%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG046+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 : n003.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 16:35:50 EDT 2023 % Result : Unsatisfiable 15.12s 2.84s % Output : Proof 133.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ALG046+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n003.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Mon Aug 28 03:22:10 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.89/1.31 Prover 4: Preprocessing ... % 3.89/1.31 Prover 1: Preprocessing ... % 4.40/1.36 Prover 3: Preprocessing ... % 4.40/1.36 Prover 2: Preprocessing ... % 4.40/1.36 Prover 0: Preprocessing ... % 4.40/1.36 Prover 6: Preprocessing ... % 4.40/1.36 Prover 5: Preprocessing ... % 7.72/1.80 Prover 3: Constructing countermodel ... % 7.72/1.80 Prover 2: Constructing countermodel ... % 7.72/1.85 Prover 1: Constructing countermodel ... % 8.17/1.86 Prover 4: Constructing countermodel ... % 8.17/1.86 Prover 0: Constructing countermodel ... % 8.26/1.88 Prover 6: Constructing countermodel ... % 10.42/2.22 Prover 5: Constructing countermodel ... % 15.12/2.84 Prover 6: proved (2189ms) % 15.12/2.84 % 15.12/2.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.12/2.84 % 15.12/2.85 Prover 2: stopped % 15.12/2.85 Prover 3: stopped % 15.12/2.85 Prover 0: stopped % 15.12/2.85 Prover 5: stopped % 15.12/2.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.12/2.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.12/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.12/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.12/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.81/3.05 Prover 8: Preprocessing ... % 16.81/3.09 Prover 13: Preprocessing ... % 16.81/3.10 Prover 7: Preprocessing ... % 16.81/3.11 Prover 10: Preprocessing ... % 17.37/3.12 Prover 11: Preprocessing ... % 17.93/3.22 Prover 8: Constructing countermodel ... % 18.68/3.32 Prover 7: Constructing countermodel ... % 18.68/3.34 Prover 10: Constructing countermodel ... % 18.68/3.34 Prover 13: Constructing countermodel ... % 18.68/3.35 Prover 11: Constructing countermodel ... % 61.75/8.98 Prover 13: stopped % 62.43/8.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 62.69/9.08 Prover 16: Preprocessing ... % 64.01/9.24 Prover 16: Constructing countermodel ... % 108.55/15.01 Prover 16: stopped % 108.55/15.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 108.55/15.07 Prover 19: Preprocessing ... % 109.15/15.17 Prover 19: Constructing countermodel ... % 115.37/16.00 Prover 1: stopped % 125.22/17.29 Prover 7: Found proof (size 29968) % 125.22/17.29 Prover 7: proved (14330ms) % 125.22/17.29 Prover 10: stopped % 125.22/17.29 Prover 11: stopped % 125.22/17.30 Prover 4: stopped % 125.22/17.30 Prover 8: stopped % 125.22/17.30 Prover 19: stopped % 125.22/17.30 % 125.22/17.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 125.22/17.30 % 126.35/17.55 % SZS output start Proof for theBenchmark % 126.62/17.59 Assumptions after simplification: % 126.62/17.59 --------------------------------- % 126.62/17.59 % 126.62/17.59 (ax1) % 126.79/17.64 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.79/17.64 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 126.79/17.64 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 126.79/17.64 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 126.79/17.64 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 126.79/17.64 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 126.79/17.64 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 126.79/17.64 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 126.79/17.64 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 126.79/17.64 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 126.79/17.64 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 126.79/17.64 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 126.79/17.64 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 126.79/17.64 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 126.79/17.64 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 126.79/17.64 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 126.79/17.64 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 126.79/17.64 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 126.79/17.64 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 126.79/17.64 % 126.79/17.64 (ax10) % 126.79/17.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.79/17.65 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e2, e1) = v1 & $i(v1) & ( ~ % 126.79/17.65 (v1 = e3) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)))))) % 126.79/17.65 % 126.79/17.65 (ax11) % 126.93/17.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.65 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e3, e2) = v1 & $i(v1) & ( ~ % 126.93/17.65 (v1 = e1) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)))))) % 126.93/17.65 % 126.93/17.65 (ax12) % 126.93/17.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.65 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e3, e1) = v1 & $i(v1) & ( ~ % 126.93/17.65 (v1 = e2) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)))))) % 126.93/17.65 % 126.93/17.65 (ax13) % 126.93/17.65 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.65 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e0, e3) = v1 & $i(v1) & ( ~ % 126.93/17.65 (v1 = e2) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)))))) % 126.93/17.65 % 126.93/17.65 (ax14) % 126.93/17.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.66 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e0, e2) = v1 & $i(v1) & ( ~ % 126.93/17.66 (v1 = e3) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)))))) % 126.93/17.66 % 126.93/17.66 (ax15) % 126.93/17.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.66 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e2, e3) = v1 & $i(v1) & ( ~ % 126.93/17.66 (v1 = e0) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)))))) % 126.93/17.66 % 126.93/17.66 (ax16) % 126.93/17.