 130.86/18.30 | | | (45), (47), (48), (52), (53), (55), (57), (58), (59), (60), % 130.86/18.30 | | | (61), (62), (64), (66), (67), (68), (69), (70), (83) are % 130.86/18.30 | | | inconsistent by sub-proof #221. % 130.86/18.30 | | | % 130.86/18.30 | | Case 2: % 130.86/18.30 | | | % 130.86/18.30 | | | (84) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, e0) = % 130.86/18.30 | | | e4) % 130.86/18.30 | | | % 130.86/18.30 | | | BETA: splitting (84) gives: % 130.86/18.30 | | | % 130.86/18.30 | | | Case 1: % 130.86/18.30 | | | | % 130.86/18.30 | | | | (85) all_9_19 = e4 & op(e1, e0) = e4 % 130.86/18.30 | | | | % 130.86/18.30 | | | | REF_CLOSE: (4), (51), (85) are inconsistent by sub-proof #220. % 130.86/18.30 | | | | % 130.86/18.30 | | | Case 2: % 130.86/18.30 | | | | % 130.86/18.30 | | | | (86) all_9_24 = e4 & op(e0, e0) = e4 % 130.86/18.30 | | | | % 130.86/18.30 | | | | ALPHA: (86) implies: % 130.86/18.30 | | | | (87) all_9_24 = e4 % 130.86/18.30 | | | | % 130.86/18.30 | | | | BETA: splitting (63) gives: % 130.86/18.30 | | | | % 130.86/18.30 | | | | Case 1: % 130.86/18.30 | | | | | % 130.86/18.30 | | | | | (88) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, % 130.86/18.30 | | | | | e0) = e3) % 130.86/18.30 | | | | | % 130.86/18.30 | | | | | REF_CLOSE: (2), (12), (16), (30), (39), (88) are inconsistent by % 130.86/18.30 | | | | | sub-proof #227. % 130.86/18.30 | | | | | % 130.86/18.30 | | | | Case 2: % 130.86/18.30 | | | | | % 130.86/18.30 | | | | | (89) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, % 130.86/18.30 | | | | | e0) = e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.30 | | | | | % 130.86/18.30 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 130.86/18.30 | | | | | (15), (17), (18), (19), (20), (22), (24), (25), (28), (29), % 130.86/18.30 | | | | | (31), (32), (33), (34), (35), (37), (38), (39), (40), (41), % 130.86/18.30 | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 130.86/18.30 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), % 130.86/18.30 | | | | | (62), (64), (65), (66), (67), (68), (70), (87), (89) are % 130.86/18.30 | | | | | inconsistent by sub-proof #216. % 130.86/18.30 | | | | | % 130.86/18.30 | | | | End of split % 130.86/18.30 | | | | % 130.86/18.30 | | | End of split % 130.86/18.30 | | | % 130.86/18.30 | | End of split % 130.86/18.30 | | % 130.86/18.30 | End of split % 130.86/18.30 | % 130.86/18.30 End of proof % 130.86/18.30 % 130.86/18.30 Sub-proof #205 shows that the following formulas are inconsistent: % 130.86/18.30 ---------------------------------------------------------------- % 130.86/18.30 (1) all_9_8 = e4 % 130.86/18.30 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.30 (3) all_6_9 = all_4_21 % 130.86/18.30 (4) all_6_5 = e1 % 130.86/18.30 (5) ~ (e4 = e0) % 130.86/18.30 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.30 (7) all_9_20 = e2 % 130.86/18.30 (8) all_6_10 = e3 % 130.86/18.30 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.30 (10) ~ (all_4_3 = all_4_4) % 130.86/18.30 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.30 (12) ~ (e4 = e2) % 130.86/18.30 (13) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.30 (14) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.30 (15) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.30 (16) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (17) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.30 (18) ~ (all_4_21 = e3) % 130.86/18.30 (19) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.30 (20) ~ (all_4_3 = e3) % 130.86/18.30 (21) all_6_20 = all_4_4 % 130.86/18.30 (22) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.30 (23) all_9_11 = e2 % 130.86/18.30 (24) ~ (e3 = e0) % 130.86/18.30 (25) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.30 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.30 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.30 (26) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.30 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.30 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.30 (27) all_6_22 = all_4_14 % 130.86/18.30 (28) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (29) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.30 = e0 % 130.86/18.30 (30) ~ (all_4_14 = e2) % 130.86/18.30 (31) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.30 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.30 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.30 (32) ~ (e2 = e0) % 130.86/18.30 (33) all_9_0 = e0 % 130.86/18.30 (34) ~ (all_4_22 = e2) % 130.86/18.30 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.30 (36) ~ (all_4_4 = e3) % 130.86/18.30 (37) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.30 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.30 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.30 (38) ~ (all_4_22 = e3) % 130.86/18.30 (39) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.30 (40) all_9_6 = e3 % 130.86/18.30 (41) ~ (e1 = e0) % 130.86/18.30 (42) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.30 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.30 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.30 (43) ~ (e3 = e2) % 130.86/18.30 (44) all_9_14 = e2 % 130.86/18.30 (45) all_9_13 = e3 % 130.86/18.30 (46) all_9_12 = e4 % 130.86/18.30 (47) op(e0, e4) = all_4_4 % 130.86/18.30 (48) ~ (e4 = e1) % 130.86/18.30 (49) ~ (all_4_3 = e0) % 130.86/18.30 (50) all_9_15 = e1 % 130.86/18.30 (51) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.30 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.30 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.30 (52) ~ (e3 = e1) % 130.86/18.30 (53) op(e3, e4) = e1 % 130.86/18.30 (54) op(e1, e4) = all_4_3 % 130.86/18.30 (55) all_4_11 = e0 % 130.86/18.30 (56) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.30 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.30 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.30 (57) op(e2, e0) = all_4_22 % 130.86/18.30 (58) all_9_19 = e0 % 130.86/18.30 (59) ~ (e4 = e3) % 130.86/18.30 (60) ~ (all_4_4 = e0) % 130.86/18.30 (61) ~ (all_4_3 = e1) % 130.86/18.30 (62) all_6_2 = all_4_10 % 130.86/18.30 (63) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.30 (64) op(e2, e4) = e3 % 130.86/18.30 (65) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.30 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.30 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.30 (66) all_9_2 = e1 % 130.86/18.30 (67) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.30 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.30 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.30 (68) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.30 = e0 % 130.86/18.30 (69) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.30 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.30 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.30 (70) ~ (all_4_4 = e1) % 130.86/18.30 (71) ~ (all_4_10 = e2) % 130.86/18.30 (72) all_4_0 = e0 % 130.86/18.30 (73) ~ (e2 = e1) % 130.86/18.30 (74) all_6_15 = all_4_3 % 130.86/18.30 (75) all_9_7 = e0 % 130.86/18.30 (76) op(e4, e4) = e0 % 130.86/18.30 (77) all_9_24 = e1 % 130.86/18.30 % 130.86/18.30 Begin of proof % 130.86/18.30 | % 130.86/18.30 | BETA: splitting (69) gives: % 130.86/18.30 | % 130.86/18.30 | Case 1: % 130.86/18.30 | | % 130.86/18.30 | | (78) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = % 130.86/18.30 | | e3) % 130.86/18.30 | | % 130.86/18.30 | | BETA: splitting (78) gives: % 130.86/18.30 | | % 130.86/18.30 | | Case 1: % 130.86/18.30 | | | % 130.86/18.30 | | | (79) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (79) implies: % 130.86/18.30 | | | (80) all_9_16 = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 130.86/18.30 | | | (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 130.86/18.30 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 130.86/18.30 | | | (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), % 130.86/18.30 | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.86/18.30 | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 130.86/18.30 | | | (68), (70), (71), (72), (73), (74), (75), (76), (77), (80) are % 130.86/18.30 | | | inconsistent by sub-proof #207. % 130.86/18.30 | | | % 130.86/18.30 | | Case 2: % 130.86/18.30 | | | % 130.86/18.30 | | | (81) all_9_17 = e3 & op(e3, e0) = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (81) implies: % 130.86/18.30 | | | (82) op(e3, e0) = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | REF_CLOSE: (3), (13), (18), (82) are inconsistent by sub-proof #228. % 130.86/18.30 | | | % 130.86/18.30 | | End of split % 130.86/18.30 | | % 130.86/18.30 | Case 2: % 130.86/18.30 | | % 130.86/18.30 | | (83) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = % 130.86/18.30 | | e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.30 | | % 130.86/18.30 | | BETA: splitting (83) gives: % 130.86/18.30 | | % 130.86/18.30 | | Case 1: % 130.86/18.30 | | | % 130.86/18.30 | | | (84) all_9_18 = e3 & op(e2, e0) = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | ALPHA: (84) implies: % 130.86/18.30 | | | (85) op(e2, e0) = e3 % 130.86/18.30 | | | % 130.86/18.30 | | | REF_CLOSE: (35), (38), (57), (85) are inconsistent by sub-proof #226. % 130.86/18.30 | | | % 130.86/18.30 | | Case 2: % 130.86/18.30 | | | % 130.86/18.30 | | | (86) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = % 130.86/18.30 | | | e3) % 130.86/18.30 | | | % 130.86/18.30 | | | BETA: splitting (86) gives: % 130.86/18.30 | | | % 130.86/18.30 | | | Case 1: % 130.86/18.30 | | | | % 130.86/18.30 | | | | (87) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.30 | | | | % 130.86/18.30 | | | | REF_CLOSE: (24), (58), (87) are inconsistent by sub-proof #206. % 130.86/18.30 | | | | % 130.86/18.30 | | | Case 2: % 130.86/18.30 | | | | % 130.86/18.30 | | | | (88) all_9_24 = e3 & op(e0, e0) = e3 % 130.86/18.30 | | | | % 130.86/18.30 | | | | ALPHA: (88) implies: % 130.86/18.30 | | | | (89) all_9_24 = e3 % 130.86/18.30 | | | | % 130.86/18.30 | | | | COMBINE_EQS: (77), (89) imply: % 130.86/18.30 | | | | (90) e3 = e1 % 130.86/18.30 | | | | % 130.86/18.30 | | | | SIMP: (90) implies: % 130.86/18.30 | | | | (91) e3 = e1 % 130.86/18.30 | | | | % 130.86/18.30 | | | | REDUCE: (52), (91) imply: % 130.86/18.30 | | | | (92) $false % 130.86/18.30 | | | | % 130.86/18.30 | | | | CLOSE: (92) is inconsistent. % 130.86/18.30 | | | | % 130.86/18.30 | | | End of split % 130.86/18.30 | | | % 130.86/18.30 | | End of split % 130.86/18.30 | | % 130.86/18.30 | End of split % 130.86/18.30 | % 130.86/18.30 End of proof % 130.86/18.30 % 130.86/18.30 Sub-proof #206 shows that the following formulas are inconsistent: % 130.86/18.30 ---------------------------------------------------------------- % 130.86/18.30 (1) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.30 (2) all_9_19 = e0 % 130.86/18.30 (3) ~ (e3 = e0) % 130.86/18.30 % 130.86/18.30 Begin of proof % 130.86/18.30 | % 130.86/18.30 | ALPHA: (1) implies: % 130.86/18.30 | (4) all_9_19 = e3 % 130.86/18.30 | % 130.86/18.30 | COMBINE_EQS: (2), (4) imply: % 130.86/18.30 | (5) e3 = e0 % 130.86/18.30 | % 130.86/18.30 | SIMP: (5) implies: % 130.86/18.30 | (6) e3 = e0 % 130.86/18.30 | % 130.86/18.30 | REDUCE: (3), (6) imply: % 130.86/18.30 | (7) $false % 130.86/18.30 | % 130.86/18.30 | CLOSE: (7) is inconsistent. % 130.86/18.30 | % 130.86/18.30 End of proof % 130.86/18.30 % 130.86/18.30 Sub-proof #207 shows that the following formulas are inconsistent: % 130.86/18.30 ---------------------------------------------------------------- % 130.86/18.30 (1) all_9_8 = e4 % 130.86/18.30 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.30 (3) all_6_5 = e1 % 130.86/18.30 (4) ~ (e4 = e0) % 130.86/18.30 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.30 (6) all_9_20 = e2 % 130.86/18.30 (7) all_6_10 = e3 % 130.86/18.30 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.30 (9) ~ (all_4_3 = all_4_4) % 130.86/18.30 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.30 (11) ~ (e4 = e2) % 130.86/18.30 (12) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.30 (13) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.30 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.30 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.30 (17) ~ (all_4_3 = e3) % 130.86/18.30 (18) all_6_20 = all_4_4 % 130.86/18.30 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.30 (20) all_9_11 = e2 % 130.86/18.30 (21) ~ (e3 = e0) % 130.86/18.30 (22) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.30 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.30 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.30 (23) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.30 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.30 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.30 (24) all_9_16 = e3 % 130.86/18.30 (25) all_6_22 = all_4_14 % 130.86/18.30 (26) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.30 (27) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.30 = e0 % 130.86/18.30 (28) ~ (all_4_14 = e2) % 130.86/18.30 (29) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.30 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.30 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.30 (30) ~ (e2 = e0) % 130.86/18.30 (31) all_9_0 = e0 % 130.86/18.30 (32) ~ (all_4_22 = e2) % 130.86/18.30 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.30 (34) ~ (all_4_4 = e3) % 130.86/18.30 (35) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.30 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.30 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.30 (36) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.30 (37) all_9_6 = e3 % 130.86/18.30 (38) ~ (e1 = e0) % 130.86/18.30 (39) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.30 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.30 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.30 (40) ~ (e3 = e2) % 130.86/18.30 (41) all_9_14 = e2 % 130.86/18.30 (42) all_9_13 = e3 % 130.86/18.30 (43) all_9_12 = e4 % 130.86/18.30 (44) op(e0, e4) = all_4_4 % 130.86/18.30 (45) ~ (e4 = e1) % 130.86/18.30 (46) ~ (all_4_3 = e0) % 130.86/18.30 (47) all_9_15 = e1 % 130.86/18.30 (48) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.30 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.30 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.30 (49) ~ (e3 = e1) % 130.86/18.30 (50) op(e3, e4) = e1 % 130.86/18.30 (51) op(e1, e4) = all_4_3 % 130.86/18.30 (52) all_4_11 = e0 % 130.86/18.30 (53) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.30 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.30 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.30 (54) all_9_19 = e0 % 130.86/18.30 (55) ~ (e4 = e3) % 130.86/18.30 (56) ~ (all_4_4 = e0) % 130.86/18.30 (57) ~ (all_4_3 = e1) % 130.86/18.30 (58) all_6_2 = all_4_10 % 130.86/18.30 (59) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.30 (60) op(e2, e4) = e3 % 130.86/18.30 (61) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.30 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.30 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.30 (62) all_9_2 = e1 % 130.86/18.30 (63) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.30 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.30 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.31 (64) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.31 = e0 % 130.86/18.31 (65) ~ (all_4_4 = e1) % 130.86/18.31 (66) ~ (all_4_10 = e2) % 130.86/18.31 (67) all_4_0 = e0 % 130.86/18.31 (68) ~ (e2 = e1) % 130.86/18.31 (69) all_6_15 = all_4_3 % 130.86/18.31 (70) all_9_7 = e0 % 130.86/18.31 (71) op(e4, e4) = e0 % 130.86/18.31 (72) all_9_24 = e1 % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | BETA: splitting (22) gives: % 130.86/18.31 | % 130.86/18.31 | Case 1: % 130.86/18.31 | | % 130.86/18.31 | | (73) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = % 130.86/18.31 | | e4) % 130.86/18.31 | | % 130.86/18.31 | | BETA: splitting (73) gives: % 130.86/18.31 | | % 130.86/18.31 | | Case 1: % 130.86/18.31 | | | % 130.86/18.31 | | | (74) all_9_16 = e4 & op(e4, e0) = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (74) implies: % 130.86/18.31 | | | (75) all_9_16 = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | COMBINE_EQS: (24), (75) imply: % 130.86/18.31 | | | (76) e4 = e3 % 130.86/18.31 | | | % 130.86/18.31 | | | REF_CLOSE: (3), (4), (6), (8), (10), (11), (13), (43), (45), (55), (61), % 130.86/18.31 | | | (67), (76) are inconsistent by sub-proof #217. % 130.86/18.31 | | | % 130.86/18.31 | | Case 2: % 130.86/18.31 | | | % 130.86/18.31 | | | (77) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (77) implies: % 130.86/18.31 | | | (78) all_9_17 = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | BETA: splitting (35) gives: % 130.86/18.31 | | | % 130.86/18.31 | | | Case 1: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (79) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) % 130.86/18.31 | | | | = e2) % 130.86/18.31 | | | | % 130.86/18.31 | | | | BETA: splitting (79) gives: % 130.86/18.31 | | | | % 130.86/18.31 | | | | Case 1: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (80) all_9_16 = e2 & op(e4, e0) = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | ALPHA: (80) implies: % 130.86/18.31 | | | | | (81) all_9_16 = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | REF_CLOSE: (24), (40), (81) are inconsistent by sub-proof #229. % 130.86/18.31 | | | | | % 130.86/18.31 | | | | Case 2: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (82) all_9_17 = e2 & op(e3, e0) = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | ALPHA: (82) implies: % 130.86/18.31 | | | | | (83) all_9_17 = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | REF_CLOSE: (11), (78), (83) are inconsistent by sub-proof #210. % 130.86/18.31 | | | | | % 130.86/18.31 | | | | End of split % 130.86/18.31 | | | | % 130.86/18.31 | | | Case 2: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (84) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) % 130.86/18.31 | | | | = e2) | (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.31 | | | | % 130.86/18.31 | | | | BETA: splitting (84) gives: % 130.86/18.31 | | | | % 130.86/18.31 | | | | Case 1: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (85) all_9_18 = e2 & op(e2, e0) = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | ALPHA: (85) implies: % 130.86/18.31 | | | | | (86) op(e2, e0) = e2 % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | REF_CLOSE: (12), (32), (86) are inconsistent by sub-proof #214. % 130.86/18.31 | | | | | % 130.86/18.31 | | | | Case 2: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (87) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, % 130.86/18.31 | | | | | e0) = e2) % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | BETA: splitting (87) gives: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | Case 1: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (88) all_9_19 = e2 & op(e1, e0) = e2 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), % 130.86/18.31 | | | | | | (15), (19), (23), (25), (28), (30), (31), (33), (36), % 130.86/18.31 | | | | | | (40), (41), (42), (43), (45), (47), (48), (50), (52), % 130.86/18.31 | | | | | | (53), (54), (55), (58), (61), (66), (67), (68), (88) are % 130.86/18.31 | | | | | | inconsistent by sub-proof #209. % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | Case 2: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (89) all_9_24 = e2 & op(e0, e0) = e2 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | ALPHA: (89) implies: % 130.86/18.31 | | | | | | (90) all_9_24 = e2 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | COMBINE_EQS: (72), (90) imply: % 130.86/18.31 | | | | | | (91) e2 = e1 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | COMBINE_EQS: (6), (91) imply: % 130.86/18.31 | | | | | | (92) all_9_20 = e1 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (11), (13), (30), (31), % 130.86/18.31 | | | | | | (33), (40), (45), (50), (53), (55), (61), (67), (68), % 130.86/18.31 | | | | | | (92) are inconsistent by sub-proof #283. % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | End of split % 130.86/18.31 | | | | | % 130.86/18.31 | | | | End of split % 130.86/18.31 | | | | % 130.86/18.31 | | | End of split % 130.86/18.31 | | | % 130.86/18.31 | | End of split % 130.86/18.31 | | % 130.86/18.31 | Case 2: % 130.86/18.31 | | % 130.86/18.31 | | (93) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = % 130.86/18.31 | | e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.31 | | % 130.86/18.31 | | BETA: splitting (93) gives: % 130.86/18.31 | | % 130.86/18.31 | | Case 1: % 130.86/18.31 | | | % 130.86/18.31 | | | (94) all_9_18 = e4 & op(e2, e0) = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (94) implies: % 130.86/18.31 | | | (95) all_9_18 = e4 % 130.86/18.31 | | | % 130.86/18.31 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 130.86/18.31 | | | (16), (17), (18), (20), (21), (26), (27), (29), (30), (31), % 130.86/18.31 | | | (33), (34), (37), (38), (39), (40), (44), (45), (46), (49), % 130.86/18.31 | | | (50), (51), (53), (55), (56), (57), (59), (60), (61), (62), % 130.86/18.31 | | | (63), (64), (65), (67), (68), (69), (70), (71), (95) are % 130.86/18.31 | | | inconsistent by sub-proof #221. % 130.86/18.31 | | | % 130.86/18.31 | | Case 2: % 130.86/18.31 | | | % 130.86/18.31 | | | (96) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, e0) = % 130.86/18.31 | | | e4) % 130.86/18.31 | | | % 130.86/18.31 | | | BETA: splitting (96) gives: % 130.86/18.31 | | | % 130.86/18.31 | | | Case 1: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (97) all_9_19 = e4 & op(e1, e0) = e4 % 130.86/18.31 | | | | % 130.86/18.31 | | | | ALPHA: (97) implies: % 130.86/18.31 | | | | (98) all_9_19 = e4 % 130.86/18.31 | | | | % 130.86/18.31 | | | | COMBINE_EQS: (54), (98) imply: % 130.86/18.31 | | | | (99) e4 = e0 % 130.86/18.31 | | | | % 130.86/18.31 | | | | SIMP: (99) implies: % 130.86/18.31 | | | | (100) e4 = e0 % 130.86/18.31 | | | | % 130.86/18.31 | | | | REDUCE: (4), (100) imply: % 130.86/18.31 | | | | (101) $false % 130.86/18.31 | | | | % 130.86/18.31 | | | | CLOSE: (101) is inconsistent. % 130.86/18.31 | | | | % 130.86/18.31 | | | Case 2: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (102) all_9_24 = e4 & op(e0, e0) = e4 % 130.86/18.31 | | | | % 130.86/18.31 | | | | ALPHA: (102) implies: % 130.86/18.31 | | | | (103) all_9_24 = e4 % 130.86/18.31 | | | | % 130.86/18.31 | | | | REF_CLOSE: (45), (72), (103) are inconsistent by sub-proof #208. % 130.86/18.31 | | | | % 130.86/18.31 | | | End of split % 130.86/18.31 | | | % 130.86/18.31 | | End of split % 130.86/18.31 | | % 130.86/18.31 | End of split % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #208 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_9_24 = e4 % 130.86/18.31 (2) all_9_24 = e1 % 130.86/18.31 (3) ~ (e4 = e1) % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | COMBINE_EQS: (1), (2) imply: % 130.86/18.31 | (4) e4 = e1 % 130.86/18.31 | % 130.86/18.31 | SIMP: (4) implies: % 130.86/18.31 | (5) e4 = e1 % 130.86/18.31 | % 130.86/18.31 | REDUCE: (3), (5) imply: % 130.86/18.31 | (6) $false % 130.86/18.31 | % 130.86/18.31 | CLOSE: (6) is inconsistent. % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #209 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.31 (2) all_6_5 = e1 % 130.86/18.31 (3) ~ (e4 = e0) % 130.86/18.31 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.31 (5) all_9_20 = e2 % 130.86/18.31 (6) all_6_10 = e3 % 130.86/18.31 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.31 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.31 (9) ~ (e4 = e2) % 130.86/18.31 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.31 (11) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.31 (12) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.31 (13) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.31 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.31 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.31 (14) all_6_22 = all_4_14 % 130.86/18.31 (15) ~ (all_4_14 = e2) % 130.86/18.31 (16) ~ (e2 = e0) % 130.86/18.31 (17) all_9_0 = e0 % 130.86/18.31 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.31 (19) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.31 (20) ~ (e3 = e2) % 130.86/18.31 (21) all_9_14 = e2 % 130.86/18.31 (22) all_9_13 = e3 % 130.86/18.31 (23) all_9_12 = e4 % 130.86/18.31 (24) ~ (e4 = e1) % 130.86/18.31 (25) all_9_15 = e1 % 130.86/18.31 (26) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.31 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.31 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.31 (27) op(e3, e4) = e1 % 130.86/18.31 (28) all_4_11 = e0 % 130.86/18.31 (29) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.31 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.31 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.31 (30) all_9_19 = e0 % 130.86/18.31 (31) ~ (e4 = e3) % 130.86/18.31 (32) all_6_2 = all_4_10 % 130.86/18.31 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.31 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.31 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.31 (34) ~ (all_4_10 = e2) % 130.86/18.31 (35) all_4_0 = e0 % 130.86/18.31 (36) all_9_19 = e2 & op(e1, e0) = e2 % 130.86/18.31 (37) ~ (e2 = e1) % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | ALPHA: (36) implies: % 130.86/18.31 | (38) all_9_19 = e2 % 130.86/18.31 | % 130.86/18.31 | COMBINE_EQS: (30), (38) imply: % 130.86/18.31 | (39) e2 = e0 % 130.86/18.31 | % 130.86/18.31 | COMBINE_EQS: (21), (39) imply: % 130.86/18.31 | (40) all_9_14 = e0 % 130.86/18.31 | % 130.86/18.31 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.31 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 130.86/18.31 | (25), (26), (27), (28), (29), (31), (32), (33), (34), (35), (37), % 130.86/18.31 | (38), (40) are inconsistent by sub-proof #245. % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #210 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_9_17 = e4 % 130.86/18.31 (2) all_9_17 = e2 % 130.86/18.31 (3) ~ (e4 = e2) % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | COMBINE_EQS: (1), (2) imply: % 130.86/18.31 | (4) e4 = e2 % 130.86/18.31 | % 130.86/18.31 | SIMP: (4) implies: % 130.86/18.31 | (5) e4 = e2 % 130.86/18.31 | % 130.86/18.31 | REDUCE: (3), (5) imply: % 130.86/18.31 | (6) $false % 130.86/18.31 | % 130.86/18.31 | CLOSE: (6) is inconsistent. % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #211 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_9_8 = e4 % 130.86/18.31 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.31 (3) all_6_9 = all_4_21 % 130.86/18.31 (4) all_6_5 = e1 % 130.86/18.31 (5) ~ (e4 = e0) % 130.86/18.31 (6) all_9_16 = e1 % 130.86/18.31 (7) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.31 (8) all_9_20 = e2 % 130.86/18.31 (9) all_6_10 = e3 % 130.86/18.31 (10) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.31 (11) ~ (all_4_3 = all_4_4) % 130.86/18.31 (12) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.31 (13) ~ (e4 = e2) % 130.86/18.31 (14) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.31 (15) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.31 (16) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.31 (17) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.31 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.31 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.31 (18) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.31 (19) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.31 (20) ~ (all_4_21 = e3) % 130.86/18.31 (21) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.31 (22) ~ (all_4_3 = e3) % 130.86/18.31 (23) all_6_20 = all_4_4 % 130.86/18.31 (24) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.31 (25) all_9_11 = e2 % 130.86/18.31 (26) ~ (e3 = e0) % 130.86/18.31 (27) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.31 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.31 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.31 (28) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.31 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.31 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.31 (29) all_6_22 = all_4_14 % 130.86/18.31 (30) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.31 (31) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.31 = e0 % 130.86/18.31 (32) ~ (all_4_14 = e2) % 130.86/18.31 (33) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.31 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.31 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.31 (34) ~ (e2 = e0) % 130.86/18.31 (35) all_9_0 = e0 % 130.86/18.31 (36) ~ (all_4_22 = e2) % 130.86/18.31 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.31 (38) ~ (all_4_4 = e3) % 130.86/18.31 (39) ~ (op(e4, e3) = e3) % 130.86/18.31 (40) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = e2) | % 130.86/18.31 (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) | % 130.86/18.31 (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.31 (41) ~ (all_4_22 = e3) % 130.86/18.31 (42) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.31 (43) all_9_6 = e3 % 130.86/18.31 (44) ~ (e1 = e0) % 130.86/18.31 (45) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.31 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.31 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.31 (46) ~ (e3 = e2) % 130.86/18.31 (47) all_9_14 = e2 % 130.86/18.31 (48) all_9_13 = e3 % 130.86/18.31 (49) all_9_12 = e4 % 130.86/18.31 (50) op(e0, e4) = all_4_4 % 130.86/18.31 (51) ~ (e4 = e1) % 130.86/18.31 (52) ~ (all_4_3 = e0) % 130.86/18.31 (53) all_9_15 = e1 % 130.86/18.31 (54) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.31 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.31 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.31 (55) ~ (e3 = e1) % 130.86/18.31 (56) op(e3, e4) = e1 % 130.86/18.31 (57) all_9_9 = e4 % 130.86/18.31 (58) op(e1, e4) = all_4_3 % 130.86/18.31 (59) all_4_11 = e0 % 130.86/18.31 (60) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.31 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.31 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.31 (61) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.31 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.31 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.31 (62) op(e2, e0) = all_4_22 % 130.86/18.31 (63) all_9_19 = e0 % 130.86/18.31 (64) ~ (e4 = e3) % 130.86/18.31 (65) ~ (all_4_4 = e0) % 130.86/18.31 (66) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.31 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.31 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.31 (67) ~ (all_4_3 = e1) % 130.86/18.31 (68) all_6_2 = all_4_10 % 130.86/18.31 (69) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.31 (70) op(e2, e4) = e3 % 130.86/18.31 (71) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.31 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.31 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.31 (72) all_9_2 = e1 % 130.86/18.31 (73) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.31 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.31 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.31 (74) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.31 = e0 % 130.86/18.31 (75) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.31 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.31 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.31 (76) ~ (all_4_4 = e1) % 130.86/18.31 (77) ~ (all_4_10 = e2) % 130.86/18.31 (78) all_4_0 = e0 % 130.86/18.31 (79) ~ (e2 = e1) % 130.86/18.31 (80) all_6_15 = all_4_3 % 130.86/18.31 (81) all_9_7 = e0 % 130.86/18.31 (82) op(e4, e4) = e0 % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | BETA: splitting (40) gives: % 130.86/18.31 | % 130.86/18.31 | Case 1: % 130.86/18.31 | | % 130.86/18.31 | | (83) (all_9_16 = e2 & op(e4, e0) = e2) | (all_9_17 = e2 & op(e3, e0) = % 130.86/18.31 | | e2) % 130.86/18.31 | | % 130.86/18.31 | | BETA: splitting (83) gives: % 130.86/18.31 | | % 130.86/18.31 | | Case 1: % 130.86/18.31 | | | % 130.86/18.31 | | | (84) all_9_16 = e2 & op(e4, e0) = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (84) implies: % 130.86/18.31 | | | (85) all_9_16 = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | COMBINE_EQS: (6), (85) imply: % 130.86/18.31 | | | (86) e2 = e1 % 130.86/18.31 | | | % 130.86/18.31 | | | SIMP: (86) implies: % 130.86/18.31 | | | (87) e2 = e1 % 130.86/18.31 | | | % 130.86/18.31 | | | COMBINE_EQS: (8), (87) imply: % 130.86/18.31 | | | (88) all_9_20 = e1 % 130.86/18.31 | | | % 130.86/18.31 | | | REF_CLOSE: (4), (5), (7), (9), (10), (12), (13), (16), (34), (35), (37), % 130.86/18.31 | | | (46), (51), (56), (60), (64), (71), (78), (79), (88) are % 130.86/18.31 | | | inconsistent by sub-proof #283. % 130.86/18.31 | | | % 130.86/18.31 | | Case 2: % 130.86/18.31 | | | % 130.86/18.31 | | | (89) all_9_17 = e2 & op(e3, e0) = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (89) implies: % 130.86/18.31 | | | (90) all_9_17 = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 130.86/18.31 | | | (14), (16), (17), (18), (20), (21), (22), (23), (25), (26), % 130.86/18.31 | | | (27), (30), (31), (33), (34), (35), (37), (38), (39), (41), % 130.86/18.31 | | | (42), (43), (44), (45), (46), (49), (50), (51), (52), (55), % 130.86/18.31 | | | (56), (57), (58), (60), (61), (62), (63), (64), (65), (66), % 130.86/18.31 | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76), % 130.86/18.31 | | | (77), (78), (79), (80), (81), (82), (90) are inconsistent by % 130.86/18.31 | | | sub-proof #215. % 130.86/18.31 | | | % 130.86/18.31 | | End of split % 130.86/18.31 | | % 130.86/18.31 | Case 2: % 130.86/18.31 | | % 130.86/18.31 | | (91) (all_9_18 = e2 & op(e2, e0) = e2) | (all_9_19 = e2 & op(e1, e0) = % 130.86/18.31 | | e2) | (all_9_24 = e2 & op(e0, e0) = e2) % 130.86/18.31 | | % 130.86/18.31 | | BETA: splitting (91) gives: % 130.86/18.31 | | % 130.86/18.31 | | Case 1: % 130.86/18.31 | | | % 130.86/18.31 | | | (92) all_9_18 = e2 & op(e2, e0) = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | ALPHA: (92) implies: % 130.86/18.31 | | | (93) op(e2, e0) = e2 % 130.86/18.31 | | | % 130.86/18.31 | | | REF_CLOSE: (15), (36), (93) are inconsistent by sub-proof #214. % 130.86/18.31 | | | % 130.86/18.31 | | Case 2: % 130.86/18.31 | | | % 130.86/18.31 | | | (94) (all_9_19 = e2 & op(e1, e0) = e2) | (all_9_24 = e2 & op(e0, e0) = % 130.86/18.31 | | | e2) % 130.86/18.31 | | | % 130.86/18.31 | | | BETA: splitting (94) gives: % 130.86/18.31 | | | % 130.86/18.31 | | | Case 1: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (95) all_9_19 = e2 & op(e1, e0) = e2 % 130.86/18.31 | | | | % 130.86/18.31 | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (12), (13), (16), (19), % 130.86/18.31 | | | | (24), (28), (29), (32), (34), (35), (37), (42), (46), (47), % 130.86/18.31 | | | | (48), (49), (51), (53), (54), (56), (59), (60), (63), (64), % 130.86/18.31 | | | | (68), (71), (77), (78), (79), (95) are inconsistent by % 130.86/18.31 | | | | sub-proof #213. % 130.86/18.31 | | | | % 130.86/18.31 | | | Case 2: % 130.86/18.31 | | | | % 130.86/18.31 | | | | (96) all_9_24 = e2 & op(e0, e0) = e2 % 130.86/18.31 | | | | % 130.86/18.31 | | | | ALPHA: (96) implies: % 130.86/18.31 | | | | (97) all_9_24 = e2 % 130.86/18.31 | | | | % 130.86/18.31 | | | | BETA: splitting (61) gives: % 130.86/18.31 | | | | % 130.86/18.31 | | | | Case 1: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (98) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) % 130.86/18.31 | | | | | = e3) % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | BETA: splitting (98) gives: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | Case 1: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (99) all_9_0 = e3 & op(e4, e4) = e3 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | REF_CLOSE: (26), (35), (99) are inconsistent by sub-proof #291. % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | Case 2: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (100) all_9_1 = e3 & op(e4, e3) = e3 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | REF_CLOSE: (39), (100) are inconsistent by sub-proof #296. % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | End of split % 130.86/18.31 | | | | | % 130.86/18.31 | | | | Case 2: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | (101) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) % 130.86/18.31 | | | | | = e3) | (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | BETA: splitting (101) gives: % 130.86/18.31 | | | | | % 130.86/18.31 | | | | | Case 1: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (102) all_9_4 = e3 & op(e4, e2) = e3 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | ALPHA: (102) implies: % 130.86/18.31 | | | | | | (103) all_9_4 = e3 % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | BETA: splitting (75) gives: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | Case 1: % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | (104) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & % 130.86/18.31 | | | | | | | op(e3, e0) = e3) % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | REF_CLOSE: (3), (6), (14), (20), (55), (104) are inconsistent by % 130.86/18.31 | | | | | | | sub-proof #218. % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | Case 2: % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | (105) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & % 130.86/18.31 | | | | | | | op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | BETA: splitting (105) gives: % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | Case 1: % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | (106) all_9_18 = e3 & op(e2, e0) = e3 % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | ALPHA: (106) implies: % 130.86/18.31 | | | | | | | | (107) op(e2, e0) = e3 % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | REF_CLOSE: (37), (41), (62), (107) are inconsistent by sub-proof % 130.86/18.31 | | | | | | | | #226. % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | Case 2: % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | (108) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & % 130.86/18.31 | | | | | | | | op(e0, e0) = e3) % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | BETA: splitting (108) gives: % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | | Case 1: % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | | (109) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (12), (13), % 130.86/18.31 | | | | | | | | | (16), (17), (18), (21), (22), (23), (26), (30), % 130.86/18.31 | | | | | | | | | (31), (34), (35), (37), (38), (39), (42), (44), % 130.86/18.31 | | | | | | | | | (45), (46), (49), (50), (51), (52), (55), (56), % 130.86/18.31 | | | | | | | | | (57), (58), (60), (61), (63), (64), (65), (66), % 130.86/18.31 | | | | | | | | | (67), (68), (69), (70), (71), (72), (73), (74), % 130.86/18.31 | | | | | | | | | (76), (77), (78), (79), (80), (82), (103), (109) % 130.86/18.31 | | | | | | | | | are inconsistent by sub-proof #225. % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | Case 2: % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | | (110) all_9_24 = e3 & op(e0, e0) = e3 % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | | REF_CLOSE: (46), (97), (110) are inconsistent by sub-proof % 130.86/18.31 | | | | | | | | | #212. % 130.86/18.31 | | | | | | | | | % 130.86/18.31 | | | | | | | | End of split % 130.86/18.31 | | | | | | | | % 130.86/18.31 | | | | | | | End of split % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | End of split % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | Case 2: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | (111) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, % 130.86/18.31 | | | | | | e0) = e3) % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | BETA: splitting (111) gives: % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | | Case 1: % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | (112) all_9_9 = e3 & op(e4, e1) = e3 % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | REF_CLOSE: (4), (5), (8), (10), (12), (13), (16), (49), (51), % 130.86/18.31 | | | | | | | (57), (64), (71), (78), (112) are inconsistent by % 130.86/18.31 | | | | | | | sub-proof #289. % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | Case 2: % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | (113) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | | REF_CLOSE: (6), (55), (113) are inconsistent by sub-proof #219. % 130.86/18.31 | | | | | | | % 130.86/18.31 | | | | | | End of split % 130.86/18.31 | | | | | | % 130.86/18.31 | | | | | End of split % 130.86/18.31 | | | | | % 130.86/18.31 | | | | End of split % 130.86/18.31 | | | | % 130.86/18.31 | | | End of split % 130.86/18.31 | | | % 130.86/18.31 | | End of split % 130.86/18.31 | | % 130.86/18.31 | End of split % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #212 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_9_24 = e3 & op(e0, e0) = e3 % 130.86/18.31 (2) all_9_24 = e2 % 130.86/18.31 (3) ~ (e3 = e2) % 130.86/18.31 % 130.86/18.31 Begin of proof % 130.86/18.31 | % 130.86/18.31 | ALPHA: (1) implies: % 130.86/18.31 | (4) all_9_24 = e3 % 130.86/18.31 | % 130.86/18.31 | COMBINE_EQS: (2), (4) imply: % 130.86/18.31 | (5) e3 = e2 % 130.86/18.31 | % 130.86/18.31 | REDUCE: (3), (5) imply: % 130.86/18.31 | (6) $false % 130.86/18.31 | % 130.86/18.31 | CLOSE: (6) is inconsistent. % 130.86/18.31 | % 130.86/18.31 End of proof % 130.86/18.31 % 130.86/18.31 Sub-proof #213 shows that the following formulas are inconsistent: % 130.86/18.31 ---------------------------------------------------------------- % 130.86/18.31 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 130.86/18.31 (2) all_6_5 = e1 % 130.86/18.31 (3) ~ (e4 = e0) % 130.86/18.31 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.31 (5) all_9_20 = e2 % 130.86/18.31 (6) all_6_10 = e3 % 130.86/18.31 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.31 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.31 (9) ~ (e4 = e2) % 130.86/18.31 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.31 (11) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 130.86/18.31 (12) e4 = e2 | ~ (op(e2, e2) = e2) % 130.86/18.32 (13) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 130.86/18.32 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 130.86/18.32 (all_9_19 = e2 & op(e1, e0) = e2) % 130.86/18.32 (14) all_6_22 = all_4_14 % 130.86/18.32 (15) ~ (all_4_14 = e2) % 130.86/18.32 (16) ~ (e2 = e0) % 130.86/18.32 (17) all_9_0 = e0 % 130.86/18.32 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.32 (19) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.32 (20) ~ (e3 = e2) % 130.86/18.32 (21) all_9_14 = e2 % 130.86/18.32 (22) all_9_13 = e3 % 130.86/18.32 (23) all_9_12 = e4 % 130.86/18.32 (24) ~ (e4 = e1) % 130.86/18.32 (25) all_9_15 = e1 % 130.86/18.32 (26) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 130.86/18.32 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 130.86/18.32 (all_9_22 = e2 & op(e0, e2) = e2) % 130.86/18.32 (27) op(e3, e4) = e1 % 130.86/18.32 (28) all_4_11 = e0 % 130.86/18.32 (29) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.32 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.32 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.32 (30) all_9_19 = e0 % 130.86/18.32 (31) ~ (e4 = e3) % 130.86/18.32 (32) all_6_2 = all_4_10 % 130.86/18.32 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.32 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.32 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.32 (34) ~ (all_4_10 = e2) % 130.86/18.32 (35) all_4_0 = e0 % 130.86/18.32 (36) all_9_19 = e2 & op(e1, e0) = e2 % 130.86/18.32 (37) ~ (e2 = e1) % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | ALPHA: (36) implies: % 130.86/18.32 | (38) all_9_19 = e2 % 130.86/18.32 | % 130.86/18.32 | COMBINE_EQS: (30), (38) imply: % 130.86/18.32 | (39) e2 = e0 % 130.86/18.32 | % 130.86/18.32 | SIMP: (39) implies: % 130.86/18.32 | (40) e2 = e0 % 130.86/18.32 | % 130.86/18.32 | COMBINE_EQS: (21), (40) imply: % 130.86/18.32 | (41) all_9_14 = e0 % 130.86/18.32 | % 130.86/18.32 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.32 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 130.86/18.32 | (25), (26), (27), (28), (29), (31), (32), (33), (34), (35), (37), % 130.86/18.32 | (38), (41) are inconsistent by sub-proof #245. % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #214 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_4_22 = e2 | ~ (op(e2, e0) = e2) % 130.86/18.32 (2) op(e2, e0) = e2 % 130.86/18.32 (3) ~ (all_4_22 = e2) % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | BETA: splitting (1) gives: % 130.86/18.32 | % 130.86/18.32 | Case 1: % 130.86/18.32 | | % 130.86/18.32 | | (4) ~ (op(e2, e0) = e2) % 130.86/18.32 | | % 130.86/18.32 | | PRED_UNIFY: (2), (4) imply: % 130.86/18.32 | | (5) $false % 130.86/18.32 | | % 130.86/18.32 | | CLOSE: (5) is inconsistent. % 130.86/18.32 | | % 130.86/18.32 | Case 2: % 130.86/18.32 | | % 130.86/18.32 | | (6) all_4_22 = e2 % 130.86/18.32 | | % 130.86/18.32 | | REDUCE: (3), (6) imply: % 130.86/18.32 | | (7) $false % 130.86/18.32 | | % 130.86/18.32 | | CLOSE: (7) is inconsistent. % 130.86/18.32 | | % 130.86/18.32 | End of split % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #215 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_9_8 = e4 % 130.86/18.32 (2) all_6_9 = all_4_21 % 130.86/18.32 (3) all_6_5 = e1 % 130.86/18.32 (4) ~ (e4 = e0) % 130.86/18.32 (5) all_9_16 = e1 % 130.86/18.32 (6) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.32 (7) all_9_20 = e2 % 130.86/18.32 (8) all_6_10 = e3 % 130.86/18.32 (9) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.32 (10) ~ (all_4_3 = all_4_4) % 130.86/18.32 (11) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.32 (12) ~ (e4 = e2) % 130.86/18.32 (13) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.32 (14) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.32 (15) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.32 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.32 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.32 (16) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.32 (17) ~ (all_4_21 = e3) % 130.86/18.32 (18) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.32 (19) ~ (all_4_3 = e3) % 130.86/18.32 (20) all_6_20 = all_4_4 % 130.86/18.32 (21) all_9_11 = e2 % 130.86/18.32 (22) ~ (e3 = e0) % 130.86/18.32 (23) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) = e4) | % 130.86/18.32 (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) = e4) | % 130.86/18.32 (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.32 (24) all_9_17 = e2 % 130.86/18.32 (25) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.32 (26) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.32 = e0 % 130.86/18.32 (27) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.32 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.32 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.32 (28) ~ (e2 = e0) % 130.86/18.32 (29) all_9_0 = e0 % 130.86/18.32 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.32 (31) ~ (all_4_4 = e3) % 130.86/18.32 (32) ~ (op(e4, e3) = e3) % 130.86/18.32 (33) ~ (all_4_22 = e3) % 130.86/18.32 (34) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.32 (35) all_9_6 = e3 % 130.86/18.32 (36) ~ (e1 = e0) % 130.86/18.32 (37) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.32 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.32 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.32 (38) ~ (e3 = e2) % 130.86/18.32 (39) all_9_12 = e4 % 130.86/18.32 (40) op(e0, e4) = all_4_4 % 130.86/18.32 (41) ~ (e4 = e1) % 130.86/18.32 (42) ~ (all_4_3 = e0) % 130.86/18.32 (43) ~ (e3 = e1) % 130.86/18.32 (44) op(e3, e4) = e1 % 130.86/18.32 (45) all_9_9 = e4 % 130.86/18.32 (46) op(e1, e4) = all_4_3 % 130.86/18.32 (47) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.32 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.32 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.32 (48) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.32 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.32 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.32 (49) op(e2, e0) = all_4_22 % 130.86/18.32 (50) all_9_19 = e0 % 130.86/18.32 (51) ~ (e4 = e3) % 130.86/18.32 (52) ~ (all_4_4 = e0) % 130.86/18.32 (53) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.32 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.32 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.32 (54) ~ (all_4_3 = e1) % 130.86/18.32 (55) all_6_2 = all_4_10 % 130.86/18.32 (56) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.32 (57) op(e2, e4) = e3 % 130.86/18.32 (58) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.32 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.32 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.32 (59) all_9_2 = e1 % 130.86/18.32 (60) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.32 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.32 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.32 (61) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.32 = e0 % 130.86/18.32 (62) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) | % 130.86/18.32 (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.32 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.32 (63) ~ (all_4_4 = e1) % 130.86/18.32 (64) ~ (all_4_10 = e2) % 130.86/18.32 (65) all_4_0 = e0 % 130.86/18.32 (66) ~ (e2 = e1) % 130.86/18.32 (67) all_6_15 = all_4_3 % 130.86/18.32 (68) all_9_7 = e0 % 130.86/18.32 (69) op(e4, e4) = e0 % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | BETA: splitting (48) gives: % 130.86/18.32 | % 130.86/18.32 | Case 1: % 130.86/18.32 | | % 130.86/18.32 | | (70) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) % 130.86/18.32 | | % 130.86/18.32 | | BETA: splitting (70) gives: % 130.86/18.32 | | % 130.86/18.32 | | Case 1: % 130.86/18.32 | | | % 130.86/18.32 | | | (71) all_9_0 = e3 & op(e4, e4) = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | REF_CLOSE: (22), (29), (71) are inconsistent by sub-proof #291. % 130.86/18.32 | | | % 130.86/18.32 | | Case 2: % 130.86/18.32 | | | % 130.86/18.32 | | | (72) all_9_1 = e3 & op(e4, e3) = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | REF_CLOSE: (32), (72) are inconsistent by sub-proof #296. % 130.86/18.32 | | | % 130.86/18.32 | | End of split % 130.86/18.32 | | % 130.86/18.32 | Case 2: % 130.86/18.32 | | % 130.86/18.32 | | (73) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) % 130.86/18.32 | | | (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.32 | | % 130.86/18.32 | | BETA: splitting (73) gives: % 130.86/18.32 | | % 130.86/18.32 | | Case 1: % 130.86/18.32 | | | % 130.86/18.32 | | | (74) all_9_4 = e3 & op(e4, e2) = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | ALPHA: (74) implies: % 130.86/18.32 | | | (75) all_9_4 = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | BETA: splitting (23) gives: % 130.86/18.32 | | | % 130.86/18.32 | | | Case 1: % 130.86/18.32 | | | | % 130.86/18.32 | | | | (76) (all_9_16 = e4 & op(e4, e0) = e4) | (all_9_17 = e4 & op(e3, e0) % 130.86/18.32 | | | | = e4) % 130.86/18.32 | | | | % 130.86/18.32 | | | | BETA: splitting (76) gives: % 130.86/18.32 | | | | % 130.86/18.32 | | | | Case 1: % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | (77) all_9_16 = e4 & op(e4, e0) = e4 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | ALPHA: (77) implies: % 130.86/18.32 | | | | | (78) all_9_16 = e4 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | COMBINE_EQS: (5), (78) imply: % 130.86/18.32 | | | | | (79) e4 = e1 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | SIMP: (79) implies: % 130.86/18.32 | | | | | (80) e4 = e1 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | REDUCE: (41), (80) imply: % 130.86/18.32 | | | | | (81) $false % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | CLOSE: (81) is inconsistent. % 130.86/18.32 | | | | | % 130.86/18.32 | | | | Case 2: % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | (82) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | REF_CLOSE: (12), (24), (82) are inconsistent by sub-proof #224. % 130.86/18.32 | | | | | % 130.86/18.32 | | | | End of split % 130.86/18.32 | | | | % 130.86/18.32 | | | Case 2: % 130.86/18.32 | | | | % 130.86/18.32 | | | | (83) (all_9_18 = e4 & op(e2, e0) = e4) | (all_9_19 = e4 & op(e1, e0) % 130.86/18.32 | | | | = e4) | (all_9_24 = e4 & op(e0, e0) = e4) % 130.86/18.32 | | | | % 130.86/18.32 | | | | BETA: splitting (83) gives: % 130.86/18.32 | | | | % 130.86/18.32 | | | | Case 1: % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | (84) all_9_18 = e4 & op(e2, e0) = e4 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | ALPHA: (84) implies: % 130.86/18.32 | | | | | (85) all_9_18 = e4 % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), % 130.86/18.32 | | | | | (16), (18), (19), (20), (21), (22), (25), (26), (27), (28), % 130.86/18.32 | | | | | (29), (30), (31), (35), (36), (37), (38), (40), (41), (42), % 130.86/18.32 | | | | | (43), (44), (46), (47), (51), (52), (54), (56), (57), (58), % 130.86/18.32 | | | | | (59), (60), (61), (63), (65), (66), (67), (68), (69), (85) % 130.86/18.32 | | | | | are inconsistent by sub-proof #221. % 130.86/18.32 | | | | | % 130.86/18.32 | | | | Case 2: % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | (86) (all_9_19 = e4 & op(e1, e0) = e4) | (all_9_24 = e4 & op(e0, % 130.86/18.32 | | | | | e0) = e4) % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | BETA: splitting (86) gives: % 130.86/18.32 | | | | | % 130.86/18.32 | | | | | Case 1: % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | (87) all_9_19 = e4 & op(e1, e0) = e4 % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | REF_CLOSE: (4), (50), (87) are inconsistent by sub-proof #220. % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | Case 2: % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | (88) all_9_24 = e4 & op(e0, e0) = e4 % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | ALPHA: (88) implies: % 130.86/18.32 | | | | | | (89) all_9_24 = e4 % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | BETA: splitting (62) gives: % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | | Case 1: % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | | (90) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & % 130.86/18.32 | | | | | | | op(e3, e0) = e3) % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | | REF_CLOSE: (2), (5), (13), (17), (43), (90) are inconsistent by % 130.86/18.32 | | | | | | | sub-proof #218. % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | Case 2: % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | | (91) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & % 130.86/18.32 | | | | | | | op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), % 130.86/18.32 | | | | | | | (15), (16), (18), (19), (20), (22), (25), (26), (28), % 130.86/18.32 | | | | | | | (29), (30), (31), (32), (33), (34), (36), (37), (38), % 130.86/18.32 | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47), % 130.86/18.32 | | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.86/18.32 | | | | | | | (57), (58), (59), (60), (61), (63), (64), (65), (66), % 130.86/18.32 | | | | | | | (67), (69), (75), (89), (91) are inconsistent by % 130.86/18.32 | | | | | | | sub-proof #216. % 130.86/18.32 | | | | | | | % 130.86/18.32 | | | | | | End of split % 130.86/18.32 | | | | | | % 130.86/18.32 | | | | | End of split % 130.86/18.32 | | | | | % 130.86/18.32 | | | | End of split % 130.86/18.32 | | | | % 130.86/18.32 | | | End of split % 130.86/18.32 | | | % 130.86/18.32 | | Case 2: % 130.86/18.32 | | | % 130.86/18.32 | | | (92) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 130.86/18.32 | | | e3) % 130.86/18.32 | | | % 130.86/18.32 | | | BETA: splitting (92) gives: % 130.86/18.32 | | | % 130.86/18.32 | | | Case 1: % 130.86/18.32 | | | | % 130.86/18.32 | | | | (93) all_9_9 = e3 & op(e4, e1) = e3 % 130.86/18.32 | | | | % 130.86/18.32 | | | | REF_CLOSE: (3), (4), (7), (9), (11), (12), (14), (39), (41), (45), (51), % 130.86/18.32 | | | | (58), (65), (93) are inconsistent by sub-proof #289. % 130.86/18.32 | | | | % 130.86/18.32 | | | Case 2: % 130.86/18.32 | | | | % 130.86/18.32 | | | | (94) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.32 | | | | % 130.86/18.32 | | | | REF_CLOSE: (5), (43), (94) are inconsistent by sub-proof #219. % 130.86/18.32 | | | | % 130.86/18.32 | | | End of split % 130.86/18.32 | | | % 130.86/18.32 | | End of split % 130.86/18.32 | | % 130.86/18.32 | End of split % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #216 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_6_5 = e1 % 130.86/18.32 (2) ~ (e4 = e0) % 130.86/18.32 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.32 (4) all_9_20 = e2 % 130.86/18.32 (5) all_6_10 = e3 % 130.86/18.32 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.32 (7) ~ (all_4_3 = all_4_4) % 130.86/18.32 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.32 (9) ~ (e4 = e2) % 130.86/18.32 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.32 (11) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.32 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.32 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.32 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.32 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.32 (14) ~ (all_4_3 = e3) % 130.86/18.32 (15) all_6_20 = all_4_4 % 130.86/18.32 (16) all_9_4 = e3 % 130.86/18.32 (17) ~ (e3 = e0) % 130.86/18.32 (18) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.32 (19) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.32 = e0 % 130.86/18.32 (20) ~ (e2 = e0) % 130.86/18.32 (21) all_9_0 = e0 % 130.86/18.32 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.32 (23) ~ (all_4_4 = e3) % 130.86/18.32 (24) ~ (op(e4, e3) = e3) % 130.86/18.32 (25) ~ (all_4_22 = e3) % 130.86/18.32 (26) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.32 (27) ~ (e1 = e0) % 130.86/18.32 (28) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.32 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.32 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.32 (29) ~ (e3 = e2) % 130.86/18.32 (30) all_9_12 = e4 % 130.86/18.32 (31) op(e0, e4) = all_4_4 % 130.86/18.32 (32) ~ (e4 = e1) % 130.86/18.32 (33) ~ (all_4_3 = e0) % 130.86/18.32 (34) ~ (e3 = e1) % 130.86/18.32 (35) op(e3, e4) = e1 % 130.86/18.32 (36) all_9_9 = e4 % 130.86/18.32 (37) op(e1, e4) = all_4_3 % 130.86/18.32 (38) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.32 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.32 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.32 (39) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.32 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.32 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.32 (40) all_9_24 = e4 % 130.86/18.32 (41) op(e2, e0) = all_4_22 % 130.86/18.32 (42) all_9_19 = e0 % 130.86/18.32 (43) ~ (e4 = e3) % 130.86/18.32 (44) ~ (all_4_4 = e0) % 130.86/18.32 (45) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.32 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.32 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.32 (46) ~ (all_4_3 = e1) % 130.86/18.32 (47) (all_9_18 = e3 & op(e2, e0) = e3) | (all_9_19 = e3 & op(e1, e0) = e3) | % 130.86/18.32 (all_9_24 = e3 & op(e0, e0) = e3) % 130.86/18.32 (48) all_6_2 = all_4_10 % 130.86/18.32 (49) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.32 (50) op(e2, e4) = e3 % 130.86/18.32 (51) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.32 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.32 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.32 (52) all_9_2 = e1 % 130.86/18.32 (53) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.32 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.32 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.32 (54) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.32 = e0 % 130.86/18.32 (55) ~ (all_4_4 = e1) % 130.86/18.32 (56) ~ (all_4_10 = e2) % 130.86/18.32 (57) all_4_0 = e0 % 130.86/18.32 (58) ~ (e2 = e1) % 130.86/18.32 (59) all_6_15 = all_4_3 % 130.86/18.32 (60) op(e4, e4) = e0 % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | BETA: splitting (47) gives: % 130.86/18.32 | % 130.86/18.32 | Case 1: % 130.86/18.32 | | % 130.86/18.32 | | (61) all_9_18 = e3 & op(e2, e0) = e3 % 130.86/18.32 | | % 130.86/18.32 | | ALPHA: (61) implies: % 130.86/18.32 | | (62) op(e2, e0) = e3 % 130.86/18.32 | | % 130.86/18.32 | | REF_CLOSE: (22), (25), (41), (62) are inconsistent by sub-proof #226. % 130.86/18.32 | | % 130.86/18.32 | Case 2: % 130.86/18.32 | | % 130.86/18.32 | | (63) (all_9_19 = e3 & op(e1, e0) = e3) | (all_9_24 = e3 & op(e0, e0) = % 130.86/18.32 | | e3) % 130.86/18.32 | | % 130.86/18.32 | | BETA: splitting (63) gives: % 130.86/18.32 | | % 130.86/18.32 | | Case 1: % 130.86/18.32 | | | % 130.86/18.32 | | | (64) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.32 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), % 130.86/18.32 | | | (23), (24), (26), (27), (28), (29), (30), (31), (32), (33), % 130.86/18.32 | | | (34), (35), (36), (37), (38), (39), (42), (43), (44), (45), % 130.86/18.32 | | | (46), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 130.86/18.32 | | | (57), (58), (59), (60), (64) are inconsistent by sub-proof % 130.86/18.32 | | | #225. % 130.86/18.32 | | | % 130.86/18.32 | | Case 2: % 130.86/18.32 | | | % 130.86/18.32 | | | (65) all_9_24 = e3 & op(e0, e0) = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | ALPHA: (65) implies: % 130.86/18.32 | | | (66) all_9_24 = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | COMBINE_EQS: (40), (66) imply: % 130.86/18.32 | | | (67) e4 = e3 % 130.86/18.32 | | | % 130.86/18.32 | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (30), (32), (43), (51), % 130.86/18.32 | | | (57), (67) are inconsistent by sub-proof #217. % 130.86/18.32 | | | % 130.86/18.32 | | End of split % 130.86/18.32 | | % 130.86/18.32 | End of split % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #217 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_6_5 = e1 % 130.86/18.32 (2) ~ (e4 = e0) % 130.86/18.32 (3) all_9_20 = e2 % 130.86/18.32 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.32 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.32 (6) ~ (e4 = e2) % 130.86/18.32 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.32 (8) all_9_12 = e4 % 130.86/18.32 (9) ~ (e4 = e1) % 130.86/18.32 (10) ~ (e4 = e3) % 130.86/18.32 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.32 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.32 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.32 (12) e4 = e3 % 130.86/18.32 (13) all_4_0 = e0 % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | SIMP: (12) implies: % 130.86/18.32 | (14) e4 = e3 % 130.86/18.32 | % 130.86/18.32 | COMBINE_EQS: (8), (14) imply: % 130.86/18.32 | (15) all_9_12 = e3 % 130.86/18.32 | % 130.86/18.32 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (15) are % 130.86/18.32 | inconsistent by sub-proof #303. % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #218 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_6_9 = all_4_21 % 130.86/18.32 (2) all_9_16 = e1 % 130.86/18.32 (3) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.32 (4) ~ (all_4_21 = e3) % 130.86/18.32 (5) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 130.86/18.32 (6) ~ (e3 = e1) % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | BETA: splitting (5) gives: % 130.86/18.32 | % 130.86/18.32 | Case 1: % 130.86/18.32 | | % 130.86/18.32 | | (7) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.32 | | % 130.86/18.32 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #219. % 130.86/18.32 | | % 130.86/18.32 | Case 2: % 130.86/18.32 | | % 130.86/18.32 | | (8) all_9_17 = e3 & op(e3, e0) = e3 % 130.86/18.32 | | % 130.86/18.32 | | ALPHA: (8) implies: % 130.86/18.32 | | (9) op(e3, e0) = e3 % 130.86/18.32 | | % 130.86/18.32 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #228. % 130.86/18.32 | | % 130.86/18.32 | End of split % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #219 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.32 (2) all_9_16 = e1 % 130.86/18.32 (3) ~ (e3 = e1) % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | ALPHA: (1) implies: % 130.86/18.32 | (4) all_9_16 = e3 % 130.86/18.32 | % 130.86/18.32 | COMBINE_EQS: (2), (4) imply: % 130.86/18.32 | (5) e3 = e1 % 130.86/18.32 | % 130.86/18.32 | SIMP: (5) implies: % 130.86/18.32 | (6) e3 = e1 % 130.86/18.32 | % 130.86/18.32 | REDUCE: (3), (6) imply: % 130.86/18.32 | (7) $false % 130.86/18.32 | % 130.86/18.32 | CLOSE: (7) is inconsistent. % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #220 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_9_19 = e4 & op(e1, e0) = e4 % 130.86/18.32 (2) all_9_19 = e0 % 130.86/18.32 (3) ~ (e4 = e0) % 130.86/18.32 % 130.86/18.32 Begin of proof % 130.86/18.32 | % 130.86/18.32 | ALPHA: (1) implies: % 130.86/18.32 | (4) all_9_19 = e4 % 130.86/18.32 | % 130.86/18.32 | COMBINE_EQS: (2), (4) imply: % 130.86/18.32 | (5) e4 = e0 % 130.86/18.32 | % 130.86/18.32 | REDUCE: (3), (5) imply: % 130.86/18.32 | (6) $false % 130.86/18.32 | % 130.86/18.32 | CLOSE: (6) is inconsistent. % 130.86/18.32 | % 130.86/18.32 End of proof % 130.86/18.32 % 130.86/18.32 Sub-proof #221 shows that the following formulas are inconsistent: % 130.86/18.32 ---------------------------------------------------------------- % 130.86/18.32 (1) all_9_8 = e4 % 130.86/18.32 (2) all_6_5 = e1 % 130.86/18.32 (3) ~ (e4 = e0) % 130.86/18.32 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.32 (5) all_9_20 = e2 % 130.86/18.32 (6) all_6_10 = e3 % 130.86/18.32 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.32 (8) ~ (all_4_3 = all_4_4) % 130.86/18.33 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.33 (10) ~ (e4 = e2) % 130.86/18.33 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.33 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.33 (14) ~ (all_4_3 = e3) % 130.86/18.33 (15) all_6_20 = all_4_4 % 130.86/18.33 (16) all_9_11 = e2 % 130.86/18.33 (17) ~ (e3 = e0) % 130.86/18.33 (18) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (19) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.33 = e0 % 130.86/18.33 (20) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) | % 130.86/18.33 (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) | % 130.86/18.33 (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.33 (21) ~ (e2 = e0) % 130.86/18.33 (22) all_9_0 = e0 % 130.86/18.33 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.33 (24) ~ (all_4_4 = e3) % 130.86/18.33 (25) all_9_6 = e3 % 130.86/18.33 (26) ~ (e1 = e0) % 130.86/18.33 (27) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.33 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.33 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.33 (28) ~ (e3 = e2) % 130.86/18.33 (29) op(e0, e4) = all_4_4 % 130.86/18.33 (30) ~ (e4 = e1) % 130.86/18.33 (31) ~ (all_4_3 = e0) % 130.86/18.33 (32) ~ (e3 = e1) % 130.86/18.33 (33) op(e3, e4) = e1 % 130.86/18.33 (34) op(e1, e4) = all_4_3 % 130.86/18.33 (35) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.33 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.33 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.33 (36) ~ (e4 = e3) % 130.86/18.33 (37) ~ (all_4_4 = e0) % 130.86/18.33 (38) ~ (all_4_3 = e1) % 130.86/18.33 (39) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.33 (40) all_9_18 = e4 % 130.86/18.33 (41) op(e2, e4) = e3 % 130.86/18.33 (42) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.33 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.33 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.33 (43) all_9_2 = e1 % 130.86/18.33 (44) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.33 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.33 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.33 (45) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.33 = e0 % 130.86/18.33 (46) ~ (all_4_4 = e1) % 130.86/18.33 (47) all_4_0 = e0 % 130.86/18.33 (48) ~ (e2 = e1) % 130.86/18.33 (49) all_6_15 = all_4_3 % 130.86/18.33 (50) all_9_7 = e0 % 130.86/18.33 (51) op(e4, e4) = e0 % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | BETA: splitting (20) gives: % 130.86/18.33 | % 130.86/18.33 | Case 1: % 130.86/18.33 | | % 130.86/18.33 | | (52) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_7 = e1 & op(e2, e3) = e1) % 130.86/18.33 | | % 130.86/18.33 | | BETA: splitting (52) gives: % 130.86/18.33 | | % 130.86/18.33 | | Case 1: % 130.86/18.33 | | | % 130.86/18.33 | | | (53) all_9_6 = e1 & op(e2, e4) = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | REF_CLOSE: (25), (32), (53) are inconsistent by sub-proof #223. % 130.86/18.33 | | | % 130.86/18.33 | | Case 2: % 130.86/18.33 | | | % 130.86/18.33 | | | (54) all_9_7 = e1 & op(e2, e3) = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | ALPHA: (54) implies: % 130.86/18.33 | | | (55) all_9_7 = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (11), (12), (13), (14), (15), % 130.86/18.33 | | | (17), (18), (19), (21), (23), (24), (26), (27), (28), (29), % 130.86/18.33 | | | (30), (31), (32), (34), (35), (36), (37), (38), (39), (41), % 130.86/18.33 | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 130.86/18.33 | | | (55) are inconsistent by sub-proof #222. % 130.86/18.33 | | | % 130.86/18.33 | | End of split % 130.86/18.33 | | % 130.86/18.33 | Case 2: % 130.86/18.33 | | % 130.86/18.33 | | (56) (all_9_8 = e1 & op(e2, e2) = e1) | (all_9_11 = e1 & op(e2, e1) = e1) % 130.86/18.33 | | | (all_9_18 = e1 & op(e2, e0) = e1) % 130.86/18.33 | | % 130.86/18.33 | | BETA: splitting (56) gives: % 130.86/18.33 | | % 130.86/18.33 | | Case 1: % 130.86/18.33 | | | % 130.86/18.33 | | | (57) all_9_8 = e1 & op(e2, e2) = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | ALPHA: (57) implies: % 130.86/18.33 | | | (58) all_9_8 = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | COMBINE_EQS: (1), (58) imply: % 130.86/18.33 | | | (59) e4 = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | SIMP: (59) implies: % 130.86/18.33 | | | (60) e4 = e1 % 130.86/18.33 | | | % 130.86/18.33 | | | REDUCE: (30), (60) imply: % 130.86/18.33 | | | (61) $false % 130.86/18.33 | | | % 130.86/18.33 | | | CLOSE: (61) is inconsistent. % 130.86/18.33 | | | % 130.86/18.33 | | Case 2: % 130.86/18.33 | | | % 130.86/18.33 | | | (62) (all_9_11 = e1 & op(e2, e1) = e1) | (all_9_18 = e1 & op(e2, e0) = % 130.86/18.33 | | | e1) % 130.86/18.33 | | | % 130.86/18.33 | | | BETA: splitting (62) gives: % 130.86/18.33 | | | % 130.86/18.33 | | | Case 1: % 130.86/18.33 | | | | % 130.86/18.33 | | | | (63) all_9_11 = e1 & op(e2, e1) = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | ALPHA: (63) implies: % 130.86/18.33 | | | | (64) all_9_11 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | COMBINE_EQS: (16), (64) imply: % 130.86/18.33 | | | | (65) e2 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | SIMP: (65) implies: % 130.86/18.33 | | | | (66) e2 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | COMBINE_EQS: (5), (66) imply: % 130.86/18.33 | | | | (67) all_9_20 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (21), (22), (23), % 130.86/18.33 | | | | (28), (30), (33), (35), (36), (42), (47), (48), (67) are % 130.86/18.33 | | | | inconsistent by sub-proof #283. % 130.86/18.33 | | | | % 130.86/18.33 | | | Case 2: % 130.86/18.33 | | | | % 130.86/18.33 | | | | (68) all_9_18 = e1 & op(e2, e0) = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | ALPHA: (68) implies: % 130.86/18.33 | | | | (69) all_9_18 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | COMBINE_EQS: (40), (69) imply: % 130.86/18.33 | | | | (70) e4 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | SIMP: (70) implies: % 130.86/18.33 | | | | (71) e4 = e1 % 130.86/18.33 | | | | % 130.86/18.33 | | | | REDUCE: (30), (71) imply: % 130.86/18.33 | | | | (72) $false % 130.86/18.33 | | | | % 130.86/18.33 | | | | CLOSE: (72) is inconsistent. % 130.86/18.33 | | | | % 130.86/18.33 | | | End of split % 130.86/18.33 | | | % 130.86/18.33 | | End of split % 130.86/18.33 | | % 130.86/18.33 | End of split % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #222 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) ~ (e4 = e0) % 130.86/18.33 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.33 (3) all_6_10 = e3 % 130.86/18.33 (4) ~ (all_4_3 = all_4_4) % 130.86/18.33 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.33 (6) ~ (e4 = e2) % 130.86/18.33 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.33 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (9) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.33 (10) ~ (all_4_3 = e3) % 130.86/18.33 (11) all_6_20 = all_4_4 % 130.86/18.33 (12) ~ (e3 = e0) % 130.86/18.33 (13) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.33 = e0 % 130.86/18.33 (15) ~ (e2 = e0) % 130.86/18.33 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.33 (17) ~ (all_4_4 = e3) % 130.86/18.33 (18) all_9_7 = e1 % 130.86/18.33 (19) ~ (e1 = e0) % 130.86/18.33 (20) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.33 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.33 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.33 (21) ~ (e3 = e2) % 130.86/18.33 (22) op(e0, e4) = all_4_4 % 130.86/18.33 (23) ~ (e4 = e1) % 130.86/18.33 (24) ~ (all_4_3 = e0) % 130.86/18.33 (25) ~ (e3 = e1) % 130.86/18.33 (26) op(e1, e4) = all_4_3 % 130.86/18.33 (27) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.33 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.33 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.33 (28) ~ (e4 = e3) % 130.86/18.33 (29) ~ (all_4_4 = e0) % 130.86/18.33 (30) ~ (all_4_3 = e1) % 130.86/18.33 (31) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.33 (32) op(e2, e4) = e3 % 130.86/18.33 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.33 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.33 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.33 (34) all_9_2 = e1 % 130.86/18.33 (35) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.33 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.33 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.33 (36) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.33 = e0 % 130.86/18.33 (37) ~ (all_4_4 = e1) % 130.86/18.33 (38) all_4_0 = e0 % 130.86/18.33 (39) ~ (e2 = e1) % 130.86/18.33 (40) all_6_15 = all_4_3 % 130.86/18.33 (41) all_9_7 = e0 % 130.86/18.33 (42) op(e4, e4) = e0 % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (18), (41) imply: % 130.86/18.33 | (43) e1 = e0 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (34), (43) imply: % 130.86/18.33 | (44) all_9_2 = e0 % 130.86/18.33 | % 130.86/18.33 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 130.86/18.33 | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), % 130.86/18.33 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 130.86/18.33 | (37), (38), (39), (40), (42), (44) are inconsistent by sub-proof % 130.86/18.33 | #265. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #223 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_6 = e1 & op(e2, e4) = e1 % 130.86/18.33 (2) all_9_6 = e3 % 130.86/18.33 (3) ~ (e3 = e1) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (1) implies: % 130.86/18.33 | (4) all_9_6 = e1 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (2), (4) imply: % 130.86/18.33 | (5) e3 = e1 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #224 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_17 = e4 & op(e3, e0) = e4 % 130.86/18.33 (2) all_9_17 = e2 % 130.86/18.33 (3) ~ (e4 = e2) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (1) implies: % 130.86/18.33 | (4) all_9_17 = e4 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (2), (4) imply: % 130.86/18.33 | (5) e4 = e2 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #225 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_5 = e1 % 130.86/18.33 (2) ~ (e4 = e0) % 130.86/18.33 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 130.86/18.33 (4) all_9_20 = e2 % 130.86/18.33 (5) all_6_10 = e3 % 130.86/18.33 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.33 (7) ~ (all_4_3 = all_4_4) % 130.86/18.33 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.33 (9) ~ (e4 = e2) % 130.86/18.33 (10) all_9_19 = e3 & op(e1, e0) = e3 % 130.86/18.33 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.33 (12) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 130.86/18.33 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 130.86/18.33 (all_9_16 = e2 & op(e4, e0) = e2) % 130.86/18.33 (13) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (14) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 130.86/18.33 (15) ~ (all_4_3 = e3) % 130.86/18.33 (16) all_6_20 = all_4_4 % 130.86/18.33 (17) all_9_4 = e3 % 130.86/18.33 (18) ~ (e3 = e0) % 130.86/18.33 (19) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 130.86/18.33 (20) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 130.86/18.33 = e0 % 130.86/18.33 (21) ~ (e2 = e0) % 130.86/18.33 (22) all_9_0 = e0 % 130.86/18.33 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.33 (24) ~ (all_4_4 = e3) % 130.86/18.33 (25) ~ (op(e4, e3) = e3) % 130.86/18.33 (26) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 130.86/18.33 (27) ~ (e1 = e0) % 130.86/18.33 (28) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 130.86/18.33 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 130.86/18.33 (all_9_20 = e3 & op(e0, e4) = e3) % 130.86/18.33 (29) ~ (e3 = e2) % 130.86/18.33 (30) all_9_12 = e4 % 130.86/18.33 (31) op(e0, e4) = all_4_4 % 130.86/18.33 (32) ~ (e4 = e1) % 130.86/18.33 (33) ~ (all_4_3 = e0) % 130.86/18.33 (34) ~ (e3 = e1) % 130.86/18.33 (35) op(e3, e4) = e1 % 130.86/18.33 (36) all_9_9 = e4 % 130.86/18.33 (37) op(e1, e4) = all_4_3 % 130.86/18.33 (38) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 130.86/18.33 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 130.86/18.33 (all_9_20 = e2 & op(e0, e4) = e2) % 130.86/18.33 (39) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 130.86/18.33 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 130.86/18.33 (all_9_16 = e3 & op(e4, e0) = e3) % 130.86/18.33 (40) all_9_19 = e0 % 130.86/18.33 (41) ~ (e4 = e3) % 130.86/18.33 (42) ~ (all_4_4 = e0) % 130.86/18.33 (43) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 130.86/18.33 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 130.86/18.33 (all_9_16 = e1 & op(e4, e0) = e1) % 130.86/18.33 (44) ~ (all_4_3 = e1) % 130.86/18.33 (45) all_6_2 = all_4_10 % 130.86/18.33 (46) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 130.86/18.33 (47) op(e2, e4) = e3 % 130.86/18.33 (48) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.33 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.33 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.33 (49) all_9_2 = e1 % 130.86/18.33 (50) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 130.86/18.33 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 130.86/18.33 (all_9_20 = e1 & op(e0, e4) = e1) % 130.86/18.33 (51) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 130.86/18.33 = e0 % 130.86/18.33 (52) ~ (all_4_4 = e1) % 130.86/18.33 (53) ~ (all_4_10 = e2) % 130.86/18.33 (54) all_4_0 = e0 % 130.86/18.33 (55) ~ (e2 = e1) % 130.86/18.33 (56) all_6_15 = all_4_3 % 130.86/18.33 (57) op(e4, e4) = e0 % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (10) implies: % 130.86/18.33 | (58) all_9_19 = e3 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (40), (58) imply: % 130.86/18.33 | (59) e3 = e0 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (17), (59) imply: % 130.86/18.33 | (60) all_9_4 = e0 % 130.86/18.33 | % 130.86/18.33 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 130.86/18.33 | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), % 130.86/18.33 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 130.86/18.33 | (37), (38), (39), (41), (42), (43), (44), (45), (46), (47), (48), % 130.86/18.33 | (49), (50), (51), (52), (53), (54), (55), (56), (57), (60) are % 130.86/18.33 | inconsistent by sub-proof #258. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #226 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.86/18.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.86/18.33 (2) op(e2, e0) = all_4_22 % 130.86/18.33 (3) op(e2, e0) = e3 % 130.86/18.33 (4) ~ (all_4_22 = e3) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | GROUND_INST: instantiating (1) with all_4_22, e3, e0, e2, simplifying with % 130.86/18.33 | (2), (3) gives: % 130.86/18.33 | (5) all_4_22 = e3 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (4), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #227 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_9 = all_4_21 % 130.86/18.33 (2) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.33 (3) ~ (all_4_21 = e3) % 130.86/18.33 (4) all_9_16 = e2 % 130.86/18.33 (5) ~ (e3 = e2) % 130.86/18.33 (6) (all_9_16 = e3 & op(e4, e0) = e3) | (all_9_17 = e3 & op(e3, e0) = e3) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | BETA: splitting (6) gives: % 130.86/18.33 | % 130.86/18.33 | Case 1: % 130.86/18.33 | | % 130.86/18.33 | | (7) all_9_16 = e3 & op(e4, e0) = e3 % 130.86/18.33 | | % 130.86/18.33 | | ALPHA: (7) implies: % 130.86/18.33 | | (8) all_9_16 = e3 % 130.86/18.33 | | % 130.86/18.33 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #229. % 130.86/18.33 | | % 130.86/18.33 | Case 2: % 130.86/18.33 | | % 130.86/18.33 | | (9) all_9_17 = e3 & op(e3, e0) = e3 % 130.86/18.33 | | % 130.86/18.33 | | ALPHA: (9) implies: % 130.86/18.33 | | (10) op(e3, e0) = e3 % 130.86/18.33 | | % 130.86/18.33 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #228. % 130.86/18.33 | | % 130.86/18.33 | End of split % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #228 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_9 = e3 | ~ (op(e3, e0) = e3) % 130.86/18.33 (2) op(e3, e0) = e3 % 130.86/18.33 (3) all_6_9 = all_4_21 % 130.86/18.33 (4) ~ (all_4_21 = e3) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | BETA: splitting (1) gives: % 130.86/18.33 | % 130.86/18.33 | Case 1: % 130.86/18.33 | | % 130.86/18.33 | | (5) ~ (op(e3, e0) = e3) % 130.86/18.33 | | % 130.86/18.33 | | PRED_UNIFY: (2), (5) imply: % 130.86/18.33 | | (6) $false % 130.86/18.33 | | % 130.86/18.33 | | CLOSE: (6) is inconsistent. % 130.86/18.33 | | % 130.86/18.33 | Case 2: % 130.86/18.33 | | % 130.86/18.33 | | (7) all_6_9 = e3 % 130.86/18.33 | | % 130.86/18.33 | | COMBINE_EQS: (3), (7) imply: % 130.86/18.33 | | (8) all_4_21 = e3 % 130.86/18.33 | | % 130.86/18.33 | | SIMP: (8) implies: % 130.86/18.33 | | (9) all_4_21 = e3 % 130.86/18.33 | | % 130.86/18.33 | | REDUCE: (4), (9) imply: % 130.86/18.33 | | (10) $false % 130.86/18.33 | | % 130.86/18.33 | | CLOSE: (10) is inconsistent. % 130.86/18.33 | | % 130.86/18.33 | End of split % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #229 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_16 = e3 % 130.86/18.33 (2) all_9_16 = e2 % 130.86/18.33 (3) ~ (e3 = e2) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (1), (2) imply: % 130.86/18.33 | (4) e3 = e2 % 130.86/18.33 | % 130.86/18.33 | SIMP: (4) implies: % 130.86/18.33 | (5) e3 = e2 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #230 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_5 = e1 % 130.86/18.33 (2) ~ (e4 = e0) % 130.86/18.33 (3) all_9_20 = e2 % 130.86/18.33 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.33 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 130.86/18.33 (6) ~ (e4 = e2) % 130.86/18.33 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 130.86/18.33 (8) all_9_10 = e3 % 130.86/18.33 (9) all_9_12 = e4 % 130.86/18.33 (10) ~ (e4 = e1) % 130.86/18.33 (11) all_9_10 = e4 & op(e3, e1) = e4 % 130.86/18.33 (12) ~ (e4 = e3) % 130.86/18.33 (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 130.86/18.33 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 130.86/18.33 (all_9_20 = e4 & op(e0, e4) = e4) % 130.86/18.33 (14) all_4_0 = e0 % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (11) implies: % 130.86/18.33 | (15) all_9_10 = e4 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (8), (15) imply: % 130.86/18.33 | (16) e4 = e3 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (9), (16) imply: % 130.86/18.33 | (17) all_9_12 = e3 % 130.86/18.33 | % 130.86/18.33 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (13), (14), (17) are % 130.86/18.33 | inconsistent by sub-proof #303. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #231 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_5 = e4 & op(e3, e2) = e4 % 130.86/18.33 (2) all_9_5 = e0 % 130.86/18.33 (3) ~ (e4 = e0) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (1) implies: % 130.86/18.33 | (4) all_9_5 = e4 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (2), (4) imply: % 130.86/18.33 | (5) e4 = e0 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #232 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_5 = e1 % 130.86/18.33 (2) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 130.86/18.33 (3) ~ (e4 = e2) % 130.86/18.33 (4) all_9_3 = e2 % 130.86/18.33 (5) ~ (e4 = e1) % 130.86/18.33 (6) (all_9_2 = e4 & op(e3, e4) = e4) | (all_9_3 = e4 & op(e3, e3) = e4) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | BETA: splitting (6) gives: % 130.86/18.33 | % 130.86/18.33 | Case 1: % 130.86/18.33 | | % 130.86/18.33 | | (7) all_9_2 = e4 & op(e3, e4) = e4 % 130.86/18.33 | | % 130.86/18.33 | | ALPHA: (7) implies: % 130.86/18.33 | | (8) op(e3, e4) = e4 % 130.86/18.33 | | % 130.86/18.33 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #316. % 130.86/18.33 | | % 130.86/18.33 | Case 2: % 130.86/18.33 | | % 130.86/18.33 | | (9) all_9_3 = e4 & op(e3, e3) = e4 % 130.86/18.33 | | % 130.86/18.33 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #233. % 130.86/18.33 | | % 130.86/18.33 | End of split % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #233 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_3 = e4 & op(e3, e3) = e4 % 130.86/18.33 (2) all_9_3 = e2 % 130.86/18.33 (3) ~ (e4 = e2) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (1) implies: % 130.86/18.33 | (4) all_9_3 = e4 % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (2), (4) imply: % 130.86/18.33 | (5) e4 = e2 % 130.86/18.33 | % 130.86/18.33 | SIMP: (5) implies: % 130.86/18.33 | (6) e4 = e2 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (6) imply: % 130.86/18.33 | (7) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (7) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #234 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_11 = all_4_7 % 130.86/18.33 (2) all_6_11 = e1 % 130.86/18.33 (3) ~ (all_4_7 = e1) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (1), (2) imply: % 130.86/18.33 | (4) all_4_7 = e1 % 130.86/18.33 | % 130.86/18.33 | SIMP: (4) implies: % 130.86/18.33 | (5) all_4_7 = e1 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #235 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_11 = all_4_7 % 130.86/18.33 (2) all_6_11 = e3 % 130.86/18.33 (3) ~ (all_4_7 = e3) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (1), (2) imply: % 130.86/18.33 | (4) all_4_7 = e3 % 130.86/18.33 | % 130.86/18.33 | SIMP: (4) implies: % 130.86/18.33 | (5) all_4_7 = e3 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #236 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_11 = all_4_7 % 130.86/18.33 (2) all_6_11 = e2 % 130.86/18.33 (3) ~ (all_4_7 = e2) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (1), (2) imply: % 130.86/18.33 | (4) all_4_7 = e2 % 130.86/18.33 | % 130.86/18.33 | SIMP: (4) implies: % 130.86/18.33 | (5) all_4_7 = e2 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #237 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_6_11 = all_4_7 % 130.86/18.33 (2) all_6_11 = e4 % 130.86/18.33 (3) ~ (all_4_7 = e4) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | COMBINE_EQS: (1), (2) imply: % 130.86/18.33 | (4) all_4_7 = e4 % 130.86/18.33 | % 130.86/18.33 | SIMP: (4) implies: % 130.86/18.33 | (5) all_4_7 = e4 % 130.86/18.33 | % 130.86/18.33 | REDUCE: (3), (5) imply: % 130.86/18.33 | (6) $false % 130.86/18.33 | % 130.86/18.33 | CLOSE: (6) is inconsistent. % 130.86/18.33 | % 130.86/18.33 End of proof % 130.86/18.33 % 130.86/18.33 Sub-proof #238 shows that the following formulas are inconsistent: % 130.86/18.33 ---------------------------------------------------------------- % 130.86/18.33 (1) all_9_22 = e0 & op(e0, e2) = e0 % 130.86/18.33 (2) all_4_14 = e0 | ~ (op(e0, e2) = e0) % 130.86/18.33 (3) ~ (all_4_14 = e0) % 130.86/18.33 % 130.86/18.33 Begin of proof % 130.86/18.33 | % 130.86/18.33 | ALPHA: (1) implies: % 130.86/18.33 | (4) op(e0, e2) = e0 % 130.86/18.33 | % 130.86/18.33 | BETA: splitting (2) gives: % 130.86/18.33 | % 130.86/18.33 | Case 1: % 130.86/18.33 | | % 130.86/18.33 | | (5) ~ (op(e0, e2) = e0) % 130.86/18.33 | | % 130.86/18.33 | | PRED_UNIFY: (4), (5) imply: % 131.10/18.33 | | (6) $false % 131.10/18.33 | | % 131.10/18.33 | | CLOSE: (6) is inconsistent. % 131.10/18.33 | | % 131.10/18.33 | Case 2: % 131.10/18.33 | | % 131.10/18.33 | | (7) all_4_14 = e0 % 131.10/18.33 | | % 131.10/18.33 | | REDUCE: (3), (7) imply: % 131.10/18.34 | | (8) $false % 131.10/18.34 | | % 131.10/18.34 | | CLOSE: (8) is inconsistent. % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #239 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_9_20 = e0 & op(e0, e4) = e0 % 131.10/18.34 (2) all_9_20 = e2 % 131.10/18.34 (3) ~ (e2 = e0) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | ALPHA: (1) implies: % 131.10/18.34 | (4) all_9_20 = e0 % 131.10/18.34 | % 131.10/18.34 | COMBINE_EQS: (2), (4) imply: % 131.10/18.34 | (5) e2 = e0 % 131.10/18.34 | % 131.10/18.34 | REDUCE: (3), (5) imply: % 131.10/18.34 | (6) $false % 131.10/18.34 | % 131.10/18.34 | CLOSE: (6) is inconsistent. % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #240 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_6_24 = e0 | ~ (op(e0, e0) = e0) % 131.10/18.34 (2) op(e0, e0) = e0 % 131.10/18.34 (3) all_6_24 = all_4_24 % 131.10/18.34 (4) ~ (all_4_24 = e0) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (1) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (5) ~ (op(e0, e0) = e0) % 131.10/18.34 | | % 131.10/18.34 | | PRED_UNIFY: (2), (5) imply: % 131.10/18.34 | | (6) $false % 131.10/18.34 | | % 131.10/18.34 | | CLOSE: (6) is inconsistent. % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (7) all_6_24 = e0 % 131.10/18.34 | | % 131.10/18.34 | | COMBINE_EQS: (3), (7) imply: % 131.10/18.34 | | (8) all_4_24 = e0 % 131.10/18.34 | | % 131.10/18.34 | | REDUCE: (4), (8) imply: % 131.10/18.34 | | (9) $false % 131.10/18.34 | | % 131.10/18.34 | | CLOSE: (9) is inconsistent. % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #241 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_6_17 = e2 % 131.10/18.34 (2) all_6_5 = e1 % 131.10/18.34 (3) ~ (e4 = e0) % 131.10/18.34 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.34 (5) all_9_20 = e2 % 131.10/18.34 (6) all_6_10 = e3 % 131.10/18.34 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.34 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.34 (9) ~ (e4 = e2) % 131.10/18.34 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.34 (11) all_6_17 = e1 | ~ (op(e1, e2) = e1) % 131.10/18.34 (12) ~ (e2 = e0) % 131.10/18.34 (13) all_9_0 = e0 % 131.10/18.34 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.34 (15) ~ (e3 = e2) % 131.10/18.34 (16) ~ (e4 = e1) % 131.10/18.34 (17) op(e3, e4) = e1 % 131.10/18.34 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.34 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.34 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.34 (19) all_9_14 = e1 & op(e1, e2) = e1 % 131.10/18.34 (20) ~ (e4 = e3) % 131.10/18.34 (21) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.34 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.34 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.34 (22) all_4_0 = e0 % 131.10/18.34 (23) ~ (e2 = e1) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | ALPHA: (19) implies: % 131.10/18.34 | (24) op(e1, e2) = e1 % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (11) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (25) ~ (op(e1, e2) = e1) % 131.10/18.34 | | % 131.10/18.34 | | PRED_UNIFY: (24), (25) imply: % 131.10/18.34 | | (26) $false % 131.10/18.34 | | % 131.10/18.34 | | CLOSE: (26) is inconsistent. % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (27) all_6_17 = e1 % 131.10/18.34 | | % 131.10/18.34 | | COMBINE_EQS: (1), (27) imply: % 131.10/18.34 | | (28) e2 = e1 % 131.10/18.34 | | % 131.10/18.34 | | SIMP: (28) implies: % 131.10/18.34 | | (29) e2 = e1 % 131.10/18.34 | | % 131.10/18.34 | | COMBINE_EQS: (5), (29) imply: % 131.10/18.34 | | (30) all_9_20 = e1 % 131.10/18.34 | | % 131.10/18.34 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15), % 131.10/18.34 | | (16), (17), (18), (20), (21), (22), (23), (30) are inconsistent % 131.10/18.34 | | by sub-proof #283. % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #242 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_6_16 = all_4_8 % 131.10/18.34 (2) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 131.10/18.34 (3) all_6_5 = e1 % 131.10/18.34 (4) ~ (e4 = e0) % 131.10/18.34 (5) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.34 (6) all_9_20 = e2 % 131.10/18.34 (7) all_6_10 = e3 % 131.10/18.34 (8) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.34 (9) ~ (all_4_3 = all_4_4) % 131.10/18.34 (10) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.34 (11) ~ (e4 = e2) % 131.10/18.34 (12) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.34 (13) all_6_19 = e0 % 131.10/18.34 (14) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.34 (15) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 131.10/18.34 (16) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.34 (17) ~ (all_4_3 = e3) % 131.10/18.34 (18) all_6_20 = all_4_4 % 131.10/18.34 (19) e4 = e2 | ~ (op(e2, e2) = e2) % 131.10/18.34 (20) ~ (e3 = e0) % 131.10/18.34 (21) ~ (all_4_8 = e1) % 131.10/18.34 (22) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 131.10/18.34 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 131.10/18.34 (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.34 (23) all_6_22 = all_4_14 % 131.10/18.34 (24) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.34 (25) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.34 = e0 % 131.10/18.34 (26) ~ (all_4_14 = e2) % 131.10/18.34 (27) ~ (e2 = e0) % 131.10/18.34 (28) all_9_0 = e0 % 131.10/18.34 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.34 (30) ~ (all_4_4 = e3) % 131.10/18.34 (31) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 131.10/18.34 (32) ~ (e1 = e0) % 131.10/18.34 (33) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.34 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.34 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.34 (34) ~ (e3 = e2) % 131.10/18.34 (35) all_9_13 = e3 % 131.10/18.34 (36) all_9_12 = e4 % 131.10/18.34 (37) op(e0, e4) = all_4_4 % 131.10/18.34 (38) ~ (e4 = e1) % 131.10/18.34 (39) ~ (all_4_3 = e0) % 131.10/18.34 (40) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 131.10/18.34 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 131.10/18.34 (all_9_22 = e2 & op(e0, e2) = e2) % 131.10/18.34 (41) ~ (e3 = e1) % 131.10/18.34 (42) op(e3, e4) = e1 % 131.10/18.34 (43) op(e1, e4) = all_4_3 % 131.10/18.34 (44) all_4_11 = e0 % 131.10/18.34 (45) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.34 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.34 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.34 (46) ~ (e4 = e3) % 131.10/18.34 (47) all_9_14 = e0 % 131.10/18.34 (48) ~ (all_4_4 = e0) % 131.10/18.34 (49) ~ (all_4_3 = e1) % 131.10/18.34 (50) all_6_2 = all_4_10 % 131.10/18.34 (51) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.34 (52) op(e2, e4) = e3 % 131.10/18.34 (53) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.34 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.34 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.34 (54) all_9_2 = e1 % 131.10/18.34 (55) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.34 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.34 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.34 (56) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.34 = e0 % 131.10/18.34 (57) ~ (all_4_4 = e1) % 131.10/18.34 (58) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 131.10/18.34 (59) ~ (all_4_10 = e2) % 131.10/18.34 (60) all_4_0 = e0 % 131.10/18.34 (61) all_6_16 = e1 | ~ (op(e1, e3) = e1) % 131.10/18.34 (62) ~ (e2 = e1) % 131.10/18.34 (63) all_6_15 = all_4_3 % 131.10/18.34 (64) op(e4, e4) = e0 % 131.10/18.34 (65) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) | % 131.10/18.34 (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = e1) | % 131.10/18.34 (all_9_19 = e1 & op(e1, e0) = e1) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (65) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (66) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = % 131.10/18.34 | | e1) % 131.10/18.34 | | % 131.10/18.34 | | REF_CLOSE: (1), (16), (21), (49), (61), (66) are inconsistent by sub-proof % 131.10/18.34 | | #253. % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (67) (all_9_14 = e1 & op(e1, e2) = e1) | (all_9_15 = e1 & op(e1, e1) = % 131.10/18.34 | | e1) | (all_9_19 = e1 & op(e1, e0) = e1) % 131.10/18.34 | | % 131.10/18.34 | | BETA: splitting (67) gives: % 131.10/18.34 | | % 131.10/18.34 | | Case 1: % 131.10/18.34 | | | % 131.10/18.34 | | | (68) all_9_14 = e1 & op(e1, e2) = e1 % 131.10/18.34 | | | % 131.10/18.34 | | | ALPHA: (68) implies: % 131.10/18.34 | | | (69) all_9_14 = e1 % 131.10/18.34 | | | % 131.10/18.34 | | | COMBINE_EQS: (47), (69) imply: % 131.10/18.34 | | | (70) e1 = e0 % 131.10/18.34 | | | % 131.10/18.34 | | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (12), (14), (16), (17), (18), % 131.10/18.34 | | | (20), (24), (25), (27), (29), (30), (32), (33), (34), (37), % 131.10/18.34 | | | (38), (39), (41), (43), (45), (46), (48), (49), (51), (52), % 131.10/18.34 | | | (53), (54), (55), (56), (57), (60), (62), (63), (64), (70) are % 131.10/18.34 | | | inconsistent by sub-proof #264. % 131.10/18.34 | | | % 131.10/18.34 | | Case 2: % 131.10/18.34 | | | % 131.10/18.34 | | | (71) (all_9_15 = e1 & op(e1, e1) = e1) | (all_9_19 = e1 & op(e1, e0) = % 131.10/18.34 | | | e1) % 131.10/18.34 | | | % 131.10/18.34 | | | BETA: splitting (71) gives: % 131.10/18.34 | | | % 131.10/18.34 | | | Case 1: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (72) all_9_15 = e1 & op(e1, e1) = e1 % 131.10/18.34 | | | | % 131.10/18.34 | | | | ALPHA: (72) implies: % 131.10/18.34 | | | | (73) all_9_15 = e1 % 131.10/18.34 | | | | % 131.10/18.34 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15), % 131.10/18.34 | | | | (19), (22), (23), (26), (27), (28), (29), (31), (34), (35), % 131.10/18.34 | | | | (36), (38), (40), (42), (44), (45), (46), (47), (50), (53), % 131.10/18.34 | | | | (59), (60), (62), (73) are inconsistent by sub-proof #244. % 131.10/18.34 | | | | % 131.10/18.34 | | | Case 2: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (74) all_9_19 = e1 & op(e1, e0) = e1 % 131.10/18.34 | | | | % 131.10/18.34 | | | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (12), (13), (14), (16), (17), % 131.10/18.34 | | | | (18), (20), (24), (25), (27), (29), (30), (32), (33), (34), % 131.10/18.34 | | | | (37), (38), (39), (41), (43), (45), (46), (48), (49), (51), % 131.10/18.34 | | | | (52), (53), (54), (55), (56), (57), (58), (60), (62), (63), % 131.10/18.34 | | | | (64), (74) are inconsistent by sub-proof #243. % 131.10/18.34 | | | | % 131.10/18.34 | | | End of split % 131.10/18.34 | | | % 131.10/18.34 | | End of split % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #243 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_9_19 = e1 & op(e1, e0) = e1 % 131.10/18.34 (2) ~ (e4 = e0) % 131.10/18.34 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.34 (4) all_6_10 = e3 % 131.10/18.34 (5) ~ (all_4_3 = all_4_4) % 131.10/18.34 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.34 (7) ~ (e4 = e2) % 131.10/18.34 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.34 (9) all_6_19 = e0 % 131.10/18.34 (10) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.34 (11) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.34 (12) ~ (all_4_3 = e3) % 131.10/18.34 (13) all_6_20 = all_4_4 % 131.10/18.34 (14) ~ (e3 = e0) % 131.10/18.34 (15) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.34 (16) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.34 = e0 % 131.10/18.34 (17) ~ (e2 = e0) % 131.10/18.34 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.34 (19) ~ (all_4_4 = e3) % 131.10/18.34 (20) ~ (e1 = e0) % 131.10/18.34 (21) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.34 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.34 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.34 (22) ~ (e3 = e2) % 131.10/18.34 (23) op(e0, e4) = all_4_4 % 131.10/18.34 (24) ~ (e4 = e1) % 131.10/18.34 (25) ~ (all_4_3 = e0) % 131.10/18.34 (26) ~ (e3 = e1) % 131.10/18.34 (27) op(e1, e4) = all_4_3 % 131.10/18.34 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.34 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.34 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.34 (29) ~ (e4 = e3) % 131.10/18.34 (30) ~ (all_4_4 = e0) % 131.10/18.34 (31) ~ (all_4_3 = e1) % 131.10/18.34 (32) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.34 (33) op(e2, e4) = e3 % 131.10/18.34 (34) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.34 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.34 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.34 (35) all_9_2 = e1 % 131.10/18.34 (36) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.34 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.34 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.34 (37) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.34 = e0 % 131.10/18.34 (38) ~ (all_4_4 = e1) % 131.10/18.34 (39) all_6_19 = e1 | ~ (op(e1, e0) = e1) % 131.10/18.34 (40) all_4_0 = e0 % 131.10/18.34 (41) ~ (e2 = e1) % 131.10/18.34 (42) all_6_15 = all_4_3 % 131.10/18.34 (43) op(e4, e4) = e0 % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | ALPHA: (1) implies: % 131.10/18.34 | (44) op(e1, e0) = e1 % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (39) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (45) ~ (op(e1, e0) = e1) % 131.10/18.34 | | % 131.10/18.34 | | PRED_UNIFY: (44), (45) imply: % 131.10/18.34 | | (46) $false % 131.10/18.34 | | % 131.10/18.34 | | CLOSE: (46) is inconsistent. % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (47) all_6_19 = e1 % 131.10/18.34 | | % 131.10/18.34 | | COMBINE_EQS: (9), (47) imply: % 131.10/18.34 | | (48) e1 = e0 % 131.10/18.34 | | % 131.10/18.34 | | COMBINE_EQS: (35), (48) imply: % 131.10/18.34 | | (49) all_9_2 = e0 % 131.10/18.34 | | % 131.10/18.34 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), % 131.10/18.34 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 131.10/18.34 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), % 131.10/18.34 | | (38), (40), (41), (42), (43), (49) are inconsistent by sub-proof % 131.10/18.34 | | #265. % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #244 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 131.10/18.34 (2) all_6_5 = e1 % 131.10/18.34 (3) ~ (e4 = e0) % 131.10/18.34 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.34 (5) all_9_20 = e2 % 131.10/18.34 (6) all_6_10 = e3 % 131.10/18.34 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.34 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.34 (9) ~ (e4 = e2) % 131.10/18.34 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.34 (11) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 131.10/18.34 (12) e4 = e2 | ~ (op(e2, e2) = e2) % 131.10/18.34 (13) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 131.10/18.34 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 131.10/18.34 (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.34 (14) all_6_22 = all_4_14 % 131.10/18.34 (15) ~ (all_4_14 = e2) % 131.10/18.34 (16) ~ (e2 = e0) % 131.10/18.34 (17) all_9_0 = e0 % 131.10/18.34 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.34 (19) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 131.10/18.34 (20) ~ (e3 = e2) % 131.10/18.34 (21) all_9_13 = e3 % 131.10/18.34 (22) all_9_12 = e4 % 131.10/18.34 (23) ~ (e4 = e1) % 131.10/18.34 (24) all_9_15 = e1 % 131.10/18.34 (25) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 131.10/18.34 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 131.10/18.34 (all_9_22 = e2 & op(e0, e2) = e2) % 131.10/18.34 (26) op(e3, e4) = e1 % 131.10/18.34 (27) all_4_11 = e0 % 131.10/18.34 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.34 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.34 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.34 (29) ~ (e4 = e3) % 131.10/18.34 (30) all_9_14 = e0 % 131.10/18.34 (31) all_6_2 = all_4_10 % 131.10/18.34 (32) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.34 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.34 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.34 (33) ~ (all_4_10 = e2) % 131.10/18.34 (34) all_4_0 = e0 % 131.10/18.34 (35) ~ (e2 = e1) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (13) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (36) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = % 131.10/18.34 | | e2) % 131.10/18.34 | | % 131.10/18.34 | | REF_CLOSE: (9), (20), (21), (22), (36) are inconsistent by sub-proof #252. % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (37) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 131.10/18.34 | | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.34 | | % 131.10/18.34 | | BETA: splitting (37) gives: % 131.10/18.34 | | % 131.10/18.34 | | Case 1: % 131.10/18.34 | | | % 131.10/18.34 | | | (38) all_9_14 = e2 & op(e1, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | REF_CLOSE: (16), (30), (38) are inconsistent by sub-proof #251. % 131.10/18.34 | | | % 131.10/18.34 | | Case 2: % 131.10/18.34 | | | % 131.10/18.34 | | | (39) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = % 131.10/18.34 | | | e2) % 131.10/18.34 | | | % 131.10/18.34 | | | BETA: splitting (39) gives: % 131.10/18.34 | | | % 131.10/18.34 | | | Case 1: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (40) all_9_15 = e2 & op(e1, e1) = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (16), (17), % 131.10/18.34 | | | | (18), (20), (23), (24), (26), (28), (29), (32), (34), (35), % 131.10/18.34 | | | | (40) are inconsistent by sub-proof #250. % 131.10/18.34 | | | | % 131.10/18.34 | | | Case 2: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (41) all_9_19 = e2 & op(e1, e0) = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | ALPHA: (41) implies: % 131.10/18.34 | | | | (42) all_9_19 = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 131.10/18.34 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 131.10/18.34 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), % 131.10/18.34 | | | | (32), (33), (34), (35), (42) are inconsistent by sub-proof % 131.10/18.34 | | | | #245. % 131.10/18.34 | | | | % 131.10/18.34 | | | End of split % 131.10/18.34 | | | % 131.10/18.34 | | End of split % 131.10/18.34 | | % 131.10/18.34 | End of split % 131.10/18.34 | % 131.10/18.34 End of proof % 131.10/18.34 % 131.10/18.34 Sub-proof #245 shows that the following formulas are inconsistent: % 131.10/18.34 ---------------------------------------------------------------- % 131.10/18.34 (1) all_4_11 = e2 | ~ (op(e3, e2) = e2) % 131.10/18.34 (2) all_6_5 = e1 % 131.10/18.34 (3) ~ (e4 = e0) % 131.10/18.34 (4) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.34 (5) all_9_20 = e2 % 131.10/18.34 (6) all_6_10 = e3 % 131.10/18.34 (7) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.34 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.34 (9) ~ (e4 = e2) % 131.10/18.34 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.34 (11) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 131.10/18.34 (12) e4 = e2 | ~ (op(e2, e2) = e2) % 131.10/18.34 (13) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 131.10/18.34 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 131.10/18.34 (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.34 (14) all_6_22 = all_4_14 % 131.10/18.34 (15) ~ (all_4_14 = e2) % 131.10/18.34 (16) ~ (e2 = e0) % 131.10/18.34 (17) all_9_0 = e0 % 131.10/18.34 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.34 (19) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 131.10/18.34 (20) ~ (e3 = e2) % 131.10/18.34 (21) all_9_13 = e3 % 131.10/18.34 (22) all_9_12 = e4 % 131.10/18.34 (23) ~ (e4 = e1) % 131.10/18.34 (24) all_9_15 = e1 % 131.10/18.34 (25) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) | % 131.10/18.34 (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) | % 131.10/18.34 (all_9_22 = e2 & op(e0, e2) = e2) % 131.10/18.34 (26) op(e3, e4) = e1 % 131.10/18.34 (27) all_4_11 = e0 % 131.10/18.34 (28) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.34 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.34 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.34 (29) ~ (e4 = e3) % 131.10/18.34 (30) all_9_14 = e0 % 131.10/18.34 (31) all_9_19 = e2 % 131.10/18.34 (32) all_6_2 = all_4_10 % 131.10/18.34 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.34 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.34 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.34 (34) ~ (all_4_10 = e2) % 131.10/18.34 (35) all_4_0 = e0 % 131.10/18.34 (36) ~ (e2 = e1) % 131.10/18.34 % 131.10/18.34 Begin of proof % 131.10/18.34 | % 131.10/18.34 | BETA: splitting (25) gives: % 131.10/18.34 | % 131.10/18.34 | Case 1: % 131.10/18.34 | | % 131.10/18.34 | | (37) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_5 = e2 & op(e3, e2) = e2) % 131.10/18.34 | | % 131.10/18.34 | | BETA: splitting (37) gives: % 131.10/18.34 | | % 131.10/18.34 | | Case 1: % 131.10/18.34 | | | % 131.10/18.34 | | | (38) all_9_4 = e2 & op(e4, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | ALPHA: (38) implies: % 131.10/18.34 | | | (39) op(e4, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | REF_CLOSE: (19), (32), (34), (39) are inconsistent by sub-proof #261. % 131.10/18.34 | | | % 131.10/18.34 | | Case 2: % 131.10/18.34 | | | % 131.10/18.34 | | | (40) all_9_5 = e2 & op(e3, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | ALPHA: (40) implies: % 131.10/18.34 | | | (41) op(e3, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | BETA: splitting (1) gives: % 131.10/18.34 | | | % 131.10/18.34 | | | Case 1: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (42) ~ (op(e3, e2) = e2) % 131.10/18.34 | | | | % 131.10/18.34 | | | | PRED_UNIFY: (41), (42) imply: % 131.10/18.34 | | | | (43) $false % 131.10/18.34 | | | | % 131.10/18.34 | | | | CLOSE: (43) is inconsistent. % 131.10/18.34 | | | | % 131.10/18.34 | | | Case 2: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (44) all_4_11 = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | COMBINE_EQS: (27), (44) imply: % 131.10/18.34 | | | | (45) e2 = e0 % 131.10/18.34 | | | | % 131.10/18.34 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (16), % 131.10/18.34 | | | | (17), (18), (20), (21), (22), (23), (24), (26), (28), (29), % 131.10/18.34 | | | | (30), (31), (33), (35), (36), (45) are inconsistent by % 131.10/18.34 | | | | sub-proof #248. % 131.10/18.34 | | | | % 131.10/18.34 | | | End of split % 131.10/18.34 | | | % 131.10/18.34 | | End of split % 131.10/18.34 | | % 131.10/18.34 | Case 2: % 131.10/18.34 | | % 131.10/18.34 | | (46) (all_9_8 = e2 & op(e2, e2) = e2) | (all_9_14 = e2 & op(e1, e2) = e2) % 131.10/18.34 | | | (all_9_22 = e2 & op(e0, e2) = e2) % 131.10/18.34 | | % 131.10/18.34 | | BETA: splitting (46) gives: % 131.10/18.34 | | % 131.10/18.34 | | Case 1: % 131.10/18.34 | | | % 131.10/18.34 | | | (47) all_9_8 = e2 & op(e2, e2) = e2 % 131.10/18.34 | | | % 131.10/18.34 | | | REF_CLOSE: (9), (12), (47) are inconsistent by sub-proof #306. % 131.10/18.34 | | | % 131.10/18.34 | | Case 2: % 131.10/18.34 | | | % 131.10/18.34 | | | (48) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_22 = e2 & op(e0, e2) = % 131.10/18.34 | | | e2) % 131.10/18.34 | | | % 131.10/18.34 | | | BETA: splitting (48) gives: % 131.10/18.34 | | | % 131.10/18.34 | | | Case 1: % 131.10/18.34 | | | | % 131.10/18.34 | | | | (49) all_9_14 = e2 & op(e1, e2) = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | ALPHA: (49) implies: % 131.10/18.34 | | | | (50) all_9_14 = e2 % 131.10/18.34 | | | | % 131.10/18.34 | | | | COMBINE_EQS: (30), (50) imply: % 131.10/18.34 | | | | (51) e2 = e0 % 131.10/18.34 | | | | % 131.10/18.34 | | | | SIMP: (51) implies: % 131.10/18.34 | | | | (52) e2 = e0 % 131.10/18.34 | | | | % 131.10/18.35 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (16), % 131.10/18.35 | | | | (17), (18), (20), (21), (22), (23), (24), (26), (28), (29), % 131.10/18.35 | | | | (30), (31), (33), (35), (36), (52) are inconsistent by % 131.10/18.35 | | | | sub-proof #248. % 131.10/18.35 | | | | % 131.10/18.35 | | | Case 2: % 131.10/18.35 | | | | % 131.10/18.35 | | | | (53) all_9_22 = e2 & op(e0, e2) = e2 % 131.10/18.35 | | | | % 131.10/18.35 | | | | ALPHA: (53) implies: % 131.10/18.35 | | | | (54) op(e0, e2) = e2 % 131.10/18.35 | | | | % 131.10/18.35 | | | | REF_CLOSE: (11), (14), (15), (54) are inconsistent by sub-proof #246. % 131.10/18.35 | | | | % 131.10/18.35 | | | End of split % 131.10/18.35 | | | % 131.10/18.35 | | End of split % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #246 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_22 = e2 | ~ (op(e0, e2) = e2) % 131.10/18.35 (2) op(e0, e2) = e2 % 131.10/18.35 (3) all_6_22 = all_4_14 % 131.10/18.35 (4) ~ (all_4_14 = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (1) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (5) ~ (op(e0, e2) = e2) % 131.10/18.35 | | % 131.10/18.35 | | PRED_UNIFY: (2), (5) imply: % 131.10/18.35 | | (6) $false % 131.10/18.35 | | % 131.10/18.35 | | CLOSE: (6) is inconsistent. % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (7) all_6_22 = e2 % 131.10/18.35 | | % 131.10/18.35 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #247. % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #247 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_22 = all_4_14 % 131.10/18.35 (2) all_6_22 = e2 % 131.10/18.35 (3) ~ (all_4_14 = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (1), (2) imply: % 131.10/18.35 | (4) all_4_14 = e2 % 131.10/18.35 | % 131.10/18.35 | SIMP: (4) implies: % 131.10/18.35 | (5) all_4_14 = e2 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #248 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_5 = e1 % 131.10/18.35 (2) ~ (e4 = e0) % 131.10/18.35 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.35 (4) all_9_20 = e2 % 131.10/18.35 (5) all_6_10 = e3 % 131.10/18.35 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.35 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.35 (8) ~ (e4 = e2) % 131.10/18.35 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.35 (10) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) | % 131.10/18.35 (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = e2) | % 131.10/18.35 (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.35 (11) ~ (e2 = e0) % 131.10/18.35 (12) e2 = e0 % 131.10/18.35 (13) all_9_0 = e0 % 131.10/18.35 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.35 (15) ~ (e3 = e2) % 131.10/18.35 (16) all_9_13 = e3 % 131.10/18.35 (17) all_9_12 = e4 % 131.10/18.35 (18) ~ (e4 = e1) % 131.10/18.35 (19) all_9_15 = e1 % 131.10/18.35 (20) op(e3, e4) = e1 % 131.10/18.35 (21) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.35 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.35 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.35 (22) ~ (e4 = e3) % 131.10/18.35 (23) all_9_14 = e0 % 131.10/18.35 (24) all_9_19 = e2 % 131.10/18.35 (25) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.35 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.35 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.35 (26) all_4_0 = e0 % 131.10/18.35 (27) ~ (e2 = e1) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (12), (24) imply: % 131.10/18.35 | (28) all_9_19 = e0 % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (10) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (29) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = % 131.10/18.35 | | e2) % 131.10/18.35 | | % 131.10/18.35 | | REF_CLOSE: (8), (15), (16), (17), (29) are inconsistent by sub-proof #252. % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (30) (all_9_14 = e2 & op(e1, e2) = e2) | (all_9_15 = e2 & op(e1, e1) = % 131.10/18.35 | | e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.35 | | % 131.10/18.35 | | BETA: splitting (30) gives: % 131.10/18.35 | | % 131.10/18.35 | | Case 1: % 131.10/18.35 | | | % 131.10/18.35 | | | (31) all_9_14 = e2 & op(e1, e2) = e2 % 131.10/18.35 | | | % 131.10/18.35 | | | REF_CLOSE: (11), (23), (31) are inconsistent by sub-proof #251. % 131.10/18.35 | | | % 131.10/18.35 | | Case 2: % 131.10/18.35 | | | % 131.10/18.35 | | | (32) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = % 131.10/18.35 | | | e2) % 131.10/18.35 | | | % 131.10/18.35 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), % 131.10/18.35 | | | (15), (18), (19), (20), (21), (22), (25), (26), (27), (28), % 131.10/18.35 | | | (32) are inconsistent by sub-proof #249. % 131.10/18.35 | | | % 131.10/18.35 | | End of split % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #249 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_5 = e1 % 131.10/18.35 (2) ~ (e4 = e0) % 131.10/18.35 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.35 (4) all_9_20 = e2 % 131.10/18.35 (5) all_6_10 = e3 % 131.10/18.35 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.35 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.35 (8) ~ (e4 = e2) % 131.10/18.35 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.35 (10) ~ (e2 = e0) % 131.10/18.35 (11) all_9_0 = e0 % 131.10/18.35 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.35 (13) ~ (e3 = e2) % 131.10/18.35 (14) ~ (e4 = e1) % 131.10/18.35 (15) all_9_15 = e1 % 131.10/18.35 (16) (all_9_15 = e2 & op(e1, e1) = e2) | (all_9_19 = e2 & op(e1, e0) = e2) % 131.10/18.35 (17) op(e3, e4) = e1 % 131.10/18.35 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.35 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.35 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.35 (19) all_9_19 = e0 % 131.10/18.35 (20) ~ (e4 = e3) % 131.10/18.35 (21) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.35 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.35 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.35 (22) all_4_0 = e0 % 131.10/18.35 (23) ~ (e2 = e1) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (16) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (24) all_9_15 = e2 & op(e1, e1) = e2 % 131.10/18.35 | | % 131.10/18.35 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 131.10/18.35 | | (13), (14), (15), (17), (18), (20), (21), (22), (23), (24) are % 131.10/18.35 | | inconsistent by sub-proof #250. % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (25) all_9_19 = e2 & op(e1, e0) = e2 % 131.10/18.35 | | % 131.10/18.35 | | ALPHA: (25) implies: % 131.10/18.35 | | (26) all_9_19 = e2 % 131.10/18.35 | | % 131.10/18.35 | | COMBINE_EQS: (19), (26) imply: % 131.10/18.35 | | (27) e2 = e0 % 131.10/18.35 | | % 131.10/18.35 | | SIMP: (27) implies: % 131.10/18.35 | | (28) e2 = e0 % 131.10/18.35 | | % 131.10/18.35 | | REDUCE: (10), (28) imply: % 131.10/18.35 | | (29) $false % 131.10/18.35 | | % 131.10/18.35 | | CLOSE: (29) is inconsistent. % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #250 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_5 = e1 % 131.10/18.35 (2) ~ (e4 = e0) % 131.10/18.35 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.35 (4) all_9_20 = e2 % 131.10/18.35 (5) all_6_10 = e3 % 131.10/18.35 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.35 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.35 (8) ~ (e4 = e2) % 131.10/18.35 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.35 (10) ~ (e2 = e0) % 131.10/18.35 (11) all_9_0 = e0 % 131.10/18.35 (12) all_9_15 = e2 & op(e1, e1) = e2 % 131.10/18.35 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.35 (14) ~ (e3 = e2) % 131.10/18.35 (15) ~ (e4 = e1) % 131.10/18.35 (16) all_9_15 = e1 % 131.10/18.35 (17) op(e3, e4) = e1 % 131.10/18.35 (18) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.35 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.35 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.35 (19) ~ (e4 = e3) % 131.10/18.35 (20) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.35 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.35 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.35 (21) all_4_0 = e0 % 131.10/18.35 (22) ~ (e2 = e1) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (12) implies: % 131.10/18.35 | (23) all_9_15 = e2 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (16), (23) imply: % 131.10/18.35 | (24) e2 = e1 % 131.10/18.35 | % 131.10/18.35 | SIMP: (24) implies: % 131.10/18.35 | (25) e2 = e1 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (4), (25) imply: % 131.10/18.35 | (26) all_9_20 = e1 % 131.10/18.35 | % 131.10/18.35 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 131.10/18.35 | (15), (17), (18), (19), (20), (21), (22), (26) are inconsistent by % 131.10/18.35 | sub-proof #283. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #251 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_9_14 = e2 & op(e1, e2) = e2 % 131.10/18.35 (2) all_9_14 = e0 % 131.10/18.35 (3) ~ (e2 = e0) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (1) implies: % 131.10/18.35 | (4) all_9_14 = e2 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (2), (4) imply: % 131.10/18.35 | (5) e2 = e0 % 131.10/18.35 | % 131.10/18.35 | SIMP: (5) implies: % 131.10/18.35 | (6) e2 = e0 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (6) imply: % 131.10/18.35 | (7) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (7) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #252 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) ~ (e4 = e2) % 131.10/18.35 (2) ~ (e3 = e2) % 131.10/18.35 (3) all_9_13 = e3 % 131.10/18.35 (4) all_9_12 = e4 % 131.10/18.35 (5) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_13 = e2 & op(e1, e3) = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (5) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (6) all_9_12 = e2 & op(e1, e4) = e2 % 131.10/18.35 | | % 131.10/18.35 | | ALPHA: (6) implies: % 131.10/18.35 | | (7) all_9_12 = e2 % 131.10/18.35 | | % 131.10/18.35 | | COMBINE_EQS: (4), (7) imply: % 131.10/18.35 | | (8) e4 = e2 % 131.10/18.35 | | % 131.10/18.35 | | REDUCE: (1), (8) imply: % 131.10/18.35 | | (9) $false % 131.10/18.35 | | % 131.10/18.35 | | CLOSE: (9) is inconsistent. % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (10) all_9_13 = e2 & op(e1, e3) = e2 % 131.10/18.35 | | % 131.10/18.35 | | ALPHA: (10) implies: % 131.10/18.35 | | (11) all_9_13 = e2 % 131.10/18.35 | | % 131.10/18.35 | | COMBINE_EQS: (3), (11) imply: % 131.10/18.35 | | (12) e3 = e2 % 131.10/18.35 | | % 131.10/18.35 | | REDUCE: (2), (12) imply: % 131.10/18.35 | | (13) $false % 131.10/18.35 | | % 131.10/18.35 | | CLOSE: (13) is inconsistent. % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #253 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_16 = all_4_8 % 131.10/18.35 (2) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_13 = e1 & op(e1, e3) = e1) % 131.10/18.35 (3) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.35 (4) ~ (all_4_8 = e1) % 131.10/18.35 (5) ~ (all_4_3 = e1) % 131.10/18.35 (6) all_6_16 = e1 | ~ (op(e1, e3) = e1) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (2) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (7) all_9_12 = e1 & op(e1, e4) = e1 % 131.10/18.35 | | % 131.10/18.35 | | ALPHA: (7) implies: % 131.10/18.35 | | (8) op(e1, e4) = e1 % 131.10/18.35 | | % 131.10/18.35 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #268. % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (9) all_9_13 = e1 & op(e1, e3) = e1 % 131.10/18.35 | | % 131.10/18.35 | | ALPHA: (9) implies: % 131.10/18.35 | | (10) op(e1, e3) = e1 % 131.10/18.35 | | % 131.10/18.35 | | BETA: splitting (6) gives: % 131.10/18.35 | | % 131.10/18.35 | | Case 1: % 131.10/18.35 | | | % 131.10/18.35 | | | (11) ~ (op(e1, e3) = e1) % 131.10/18.35 | | | % 131.10/18.35 | | | PRED_UNIFY: (10), (11) imply: % 131.10/18.35 | | | (12) $false % 131.10/18.35 | | | % 131.10/18.35 | | | CLOSE: (12) is inconsistent. % 131.10/18.35 | | | % 131.10/18.35 | | Case 2: % 131.10/18.35 | | | % 131.10/18.35 | | | (13) all_6_16 = e1 % 131.10/18.35 | | | % 131.10/18.35 | | | COMBINE_EQS: (1), (13) imply: % 131.10/18.35 | | | (14) all_4_8 = e1 % 131.10/18.35 | | | % 131.10/18.35 | | | SIMP: (14) implies: % 131.10/18.35 | | | (15) all_4_8 = e1 % 131.10/18.35 | | | % 131.10/18.35 | | | REDUCE: (4), (15) imply: % 131.10/18.35 | | | (16) $false % 131.10/18.35 | | | % 131.10/18.35 | | | CLOSE: (16) is inconsistent. % 131.10/18.35 | | | % 131.10/18.35 | | End of split % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #254 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_9_12 = e0 & op(e1, e4) = e0 % 131.10/18.35 (2) all_9_12 = e4 % 131.10/18.35 (3) ~ (e4 = e0) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (1) implies: % 131.10/18.35 | (4) all_9_12 = e0 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (2), (4) imply: % 131.10/18.35 | (5) e4 = e0 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #255 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_14 = all_4_22 % 131.10/18.35 (2) all_6_14 = e3 % 131.10/18.35 (3) ~ (all_4_22 = e3) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (1), (2) imply: % 131.10/18.35 | (4) all_4_22 = e3 % 131.10/18.35 | % 131.10/18.35 | SIMP: (4) implies: % 131.10/18.35 | (5) all_4_22 = e3 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #256 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_9_6 = e0 & op(e2, e4) = e0 % 131.10/18.35 (2) all_9_6 = e3 % 131.10/18.35 (3) ~ (e3 = e0) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (1) implies: % 131.10/18.35 | (4) all_9_6 = e0 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (2), (4) imply: % 131.10/18.35 | (5) e3 = e0 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #257 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_14 = all_4_22 % 131.10/18.35 (2) all_6_14 = e2 % 131.10/18.35 (3) ~ (all_4_22 = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (1), (2) imply: % 131.10/18.35 | (4) all_4_22 = e2 % 131.10/18.35 | % 131.10/18.35 | SIMP: (4) implies: % 131.10/18.35 | (5) all_4_22 = e2 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #258 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_5 = e1 % 131.10/18.35 (2) ~ (e4 = e0) % 131.10/18.35 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.35 (4) all_9_20 = e2 % 131.10/18.35 (5) all_6_10 = e3 % 131.10/18.35 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.35 (7) ~ (all_4_3 = all_4_4) % 131.10/18.35 (8) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.35 (9) ~ (e4 = e2) % 131.10/18.35 (10) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.35 (11) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) = e2) | % 131.10/18.35 (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) = e2) | % 131.10/18.35 (all_9_16 = e2 & op(e4, e0) = e2) % 131.10/18.35 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.35 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.35 (14) ~ (all_4_3 = e3) % 131.10/18.35 (15) all_6_20 = all_4_4 % 131.10/18.35 (16) ~ (e3 = e0) % 131.10/18.35 (17) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.35 (18) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.35 = e0 % 131.10/18.35 (19) ~ (e2 = e0) % 131.10/18.35 (20) all_9_0 = e0 % 131.10/18.35 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.35 (22) ~ (all_4_4 = e3) % 131.10/18.35 (23) ~ (op(e4, e3) = e3) % 131.10/18.35 (24) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 131.10/18.35 (25) ~ (e1 = e0) % 131.10/18.35 (26) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.35 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.35 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.35 (27) ~ (e3 = e2) % 131.10/18.35 (28) all_9_12 = e4 % 131.10/18.35 (29) op(e0, e4) = all_4_4 % 131.10/18.35 (30) ~ (e4 = e1) % 131.10/18.35 (31) ~ (all_4_3 = e0) % 131.10/18.35 (32) ~ (e3 = e1) % 131.10/18.35 (33) op(e3, e4) = e1 % 131.10/18.35 (34) all_9_9 = e4 % 131.10/18.35 (35) op(e1, e4) = all_4_3 % 131.10/18.35 (36) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.35 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.35 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.35 (37) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) | % 131.10/18.35 (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) | % 131.10/18.35 (all_9_16 = e3 & op(e4, e0) = e3) % 131.10/18.35 (38) ~ (e4 = e3) % 131.10/18.35 (39) ~ (all_4_4 = e0) % 131.10/18.35 (40) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 131.10/18.35 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 131.10/18.35 (all_9_16 = e1 & op(e4, e0) = e1) % 131.10/18.35 (41) ~ (all_4_3 = e1) % 131.10/18.35 (42) all_6_2 = all_4_10 % 131.10/18.35 (43) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.35 (44) op(e2, e4) = e3 % 131.10/18.35 (45) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.35 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.35 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.35 (46) all_9_4 = e0 % 131.10/18.35 (47) all_9_2 = e1 % 131.10/18.35 (48) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.35 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.35 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.35 (49) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.35 = e0 % 131.10/18.35 (50) ~ (all_4_4 = e1) % 131.10/18.35 (51) ~ (all_4_10 = e2) % 131.10/18.35 (52) all_4_0 = e0 % 131.10/18.35 (53) ~ (e2 = e1) % 131.10/18.35 (54) all_6_15 = all_4_3 % 131.10/18.35 (55) op(e4, e4) = e0 % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | BETA: splitting (37) gives: % 131.10/18.35 | % 131.10/18.35 | Case 1: % 131.10/18.35 | | % 131.10/18.35 | | (56) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_1 = e3 & op(e4, e3) = e3) % 131.10/18.35 | | % 131.10/18.35 | | BETA: splitting (56) gives: % 131.10/18.35 | | % 131.10/18.35 | | Case 1: % 131.10/18.35 | | | % 131.10/18.35 | | | (57) all_9_0 = e3 & op(e4, e4) = e3 % 131.10/18.35 | | | % 131.10/18.35 | | | REF_CLOSE: (16), (20), (57) are inconsistent by sub-proof #291. % 131.10/18.35 | | | % 131.10/18.35 | | Case 2: % 131.10/18.35 | | | % 131.10/18.35 | | | (58) all_9_1 = e3 & op(e4, e3) = e3 % 131.10/18.35 | | | % 131.10/18.35 | | | REF_CLOSE: (23), (58) are inconsistent by sub-proof #296. % 131.10/18.35 | | | % 131.10/18.35 | | End of split % 131.10/18.35 | | % 131.10/18.35 | Case 2: % 131.10/18.35 | | % 131.10/18.35 | | (59) (all_9_4 = e3 & op(e4, e2) = e3) | (all_9_9 = e3 & op(e4, e1) = e3) % 131.10/18.35 | | | (all_9_16 = e3 & op(e4, e0) = e3) % 131.10/18.35 | | % 131.10/18.35 | | BETA: splitting (59) gives: % 131.10/18.35 | | % 131.10/18.35 | | Case 1: % 131.10/18.35 | | | % 131.10/18.35 | | | (60) all_9_4 = e3 & op(e4, e2) = e3 % 131.10/18.35 | | | % 131.10/18.35 | | | REF_CLOSE: (16), (46), (60) are inconsistent by sub-proof #290. % 131.10/18.35 | | | % 131.10/18.35 | | Case 2: % 131.10/18.35 | | | % 131.10/18.35 | | | (61) (all_9_9 = e3 & op(e4, e1) = e3) | (all_9_16 = e3 & op(e4, e0) = % 131.10/18.35 | | | e3) % 131.10/18.35 | | | % 131.10/18.35 | | | BETA: splitting (61) gives: % 131.10/18.35 | | | % 131.10/18.35 | | | Case 1: % 131.10/18.35 | | | | % 131.10/18.35 | | | | (62) all_9_9 = e3 & op(e4, e1) = e3 % 131.10/18.35 | | | | % 131.10/18.35 | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (28), (30), (34), (38), % 131.10/18.35 | | | | (45), (52), (62) are inconsistent by sub-proof #289. % 131.10/18.35 | | | | % 131.10/18.35 | | | Case 2: % 131.10/18.35 | | | | % 131.10/18.35 | | | | (63) all_9_16 = e3 & op(e4, e0) = e3 % 131.10/18.35 | | | | % 131.10/18.35 | | | | ALPHA: (63) implies: % 131.10/18.35 | | | | (64) all_9_16 = e3 % 131.10/18.35 | | | | % 131.10/18.35 | | | | BETA: splitting (11) gives: % 131.10/18.35 | | | | % 131.10/18.35 | | | | Case 1: % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | (65) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_1 = e2 & op(e4, e3) % 131.10/18.35 | | | | | = e2) % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | BETA: splitting (65) gives: % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | Case 1: % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | (66) all_9_0 = e2 & op(e4, e4) = e2 % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | REF_CLOSE: (19), (20), (66) are inconsistent by sub-proof #314. % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | Case 2: % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | (67) all_9_1 = e2 & op(e4, e3) = e2 % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | ALPHA: (67) implies: % 131.10/18.35 | | | | | | (68) all_9_1 = e2 % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), % 131.10/18.35 | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), % 131.10/18.35 | | | | | | (22), (25), (26), (27), (29), (30), (31), (32), (33), % 131.10/18.35 | | | | | | (34), (35), (36), (38), (39), (40), (41), (43), (44), % 131.10/18.35 | | | | | | (45), (46), (47), (48), (49), (50), (52), (53), (54), % 131.10/18.35 | | | | | | (55), (64), (68) are inconsistent by sub-proof #262. % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | End of split % 131.10/18.35 | | | | | % 131.10/18.35 | | | | Case 2: % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | (69) (all_9_4 = e2 & op(e4, e2) = e2) | (all_9_9 = e2 & op(e4, e1) % 131.10/18.35 | | | | | = e2) | (all_9_16 = e2 & op(e4, e0) = e2) % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | BETA: splitting (69) gives: % 131.10/18.35 | | | | | % 131.10/18.35 | | | | | Case 1: % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | (70) all_9_4 = e2 & op(e4, e2) = e2 % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | ALPHA: (70) implies: % 131.10/18.35 | | | | | | (71) op(e4, e2) = e2 % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | REF_CLOSE: (24), (42), (51), (71) are inconsistent by sub-proof % 131.10/18.35 | | | | | | #261. % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | Case 2: % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | (72) (all_9_9 = e2 & op(e4, e1) = e2) | (all_9_16 = e2 & op(e4, % 131.10/18.35 | | | | | | e0) = e2) % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | BETA: splitting (72) gives: % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | | Case 1: % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | | (73) all_9_9 = e2 & op(e4, e1) = e2 % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | | REF_CLOSE: (9), (34), (73) are inconsistent by sub-proof #260. % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | Case 2: % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | | (74) all_9_16 = e2 & op(e4, e0) = e2 % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | | REF_CLOSE: (27), (64), (74) are inconsistent by sub-proof #259. % 131.10/18.35 | | | | | | | % 131.10/18.35 | | | | | | End of split % 131.10/18.35 | | | | | | % 131.10/18.35 | | | | | End of split % 131.10/18.35 | | | | | % 131.10/18.35 | | | | End of split % 131.10/18.35 | | | | % 131.10/18.35 | | | End of split % 131.10/18.35 | | | % 131.10/18.35 | | End of split % 131.10/18.35 | | % 131.10/18.35 | End of split % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #259 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_9_16 = e2 & op(e4, e0) = e2 % 131.10/18.35 (2) all_9_16 = e3 % 131.10/18.35 (3) ~ (e3 = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (1) implies: % 131.10/18.35 | (4) all_9_16 = e2 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (2), (4) imply: % 131.10/18.35 | (5) e3 = e2 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #260 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_9_9 = e2 & op(e4, e1) = e2 % 131.10/18.35 (2) all_9_9 = e4 % 131.10/18.35 (3) ~ (e4 = e2) % 131.10/18.35 % 131.10/18.35 Begin of proof % 131.10/18.35 | % 131.10/18.35 | ALPHA: (1) implies: % 131.10/18.35 | (4) all_9_9 = e2 % 131.10/18.35 | % 131.10/18.35 | COMBINE_EQS: (2), (4) imply: % 131.10/18.35 | (5) e4 = e2 % 131.10/18.35 | % 131.10/18.35 | REDUCE: (3), (5) imply: % 131.10/18.35 | (6) $false % 131.10/18.35 | % 131.10/18.35 | CLOSE: (6) is inconsistent. % 131.10/18.35 | % 131.10/18.35 End of proof % 131.10/18.35 % 131.10/18.35 Sub-proof #261 shows that the following formulas are inconsistent: % 131.10/18.35 ---------------------------------------------------------------- % 131.10/18.35 (1) all_6_2 = e2 | ~ (op(e4, e2) = e2) % 131.10/18.35 (2) op(e4, e2) = e2 % 131.10/18.35 (3) all_6_2 = all_4_10 % 131.10/18.35 (4) ~ (all_4_10 = e2) % 131.10/18.36 % 131.10/18.36 Begin of proof % 131.10/18.36 | % 131.10/18.36 | BETA: splitting (1) gives: % 131.10/18.36 | % 131.10/18.36 | Case 1: % 131.10/18.36 | | % 131.10/18.36 | | (5) ~ (op(e4, e2) = e2) % 131.10/18.36 | | % 131.10/18.36 | | PRED_UNIFY: (2), (5) imply: % 131.10/18.36 | | (6) $false % 131.10/18.36 | | % 131.10/18.36 | | CLOSE: (6) is inconsistent. % 131.10/18.36 | | % 131.10/18.36 | Case 2: % 131.10/18.36 | | % 131.10/18.36 | | (7) all_6_2 = e2 % 131.10/18.36 | | % 131.10/18.36 | | COMBINE_EQS: (3), (7) imply: % 131.10/18.36 | | (8) all_4_10 = e2 % 131.10/18.36 | | % 131.10/18.36 | | SIMP: (8) implies: % 131.10/18.36 | | (9) all_4_10 = e2 % 131.10/18.36 | | % 131.10/18.36 | | REDUCE: (4), (9) imply: % 131.10/18.36 | | (10) $false % 131.10/18.36 | | % 131.10/18.36 | | CLOSE: (10) is inconsistent. % 131.10/18.36 | | % 131.10/18.36 | End of split % 131.10/18.36 | % 131.10/18.36 End of proof % 131.10/18.36 % 131.10/18.36 Sub-proof #262 shows that the following formulas are inconsistent: % 131.10/18.36 ---------------------------------------------------------------- % 131.10/18.36 (1) all_6_5 = e1 % 131.10/18.36 (2) ~ (e4 = e0) % 131.10/18.36 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.36 (4) all_9_20 = e2 % 131.10/18.36 (5) all_6_10 = e3 % 131.10/18.36 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.10/18.36 (7) ~ (all_4_3 = all_4_4) % 131.10/18.36 (8) all_9_1 = e2 % 131.10/18.36 (9) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.36 (10) ~ (e4 = e2) % 131.10/18.36 (11) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.36 (12) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (13) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.36 (14) ~ (all_4_3 = e3) % 131.10/18.36 (15) all_6_20 = all_4_4 % 131.10/18.36 (16) ~ (e3 = e0) % 131.10/18.36 (17) all_9_16 = e3 % 131.10/18.36 (18) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (19) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.36 = e0 % 131.10/18.36 (20) ~ (e2 = e0) % 131.10/18.36 (21) all_9_0 = e0 % 131.10/18.36 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.36 (23) ~ (all_4_4 = e3) % 131.10/18.36 (24) ~ (e1 = e0) % 131.10/18.36 (25) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.36 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.36 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.36 (26) ~ (e3 = e2) % 131.10/18.36 (27) op(e0, e4) = all_4_4 % 131.10/18.36 (28) ~ (e4 = e1) % 131.10/18.36 (29) ~ (all_4_3 = e0) % 131.10/18.36 (30) ~ (e3 = e1) % 131.10/18.36 (31) op(e3, e4) = e1 % 131.10/18.36 (32) all_9_9 = e4 % 131.10/18.36 (33) op(e1, e4) = all_4_3 % 131.10/18.36 (34) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.36 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.36 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.36 (35) ~ (e4 = e3) % 131.10/18.36 (36) ~ (all_4_4 = e0) % 131.10/18.36 (37) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) | % 131.10/18.36 (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) | % 131.10/18.36 (all_9_16 = e1 & op(e4, e0) = e1) % 131.10/18.36 (38) ~ (all_4_3 = e1) % 131.10/18.36 (39) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.36 (40) op(e2, e4) = e3 % 131.10/18.36 (41) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.36 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.36 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.36 (42) all_9_4 = e0 % 131.10/18.36 (43) all_9_2 = e1 % 131.10/18.36 (44) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.36 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.36 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.36 (45) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.36 = e0 % 131.10/18.36 (46) ~ (all_4_4 = e1) % 131.10/18.36 (47) all_4_0 = e0 % 131.10/18.36 (48) ~ (e2 = e1) % 131.10/18.36 (49) all_6_15 = all_4_3 % 131.10/18.36 (50) op(e4, e4) = e0 % 131.10/18.36 % 131.10/18.36 Begin of proof % 131.10/18.36 | % 131.10/18.36 | BETA: splitting (37) gives: % 131.10/18.36 | % 131.10/18.36 | Case 1: % 131.10/18.36 | | % 131.10/18.36 | | (51) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_1 = e1 & op(e4, e3) = e1) % 131.10/18.36 | | % 131.10/18.36 | | BETA: splitting (51) gives: % 131.10/18.36 | | % 131.10/18.36 | | Case 1: % 131.10/18.36 | | | % 131.10/18.36 | | | (52) all_9_0 = e1 & op(e4, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (52) implies: % 131.10/18.36 | | | (53) op(e4, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | REF_CLOSE: (22), (24), (50), (53) are inconsistent by sub-proof #321. % 131.10/18.36 | | | % 131.10/18.36 | | Case 2: % 131.10/18.36 | | | % 131.10/18.36 | | | (54) all_9_1 = e1 & op(e4, e3) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (54) implies: % 131.10/18.36 | | | (55) all_9_1 = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | COMBINE_EQS: (8), (55) imply: % 131.10/18.36 | | | (56) e2 = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | COMBINE_EQS: (4), (56) imply: % 131.10/18.36 | | | (57) all_9_20 = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (20), (21), (22), % 131.10/18.36 | | | (26), (28), (31), (34), (35), (41), (47), (48), (57) are % 131.10/18.36 | | | inconsistent by sub-proof #283. % 131.10/18.36 | | | % 131.10/18.36 | | End of split % 131.10/18.36 | | % 131.10/18.36 | Case 2: % 131.10/18.36 | | % 131.10/18.36 | | (58) (all_9_4 = e1 & op(e4, e2) = e1) | (all_9_9 = e1 & op(e4, e1) = e1) % 131.10/18.36 | | | (all_9_16 = e1 & op(e4, e0) = e1) % 131.10/18.36 | | % 131.10/18.36 | | BETA: splitting (58) gives: % 131.10/18.36 | | % 131.10/18.36 | | Case 1: % 131.10/18.36 | | | % 131.10/18.36 | | | (59) all_9_4 = e1 & op(e4, e2) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (59) implies: % 131.10/18.36 | | | (60) all_9_4 = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | COMBINE_EQS: (42), (60) imply: % 131.10/18.36 | | | (61) e1 = e0 % 131.10/18.36 | | | % 131.10/18.36 | | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (11), (12), (13), (14), (15), % 131.10/18.36 | | | (16), (18), (19), (20), (22), (23), (24), (25), (26), (27), % 131.10/18.36 | | | (28), (29), (30), (33), (34), (35), (36), (38), (39), (40), % 131.10/18.36 | | | (41), (43), (44), (45), (46), (47), (48), (49), (50), (61) are % 131.10/18.36 | | | inconsistent by sub-proof #264. % 131.10/18.36 | | | % 131.10/18.36 | | Case 2: % 131.10/18.36 | | | % 131.10/18.36 | | | (62) (all_9_9 = e1 & op(e4, e1) = e1) | (all_9_16 = e1 & op(e4, e0) = % 131.10/18.36 | | | e1) % 131.10/18.36 | | | % 131.10/18.36 | | | BETA: splitting (62) gives: % 131.10/18.36 | | | % 131.10/18.36 | | | Case 1: % 131.10/18.36 | | | | % 131.10/18.36 | | | | (63) all_9_9 = e1 & op(e4, e1) = e1 % 131.10/18.36 | | | | % 131.10/18.36 | | | | REF_CLOSE: (28), (32), (63) are inconsistent by sub-proof #263. % 131.10/18.36 | | | | % 131.10/18.36 | | | Case 2: % 131.10/18.36 | | | | % 131.10/18.36 | | | | (64) all_9_16 = e1 & op(e4, e0) = e1 % 131.10/18.36 | | | | % 131.10/18.36 | | | | ALPHA: (64) implies: % 131.10/18.36 | | | | (65) all_9_16 = e1 % 131.10/18.36 | | | | % 131.10/18.36 | | | | COMBINE_EQS: (17), (65) imply: % 131.10/18.36 | | | | (66) e3 = e1 % 131.10/18.36 | | | | % 131.10/18.36 | | | | REDUCE: (30), (66) imply: % 131.10/18.36 | | | | (67) $false % 131.10/18.36 | | | | % 131.10/18.36 | | | | CLOSE: (67) is inconsistent. % 131.10/18.36 | | | | % 131.10/18.36 | | | End of split % 131.10/18.36 | | | % 131.10/18.36 | | End of split % 131.10/18.36 | | % 131.10/18.36 | End of split % 131.10/18.36 | % 131.10/18.36 End of proof % 131.10/18.36 % 131.10/18.36 Sub-proof #263 shows that the following formulas are inconsistent: % 131.10/18.36 ---------------------------------------------------------------- % 131.10/18.36 (1) all_9_9 = e1 & op(e4, e1) = e1 % 131.10/18.36 (2) all_9_9 = e4 % 131.10/18.36 (3) ~ (e4 = e1) % 131.10/18.36 % 131.10/18.36 Begin of proof % 131.10/18.36 | % 131.10/18.36 | ALPHA: (1) implies: % 131.10/18.36 | (4) all_9_9 = e1 % 131.10/18.36 | % 131.10/18.36 | COMBINE_EQS: (2), (4) imply: % 131.10/18.36 | (5) e4 = e1 % 131.10/18.36 | % 131.10/18.36 | REDUCE: (3), (5) imply: % 131.10/18.36 | (6) $false % 131.10/18.36 | % 131.10/18.36 | CLOSE: (6) is inconsistent. % 131.10/18.36 | % 131.10/18.36 End of proof % 131.10/18.36 % 131.10/18.36 Sub-proof #264 shows that the following formulas are inconsistent: % 131.10/18.36 ---------------------------------------------------------------- % 131.10/18.36 (1) ~ (e4 = e0) % 131.10/18.36 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.36 (3) all_6_10 = e3 % 131.10/18.36 (4) ~ (all_4_3 = all_4_4) % 131.10/18.36 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.36 (6) ~ (e4 = e2) % 131.10/18.36 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.36 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (9) e1 = e0 % 131.10/18.36 (10) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.36 (11) ~ (all_4_3 = e3) % 131.10/18.36 (12) all_6_20 = all_4_4 % 131.10/18.36 (13) ~ (e3 = e0) % 131.10/18.36 (14) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (15) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.36 = e0 % 131.10/18.36 (16) ~ (e2 = e0) % 131.10/18.36 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.36 (18) ~ (all_4_4 = e3) % 131.10/18.36 (19) ~ (e1 = e0) % 131.10/18.36 (20) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.36 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.36 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.36 (21) ~ (e3 = e2) % 131.10/18.36 (22) op(e0, e4) = all_4_4 % 131.10/18.36 (23) ~ (e4 = e1) % 131.10/18.36 (24) ~ (all_4_3 = e0) % 131.10/18.36 (25) ~ (e3 = e1) % 131.10/18.36 (26) op(e1, e4) = all_4_3 % 131.10/18.36 (27) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.36 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.36 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.36 (28) ~ (e4 = e3) % 131.10/18.36 (29) ~ (all_4_4 = e0) % 131.10/18.36 (30) ~ (all_4_3 = e1) % 131.10/18.36 (31) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.36 (32) op(e2, e4) = e3 % 131.10/18.36 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.36 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.36 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.36 (34) all_9_2 = e1 % 131.10/18.36 (35) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.36 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.36 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.36 (36) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.36 = e0 % 131.10/18.36 (37) ~ (all_4_4 = e1) % 131.10/18.36 (38) all_4_0 = e0 % 131.10/18.36 (39) ~ (e2 = e1) % 131.10/18.36 (40) all_6_15 = all_4_3 % 131.10/18.36 (41) op(e4, e4) = e0 % 131.10/18.36 % 131.10/18.36 Begin of proof % 131.10/18.36 | % 131.10/18.36 | SIMP: (9) implies: % 131.10/18.36 | (42) e1 = e0 % 131.10/18.36 | % 131.10/18.36 | COMBINE_EQS: (34), (42) imply: % 131.10/18.36 | (43) all_9_2 = e0 % 131.10/18.36 | % 131.10/18.36 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 131.10/18.36 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 131.10/18.36 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 131.10/18.36 | (37), (38), (39), (40), (41), (43) are inconsistent by sub-proof % 131.10/18.36 | #265. % 131.10/18.36 | % 131.10/18.36 End of proof % 131.10/18.36 % 131.10/18.36 Sub-proof #265 shows that the following formulas are inconsistent: % 131.10/18.36 ---------------------------------------------------------------- % 131.10/18.36 (1) ~ (e4 = e0) % 131.10/18.36 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.10/18.36 (3) all_6_10 = e3 % 131.10/18.36 (4) ~ (all_4_3 = all_4_4) % 131.10/18.36 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.10/18.36 (6) ~ (e4 = e2) % 131.10/18.36 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 131.10/18.36 (8) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (9) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.10/18.36 (10) ~ (all_4_3 = e3) % 131.10/18.36 (11) all_6_20 = all_4_4 % 131.10/18.36 (12) ~ (e3 = e0) % 131.10/18.36 (13) all_4_3 = e4 | ~ (op(e1, e4) = e4) % 131.10/18.36 (14) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.10/18.36 = e0 % 131.10/18.36 (15) ~ (e2 = e0) % 131.10/18.36 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.10/18.