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.66 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e2, e0) = v1 & $i(v1) & ( ~ % 126.93/17.66 (v1 = e3) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)))))) % 126.93/17.66 % 126.93/17.66 (ax17) % 126.93/17.66 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.66 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e3, e2) = v1 & $i(v1) & ( ~ % 126.93/17.67 (v1 = e0) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)))))) % 126.93/17.67 % 126.93/17.67 (ax18) % 126.93/17.67 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.67 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e3, e0) = v1 & $i(v1) & ( ~ % 126.93/17.67 (v1 = e2) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)))))) % 126.93/17.67 % 126.93/17.67 (ax19) % 126.93/17.67 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.67 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e0, e3) = v1 & $i(v1) & ( ~ % 126.93/17.67 (v1 = e1) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)))))) % 126.93/17.67 % 126.93/17.67 (ax2) % 126.93/17.67 op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 % 126.93/17.67 & op(e3, unit) = e3 & op(e2, unit) = e2 & op(e1, unit) = e1 & op(e0, unit) = % 126.93/17.67 e0 & $i(unit) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & (unit = e3 | unit = e2 | % 126.93/17.67 unit = e1 | unit = e0) % 126.93/17.67 % 126.93/17.67 (ax20) % 126.93/17.67 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.67 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e0, e1) = v1 & $i(v1) & ( ~ % 126.93/17.67 (v1 = e3) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)))))) % 126.93/17.67 % 126.93/17.67 (ax21) % 126.93/17.68 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.68 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e1, e3) = v1 & $i(v1) & ( ~ % 126.93/17.68 (v1 = e0) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)))))) % 126.93/17.68 % 126.93/17.68 (ax22) % 126.93/17.68 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.68 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e1, e0) = v1 & $i(v1) & ( ~ % 126.93/17.68 (v1 = e3) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)))))) % 126.93/17.68 % 126.93/17.68 (ax23) % 126.93/17.68 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.68 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e3, e1) = v1 & $i(v1) & ( ~ % 126.93/17.68 (v1 = e0) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)))))) % 126.93/17.68 % 126.93/17.68 (ax24) % 126.93/17.68 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.68 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e3, e0) = v1 & $i(v1) & ( ~ % 126.93/17.68 (v1 = e1) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)))))) % 126.93/17.68 % 126.93/17.68 (ax25) % 126.93/17.69 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.69 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e0, e2) = v1 & $i(v1) & ( ~ % 126.93/17.69 (v1 = e1) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)))))) % 126.93/17.69 % 126.93/17.69 (ax26) % 126.93/17.69 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.69 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e0, e1) = v1 & $i(v1) & ( ~ % 126.93/17.69 (v1 = e2) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)))))) % 126.93/17.69 % 126.93/17.69 (ax27) % 126.93/17.69 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.69 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e1, e2) = v1 & $i(v1) & ( ~ % 126.93/17.69 (v1 = e0) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)))))) % 126.93/17.69 % 126.93/17.69 (ax28) % 126.93/17.69 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.69 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e1, e0) = v1 & $i(v1) & ( ~ % 126.93/17.69 (v1 = e2) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)))))) % 126.93/17.69 % 126.93/17.69 (ax29) % 126.93/17.70 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.70 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e2, e1) = v1 & $i(v1) & ( ~ % 126.93/17.70 (v1 = e0) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)))))) % 126.93/17.70 % 126.93/17.70 (ax3) % 126.93/17.72 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.72 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 126.93/17.72 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 126.93/17.72 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = % 126.93/17.72 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, % 126.93/17.72 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) = % 126.93/17.72 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15 % 126.93/17.72 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 & % 126.93/17.72 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3, % 126.93/17.72 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2) % 126.93/17.72 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1 % 126.93/17.72 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3, % 126.93/17.72 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = % 126.93/17.72 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 % 126.93/17.72 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 & % 126.93/17.72 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3, % 126.93/17.72 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0) % 126.93/17.72 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3 % 126.93/17.72 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) % 126.93/17.72 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 126.93/17.72 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 & % 126.93/17.72 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2) % 126.93/17.72 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) | % 126.93/17.72 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 126.93/17.72 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2, % 126.93/17.72 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = % 126.93/17.72 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 126.93/17.72 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 & % 126.93/17.72 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1) % 126.93/17.72 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) | % 126.93/17.72 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 & % 126.93/17.72 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2, % 126.93/17.72 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) % 126.93/17.72 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 & % 126.93/17.72 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3, % 126.93/17.72 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1) % 126.93/17.72 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0 % 126.93/17.72 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) % 126.93/17.72 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | % 126.93/17.72 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 & % 126.93/17.72 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) = % 126.93/17.72 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8 % 126.93/17.72 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 & % 126.93/17.72 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) % 126.93/17.72 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & % 126.93/17.72 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 & % 126.93/17.72 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0) % 126.93/17.72 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0 % 126.93/17.72 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 & % 126.93/17.72 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = % 126.93/17.72 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 126.93/17.72 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 & % 126.93/17.72 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = % 126.93/17.72 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2 % 126.93/17.72 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 126.93/17.72 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3, % 126.93/17.72 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = % 126.93/17.72 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | % 126.93/17.72 (v1 = e0 & op(e0, e1) = e0))))) % 126.93/17.72 % 126.93/17.72 (ax30) % 126.93/17.72 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 126.93/17.72 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e2, e0) = v1 & $i(v1) & ( ~ % 126.93/17.72 (v1 = e1) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)))))) % 126.93/17.72 % 126.93/17.72 (ax4) % 127.31/17.73 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 127.31/17.73 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 127.31/17.73 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 127.31/17.73 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 127.31/17.73 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 127.31/17.73 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 127.31/17.73 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 127.31/17.73 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 127.31/17.73 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 127.31/17.73 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 127.31/17.73 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 127.31/17.73 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 127.31/17.73 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 127.31/17.73 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 127.31/17.73 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 127.31/17.73 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 127.31/17.73 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 127.31/17.73 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 127.31/17.73 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 127.31/17.73 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 127.31/17.73 % 127.31/17.73 (ax5) % 127.31/17.73 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 127.31/17.73 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 127.31/17.73 % 127.31/17.73 (ax6) % 127.31/17.74 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 127.31/17.74 ? [v3: $i] : ((( ~ (v3 = e3) & op(e3, e3) = v3 & $i(v3)) | ( ~ (v2 = e3) & % 127.31/17.74 op(e2, e2) = v2 & $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)) | % 127.31/17.74 ( ~ (v0 = e3) & op(e0, e0) = v0 & $i(v0))) & (( ~ (v3 = e2) & op(e3, e3) = % 127.31/17.74 v3 & $i(v3)) | ( ~ (v2 = e2) & op(e2, e2) = v2 & $i(v2)) | ( ~ (v1 = e2) % 127.31/17.74 & op(e1, e1) = v1 & $i(v1)) | ( ~ (v0 = e2) & op(e0, e0) = v0 & $i(v0))) % 127.31/17.74 & (( ~ (v3 = e1) & op(e3, e3) = v3 & $i(v3)) | ( ~ (v2 = e1) & op(e2, e2) = % 127.31/17.74 v2 & $i(v2)) | ( ~ (v1 = e1) & op(e1, e1) = v1 & $i(v1)) | ( ~ (v0 = e1) % 127.31/17.74 & op(e0, e0) = v0 & $i(v0))) & (( ~ (v3 = e0) & op(e3, e3) = v3 & % 127.31/17.74 $i(v3)) | ( ~ (v2 = e0) & op(e2, e2) = v2 & $i(v2)) | ( ~ (v1 = e0) & % 127.31/17.74 op(e1, e1) = v1 & $i(v1)) | ( ~ (v0 = e0) & op(e0, e0) = v0 & $i(v0)))) % 127.31/17.74 % 127.31/17.74 (ax7) % 127.31/17.74 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 127.31/17.74 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e1, e3) = v1 & $i(v1) & ( ~ % 127.31/17.74 (v1 = e2) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)))))) % 127.31/17.74 % 127.31/17.74 (ax8) % 127.31/17.74 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 127.31/17.74 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e1, e2) = v1 & $i(v1) & ( ~ % 127.31/17.74 (v1 = e3) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)))))) % 127.31/17.74 % 127.31/17.74 (ax9) % 127.31/17.74 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 127.31/17.74 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e2, e3) = v1 & $i(v1) & ( ~ % 127.31/17.74 (v1 = e1) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)))))) % 127.31/17.74 % 127.31/17.74 (function-axioms) % 127.31/17.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 127.31/17.74 v2) = v1) | ~ (op(v3, v2) = v0)) % 127.31/17.74 % 127.31/17.74 Those formulas are unsatisfiable: % 127.31/17.74 --------------------------------- % 127.31/17.74 % 127.31/17.74 Begin of proof % 127.31/17.74 | % 127.31/17.74 | ALPHA: (ax1) implies: % 127.31/17.75 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 127.31/17.75 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 127.31/17.75 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 127.31/17.75 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 127.31/17.75 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 127.31/17.75 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 127.31/17.75 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 127.31/17.75 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 127.31/17.75 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 127.31/17.75 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 127.31/17.75 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 127.31/17.75 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 127.31/17.75 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 