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.10/18.36 (17) ~ (all_4_4 = e3) % 131.10/18.36 (18) all_9_2 = e0 % 131.10/18.36 (19) ~ (e1 = e0) % 131.10/18.36 (20) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = e3) | % 131.10/18.36 (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = e3) | % 131.10/18.36 (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.36 (21) ~ (e3 = e2) % 131.10/18.36 (22) op(e0, e4) = all_4_4 % 131.10/18.36 (23) ~ (e4 = e1) % 131.10/18.36 (24) ~ (all_4_3 = e0) % 131.10/18.36 (25) ~ (e3 = e1) % 131.10/18.36 (26) op(e1, e4) = all_4_3 % 131.10/18.36 (27) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.10/18.36 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.10/18.36 (all_9_20 = e2 & op(e0, e4) = e2) % 131.10/18.36 (28) ~ (e4 = e3) % 131.10/18.36 (29) ~ (all_4_4 = e0) % 131.10/18.36 (30) ~ (all_4_3 = e1) % 131.10/18.36 (31) all_6_20 = e4 | ~ (op(e0, e4) = e4) % 131.10/18.36 (32) op(e2, e4) = e3 % 131.10/18.36 (33) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.10/18.36 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.10/18.36 (all_9_20 = e4 & op(e0, e4) = e4) % 131.10/18.36 (34) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) | % 131.10/18.36 (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) | % 131.10/18.36 (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.36 (35) all_6_15 = e4 | all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | all_6_15 % 131.10/18.36 = e0 % 131.10/18.36 (36) ~ (all_4_4 = e1) % 131.10/18.36 (37) all_4_0 = e0 % 131.10/18.36 (38) ~ (e2 = e1) % 131.10/18.36 (39) all_6_15 = all_4_3 % 131.10/18.36 (40) op(e4, e4) = e0 % 131.10/18.36 % 131.10/18.36 Begin of proof % 131.10/18.36 | % 131.10/18.36 | BETA: splitting (34) gives: % 131.10/18.36 | % 131.10/18.36 | Case 1: % 131.10/18.36 | | % 131.10/18.36 | | (41) (all_9_0 = e1 & op(e4, e4) = e1) | (all_9_2 = e1 & op(e3, e4) = e1) % 131.10/18.36 | | % 131.10/18.36 | | BETA: splitting (41) gives: % 131.10/18.36 | | % 131.10/18.36 | | Case 1: % 131.10/18.36 | | | % 131.10/18.36 | | | (42) all_9_0 = e1 & op(e4, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (42) implies: % 131.10/18.36 | | | (43) op(e4, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | REF_CLOSE: (16), (19), (40), (43) are inconsistent by sub-proof #321. % 131.10/18.36 | | | % 131.10/18.36 | | Case 2: % 131.10/18.36 | | | % 131.10/18.36 | | | (44) all_9_2 = e1 & op(e3, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (44) implies: % 131.10/18.36 | | | (45) all_9_2 = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | COMBINE_EQS: (18), (45) imply: % 131.10/18.36 | | | (46) e1 = e0 % 131.10/18.36 | | | % 131.10/18.36 | | | SIMP: (46) implies: % 131.10/18.36 | | | (47) e1 = e0 % 131.10/18.36 | | | % 131.10/18.36 | | | REDUCE: (19), (47) imply: % 131.10/18.36 | | | (48) $false % 131.10/18.36 | | | % 131.10/18.36 | | | CLOSE: (48) is inconsistent. % 131.10/18.36 | | | % 131.10/18.36 | | End of split % 131.10/18.36 | | % 131.10/18.36 | Case 2: % 131.10/18.36 | | % 131.10/18.36 | | (49) (all_9_6 = e1 & op(e2, e4) = e1) | (all_9_12 = e1 & op(e1, e4) = e1) % 131.10/18.36 | | | (all_9_20 = e1 & op(e0, e4) = e1) % 131.10/18.36 | | % 131.10/18.36 | | BETA: splitting (49) gives: % 131.10/18.36 | | % 131.10/18.36 | | Case 1: % 131.10/18.36 | | | % 131.10/18.36 | | | (50) all_9_6 = e1 & op(e2, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | ALPHA: (50) implies: % 131.10/18.36 | | | (51) all_9_6 = e1 % 131.10/18.36 | | | (52) op(e2, e4) = e1 % 131.10/18.36 | | | % 131.10/18.36 | | | BETA: splitting (20) gives: % 131.10/18.36 | | | % 131.10/18.36 | | | Case 1: % 131.10/18.36 | | | | % 131.10/18.36 | | | | (53) (all_9_0 = e3 & op(e4, e4) = e3) | (all_9_2 = e3 & op(e3, e4) = % 131.10/18.36 | | | | e3) % 131.10/18.36 | | | | % 131.10/18.36 | | | | BETA: splitting (53) gives: % 131.10/18.36 | | | | % 131.10/18.36 | | | | Case 1: % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | (54) all_9_0 = e3 & op(e4, e4) = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | ALPHA: (54) implies: % 131.10/18.36 | | | | | (55) op(e4, e4) = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | GROUND_INST: instantiating (16) with e3, e1, e4, e2, simplifying with % 131.10/18.36 | | | | | (32), (52) gives: % 131.10/18.36 | | | | | (56) e3 = e1 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | GROUND_INST: instantiating (16) with e0, e3, e4, e4, simplifying with % 131.10/18.36 | | | | | (40), (55) gives: % 131.10/18.36 | | | | | (57) e3 = e0 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | COMBINE_EQS: (56), (57) imply: % 131.10/18.36 | | | | | (58) e1 = e0 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | REDUCE: (19), (58) imply: % 131.10/18.36 | | | | | (59) $false % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | CLOSE: (59) is inconsistent. % 131.10/18.36 | | | | | % 131.10/18.36 | | | | Case 2: % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | (60) all_9_2 = e3 & op(e3, e4) = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | ALPHA: (60) implies: % 131.10/18.36 | | | | | (61) all_9_2 = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | COMBINE_EQS: (18), (61) imply: % 131.10/18.36 | | | | | (62) e3 = e0 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | SIMP: (62) implies: % 131.10/18.36 | | | | | (63) e3 = e0 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | REDUCE: (12), (63) imply: % 131.10/18.36 | | | | | (64) $false % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | CLOSE: (64) is inconsistent. % 131.10/18.36 | | | | | % 131.10/18.36 | | | | End of split % 131.10/18.36 | | | | % 131.10/18.36 | | | Case 2: % 131.10/18.36 | | | | % 131.10/18.36 | | | | (65) (all_9_6 = e3 & op(e2, e4) = e3) | (all_9_12 = e3 & op(e1, e4) = % 131.10/18.36 | | | | e3) | (all_9_20 = e3 & op(e0, e4) = e3) % 131.10/18.36 | | | | % 131.10/18.36 | | | | BETA: splitting (65) gives: % 131.10/18.36 | | | | % 131.10/18.36 | | | | Case 1: % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | (66) all_9_6 = e3 & op(e2, e4) = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | ALPHA: (66) implies: % 131.10/18.36 | | | | | (67) all_9_6 = e3 % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | REF_CLOSE: (25), (51), (67) are inconsistent by sub-proof #282. % 131.10/18.36 | | | | | % 131.10/18.36 | | | | Case 2: % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | (68) (all_9_12 = e3 & op(e1, e4) = e3) | (all_9_20 = e3 & op(e0, % 131.10/18.36 | | | | | e4) = e3) % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | BETA: splitting (68) gives: % 131.10/18.36 | | | | | % 131.10/18.36 | | | | | Case 1: % 131.10/18.36 | | | | | | % 131.16/18.36 | | | | | | (69) all_9_12 = e3 & op(e1, e4) = e3 % 131.16/18.36 | | | | | | % 131.16/18.36 | | | | | | ALPHA: (69) implies: % 131.16/18.36 | | | | | | (70) all_9_12 = e3 % 131.16/18.36 | | | | | | (71) op(e1, e4) = e3 % 131.16/18.36 | | | | | | % 131.16/18.36 | | | | | | BETA: splitting (33) gives: % 131.16/18.36 | | | | | | % 131.16/18.36 | | | | | | Case 1: % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | | (72) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, % 131.16/18.36 | | | | | | | e4) = e4) % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | | REF_CLOSE: (1), (5), (18), (37), (72) are inconsistent by % 131.16/18.36 | | | | | | | sub-proof #280. % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | Case 2: % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | | (73) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, % 131.16/18.36 | | | | | | | e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | | BETA: splitting (73) gives: % 131.16/18.36 | | | | | | | % 131.16/18.36 | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | | (74) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | | REF_CLOSE: (23), (51), (74) are inconsistent by sub-proof #279. % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | | (75) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 131.16/18.36 | | | | | | | | op(e0, e4) = e4) % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | | BETA: splitting (75) gives: % 131.16/18.36 | | | | | | | | % 131.16/18.36 | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | (76) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | REF_CLOSE: (28), (70), (76) are inconsistent by sub-proof % 131.16/18.36 | | | | | | | | | #305. % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | (77) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | ALPHA: (77) implies: % 131.16/18.36 | | | | | | | | | (78) op(e0, e4) = e4 % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | BETA: splitting (31) gives: % 131.16/18.36 | | | | | | | | | % 131.16/18.36 | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | (79) ~ (op(e0, e4) = e4) % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | PRED_UNIFY: (78), (79) imply: % 131.16/18.36 | | | | | | | | | | (80) $false % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | CLOSE: (80) is inconsistent. % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | (81) all_6_20 = e4 % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | COMBINE_EQS: (11), (81) imply: % 131.16/18.36 | | | | | | | | | | (82) all_4_4 = e4 % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | SIMP: (82) implies: % 131.16/18.36 | | | | | | | | | | (83) all_4_4 = e4 % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | REDUCE: (4), (83) imply: % 131.16/18.36 | | | | | | | | | | (84) ~ (all_4_3 = e4) % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | BETA: splitting (35) gives: % 131.16/18.36 | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | (85) all_6_15 = e4 % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | REF_CLOSE: (39), (84), (85) are inconsistent by sub-proof % 131.16/18.36 | | | | | | | | | | | #278. % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | (86) all_6_15 = e3 | all_6_15 = e2 | all_6_15 = e1 | % 131.16/18.36 | | | | | | | | | | | all_6_15 = e0 % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | BETA: splitting (27) gives: % 131.16/18.36 | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | (87) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & % 131.16/18.36 | | | | | | | | | | | | op(e3, e4) = e2) % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | BETA: splitting (87) gives: % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | (88) all_9_0 = e2 & op(e4, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | ALPHA: (88) implies: % 131.16/18.36 | | | | | | | | | | | | | (89) op(e4, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | BETA: splitting (86) gives: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | (90) all_6_15 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | COMBINE_EQS: (39), (90) imply: % 131.16/18.36 | | | | | | | | | | | | | | (91) all_4_3 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | REDUCE: (26), (91) imply: % 131.16/18.36 | | | | | | | | | | | | | | (92) op(e1, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e2, e3, e4, e1, % 131.16/18.36 | | | | | | | | | | | | | | simplifying with (71), (92) gives: % 131.16/18.36 | | | | | | | | | | | | | | (93) e3 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e3, e1, e4, e2, % 131.16/18.36 | | | | | | | | | | | | | | simplifying with (32), (52) gives: % 131.16/18.36 | | | | | | | | | | | | | | (94) e3 = e1 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e0, e2, e4, e4, % 131.16/18.36 | | | | | | | | | | | | | | simplifying with (40), (89) gives: % 131.16/18.36 | | | | | | | | | | | | | | (95) e2 = e0 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | COMBINE_EQS: (93), (94) imply: % 131.16/18.36 | | | | | | | | | | | | | | (96) e2 = e1 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | REF_CLOSE: (19), (95), (96) are inconsistent by sub-proof % 131.16/18.36 | | | | | | | | | | | | | | #277. % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | (97) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | REF_CLOSE: (10), (24), (30), (39), (97) are inconsistent by % 131.16/18.36 | | | | | | | | | | | | | | sub-proof #276. % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | End of split % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | (98) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | REF_CLOSE: (15), (18), (98) are inconsistent by sub-proof % 131.16/18.36 | | | | | | | | | | | | | #275. % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | End of split % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | (99) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 % 131.16/18.36 | | | | | | | | | | | | & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 131.16/18.36 | | | | | | | | | | | | = e2) % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | BETA: splitting (99) gives: % 131.16/18.36 | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | (100) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (21), (100) are inconsistent by % 131.16/18.36 | | | | | | | | | | | | | sub-proof #311. % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | (101) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 131.16/18.36 | | | | | | | | | | | | | & op(e0, e4) = e2) % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | BETA: splitting (101) gives: % 131.16/18.36 | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | (102) all_9_12 = e2 & op(e1, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | ALPHA: (102) implies: % 131.16/18.36 | | | | | | | | | | | | | | (103) all_9_12 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | COMBINE_EQS: (70), (103) imply: % 131.16/18.36 | | | | | | | | | | | | | | (104) e3 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | SIMP: (104) implies: % 131.16/18.36 | | | | | | | | | | | | | | (105) e3 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | REDUCE: (21), (105) imply: % 131.16/18.36 | | | | | | | | | | | | | | (106) $false % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | (107) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | ALPHA: (107) implies: % 131.16/18.36 | | | | | | | | | | | | | | (108) all_9_20 = e2 % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | BETA: splitting (33) gives: % 131.16/18.36 | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | (109) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 131.16/18.36 | | | | | | | | | | | | | | | op(e3, e4) = e4) % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (18), (37), (109) are inconsistent by % 131.16/18.36 | | | | | | | | | | | | | | | sub-proof #280. % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 131.16/18.36 | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | (110) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | REF_CLOSE: (23), (51), (110) are inconsistent by sub-proof % 131.16/18.36 | | | | | | | | | | | | | | | | #274. % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 131.16/18.36 | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | Case 1: % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | (111) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | ALPHA: (111) implies: % 131.16/18.36 | | | | | | | | | | | | | | | | | (112) all_9_12 = e4 % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (112) imply: % 131.16/18.36 | | | | | | | | | | | | | | | | | (113) e4 = e3 % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | REDUCE: (28), (113) imply: % 131.16/18.36 | | | | | | | | | | | | | | | | | (114) $false % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | CLOSE: (114) is inconsistent. % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | Case 2: % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | % 131.16/18.36 | | | | | | | | | | | | | | | | | ALPHA: (77) implies: % 131.16/18.37 | | | | | | | | | | | | | | | | | (115) all_9_20 = e4 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (115) imply: % 131.16/18.37 | | | | | | | | | | | | | | | | | (116) e4 = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | SIMP: (116) implies: % 131.16/18.37 | | | | | | | | | | | | | | | | | (117) e4 = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | REDUCE: (6), (117) imply: % 131.16/18.37 | | | | | | | | | | | | | | | | | (118) $false % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | CLOSE: (118) is inconsistent. % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | End of split % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | End of split % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | End of split % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | Case 2: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | (119) all_9_20 = e3 & op(e0, e4) = e3 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | ALPHA: (119) implies: % 131.16/18.37 | | | | | | (120) all_9_20 = e3 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | BETA: splitting (27) gives: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | Case 1: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (121) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, % 131.16/18.37 | | | | | | | e4) = e2) % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | BETA: splitting (121) gives: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (122) all_9_0 = e2 & op(e4, e4) = e2 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | ALPHA: (122) implies: % 131.16/18.37 | | | | | | | | (123) all_9_0 = e2 % 131.16/18.37 | | | | | | | | (124) op(e4, e4) = e2 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | BETA: splitting (33) gives: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (125) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 131.16/18.37 | | | | | | | | | op(e3, e4) = e4) % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | BETA: splitting (125) gives: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (126) all_9_0 = e4 & op(e4, e4) = e4 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | ALPHA: (126) implies: % 131.16/18.37 | | | | | | | | | | (127) op(e4, e4) = e4 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | REF_CLOSE: (1), (5), (37), (127) are inconsistent by % 131.16/18.37 | | | | | | | | | | sub-proof #317. % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (128) all_9_2 = e4 & op(e3, e4) = e4 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | ALPHA: (128) implies: % 131.16/18.37 | | | | | | | | | | (129) all_9_2 = e4 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | COMBINE_EQS: (18), (129) imply: % 131.16/18.37 | | | | | | | | | | (130) e4 = e0 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | REDUCE: (1), (130) imply: % 131.16/18.37 | | | | | | | | | | (131) $false % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | CLOSE: (131) is inconsistent. % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (132) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 131.16/18.37 | | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 131.16/18.37 | | | | | | | | | e4) % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | BETA: splitting (132) gives: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (133) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | REF_CLOSE: (23), (51), (133) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | #279. % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (134) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 131.16/18.37 | | | | | | | | | | & op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | BETA: splitting (134) gives: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (135) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | ALPHA: (135) implies: % 131.16/18.37 | | | | | | | | | | | (136) op(e1, e4) = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | BETA: splitting (13) gives: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | (137) ~ (op(e1, e4) = e4) % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | PRED_UNIFY: (136), (137) imply: % 131.16/18.37 | | | | | | | | | | | | (138) $false % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | (139) all_4_3 = e4 % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | REDUCE: (4), (139) imply: % 131.16/18.37 | | | | | | | | | | | | (140) ~ (all_4_4 = e4) % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | SIMP: (140) implies: % 131.16/18.37 | | | | | | | | | | | | (141) ~ (all_4_4 = e4) % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | BETA: splitting (14) gives: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | (142) all_6_20 = e4 % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | REF_CLOSE: (11), (141), (142) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | #309. % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | (143) ~ (all_6_20 = e4) % 131.16/18.37 | | | | | | | | | | | | | (144) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | % 131.16/18.37 | | | | | | | | | | | | | all_6_20 = e0 % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | BETA: splitting (144) gives: % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | (145) all_6_20 = e2 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | COMBINE_EQS: (11), (145) imply: % 131.16/18.37 | | | | | | | | | | | | | | (146) all_4_4 = e2 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | SIMP: (146) implies: % 131.16/18.37 | | | | | | | | | | | | | | (147) all_4_4 = e2 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | REDUCE: (141), (147) imply: % 131.16/18.37 | | | | | | | | | | | | | | (148) ~ (e4 = e2) % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | REDUCE: (17), (147) imply: % 131.16/18.37 | | | | | | | | | | | | | | (149) ~ (e3 = e2) % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e0, e2, e4, e4, % 131.16/18.37 | | | | | | | | | | | | | | simplifying with (40), (124) gives: % 131.16/18.37 | | | | | | | | | | | | | | (150) e2 = e0 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | COMBINE_EQS: (123), (150) imply: % 131.16/18.37 | | | | | | | | | | | | | | (151) all_9_0 = e0 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | BETA: splitting (27) gives: % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (122), (151) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | | | | #314. % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | (152) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (152) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | | | | #275. % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | (153) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 % 131.16/18.37 | | | | | | | | | | | | | | | & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) % 131.16/18.37 | | | | | | | | | | | | | | | = e2) % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | BETA: splitting (153) gives: % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | (154) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (21), (154) are inconsistent by % 131.16/18.37 | | | | | | | | | | | | | | | | sub-proof #311. % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | (155) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | & op(e0, e4) = e2) % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | (156) all_9_12 = e2 & op(e1, e4) = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 131.16/18.37 | | | | | | | | | | | | | | | | | (157) all_9_12 = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (18), (23), (28), (33), (37), (51), % 131.16/18.37 | | | | | | | | | | | | | | | | | (120), (157) are inconsistent by sub-proof #271. % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | (158) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (120), (158) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | | | | | #270. % 131.16/18.37 | | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | (159) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | | REF_CLOSE: (11), (17), (29), (36), (159) are inconsistent by % 131.16/18.37 | | | | | | | | | | | | | | sub-proof #269. % 131.16/18.37 | | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (160) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | REF_CLOSE: (28), (120), (160) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | #272. % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | End of split % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (161) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | REF_CLOSE: (15), (18), (161) are inconsistent by sub-proof #275. % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | End of split % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | Case 2: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (162) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & % 131.16/18.37 | | | | | | | op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | BETA: splitting (162) gives: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (163) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | REF_CLOSE: (2), (3), (21), (163) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | #311. % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (164) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & % 131.16/18.37 | | | | | | | | op(e0, e4) = e2) % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | BETA: splitting (164) gives: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (165) all_9_12 = e2 & op(e1, e4) = e2 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | ALPHA: (165) implies: % 131.16/18.37 | | | | | | | | | (166) all_9_12 = e2 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | REF_CLOSE: (1), (5), (6), (18), (23), (28), (33), (37), (51), % 131.16/18.37 | | | | | | | | | (120), (166) are inconsistent by sub-proof #271. % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (167) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | REF_CLOSE: (21), (120), (167) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | #270. % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | End of split % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | End of split % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | End of split % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | End of split % 131.16/18.37 | | | | | % 131.16/18.37 | | | | End of split % 131.16/18.37 | | | | % 131.16/18.37 | | | End of split % 131.16/18.37 | | | % 131.16/18.37 | | Case 2: % 131.16/18.37 | | | % 131.16/18.37 | | | (168) (all_9_12 = e1 & op(e1, e4) = e1) | (all_9_20 = e1 & op(e0, e4) = % 131.16/18.37 | | | e1) % 131.16/18.37 | | | % 131.16/18.37 | | | BETA: splitting (168) gives: % 131.16/18.37 | | | % 131.16/18.37 | | | Case 1: % 131.16/18.37 | | | | % 131.16/18.37 | | | | (169) all_9_12 = e1 & op(e1, e4) = e1 % 131.16/18.37 | | | | % 131.16/18.37 | | | | ALPHA: (169) implies: % 131.16/18.37 | | | | (170) op(e1, e4) = e1 % 131.16/18.37 | | | | % 131.16/18.37 | | | | REF_CLOSE: (9), (30), (170) are inconsistent by sub-proof #268. % 131.16/18.37 | | | | % 131.16/18.37 | | | Case 2: % 131.16/18.37 | | | | % 131.16/18.37 | | | | (171) all_9_20 = e1 & op(e0, e4) = e1 % 131.16/18.37 | | | | % 131.16/18.37 | | | | ALPHA: (171) implies: % 131.16/18.37 | | | | (172) all_9_20 = e1 % 131.16/18.37 | | | | (173) op(e0, e4) = e1 % 131.16/18.37 | | | | % 131.16/18.37 | | | | BETA: splitting (27) gives: % 131.16/18.37 | | | | % 131.16/18.37 | | | | Case 1: % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | (174) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) % 131.16/18.37 | | | | | = e2) % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | BETA: splitting (174) gives: % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | Case 1: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | (175) all_9_0 = e2 & op(e4, e4) = e2 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | ALPHA: (175) implies: % 131.16/18.37 | | | | | | (176) all_9_0 = e2 % 131.16/18.37 | | | | | | (177) op(e4, e4) = e2 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | BETA: splitting (33) gives: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | Case 1: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (178) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, % 131.16/18.37 | | | | | | | e4) = e4) % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | REF_CLOSE: (1), (5), (18), (37), (178) are inconsistent by % 131.16/18.37 | | | | | | | sub-proof #280. % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | Case 2: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (179) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 131.16/18.37 | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | BETA: splitting (179) gives: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (180) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | ALPHA: (180) implies: % 131.16/18.37 | | | | | | | | (181) all_9_6 = e4 % 131.16/18.37 | | | | | | | | (182) op(e2, e4) = e4 % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | BETA: splitting (7) gives: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (183) ~ (op(e2, e4) = e4) % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | PRED_UNIFY: (182), (183) imply: % 131.16/18.37 | | | | | | | | | (184) $false % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | CLOSE: (184) is inconsistent. % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (185) e4 = e3 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | COMBINE_EQS: (181), (185) imply: % 131.16/18.37 | | | | | | | | | (186) all_9_6 = e3 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | BETA: splitting (33) gives: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (187) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 131.16/18.37 | | | | | | | | | | op(e3, e4) = e4) % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | BETA: splitting (187) gives: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (188) all_9_0 = e4 & op(e4, e4) = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | ALPHA: (188) implies: % 131.16/18.37 | | | | | | | | | | | (189) all_9_0 = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | COMBINE_EQS: (176), (189) imply: % 131.16/18.37 | | | | | | | | | | | (190) e4 = e2 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | SIMP: (190) implies: % 131.16/18.37 | | | | | | | | | | | (191) e4 = e2 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | REDUCE: (6), (191) imply: % 131.16/18.37 | | | | | | | | | | | (192) $false % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | CLOSE: (192) is inconsistent. % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (193) all_9_2 = e4 & op(e3, e4) = e4 % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | REF_CLOSE: (1), (18), (193) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | #281. % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | BETA: splitting (179) gives: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | REDUCE: (28), (185) imply: % 131.16/18.37 | | | | | | | | | | | (194) $false % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | CLOSE: (194) is inconsistent. % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (195) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 131.16/18.37 | | | | | | | | | | | & op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | BETA: splitting (195) gives: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | (196) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | ALPHA: (196) implies: % 131.16/18.37 | | | | | | | | | | | | (197) op(e1, e4) = e4 % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | REF_CLOSE: (4), (8), (11), (14), (16), (17), (19), (22), % 131.16/18.37 | | | | | | | | | | | | (29), (36), (39), (40), (173), (177), (197) are % 131.16/18.37 | | | | | | | | | | | | inconsistent by sub-proof #267. % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | (198) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | REF_CLOSE: (23), (172), (198) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | #288. % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | End of split % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (199) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 131.16/18.37 | | | | | | | | op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | REF_CLOSE: (4), (8), (11), (14), (16), (17), (19), (22), (23), % 131.16/18.37 | | | | | | | | (29), (36), (39), (40), (172), (173), (177), (199) % 131.16/18.37 | | | | | | | | are inconsistent by sub-proof #266. % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | End of split % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | End of split % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | Case 2: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | (200) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | REF_CLOSE: (15), (18), (200) are inconsistent by sub-proof #275. % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | End of split % 131.16/18.37 | | | | | % 131.16/18.37 | | | | Case 2: % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | (201) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, % 131.16/18.37 | | | | | e4) = e2) | (all_9_20 = e2 & op(e0, e4) = e2) % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | BETA: splitting (201) gives: % 131.16/18.37 | | | | | % 131.16/18.37 | | | | | Case 1: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | (202) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | REF_CLOSE: (2), (3), (21), (202) are inconsistent by sub-proof #311. % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | Case 2: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | (203) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, % 131.16/18.37 | | | | | | e4) = e2) % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | BETA: splitting (203) gives: % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | | Case 1: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (204) all_9_12 = e2 & op(e1, e4) = e2 % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | ALPHA: (204) implies: % 131.16/18.37 | | | | | | | (205) all_9_12 = e2 % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | BETA: splitting (33) gives: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (206) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 131.16/18.37 | | | | | | | | op(e3, e4) = e4) % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | REF_CLOSE: (1), (5), (18), (37), (206) are inconsistent by % 131.16/18.37 | | | | | | | | sub-proof #280. % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | (207) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & % 131.16/18.37 | | | | | | | | op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | BETA: splitting (207) gives: % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (208) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | ALPHA: (208) implies: % 131.16/18.37 | | | | | | | | | (209) all_9_6 = e4 % 131.16/18.37 | | | | | | | | | (210) op(e2, e4) = e4 % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | BETA: splitting (7) gives: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (211) ~ (op(e2, e4) = e4) % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | PRED_UNIFY: (210), (211) imply: % 131.16/18.37 | | | | | | | | | | (212) $false % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | CLOSE: (212) is inconsistent. % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | (213) e4 = e3 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | COMBINE_EQS: (209), (213) imply: % 131.16/18.37 | | | | | | | | | | (214) all_9_6 = e3 % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | BETA: splitting (33) gives: % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | (215) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & % 131.16/18.37 | | | | | | | | | | | op(e3, e4) = e4) % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | REF_CLOSE: (1), (5), (18), (37), (215) are inconsistent by % 131.16/18.37 | | | | | | | | | | | sub-proof #280. % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | BETA: splitting (207) gives: % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | COMBINE_EQS: (209), (214) imply: % 131.16/18.37 | | | | | | | | | | | | (216) e4 = e3 % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | REDUCE: (28), (213) imply: % 131.16/18.37 | | | | | | | | | | | | (217) $false % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | (218) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 % 131.16/18.37 | | | | | | | | | | | | & op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | BETA: splitting (218) gives: % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | Case 1: % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | (219) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | REF_CLOSE: (6), (205), (219) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | #273. % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | (220) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | | REF_CLOSE: (23), (172), (220) are inconsistent by sub-proof % 131.16/18.37 | | | | | | | | | | | | | #288. % 131.16/18.37 | | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | | % 131.16/18.37 | | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | | % 131.16/18.37 | | | | | | | | | End of split % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | Case 2: % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | (221) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & % 131.16/18.37 | | | | | | | | | op(e0, e4) = e4) % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | | REF_CLOSE: (6), (23), (172), (205), (221) are inconsistent by % 131.16/18.37 | | | | | | | | | sub-proof #287. % 131.16/18.37 | | | | | | | | | % 131.16/18.37 | | | | | | | | End of split % 131.16/18.37 | | | | | | | | % 131.16/18.37 | | | | | | | End of split % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | Case 2: % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | (222) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | | REF_CLOSE: (38), (172), (222) are inconsistent by sub-proof #285. % 131.16/18.37 | | | | | | | % 131.16/18.37 | | | | | | End of split % 131.16/18.37 | | | | | | % 131.16/18.37 | | | | | End of split % 131.16/18.37 | | | | | % 131.16/18.37 | | | | End of split % 131.16/18.37 | | | | % 131.16/18.37 | | | End of split % 131.16/18.37 | | | % 131.16/18.37 | | End of split % 131.16/18.37 | | % 131.16/18.37 | End of split % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #266 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) ~ (all_4_3 = all_4_4) % 131.16/18.37 (2) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.16/18.37 (3) all_6_20 = all_4_4 % 131.16/18.37 (4) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.16/18.37 = e0 % 131.16/18.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.37 (6) all_9_20 = e1 % 131.16/18.37 (7) ~ (all_4_4 = e3) % 131.16/18.37 (8) ~ (e1 = e0) % 131.16/18.37 (9) op(e0, e4) = all_4_4 % 131.16/18.37 (10) ~ (e4 = e1) % 131.16/18.37 (11) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.37 (12) op(e0, e4) = e1 % 131.16/18.37 (13) ~ (all_4_4 = e0) % 131.16/18.37 (14) ~ (all_4_4 = e1) % 131.16/18.37 (15) all_6_15 = all_4_3 % 131.16/18.37 (16) op(e4, e4) = e0 % 131.16/18.37 (17) op(e4, e4) = e2 % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | BETA: splitting (11) gives: % 131.16/18.37 | % 131.16/18.37 | Case 1: % 131.16/18.37 | | % 131.16/18.37 | | (18) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.37 | | % 131.16/18.37 | | ALPHA: (18) implies: % 131.16/18.37 | | (19) op(e1, e4) = e4 % 131.16/18.37 | | % 131.16/18.37 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (12), (13), (14), (15), % 131.16/18.37 | | (16), (17), (19) are inconsistent by sub-proof #267. % 131.16/18.37 | | % 131.16/18.37 | Case 2: % 131.16/18.37 | | % 131.16/18.37 | | (20) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.37 | | % 131.16/18.37 | | REF_CLOSE: (6), (10), (20) are inconsistent by sub-proof #288. % 131.16/18.37 | | % 131.16/18.37 | End of split % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #267 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) ~ (all_4_3 = all_4_4) % 131.16/18.37 (2) all_6_15 = e4 | ~ (op(e1, e4) = e4) % 131.16/18.37 (3) all_6_20 = all_4_4 % 131.16/18.37 (4) op(e1, e4) = e4 % 131.16/18.37 (5) all_6_20 = e4 | all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 % 131.16/18.37 = e0 % 131.16/18.37 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.37 (7) ~ (all_4_4 = e3) % 131.16/18.37 (8) ~ (e1 = e0) % 131.16/18.37 (9) op(e0, e4) = all_4_4 % 131.16/18.37 (10) op(e0, e4) = e1 % 131.16/18.37 (11) ~ (all_4_4 = e0) % 131.16/18.37 (12) ~ (all_4_4 = e1) % 131.16/18.37 (13) all_6_15 = all_4_3 % 131.16/18.37 (14) op(e4, e4) = e0 % 131.16/18.37 (15) op(e4, e4) = e2 % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | BETA: splitting (2) gives: % 131.16/18.37 | % 131.16/18.37 | Case 1: % 131.16/18.37 | | % 131.16/18.37 | | (16) ~ (op(e1, e4) = e4) % 131.16/18.37 | | % 131.16/18.37 | | PRED_UNIFY: (4), (16) imply: % 131.16/18.37 | | (17) $false % 131.16/18.37 | | % 131.16/18.37 | | CLOSE: (17) is inconsistent. % 131.16/18.37 | | % 131.16/18.37 | Case 2: % 131.16/18.37 | | % 131.16/18.37 | | (18) all_6_15 = e4 % 131.16/18.37 | | % 131.16/18.37 | | COMBINE_EQS: (13), (18) imply: % 131.16/18.37 | | (19) all_4_3 = e4 % 131.16/18.37 | | % 131.16/18.37 | | SIMP: (19) implies: % 131.16/18.37 | | (20) all_4_3 = e4 % 131.16/18.37 | | % 131.16/18.37 | | REDUCE: (1), (20) imply: % 131.16/18.37 | | (21) ~ (all_4_4 = e4) % 131.16/18.37 | | % 131.16/18.37 | | SIMP: (21) implies: % 131.16/18.37 | | (22) ~ (all_4_4 = e4) % 131.16/18.37 | | % 131.16/18.37 | | BETA: splitting (5) gives: % 131.16/18.37 | | % 131.16/18.37 | | Case 1: % 131.16/18.37 | | | % 131.16/18.37 | | | (23) all_6_20 = e4 % 131.16/18.37 | | | % 131.16/18.37 | | | REF_CLOSE: (3), (22), (23) are inconsistent by sub-proof #309. % 131.16/18.37 | | | % 131.16/18.37 | | Case 2: % 131.16/18.37 | | | % 131.16/18.37 | | | (24) all_6_20 = e3 | all_6_20 = e2 | all_6_20 = e1 | all_6_20 = e0 % 131.16/18.37 | | | % 131.16/18.37 | | | BETA: splitting (24) gives: % 131.16/18.37 | | | % 131.16/18.37 | | | Case 1: % 131.16/18.37 | | | | % 131.16/18.37 | | | | (25) all_6_20 = e2 % 131.16/18.37 | | | | % 131.16/18.37 | | | | COMBINE_EQS: (3), (25) imply: % 131.16/18.37 | | | | (26) all_4_4 = e2 % 131.16/18.37 | | | | % 131.16/18.37 | | | | SIMP: (26) implies: % 131.16/18.37 | | | | (27) all_4_4 = e2 % 131.16/18.37 | | | | % 131.16/18.37 | | | | REDUCE: (9), (27) imply: % 131.16/18.37 | | | | (28) op(e0, e4) = e2 % 131.16/18.37 | | | | % 131.16/18.37 | | | | GROUND_INST: instantiating (6) with e1, e2, e4, e0, simplifying with % 131.16/18.37 | | | | (10), (28) gives: % 131.16/18.37 | | | | (29) e2 = e1 % 131.16/18.37 | | | | % 131.16/18.37 | | | | GROUND_INST: instantiating (6) with e0, e2, e4, e4, simplifying with % 131.16/18.37 | | | | (14), (15) gives: % 131.16/18.37 | | | | (30) e2 = e0 % 131.16/18.37 | | | | % 131.16/18.37 | | | | REF_CLOSE: (8), (29), (30) are inconsistent by sub-proof #277. % 131.16/18.37 | | | | % 131.16/18.37 | | | Case 2: % 131.16/18.37 | | | | % 131.16/18.37 | | | | (31) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 131.16/18.37 | | | | % 131.16/18.37 | | | | REF_CLOSE: (3), (7), (11), (12), (31) are inconsistent by sub-proof % 131.16/18.37 | | | | #269. % 131.16/18.37 | | | | % 131.16/18.37 | | | End of split % 131.16/18.37 | | | % 131.16/18.37 | | End of split % 131.16/18.37 | | % 131.16/18.37 | End of split % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #268 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) all_4_3 = e1 | ~ (op(e1, e4) = e1) % 131.16/18.37 (2) op(e1, e4) = e1 % 131.16/18.37 (3) ~ (all_4_3 = e1) % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | BETA: splitting (1) gives: % 131.16/18.37 | % 131.16/18.37 | Case 1: % 131.16/18.37 | | % 131.16/18.37 | | (4) ~ (op(e1, e4) = e1) % 131.16/18.37 | | % 131.16/18.37 | | PRED_UNIFY: (2), (4) imply: % 131.16/18.37 | | (5) $false % 131.16/18.37 | | % 131.16/18.37 | | CLOSE: (5) is inconsistent. % 131.16/18.37 | | % 131.16/18.37 | Case 2: % 131.16/18.37 | | % 131.16/18.37 | | (6) all_4_3 = e1 % 131.16/18.37 | | % 131.16/18.37 | | REDUCE: (3), (6) imply: % 131.16/18.37 | | (7) $false % 131.16/18.37 | | % 131.16/18.37 | | CLOSE: (7) is inconsistent. % 131.16/18.37 | | % 131.16/18.37 | End of split % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #269 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) all_6_20 = all_4_4 % 131.16/18.37 (2) ~ (all_4_4 = e3) % 131.16/18.37 (3) all_6_20 = e3 | all_6_20 = e1 | all_6_20 = e0 % 131.16/18.37 (4) ~ (all_4_4 = e0) % 131.16/18.37 (5) ~ (all_4_4 = e1) % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | BETA: splitting (3) gives: % 131.16/18.37 | % 131.16/18.37 | Case 1: % 131.16/18.37 | | % 131.16/18.37 | | (6) all_6_20 = e3 % 131.16/18.37 | | % 131.16/18.37 | | COMBINE_EQS: (1), (6) imply: % 131.16/18.37 | | (7) all_4_4 = e3 % 131.16/18.37 | | % 131.16/18.37 | | SIMP: (7) implies: % 131.16/18.37 | | (8) all_4_4 = e3 % 131.16/18.37 | | % 131.16/18.37 | | REDUCE: (2), (8) imply: % 131.16/18.37 | | (9) $false % 131.16/18.37 | | % 131.16/18.37 | | CLOSE: (9) is inconsistent. % 131.16/18.37 | | % 131.16/18.37 | Case 2: % 131.16/18.37 | | % 131.16/18.37 | | (10) all_6_20 = e1 | all_6_20 = e0 % 131.16/18.37 | | % 131.16/18.37 | | BETA: splitting (10) gives: % 131.16/18.37 | | % 131.16/18.37 | | Case 1: % 131.16/18.37 | | | % 131.16/18.37 | | | (11) all_6_20 = e1 % 131.16/18.37 | | | % 131.16/18.37 | | | COMBINE_EQS: (1), (11) imply: % 131.16/18.37 | | | (12) all_4_4 = e1 % 131.16/18.37 | | | % 131.16/18.37 | | | SIMP: (12) implies: % 131.16/18.37 | | | (13) all_4_4 = e1 % 131.16/18.37 | | | % 131.16/18.37 | | | REDUCE: (5), (13) imply: % 131.16/18.37 | | | (14) $false % 131.16/18.37 | | | % 131.16/18.37 | | | CLOSE: (14) is inconsistent. % 131.16/18.37 | | | % 131.16/18.37 | | Case 2: % 131.16/18.37 | | | % 131.16/18.37 | | | (15) all_6_20 = e0 % 131.16/18.37 | | | % 131.16/18.37 | | | COMBINE_EQS: (1), (15) imply: % 131.16/18.37 | | | (16) all_4_4 = e0 % 131.16/18.37 | | | % 131.16/18.37 | | | SIMP: (16) implies: % 131.16/18.37 | | | (17) all_4_4 = e0 % 131.16/18.37 | | | % 131.16/18.37 | | | REDUCE: (4), (17) imply: % 131.16/18.37 | | | (18) $false % 131.16/18.37 | | | % 131.16/18.37 | | | CLOSE: (18) is inconsistent. % 131.16/18.37 | | | % 131.16/18.37 | | End of split % 131.16/18.37 | | % 131.16/18.37 | End of split % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #270 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.37 (2) all_9_20 = e3 % 131.16/18.37 (3) ~ (e3 = e2) % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | ALPHA: (1) implies: % 131.16/18.37 | (4) all_9_20 = e2 % 131.16/18.37 | % 131.16/18.37 | COMBINE_EQS: (2), (4) imply: % 131.16/18.37 | (5) e3 = e2 % 131.16/18.37 | % 131.16/18.37 | REDUCE: (3), (5) imply: % 131.16/18.37 | (6) $false % 131.16/18.37 | % 131.16/18.37 | CLOSE: (6) is inconsistent. % 131.16/18.37 | % 131.16/18.37 End of proof % 131.16/18.37 % 131.16/18.37 Sub-proof #271 shows that the following formulas are inconsistent: % 131.16/18.37 ---------------------------------------------------------------- % 131.16/18.37 (1) ~ (e4 = e0) % 131.16/18.37 (2) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.37 (3) ~ (e4 = e2) % 131.16/18.37 (4) all_9_6 = e1 % 131.16/18.37 (5) all_9_2 = e0 % 131.16/18.37 (6) all_9_12 = e2 % 131.16/18.37 (7) ~ (e4 = e1) % 131.16/18.37 (8) ~ (e4 = e3) % 131.16/18.37 (9) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.37 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.37 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.37 (10) all_9_20 = e3 % 131.16/18.37 (11) all_4_0 = e0 % 131.16/18.37 % 131.16/18.37 Begin of proof % 131.16/18.37 | % 131.16/18.37 | BETA: splitting (9) gives: % 131.16/18.37 | % 131.16/18.37 | Case 1: % 131.16/18.37 | | % 131.16/18.37 | | (12) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 131.16/18.37 | | % 131.16/18.37 | | REF_CLOSE: (1), (2), (5), (11), (12) are inconsistent by sub-proof #280. % 131.16/18.37 | | % 131.16/18.37 | Case 2: % 131.16/18.37 | | % 131.16/18.37 | | (13) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 131.16/18.37 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.37 | | % 131.16/18.37 | | BETA: splitting (13) gives: % 131.16/18.37 | | % 131.16/18.37 | | Case 1: % 131.16/18.37 | | | % 131.16/18.37 | | | (14) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.37 | | | % 131.16/18.37 | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #274. % 131.16/18.37 | | | % 131.16/18.37 | | Case 2: % 131.16/18.37 | | | % 131.16/18.37 | | | (15) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 131.16/18.37 | | | e4) % 131.16/18.37 | | | % 131.16/18.37 | | | BETA: splitting (15) gives: % 131.16/18.37 | | | % 131.16/18.37 | | | Case 1: % 131.16/18.37 | | | | % 131.16/18.37 | | | | (16) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.37 | | | | % 131.16/18.37 | | | | REF_CLOSE: (3), (6), (16) are inconsistent by sub-proof #273. % 131.16/18.37 | | | | % 131.16/18.37 | | | Case 2: % 131.16/18.37 | | | | % 131.16/18.38 | | | | (17) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.38 | | | | % 131.16/18.38 | | | | REF_CLOSE: (8), (10), (17) are inconsistent by sub-proof #272. % 131.16/18.38 | | | | % 131.16/18.38 | | | End of split % 131.16/18.38 | | | % 131.16/18.38 | | End of split % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #272 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.38 (2) all_9_20 = e3 % 131.16/18.38 (3) ~ (e4 = e3) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_20 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e3 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e4 = e3 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #273 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.38 (2) all_9_12 = e2 % 131.16/18.38 (3) ~ (e4 = e2) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_12 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e2 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #274 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.38 (2) all_9_6 = e1 % 131.16/18.38 (3) ~ (e4 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_6 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e1 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e4 = e1 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #275 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.38 (2) all_9_2 = e0 % 131.16/18.38 (3) ~ (e2 = e0) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_2 = e2 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e2 = e0 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e2 = e0 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #276 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) ~ (all_4_3 = e3) % 131.16/18.38 (2) all_6_15 = e3 | all_6_15 = e1 | all_6_15 = e0 % 131.16/18.38 (3) ~ (all_4_3 = e0) % 131.16/18.38 (4) ~ (all_4_3 = e1) % 131.16/18.38 (5) all_6_15 = all_4_3 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (2) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_6_15 = e3 % 131.16/18.38 | | % 131.16/18.38 | | COMBINE_EQS: (5), (6) imply: % 131.16/18.38 | | (7) all_4_3 = e3 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (1), (7) imply: % 131.16/18.38 | | (8) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (8) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (9) all_6_15 = e1 | all_6_15 = e0 % 131.16/18.38 | | % 131.16/18.38 | | BETA: splitting (9) gives: % 131.16/18.38 | | % 131.16/18.38 | | Case 1: % 131.16/18.38 | | | % 131.16/18.38 | | | (10) all_6_15 = e1 % 131.16/18.38 | | | % 131.16/18.38 | | | COMBINE_EQS: (5), (10) imply: % 131.16/18.38 | | | (11) all_4_3 = e1 % 131.16/18.38 | | | % 131.16/18.38 | | | SIMP: (11) implies: % 131.16/18.38 | | | (12) all_4_3 = e1 % 131.16/18.38 | | | % 131.16/18.38 | | | REDUCE: (4), (12) imply: % 131.16/18.38 | | | (13) $false % 131.16/18.38 | | | % 131.16/18.38 | | | CLOSE: (13) is inconsistent. % 131.16/18.38 | | | % 131.16/18.38 | | Case 2: % 131.16/18.38 | | | % 131.16/18.38 | | | (14) all_6_15 = e0 % 131.16/18.38 | | | % 131.16/18.38 | | | COMBINE_EQS: (5), (14) imply: % 131.16/18.38 | | | (15) all_4_3 = e0 % 131.16/18.38 | | | % 131.16/18.38 | | | SIMP: (15) implies: % 131.16/18.38 | | | (16) all_4_3 = e0 % 131.16/18.38 | | | % 131.16/18.38 | | | REDUCE: (3), (16) imply: % 131.16/18.38 | | | (17) $false % 131.16/18.38 | | | % 131.16/18.38 | | | CLOSE: (17) is inconsistent. % 131.16/18.38 | | | % 131.16/18.38 | | End of split % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #277 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) e2 = e1 % 131.16/18.38 (2) e2 = e0 % 131.16/18.38 (3) ~ (e1 = e0) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (1), (2) imply: % 131.16/18.38 | (4) e1 = e0 % 131.16/18.38 | % 131.16/18.38 | SIMP: (4) implies: % 131.16/18.38 | (5) e1 = e0 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #278 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_15 = all_4_3 % 131.16/18.38 (2) all_6_15 = e4 % 131.16/18.38 (3) ~ (all_4_3 = e4) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (1), (2) imply: % 131.16/18.38 | (4) all_4_3 = e4 % 131.16/18.38 | % 131.16/18.38 | SIMP: (4) implies: % 131.16/18.38 | (5) all_4_3 = e4 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #279 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.38 (2) all_9_6 = e1 % 131.16/18.38 (3) ~ (e4 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_6 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e1 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #280 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) ~ (e4 = e0) % 131.16/18.38 (2) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (3) all_9_2 = e0 % 131.16/18.38 (4) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 131.16/18.38 (5) all_4_0 = e0 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (4) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_9_0 = e4 & op(e4, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | ALPHA: (6) implies: % 131.16/18.38 | | (7) op(e4, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #317. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (8) all_9_2 = e4 & op(e3, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #281. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #281 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_2 = e4 & op(e3, e4) = e4 % 131.16/18.38 (2) all_9_2 = e0 % 131.16/18.38 (3) ~ (e4 = e0) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_2 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e0 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e4 = e0 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #282 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_6 = e3 % 131.16/18.38 (2) all_9_6 = e1 % 131.16/18.38 (3) ~ (e3 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (1), (2) imply: % 131.16/18.38 | (4) e3 = e1 % 131.16/18.38 | % 131.16/18.38 | SIMP: (4) implies: % 131.16/18.38 | (5) e3 = e1 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #283 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_5 = e1 % 131.16/18.38 (2) ~ (e4 = e0) % 131.16/18.38 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.16/18.38 (4) all_6_10 = e3 % 131.16/18.38 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (7) ~ (e4 = e2) % 131.16/18.38 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (9) ~ (e2 = e0) % 131.16/18.38 (10) all_9_0 = e0 % 131.16/18.38 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.38 (12) all_9_20 = e1 % 131.16/18.38 (13) ~ (e3 = e2) % 131.16/18.38 (14) ~ (e4 = e1) % 131.16/18.38 (15) op(e3, e4) = e1 % 131.16/18.38 (16) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) | % 131.16/18.38 (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.16/18.38 (all_9_20 = e2 & op(e0, e4) = e2) % 131.16/18.38 (17) ~ (e4 = e3) % 131.16/18.38 (18) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.38 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.38 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 (19) all_4_0 = e0 % 131.16/18.38 (20) ~ (e2 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (16) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (21) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (9), (10), (11), (15), (20), (21) are inconsistent by sub-proof % 131.16/18.38 | | #312. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (22) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) % 131.16/18.38 | | | (all_9_20 = e2 & op(e0, e4) = e2) % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (13), (14), (17), % 131.16/18.38 | | (18), (19), (20), (22) are inconsistent by sub-proof #284. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #284 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_5 = e1 % 131.16/18.38 (2) ~ (e4 = e0) % 131.16/18.38 (3) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.16/18.38 (4) all_6_10 = e3 % 131.16/18.38 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (7) ~ (e4 = e2) % 131.16/18.38 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (9) all_9_20 = e1 % 131.16/18.38 (10) ~ (e3 = e2) % 131.16/18.38 (11) ~ (e4 = e1) % 131.16/18.38 (12) ~ (e4 = e3) % 131.16/18.38 (13) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_12 = e2 & op(e1, e4) = e2) | % 131.16/18.38 (all_9_20 = e2 & op(e0, e4) = e2) % 131.16/18.38 (14) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.38 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.38 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 (15) all_4_0 = e0 % 131.16/18.38 (16) ~ (e2 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (13) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (17) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (3), (4), (10), (17) are inconsistent by sub-proof #311. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (18) (all_9_12 = e2 & op(e1, e4) = e2) | (all_9_20 = e2 & op(e0, e4) = % 131.16/18.38 | | e2) % 131.16/18.38 | | % 131.16/18.38 | | BETA: splitting (18) gives: % 131.16/18.38 | | % 131.16/18.38 | | Case 1: % 131.16/18.38 | | | % 131.16/18.38 | | | (19) all_9_12 = e2 & op(e1, e4) = e2 % 131.16/18.38 | | | % 131.16/18.38 | | | ALPHA: (19) implies: % 131.16/18.38 | | | (20) all_9_12 = e2 % 131.16/18.38 | | | % 131.16/18.38 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (14), (15), (20) % 131.16/18.38 | | | are inconsistent by sub-proof #286. % 131.16/18.38 | | | % 131.16/18.38 | | Case 2: % 131.16/18.38 | | | % 131.16/18.38 | | | (21) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.38 | | | % 131.16/18.38 | | | REF_CLOSE: (9), (16), (21) are inconsistent by sub-proof #285. % 131.16/18.38 | | | % 131.16/18.38 | | End of split % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #285 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_20 = e2 & op(e0, e4) = e2 % 131.16/18.38 (2) all_9_20 = e1 % 131.16/18.38 (3) ~ (e2 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_20 = e2 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e2 = e1 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #286 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_5 = e1 % 131.16/18.38 (2) ~ (e4 = e0) % 131.16/18.38 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (5) ~ (e4 = e2) % 131.16/18.38 (6) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (7) all_9_20 = e1 % 131.16/18.38 (8) all_9_12 = e2 % 131.16/18.38 (9) ~ (e4 = e1) % 131.16/18.38 (10) ~ (e4 = e3) % 131.16/18.38 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.38 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.38 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 (12) all_4_0 = e0 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (11) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (2), (3), (4), (9), (12), (13) are inconsistent by sub-proof % 131.16/18.38 | | #315. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (14) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 131.16/18.38 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 | | % 131.16/18.38 | | BETA: splitting (14) gives: % 131.16/18.38 | | % 131.16/18.38 | | Case 1: % 131.16/18.38 | | | % 131.16/18.38 | | | (15) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.38 | | | % 131.16/18.38 | | | ALPHA: (15) implies: % 131.16/18.38 | | | (16) op(e2, e4) = e4 % 131.16/18.38 | | | % 131.16/18.38 | | | REF_CLOSE: (6), (10), (16) are inconsistent by sub-proof #320. % 131.16/18.38 | | | % 131.16/18.38 | | Case 2: % 131.16/18.38 | | | % 131.16/18.38 | | | (17) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 131.16/18.38 | | | e4) % 131.16/18.38 | | | % 131.16/18.38 | | | REF_CLOSE: (5), (7), (8), (9), (17) are inconsistent by sub-proof #287. % 131.16/18.38 | | | % 131.16/18.38 | | End of split % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #287 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) ~ (e4 = e2) % 131.16/18.38 (2) all_9_20 = e1 % 131.16/18.38 (3) all_9_12 = e2 % 131.16/18.38 (4) ~ (e4 = e1) % 131.16/18.38 (5) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (5) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | ALPHA: (6) implies: % 131.16/18.38 | | (7) all_9_12 = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #310. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (8) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #288. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #288 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.38 (2) all_9_20 = e1 % 131.16/18.38 (3) ~ (e4 = e1) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_20 = e4 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e4 = e1 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #289 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_5 = e1 % 131.16/18.38 (2) ~ (e4 = e0) % 131.16/18.38 (3) all_9_20 = e2 % 131.16/18.38 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (6) ~ (e4 = e2) % 131.16/18.38 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (8) all_9_12 = e4 % 131.16/18.38 (9) ~ (e4 = e1) % 131.16/18.38 (10) all_9_9 = e4 % 131.16/18.38 (11) all_9_9 = e3 & op(e4, e1) = e3 % 131.16/18.38 (12) ~ (e4 = e3) % 131.16/18.38 (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.38 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.38 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 (14) all_4_0 = e0 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (11) implies: % 131.16/18.38 | (15) all_9_9 = e3 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (10), (15) imply: % 131.16/18.38 | (16) e4 = e3 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (8), (16) imply: % 131.16/18.38 | (17) all_9_12 = e3 % 131.16/18.38 | % 131.16/18.38 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (14), (17) are % 131.16/18.38 | inconsistent by sub-proof #303. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #290 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_4 = e3 & op(e4, e2) = e3 % 131.16/18.38 (2) all_9_4 = e0 % 131.16/18.38 (3) ~ (e3 = e0) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_4 = e3 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e3 = e0 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e3 = e0 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #291 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_0 = e3 & op(e4, e4) = e3 % 131.16/18.38 (2) all_9_0 = e0 % 131.16/18.38 (3) ~ (e3 = e0) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (4) all_9_0 = e3 % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (2), (4) imply: % 131.16/18.38 | (5) e3 = e0 % 131.16/18.38 | % 131.16/18.38 | SIMP: (5) implies: % 131.16/18.38 | (6) e3 = e0 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (6) imply: % 131.16/18.38 | (7) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (7) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #292 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_7 = e3 | ~ (op(e3, e2) = e3) % 131.16/18.38 (2) op(e3, e2) = e3 % 131.16/18.38 (3) all_6_7 = all_4_11 % 131.16/18.38 (4) ~ (all_4_11 = e3) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (1) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (5) ~ (op(e3, e2) = e3) % 131.16/18.38 | | % 131.16/18.38 | | PRED_UNIFY: (2), (5) imply: % 131.16/18.38 | | (6) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (6) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (7) all_6_7 = e3 % 131.16/18.38 | | % 131.16/18.38 | | COMBINE_EQS: (3), (7) imply: % 131.16/18.38 | | (8) all_4_11 = e3 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (4), (8) imply: % 131.16/18.38 | | (9) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (9) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #293 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) ~ (all_4_6 = e3) % 131.16/18.38 (2) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 131.16/18.38 (3) (all_9_2 = e3 & op(e3, e4) = e3) | (all_9_3 = e3 & op(e3, e3) = e3) % 131.16/18.38 (4) ~ (e3 = e1) % 131.16/18.38 (5) all_9_2 = e1 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (3) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_9_2 = e3 & op(e3, e4) = e3 % 131.16/18.38 | | % 131.16/18.38 | | ALPHA: (6) implies: % 131.16/18.38 | | (7) all_9_2 = e3 % 131.16/18.38 | | % 131.16/18.38 | | COMBINE_EQS: (5), (7) imply: % 131.16/18.38 | | (8) e3 = e1 % 131.16/18.38 | | % 131.16/18.38 | | SIMP: (8) implies: % 131.16/18.38 | | (9) e3 = e1 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (4), (9) imply: % 131.16/18.38 | | (10) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (10) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (11) all_9_3 = e3 & op(e3, e3) = e3 % 131.16/18.38 | | % 131.16/18.38 | | ALPHA: (11) implies: % 131.16/18.38 | | (12) op(e3, e3) = e3 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #295. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #294 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_11 = e3 | ~ (op(e2, e3) = e3) % 131.16/18.38 (2) op(e2, e3) = e3 % 131.16/18.38 (3) all_6_11 = all_4_7 % 131.16/18.38 (4) ~ (all_4_7 = e3) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (1) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (5) ~ (op(e2, e3) = e3) % 131.16/18.38 | | % 131.16/18.38 | | PRED_UNIFY: (2), (5) imply: % 131.16/18.38 | | (6) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (6) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (7) all_6_11 = e3 % 131.16/18.38 | | % 131.16/18.38 | | COMBINE_EQS: (3), (7) imply: % 131.16/18.38 | | (8) all_4_7 = e3 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (4), (8) imply: % 131.16/18.38 | | (9) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (9) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #295 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_4_6 = e3 | ~ (op(e3, e3) = e3) % 131.16/18.38 (2) op(e3, e3) = e3 % 131.16/18.38 (3) ~ (all_4_6 = e3) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (1) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (4) ~ (op(e3, e3) = e3) % 131.16/18.38 | | % 131.16/18.38 | | PRED_UNIFY: (2), (4) imply: % 131.16/18.38 | | (5) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (5) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_4_6 = e3 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (3), (6) imply: % 131.16/18.38 | | (7) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (7) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #296 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_1 = e3 & op(e4, e3) = e3 % 131.16/18.38 (2) ~ (op(e4, e3) = e3) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (3) op(e4, e3) = e3 % 131.16/18.38 | % 131.16/18.38 | PRED_UNIFY: (2), (3) imply: % 131.16/18.38 | (4) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (4) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #297 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_14 = all_4_22 % 131.16/18.38 (2) all_6_14 = e4 % 131.16/18.38 (3) ~ (all_4_22 = e4) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | COMBINE_EQS: (1), (2) imply: % 131.16/18.38 | (4) all_4_22 = e4 % 131.16/18.38 | % 131.16/18.38 | SIMP: (4) implies: % 131.16/18.38 | (5) all_4_22 = e4 % 131.16/18.38 | % 131.16/18.38 | REDUCE: (3), (5) imply: % 131.16/18.38 | (6) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (6) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #298 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_6_2 = e4 | ~ (op(e4, e2) = e4) % 131.16/18.38 (2) op(e4, e2) = e4 % 131.16/18.38 (3) all_6_2 = all_4_10 % 131.16/18.38 (4) ~ (all_4_10 = e4) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (1) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (5) ~ (op(e4, e2) = e4) % 131.16/18.38 | | % 131.16/18.38 | | PRED_UNIFY: (2), (5) imply: % 131.16/18.38 | | (6) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (6) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (7) all_6_2 = e4 % 131.16/18.38 | | % 131.16/18.38 | | COMBINE_EQS: (3), (7) imply: % 131.16/18.38 | | (8) all_4_10 = e4 % 131.16/18.38 | | % 131.16/18.38 | | SIMP: (8) implies: % 131.16/18.38 | | (9) all_4_10 = e4 % 131.16/18.38 | | % 131.16/18.38 | | REDUCE: (4), (9) imply: % 131.16/18.38 | | (10) $false % 131.16/18.38 | | % 131.16/18.38 | | CLOSE: (10) is inconsistent. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #299 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) ~ (e4 = e0) % 131.16/18.38 (2) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (3) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_1 = e4 & op(e4, e3) = e4) % 131.16/18.38 (4) ~ (op(e4, e3) = e4) % 131.16/18.38 (5) all_4_0 = e0 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (3) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (6) all_9_0 = e4 & op(e4, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | ALPHA: (6) implies: % 131.16/18.38 | | (7) op(e4, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #317. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (8) all_9_1 = e4 & op(e4, e3) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (4), (8) are inconsistent by sub-proof #300. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #300 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) all_9_1 = e4 & op(e4, e3) = e4 % 131.16/18.38 (2) ~ (op(e4, e3) = e4) % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (1) implies: % 131.16/18.38 | (3) op(e4, e3) = e4 % 131.16/18.38 | % 131.16/18.38 | PRED_UNIFY: (2), (3) imply: % 131.16/18.38 | (4) $false % 131.16/18.38 | % 131.16/18.38 | CLOSE: (4) is inconsistent. % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #301 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) op(e4, e1) = e4 % 131.16/18.38 (2) all_8_40 = e3 & ~ (all_8_41 = e4) & op(e4, all_8_42) = e3 & op(e3, % 131.16/18.38 all_8_42) = all_8_41 & op(e3, e4) = all_8_42 & $i(all_8_41) & % 131.16/18.38 $i(all_8_42) % 131.16/18.38 (3) all_6_5 = e1 % 131.16/18.38 (4) ~ (e4 = e0) % 131.16/18.38 (5) all_9_20 = e2 % 131.16/18.38 (6) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (7) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (8) ~ (e4 = e2) % 131.16/18.38 (9) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.38 (11) all_9_12 = e4 % 131.16/18.38 (12) ~ (e4 = e1) % 131.16/18.38 (13) op(e3, e4) = e1 % 131.16/18.38 (14) ~ (e4 = e3) % 131.16/18.38 (15) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.38 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.38 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.38 (16) all_4_0 = e0 % 131.16/18.38 % 131.16/18.38 Begin of proof % 131.16/18.38 | % 131.16/18.38 | ALPHA: (2) implies: % 131.16/18.38 | (17) op(e3, e4) = all_8_42 % 131.16/18.38 | (18) op(e4, all_8_42) = e3 % 131.16/18.38 | % 131.16/18.38 | BETA: splitting (6) gives: % 131.16/18.38 | % 131.16/18.38 | Case 1: % 131.16/18.38 | | % 131.16/18.38 | | (19) ~ (op(e3, e4) = e4) % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 131.16/18.38 | | (15), (16), (17), (18), (19) are inconsistent by sub-proof #302. % 131.16/18.38 | | % 131.16/18.38 | Case 2: % 131.16/18.38 | | % 131.16/18.38 | | (20) op(e3, e4) = e4 % 131.16/18.38 | | % 131.16/18.38 | | REF_CLOSE: (3), (6), (12), (20) are inconsistent by sub-proof #316. % 131.16/18.38 | | % 131.16/18.38 | End of split % 131.16/18.38 | % 131.16/18.38 End of proof % 131.16/18.38 % 131.16/18.38 Sub-proof #302 shows that the following formulas are inconsistent: % 131.16/18.38 ---------------------------------------------------------------- % 131.16/18.38 (1) op(e4, e1) = e4 % 131.16/18.38 (2) all_6_5 = e1 % 131.16/18.38 (3) ~ (e4 = e0) % 131.16/18.38 (4) all_9_20 = e2 % 131.16/18.38 (5) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.38 (6) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.38 (7) ~ (e4 = e2) % 131.16/18.38 (8) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.38 (9) ~ (op(e3, e4) = e4) % 131.16/18.38 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.38 (11) op(e4, all_8_42) = e3 % 131.16/18.38 (12) all_9_12 = e4 % 131.16/18.38 (13) op(e3, e4) = e1 % 131.16/18.38 (14) ~ (e4 = e3) % 131.16/18.38 (15) op(e3, e4) = all_8_42 % 131.16/18.39 (16) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.39 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.39 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.39 (17) all_4_0 = e0 % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | GROUND_INST: instantiating (10) with e1, all_8_42, e4, e3, simplifying with % 131.16/18.39 | (13), (15) gives: % 131.16/18.39 | (18) all_8_42 = e1 % 131.16/18.39 | % 131.16/18.39 | GROUND_INST: instantiating (10) with e4, e3, e1, e4, simplifying with (1) % 131.16/18.39 | gives: % 131.16/18.39 | (19) e4 = e3 | ~ (op(e4, e1) = e3) % 131.16/18.39 | % 131.16/18.39 | PRED_UNIFY: (9), (15) imply: % 131.16/18.39 | (20) ~ (all_8_42 = e4) % 131.16/18.39 | % 131.16/18.39 | REDUCE: (18), (20) imply: % 131.16/18.39 | (21) ~ (e4 = e1) % 131.16/18.39 | % 131.16/18.39 | SIMP: (21) implies: % 131.16/18.39 | (22) ~ (e4 = e1) % 131.16/18.39 | % 131.16/18.39 | REDUCE: (11), (18) imply: % 131.16/18.39 | (23) op(e4, e1) = e3 % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (19) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (24) ~ (op(e4, e1) = e3) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (23), (24) imply: % 131.16/18.39 | | (25) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (25) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (26) e4 = e3 % 131.16/18.39 | | % 131.16/18.39 | | COMBINE_EQS: (12), (26) imply: % 131.16/18.39 | | (27) all_9_12 = e3 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (14), (16), (17), (22), (27) % 131.16/18.39 | | are inconsistent by sub-proof #303. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #303 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_6_5 = e1 % 131.16/18.39 (2) ~ (e4 = e0) % 131.16/18.39 (3) all_9_20 = e2 % 131.16/18.39 (4) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.39 (5) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.39 (6) ~ (e4 = e2) % 131.16/18.39 (7) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.39 (8) all_9_12 = e3 % 131.16/18.39 (9) ~ (e4 = e1) % 131.16/18.39 (10) ~ (e4 = e3) % 131.16/18.39 (11) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) | % 131.16/18.39 (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) | % 131.16/18.39 (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.39 (12) all_4_0 = e0 % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (11) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (13) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (1), (2), (4), (5), (9), (12), (13) are inconsistent by sub-proof % 131.16/18.39 | | #315. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (14) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_12 = e4 & op(e1, e4) = e4) % 131.16/18.39 | | | (all_9_20 = e4 & op(e0, e4) = e4) % 131.16/18.39 | | % 131.16/18.39 | | BETA: splitting (14) gives: % 131.16/18.39 | | % 131.16/18.39 | | Case 1: % 131.16/18.39 | | | % 131.16/18.39 | | | (15) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.39 | | | % 131.16/18.39 | | | ALPHA: (15) implies: % 131.16/18.39 | | | (16) op(e2, e4) = e4 % 131.16/18.39 | | | % 131.16/18.39 | | | REF_CLOSE: (7), (10), (16) are inconsistent by sub-proof #320. % 131.16/18.39 | | | % 131.16/18.39 | | Case 2: % 131.16/18.39 | | | % 131.16/18.39 | | | (17) (all_9_12 = e4 & op(e1, e4) = e4) | (all_9_20 = e4 & op(e0, e4) = % 131.16/18.39 | | | e4) % 131.16/18.39 | | | % 131.16/18.39 | | | BETA: splitting (17) gives: % 131.16/18.39 | | | % 131.16/18.39 | | | Case 1: % 131.16/18.39 | | | | % 131.16/18.39 | | | | (18) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.39 | | | | % 131.16/18.39 | | | | REF_CLOSE: (8), (10), (18) are inconsistent by sub-proof #305. % 131.16/18.39 | | | | % 131.16/18.39 | | | Case 2: % 131.16/18.39 | | | | % 131.16/18.39 | | | | (19) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.39 | | | | % 131.16/18.39 | | | | REF_CLOSE: (3), (6), (19) are inconsistent by sub-proof #304. % 131.16/18.39 | | | | % 131.16/18.39 | | | End of split % 131.16/18.39 | | | % 131.16/18.39 | | End of split % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #304 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_20 = e4 & op(e0, e4) = e4 % 131.16/18.39 (2) all_9_20 = e2 % 131.16/18.39 (3) ~ (e4 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | ALPHA: (1) implies: % 131.16/18.39 | (4) all_9_20 = e4 % 131.16/18.39 | % 131.16/18.39 | COMBINE_EQS: (2), (4) imply: % 131.16/18.39 | (5) e4 = e2 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (3), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #305 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_12 = e4 & op(e1, e4) = e4 % 131.16/18.39 (2) all_9_12 = e3 % 131.16/18.39 (3) ~ (e4 = e3) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | ALPHA: (1) implies: % 131.16/18.39 | (4) all_9_12 = e4 % 131.16/18.39 | % 131.16/18.39 | COMBINE_EQS: (2), (4) imply: % 131.16/18.39 | (5) e4 = e3 % 131.16/18.39 | % 131.16/18.39 | SIMP: (5) implies: % 131.16/18.39 | (6) e4 = e3 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (3), (6) imply: % 131.16/18.39 | (7) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (7) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #306 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_8 = e2 & op(e2, e2) = e2 % 131.16/18.39 (2) e4 = e2 | ~ (op(e2, e2) = e2) % 131.16/18.39 (3) ~ (e4 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | ALPHA: (1) implies: % 131.16/18.39 | (4) op(e2, e2) = e2 % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (2) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (5) ~ (op(e2, e2) = e2) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (4), (5) imply: % 131.16/18.39 | | (6) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (6) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (7) e4 = e2 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (3), (7) imply: % 131.16/18.39 | | (8) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (8) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #307 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.16/18.39 (2) all_6_10 = e3 % 131.16/18.39 (3) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 131.16/18.39 (4) (all_9_6 = e2 & op(e2, e4) = e2) | (all_9_7 = e2 & op(e2, e3) = e2) % 131.16/18.39 (5) ~ (e3 = e2) % 131.16/18.39 (6) ~ (all_4_7 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (4) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (7) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #311. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (8) all_9_7 = e2 & op(e2, e3) = e2 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (8) implies: % 131.16/18.39 | | (9) op(e2, e3) = e2 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #308. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #308 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_4_7 = e2 | ~ (op(e2, e3) = e2) % 131.16/18.39 (2) op(e2, e3) = e2 % 131.16/18.39 (3) ~ (all_4_7 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (1) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (4) ~ (op(e2, e3) = e2) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (2), (4) imply: % 131.16/18.39 | | (5) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (5) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (6) all_4_7 = e2 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (3), (6) imply: % 131.16/18.39 | | (7) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (7) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #309 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_6_20 = all_4_4 % 131.16/18.39 (2) all_6_20 = e4 % 131.16/18.39 (3) ~ (all_4_4 = e4) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | COMBINE_EQS: (1), (2) imply: % 131.16/18.39 | (4) all_4_4 = e4 % 131.16/18.39 | % 131.16/18.39 | SIMP: (4) implies: % 131.16/18.39 | (5) all_4_4 = e4 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (3), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #310 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_12 = e4 % 131.16/18.39 (2) all_9_12 = e2 % 131.16/18.39 (3) ~ (e4 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | COMBINE_EQS: (1), (2) imply: % 131.16/18.39 | (4) e4 = e2 % 131.16/18.39 | % 131.16/18.39 | SIMP: (4) implies: % 131.16/18.39 | (5) e4 = e2 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (3), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #311 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_6 = e2 & op(e2, e4) = e2 % 131.16/18.39 (2) all_6_10 = e2 | ~ (op(e2, e4) = e2) % 131.16/18.39 (3) all_6_10 = e3 % 131.16/18.39 (4) ~ (e3 = e2) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | ALPHA: (1) implies: % 131.16/18.39 | (5) op(e2, e4) = e2 % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (2) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (6) ~ (op(e2, e4) = e2) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (5), (6) imply: % 131.16/18.39 | | (7) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (7) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (8) all_6_10 = e2 % 131.16/18.39 | | % 131.16/18.39 | | COMBINE_EQS: (3), (8) imply: % 131.16/18.39 | | (9) e3 = e2 % 131.16/18.39 | | % 131.16/18.39 | | SIMP: (9) implies: % 131.16/18.39 | | (10) e3 = e2 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (4), (10) imply: % 131.16/18.39 | | (11) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (11) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #312 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) ~ (e2 = e0) % 131.16/18.39 (2) all_9_0 = e0 % 131.16/18.39 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.39 (4) (all_9_0 = e2 & op(e4, e4) = e2) | (all_9_2 = e2 & op(e3, e4) = e2) % 131.16/18.39 (5) op(e3, e4) = e1 % 131.16/18.39 (6) ~ (e2 = e1) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (4) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (7) all_9_0 = e2 & op(e4, e4) = e2 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #314. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (8) all_9_2 = e2 & op(e3, e4) = e2 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (8) implies: % 131.16/18.39 | | (9) op(e3, e4) = e2 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #313. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #313 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.39 (2) op(e3, e4) = e2 % 131.16/18.39 (3) op(e3, e4) = e1 % 131.16/18.39 (4) ~ (e2 = e1) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | GROUND_INST: instantiating (1) with e1, e2, e4, e3, simplifying with (2), (3) % 131.16/18.39 | gives: % 131.16/18.39 | (5) e2 = e1 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (4), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #314 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_9_0 = e2 & op(e4, e4) = e2 % 131.16/18.39 (2) all_9_0 = e0 % 131.16/18.39 (3) ~ (e2 = e0) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | ALPHA: (1) implies: % 131.16/18.39 | (4) all_9_0 = e2 % 131.16/18.39 | % 131.16/18.39 | COMBINE_EQS: (2), (4) imply: % 131.16/18.39 | (5) e2 = e0 % 131.16/18.39 | % 131.16/18.39 | SIMP: (5) implies: % 131.16/18.39 | (6) e2 = e0 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (3), (6) imply: % 131.16/18.39 | (7) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (7) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #315 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_6_5 = e1 % 131.16/18.39 (2) ~ (e4 = e0) % 131.16/18.39 (3) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.39 (4) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.39 (5) ~ (e4 = e1) % 131.16/18.39 (6) (all_9_0 = e4 & op(e4, e4) = e4) | (all_9_2 = e4 & op(e3, e4) = e4) % 131.16/18.39 (7) all_4_0 = e0 % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (6) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (8) all_9_0 = e4 & op(e4, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (8) implies: % 131.16/18.39 | | (9) op(e4, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (2), (4), (7), (9) are inconsistent by sub-proof #317. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (10) all_9_2 = e4 & op(e3, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (10) implies: % 131.16/18.39 | | (11) op(e3, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #316. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #316 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_6_5 = e4 | ~ (op(e3, e4) = e4) % 131.16/18.39 (2) op(e3, e4) = e4 % 131.16/18.39 (3) all_6_5 = e1 % 131.16/18.39 (4) ~ (e4 = e1) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (1) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (5) ~ (op(e3, e4) = e4) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (2), (5) imply: % 131.16/18.39 | | (6) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (6) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (7) all_6_5 = e4 % 131.16/18.39 | | % 131.16/18.39 | | COMBINE_EQS: (3), (7) imply: % 131.16/18.39 | | (8) e4 = e1 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (4), (8) imply: % 131.16/18.39 | | (9) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (9) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #317 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) all_4_0 = e4 | ~ (op(e4, e4) = e4) % 131.16/18.39 (2) op(e4, e4) = e4 % 131.16/18.39 (3) all_4_0 = e0 % 131.16/18.39 (4) ~ (e4 = e0) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (1) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (5) ~ (op(e4, e4) = e4) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (2), (5) imply: % 131.16/18.39 | | (6) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (6) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (7) all_4_0 = e4 % 131.16/18.39 | | % 131.16/18.39 | | COMBINE_EQS: (3), (7) imply: % 131.16/18.39 | | (8) e4 = e0 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (4), (8) imply: % 131.16/18.39 | | (9) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (9) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #318 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) op(e2, e3) = all_4_7 % 131.16/18.39 (2) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.39 (3) ~ (all_4_7 = e4) % 131.16/18.39 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.39 (5) (all_9_6 = e4 & op(e2, e4) = e4) | (all_9_7 = e4 & op(e2, e3) = e4) % 131.16/18.39 (6) ~ (e4 = e3) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (5) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (7) all_9_6 = e4 & op(e2, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (7) implies: % 131.16/18.39 | | (8) op(e2, e4) = e4 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #320. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (9) all_9_7 = e4 & op(e2, e3) = e4 % 131.16/18.39 | | % 131.16/18.39 | | ALPHA: (9) implies: % 131.16/18.39 | | (10) op(e2, e3) = e4 % 131.16/18.39 | | % 131.16/18.39 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #319. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #319 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.39 (2) op(e2, e3) = all_4_7 % 131.16/18.39 (3) op(e2, e3) = e4 % 131.16/18.39 (4) ~ (all_4_7 = e4) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | GROUND_INST: instantiating (1) with all_4_7, e4, e3, e2, simplifying with (2), % 131.16/18.39 | (3) gives: % 131.16/18.39 | (5) all_4_7 = e4 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (4), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #320 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) e4 = e3 | ~ (op(e2, e4) = e4) % 131.16/18.39 (2) op(e2, e4) = e4 % 131.16/18.39 (3) ~ (e4 = e3) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | BETA: splitting (1) gives: % 131.16/18.39 | % 131.16/18.39 | Case 1: % 131.16/18.39 | | % 131.16/18.39 | | (4) ~ (op(e2, e4) = e4) % 131.16/18.39 | | % 131.16/18.39 | | PRED_UNIFY: (2), (4) imply: % 131.16/18.39 | | (5) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (5) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | Case 2: % 131.16/18.39 | | % 131.16/18.39 | | (6) e4 = e3 % 131.16/18.39 | | % 131.16/18.39 | | REDUCE: (3), (6) imply: % 131.16/18.39 | | (7) $false % 131.16/18.39 | | % 131.16/18.39 | | CLOSE: (7) is inconsistent. % 131.16/18.39 | | % 131.16/18.39 | End of split % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % 131.16/18.39 Sub-proof #321 shows that the following formulas are inconsistent: % 131.16/18.39 ---------------------------------------------------------------- % 131.16/18.39 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.16/18.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.16/18.39 (2) op(e4, e4) = e1 % 131.16/18.39 (3) op(e4, e4) = e0 % 131.16/18.39 (4) ~ (e1 = e0) % 131.16/18.39 % 131.16/18.39 Begin of proof % 131.16/18.39 | % 131.16/18.39 | GROUND_INST: instantiating (1) with e0, e1, e4, e4, simplifying with (2), (3) % 131.16/18.39 | gives: % 131.16/18.39 | (5) e1 = e0 % 131.16/18.39 | % 131.16/18.39 | REDUCE: (4), (5) imply: % 131.16/18.39 | (6) $false % 131.16/18.39 | % 131.16/18.39 | CLOSE: (6) is inconsistent. % 131.16/18.39 | % 131.16/18.39 End of proof % 131.16/18.39 % SZS output end Proof for theBenchmark % 131.16/18.39 % 131.16/18.39 17783ms %------------------------------------------------------------------------------