127.31/17.75 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 127.31/17.75 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 127.31/17.75 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 127.31/17.75 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 127.31/17.75 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 127.31/17.75 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 127.31/17.75 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 127.31/17.75 | = e0)) % 127.31/17.75 | % 127.31/17.75 | ALPHA: (ax2) implies: % 127.31/17.75 | (2) op(e0, unit) = e0 % 127.31/17.75 | (3) op(e1, unit) = e1 % 127.31/17.75 | (4) op(e2, unit) = e2 % 127.31/17.75 | (5) op(e3, unit) = e3 % 127.31/17.75 | (6) op(unit, e0) = e0 % 127.31/17.75 | (7) op(unit, e1) = e1 % 127.31/17.75 | (8) op(unit, e2) = e2 % 127.31/17.75 | (9) op(unit, e3) = e3 % 127.31/17.75 | (10) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 127.31/17.75 | % 127.31/17.75 | ALPHA: (ax3) implies: % 127.31/17.78 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 127.31/17.78 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 127.31/17.78 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 127.31/17.78 | $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & % 127.31/17.78 | op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & % 127.31/17.78 | op(e3, e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & % 127.31/17.78 | op(e2, e3) = e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & % 127.31/17.78 | op(e0, e3) = e3)) & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & % 127.31/17.78 | op(e3, e2) = e2) | (v11 = e2 & op(e3, e1) = e2) | (v6 = e2 & % 127.31/17.78 | op(e3, e0) = e2)) & ((v15 = e2 & op(e3, e3) = e2) | (v13 = e2 & % 127.31/17.78 | op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2) | (v3 = e2 & % 127.31/17.78 | op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1 & % 127.31/17.78 | op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & % 127.31/17.78 | op(e3, e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & % 127.31/17.78 | op(e2, e3) = e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & % 127.31/17.78 | op(e0, e3) = e1)) & ((v15 = e0 & op(e3, e3) = e0) | (v14 = e0 & % 127.31/17.78 | op(e3, e2) = e0) | (v11 = e0 & op(e3, e1) = e0) | (v6 = e0 & % 127.31/17.78 | op(e3, e0) = e0)) & ((v15 = e0 & op(e3, e3) = e0) | (v13 = e0 & % 127.31/17.78 | op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0) | (v3 = e0 & % 127.31/17.78 | op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3 & % 127.31/17.78 | op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & % 127.31/17.78 | op(e0, e2) = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & % 127.31/17.78 | op(e2, e2) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & % 127.31/17.78 | op(e0, e2) = e2)) & ((v14 = e1 & op(e3, e2) = e1) | (v12 = e1 & % 127.31/17.78 | op(e2, e2) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v2 = e1 & % 127.31/17.78 | op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) | (v12 = e0 & % 127.31/17.78 | op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 127.31/17.78 | op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & % 127.31/17.78 | op(e2, e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & % 127.31/17.78 | op(e2, e0) = e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & % 127.31/17.78 | op(e2, e2) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & % 127.31/17.78 | op(e2, e0) = e2)) & ((v13 = e1 & op(e2, e3) = e1) | (v12 = e1 & % 127.31/17.78 | op(e2, e2) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v5 = e1 & % 127.31/17.78 | op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) | (v12 = e0 & % 127.31/17.78 | op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 & % 127.31/17.78 | op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & % 127.31/17.78 | op(e2, e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & % 127.31/17.78 | op(e0, e1) = e3)) & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & % 127.31/17.78 | op(e2, e1) = e2) | (v7 = e2 & op(e1, e1) = e2) | (v1 = e2 & % 127.31/17.78 | op(e0, e1) = e2)) & ((v11 = e1 & op(e3, e1) = e1) | (v10 = e1 & % 127.31/17.78 | op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v1 = e1 & % 127.31/17.78 | op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0 & % 127.31/17.78 | op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & % 127.31/17.78 | op(e0, e1) = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & % 127.31/17.78 | op(e1, e2) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & % 127.31/17.78 | op(e1, e0) = e3)) & ((v9 = e2 & op(e1, e3) = e2) | (v8 = e2 & % 127.31/17.78 | op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) = e2) | (v4 = e2 & % 127.31/17.78 | op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8 = e1 & % 127.31/17.78 | op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 & % 127.31/17.78 | op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & % 127.31/17.78 | op(e1, e2) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & % 127.31/17.78 | op(e1, e0) = e0)) & ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & % 127.31/17.78 | op(e2, e0) = e3) | (v4 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 127.31/17.78 | op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0) = e2) | (v5 = e2 & % 127.31/17.78 | op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0 = e2 & % 127.31/17.78 | op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 & % 127.31/17.78 | op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & % 127.31/17.78 | op(e0, e0) = e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & % 127.31/17.78 | op(e0, e2) = e3) | (v1 = e3 & op(e0, e1) = e3) | (v0 = e3 & % 127.31/17.78 | op(e0, e0) = e3)) & ((v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & % 127.31/17.78 | op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & % 127.31/17.78 | op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 127.31/17.78 | op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 127.31/17.78 | op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & % 127.31/17.78 | op(e3, e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & % 127.31/17.78 | op(e1, e0) = e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 % 127.31/17.78 | & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = e0))))) % 127.31/17.78 | % 127.31/17.78 | ALPHA: (ax4) implies: % 127.57/17.78 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 127.57/17.78 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 127.57/17.78 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 127.57/17.78 | $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = % 127.57/17.78 | v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 127.57/17.78 | v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = % 127.57/17.78 | v2) & ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = % 127.57/17.78 | v1) & ~ (v12 = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = % 127.57/17.78 | v10) & ~ (v11 = v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = % 127.57/17.78 | v3) & ~ (v10 = v9) & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = % 127.57/17.78 | v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & % 127.57/17.78 | ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = % 127.57/17.78 | v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & % 127.57/17.78 | ~ (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = % 127.57/17.78 | v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = % 127.57/17.78 | v15 & op(e3, e2) = v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, % 127.57/17.78 | e3) = v14 & op(e2, e2) = v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & % 127.57/17.78 | op(e1, e3) = v13 & op(e1, e2) = v9 & op(e1, e1) = v5 & op(e1, e0) = % 127.57/17.78 | v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & op(e0, e1) = v4 & op(e0, % 127.57/17.78 | e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & % 127.57/17.78 | $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 127.57/17.78 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 127.57/17.78 | % 127.57/17.78 | ALPHA: (ax5) implies: % 127.57/17.78 | (13) ~ (e1 = e0) % 127.57/17.78 | (14) ~ (e2 = e0) % 127.57/17.79 | (15) ~ (e2 = e1) % 127.57/17.79 | (16) ~ (e3 = e0) % 127.57/17.79 | (17) ~ (e3 = e1) % 127.57/17.79 | (18) ~ (e3 = e2) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax6) implies: % 127.57/17.79 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((( ~ (v3 = % 127.57/17.79 | e3) & op(e3, e3) = v3 & $i(v3)) | ( ~ (v2 = e3) & op(e2, e2) = % 127.57/17.79 | v2 & $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)) | ( ~ % 127.57/17.79 | (v0 = e3) & op(e0, e0) = v0 & $i(v0))) & (( ~ (v3 = e2) & op(e3, % 127.57/17.79 | e3) = v3 & $i(v3)) | ( ~ (v2 = e2) & op(e2, e2) = v2 & $i(v2)) % 127.57/17.79 | | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)) | ( ~ (v0 = e2) & % 127.57/17.79 | op(e0, e0) = v0 & $i(v0))) & (( ~ (v3 = e1) & op(e3, e3) = v3 & % 127.57/17.79 | $i(v3)) | ( ~ (v2 = e1) & op(e2, e2) = v2 & $i(v2)) | ( ~ (v1 = % 127.57/17.79 | e1) & op(e1, e1) = v1 & $i(v1)) | ( ~ (v0 = e1) & op(e0, e0) = % 127.57/17.79 | v0 & $i(v0))) & (( ~ (v3 = e0) & op(e3, e3) = v3 & $i(v3)) | ( ~ % 127.57/17.79 | (v2 = e0) & op(e2, e2) = v2 & $i(v2)) | ( ~ (v1 = e0) & op(e1, % 127.57/17.79 | e1) = v1 & $i(v1)) | ( ~ (v0 = e0) & op(e0, e0) = v0 & % 127.57/17.79 | $i(v0)))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax7) implies: % 127.57/17.79 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e3) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e1, e2) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax8) implies: % 127.57/17.79 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e2) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e1, e3) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax9) implies: % 127.57/17.79 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e3) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e2, e1) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax10) implies: % 127.57/17.79 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e1) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e2, e3) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax11) implies: % 127.57/17.79 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e2) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e3, e1) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.79 | ALPHA: (ax12) implies: % 127.57/17.79 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.79 | ( ~ (v0 = e1) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.79 | = e0) & op(e3, e2) = v2 & $i(v2)))))) % 127.57/17.79 | % 127.57/17.80 | ALPHA: (ax13) implies: % 127.57/17.80 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e3) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e0, e2) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax14) implies: % 127.57/17.80 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e2) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e0, e3) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax15) implies: % 127.57/17.80 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e3) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e2, e0) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax16) implies: % 127.57/17.80 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e0) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e2, e3) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax17) implies: % 127.57/17.80 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e2) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e3, e0) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax18) implies: % 127.57/17.80 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e0) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.80 | = e1) & op(e3, e2) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax19) implies: % 127.57/17.80 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e3) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e0, e1) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax20) implies: % 127.57/17.80 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e1) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e0, e3) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax21) implies: % 127.57/17.80 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e3) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e1, e0) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax22) implies: % 127.57/17.80 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e0) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e1, e3) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax23) implies: % 127.57/17.80 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e1) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e3, e0) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax24) implies: % 127.57/17.80 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 127.57/17.80 | ( ~ (v0 = e0) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.80 | = e2) & op(e3, e1) = v2 & $i(v2)))))) % 127.57/17.80 | % 127.57/17.80 | ALPHA: (ax25) implies: % 127.57/17.81 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e2) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e0, e1) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (ax26) implies: % 127.57/17.81 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e1) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e0, e2) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (ax27) implies: % 127.57/17.81 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e2) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e1, e0) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (ax28) implies: % 127.57/17.81 | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e0) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e1, e2) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (ax29) implies: % 127.57/17.81 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e1) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e2, e0) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (ax30) implies: % 127.57/17.81 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 127.57/17.81 | ( ~ (v0 = e0) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 127.57/17.81 | = e3) & op(e2, e1) = v2 & $i(v2)))))) % 127.57/17.81 | % 127.57/17.81 | DELTA: instantiating (37) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 127.57/17.81 | (44) op(e3, e3) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e0) | (op(e3, e0) % 127.57/17.81 | = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e1) | ( ~ (all_4_0 = e2) % 127.57/17.81 | & op(e3, e1) = all_4_0 & $i(all_4_0))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (44) implies: % 127.57/17.81 | (45) op(e3, e3) = all_4_2 % 127.57/17.81 | (46) ~ (all_4_2 = e0) | (op(e3, e0) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 % 127.57/17.81 | = e1) | ( ~ (all_4_0 = e2) & op(e3, e1) = all_4_0 & % 127.57/17.81 | $i(all_4_0)))) % 127.57/17.81 | % 127.57/17.81 | DELTA: instantiating (28) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 127.57/17.81 | (47) op(e2, e2) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e3) | (op(e2, e3) % 127.57/17.81 | = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e0) | ( ~ (all_6_0 = e1) % 127.57/17.81 | & op(e2, e0) = all_6_0 & $i(all_6_0))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (47) implies: % 127.57/17.81 | (48) op(e2, e2) = all_6_2 % 127.57/17.81 | (49) ~ (all_6_2 = e3) | (op(e2, e3) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 % 127.57/17.81 | = e0) | ( ~ (all_6_0 = e1) & op(e2, e0) = all_6_0 & % 127.57/17.81 | $i(all_6_0)))) % 127.57/17.81 | % 127.57/17.81 | DELTA: instantiating (39) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 127.57/17.81 | (50) op(e0, e0) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | (op(e0, e1) % 127.57/17.81 | = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) % 127.57/17.81 | & op(e0, e2) = all_8_0 & $i(all_8_0))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (50) implies: % 127.57/17.81 | (51) op(e0, e0) = all_8_2 % 127.57/17.81 | (52) ~ (all_8_2 = e1) | (op(e0, e1) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 % 127.57/17.81 | = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 127.57/17.81 | $i(all_8_0)))) % 127.57/17.81 | % 127.57/17.81 | DELTA: instantiating (26) with fresh symbols all_10_0, all_10_1, all_10_2 % 127.57/17.81 | gives: % 127.57/17.81 | (53) op(e0, e0) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e3) | (op(e0, % 127.57/17.81 | e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e2) | ( ~ % 127.57/17.81 | (all_10_0 = e1) & op(e0, e2) = all_10_0 & $i(all_10_0))))) % 127.57/17.81 | % 127.57/17.81 | ALPHA: (53) implies: % 127.57/17.81 | (54) op(e0, e0) = all_10_2 % 127.57/17.81 | (55) ~ (all_10_2 = e3) | (op(e0, e3) = all_10_1 & $i(all_10_1) & ( ~ % 127.57/17.81 | (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & % 127.57/17.81 | $i(all_10_0)))) % 127.57/17.81 | % 127.57/17.81 | DELTA: instantiating (21) with fresh symbols all_12_0, all_12_1, all_12_2 % 127.57/17.81 | gives: % 127.57/17.82 | (56) op(e1, e1) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e2) | (op(e1, % 127.57/17.82 | e2) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e3) | ( ~ % 127.57/17.82 | (all_12_0 = e0) & op(e1, e3) = all_12_0 & $i(all_12_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (56) implies: % 127.57/17.82 | (57) op(e1, e1) = all_12_2 % 127.57/17.82 | (58) ~ (all_12_2 = e2) | (op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 127.57/17.82 | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, e3) = all_12_0 & % 127.57/17.82 | $i(all_12_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (30) with fresh symbols all_14_0, all_14_1, all_14_2 % 127.57/17.82 | gives: % 127.57/17.82 | (59) op(e3, e3) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e2) | (op(e3, % 127.57/17.82 | e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = e0) | ( ~ % 127.57/17.82 | (all_14_0 = e1) & op(e3, e0) = all_14_0 & $i(all_14_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (59) implies: % 127.57/17.82 | (60) op(e3, e3) = all_14_2 % 127.57/17.82 | (61) ~ (all_14_2 = e2) | (op(e3, e2) = all_14_1 & $i(all_14_1) & ( ~ % 127.57/17.82 | (all_14_1 = e0) | ( ~ (all_14_0 = e1) & op(e3, e0) = all_14_0 & % 127.57/17.82 | $i(all_14_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (32) with fresh symbols all_16_0, all_16_1, all_16_2 % 127.57/17.82 | gives: % 127.57/17.82 | (62) op(e0, e0) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e3) | (op(e0, % 127.57/17.82 | e3) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e1) | ( ~ % 127.57/17.82 | (all_16_0 = e2) & op(e0, e1) = all_16_0 & $i(all_16_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (62) implies: % 127.57/17.82 | (63) op(e0, e0) = all_16_2 % 127.57/17.82 | (64) ~ (all_16_2 = e3) | (op(e0, e3) = all_16_1 & $i(all_16_1) & ( ~ % 127.57/17.82 | (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 127.57/17.82 | $i(all_16_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (20) with fresh symbols all_18_0, all_18_1, all_18_2 % 127.57/17.82 | gives: % 127.57/17.82 | (65) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e3) | (op(e1, % 127.57/17.82 | e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 = e2) | ( ~ % 127.57/17.82 | (all_18_0 = e0) & op(e1, e2) = all_18_0 & $i(all_18_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (65) implies: % 127.57/17.82 | (66) op(e1, e1) = all_18_2 % 127.57/17.82 | (67) ~ (all_18_2 = e3) | (op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ % 127.57/17.82 | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, e2) = all_18_0 & % 127.57/17.82 | $i(all_18_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (33) with fresh symbols all_20_0, all_20_1, all_20_2 % 127.57/17.82 | gives: % 127.57/17.82 | (68) op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e1) | (op(e0, % 127.57/17.82 | e1) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e3) | ( ~ % 127.57/17.82 | (all_20_0 = e2) & op(e0, e3) = all_20_0 & $i(all_20_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (68) implies: % 127.57/17.82 | (69) op(e0, e0) = all_20_2 % 127.57/17.82 | (70) ~ (all_20_2 = e1) | (op(e0, e1) = all_20_1 & $i(all_20_1) & ( ~ % 127.57/17.82 | (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 & % 127.57/17.82 | $i(all_20_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (35) with fresh symbols all_22_0, all_22_1, all_22_2 % 127.57/17.82 | gives: % 127.57/17.82 | (71) op(e1, e1) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e0) | (op(e1, % 127.57/17.82 | e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e3) | ( ~ % 127.57/17.82 | (all_22_0 = e2) & op(e1, e3) = all_22_0 & $i(all_22_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (71) implies: % 127.57/17.82 | (72) op(e1, e1) = all_22_2 % 127.57/17.82 | (73) ~ (all_22_2 = e0) | (op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 127.57/17.82 | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 127.57/17.82 | $i(all_22_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (34) with fresh symbols all_24_0, all_24_1, all_24_2 % 127.57/17.82 | gives: % 127.57/17.82 | (74) op(e1, e1) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e3) | (op(e1, % 127.57/17.82 | e3) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e0) | ( ~ % 127.57/17.82 | (all_24_0 = e2) & op(e1, e0) = all_24_0 & $i(all_24_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (74) implies: % 127.57/17.82 | (75) op(e1, e1) = all_24_2 % 127.57/17.82 | (76) ~ (all_24_2 = e3) | (op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 127.57/17.82 | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, e0) = all_24_0 & % 127.57/17.82 | $i(all_24_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (23) with fresh symbols all_26_0, all_26_1, all_26_2 % 127.57/17.82 | gives: % 127.57/17.82 | (77) op(e2, e2) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e1) | (op(e2, % 127.57/17.82 | e1) = all_26_1 & $i(all_26_1) & ( ~ (all_26_1 = e3) | ( ~ % 127.57/17.82 | (all_26_0 = e0) & op(e2, e3) = all_26_0 & $i(all_26_0))))) % 127.57/17.82 | % 127.57/17.82 | ALPHA: (77) implies: % 127.57/17.82 | (78) op(e2, e2) = all_26_2 % 127.57/17.82 | (79) ~ (all_26_2 = e1) | (op(e2, e1) = all_26_1 & $i(all_26_1) & ( ~ % 127.57/17.82 | (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, e3) = all_26_0 & % 127.57/17.82 | $i(all_26_0)))) % 127.57/17.82 | % 127.57/17.82 | DELTA: instantiating (38) with fresh symbols all_28_0, all_28_1, all_28_2 % 127.57/17.82 | gives: % 127.57/17.83 | (80) op(e0, e0) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e2) | (op(e0, % 127.57/17.83 | e2) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e1) | ( ~ % 127.57/17.83 | (all_28_0 = e3) & op(e0, e1) = all_28_0 & $i(all_28_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (80) implies: % 127.57/17.83 | (81) op(e0, e0) = all_28_2 % 127.57/17.83 | (82) ~ (all_28_2 = e2) | (op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 127.57/17.83 | (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 127.57/17.83 | $i(all_28_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (40) with fresh symbols all_30_0, all_30_1, all_30_2 % 127.57/17.83 | gives: % 127.57/17.83 | (83) op(e1, e1) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e2) | (op(e1, % 127.57/17.83 | e2) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 = e0) | ( ~ % 127.57/17.83 | (all_30_0 = e3) & op(e1, e0) = all_30_0 & $i(all_30_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (83) implies: % 127.57/17.83 | (84) op(e1, e1) = all_30_2 % 127.57/17.83 | (85) ~ (all_30_2 = e2) | (op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ % 127.57/17.83 | (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e1, e0) = all_30_0 & % 127.57/17.83 | $i(all_30_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1, all_32_2 % 127.57/17.83 | gives: % 127.57/17.83 | (86) op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | (op(e3, % 127.57/17.83 | e2) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 = e1) | ( ~ % 127.57/17.83 | (all_32_0 = e0) & op(e3, e1) = all_32_0 & $i(all_32_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (86) implies: % 127.57/17.83 | (87) op(e3, e3) = all_32_2 % 127.57/17.83 | (88) ~ (all_32_2 = e2) | (op(e3, e2) = all_32_1 & $i(all_32_1) & ( ~ % 127.57/17.83 | (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, e1) = all_32_0 & % 127.57/17.83 | $i(all_32_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (25) with fresh symbols all_34_0, all_34_1, all_34_2 % 127.57/17.83 | gives: % 127.57/17.83 | (89) op(e3, e3) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e1) | (op(e3, % 127.57/17.83 | e1) = all_34_1 & $i(all_34_1) & ( ~ (all_34_1 = e2) | ( ~ % 127.57/17.83 | (all_34_0 = e0) & op(e3, e2) = all_34_0 & $i(all_34_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (89) implies: % 127.57/17.83 | (90) op(e3, e3) = all_34_2 % 127.57/17.83 | (91) ~ (all_34_2 = e1) | (op(e3, e1) = all_34_1 & $i(all_34_1) & ( ~ % 127.57/17.83 | (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e3, e2) = all_34_0 & % 127.57/17.83 | $i(all_34_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (27) with fresh symbols all_36_0, all_36_1, all_36_2 % 127.57/17.83 | gives: % 127.57/17.83 | (92) op(e0, e0) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e2) | (op(e0, % 127.57/17.83 | e2) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e3) | ( ~ % 127.57/17.83 | (all_36_0 = e1) & op(e0, e3) = all_36_0 & $i(all_36_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (92) implies: % 127.57/17.83 | (93) op(e0, e0) = all_36_2 % 127.57/17.83 | (94) ~ (all_36_2 = e2) | (op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 127.57/17.83 | (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, e3) = all_36_0 & % 127.57/17.83 | $i(all_36_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (41) with fresh symbols all_38_0, all_38_1, all_38_2 % 127.57/17.83 | gives: % 127.57/17.83 | (95) op(e1, e1) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e0) | (op(e1, % 127.57/17.83 | e0) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e2) | ( ~ % 127.57/17.83 | (all_38_0 = e3) & op(e1, e2) = all_38_0 & $i(all_38_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (95) implies: % 127.57/17.83 | (96) op(e1, e1) = all_38_2 % 127.57/17.83 | (97) ~ (all_38_2 = e0) | (op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 127.57/17.83 | (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 127.57/17.83 | $i(all_38_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (42) with fresh symbols all_40_0, all_40_1, all_40_2 % 127.57/17.83 | gives: % 127.57/17.83 | (98) op(e2, e2) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e1) | (op(e2, % 127.57/17.83 | e1) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e0) | ( ~ % 127.57/17.83 | (all_40_0 = e3) & op(e2, e0) = all_40_0 & $i(all_40_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (98) implies: % 127.57/17.83 | (99) op(e2, e2) = all_40_2 % 127.57/17.83 | (100) ~ (all_40_2 = e1) | (op(e2, e1) = all_40_1 & $i(all_40_1) & ( ~ % 127.57/17.83 | (all_40_1 = e0) | ( ~ (all_40_0 = e3) & op(e2, e0) = all_40_0 & % 127.57/17.83 | $i(all_40_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (43) with fresh symbols all_42_0, all_42_1, all_42_2 % 127.57/17.83 | gives: % 127.57/17.83 | (101) op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e0) | (op(e2, % 127.57/17.83 | e0) = all_42_1 & $i(all_42_1) & ( ~ (all_42_1 = e1) | ( ~ % 127.57/17.83 | (all_42_0 = e3) & op(e2, e1) = all_42_0 & $i(all_42_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (101) implies: % 127.57/17.83 | (102) op(e2, e2) = all_42_2 % 127.57/17.83 | (103) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 127.57/17.83 | (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 127.57/17.83 | $i(all_42_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (29) with fresh symbols all_44_0, all_44_1, all_44_2 % 127.57/17.83 | gives: % 127.57/17.83 | (104) op(e2, e2) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e0) | (op(e2, % 127.57/17.83 | e0) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 = e3) | ( ~ % 127.57/17.83 | (all_44_0 = e1) & op(e2, e3) = all_44_0 & $i(all_44_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (104) implies: % 127.57/17.83 | (105) op(e2, e2) = all_44_2 % 127.57/17.83 | (106) ~ (all_44_2 = e0) | (op(e2, e0) = all_44_1 & $i(all_44_1) & ( ~ % 127.57/17.83 | (all_44_1 = e3) | ( ~ (all_44_0 = e1) & op(e2, e3) = all_44_0 & % 127.57/17.83 | $i(all_44_0)))) % 127.57/17.83 | % 127.57/17.83 | DELTA: instantiating (36) with fresh symbols all_46_0, all_46_1, all_46_2 % 127.57/17.83 | gives: % 127.57/17.83 | (107) op(e3, e3) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e1) | (op(e3, % 127.57/17.83 | e1) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e0) | ( ~ % 127.57/17.83 | (all_46_0 = e2) & op(e3, e0) = all_46_0 & $i(all_46_0))))) % 127.57/17.83 | % 127.57/17.83 | ALPHA: (107) implies: % 127.57/17.83 | (108) op(e3, e3) = all_46_2 % 127.57/17.84 | (109) ~ (all_46_2 = e1) | (op(e3, e1) = all_46_1 & $i(all_46_1) & ( ~ % 127.57/17.84 | (all_46_1 = e0) | ( ~ (all_46_0 = e2) & op(e3, e0) = all_46_0 & % 127.57/17.84 | $i(all_46_0)))) % 127.57/17.84 | % 127.57/17.84 | DELTA: instantiating (31) with fresh symbols all_48_0, all_48_1, all_48_2 % 127.57/17.84 | gives: % 127.57/17.84 | (110) op(e3, e3) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e0) | (op(e3, % 127.57/17.84 | e0) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e2) | ( ~ % 127.57/17.84 | (all_48_0 = e1) & op(e3, e2) = all_48_0 & $i(all_48_0))))) % 127.57/17.84 | % 127.57/17.84 | ALPHA: (110) implies: % 127.57/17.84 | (111) op(e3, e3) = all_48_2 % 127.57/17.84 | (112) ~ (all_48_2 = e0) | (op(e3, e0) = all_48_1 & $i(all_48_1) & ( ~ % 127.57/17.84 | (all_48_1 = e2) | ( ~ (all_48_0 = e1) & op(e3, e2) = all_48_0 & % 127.57/17.84 | $i(all_48_0)))) % 127.57/17.84 | % 127.57/17.84 | DELTA: instantiating (22) with fresh symbols all_50_0, all_50_1, all_50_2 % 127.57/17.84 | gives: % 127.57/17.84 | (113) op(e2, e2) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e3) | (op(e2, % 127.57/17.84 | e3) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e1) | ( ~ % 127.57/17.84 | (all_50_0 = e0) & op(e2, e1) = all_50_0 & $i(all_50_0))))) % 127.57/17.84 | % 127.57/17.84 | ALPHA: (113) implies: % 127.57/17.84 | (114) op(e2, e2) = all_50_2 % 127.57/17.84 | (115) ~ (all_50_2 = e3) | (op(e2, e3) = all_50_1 & $i(all_50_1) & ( ~ % 127.57/17.84 | (all_50_1 = e1) | ( ~ (all_50_0 = e0) & op(e2, e1) = all_50_0 & % 127.57/17.84 | $i(all_50_0)))) % 127.57/17.84 | % 127.57/17.84 | DELTA: instantiating (19) with fresh symbols all_52_0, all_52_1, all_52_2, % 127.57/17.84 | all_52_3 gives: % 127.57/17.84 | (116) (( ~ (all_52_0 = e3) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e3) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e3) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e3) & op(e0, e0) = all_52_3 & $i(all_52_3))) & (( ~ % 127.57/17.84 | (all_52_0 = e2) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e2) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e2) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e2) & op(e0, e0) = all_52_3 & $i(all_52_3))) & (( ~ % 127.57/17.84 | (all_52_0 = e1) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e1) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e1) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e1) & op(e0, e0) = all_52_3 & $i(all_52_3))) & (( ~ % 127.57/17.84 | (all_52_0 = e0) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e0) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e0) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e0) & op(e0, e0) = all_52_3 & $i(all_52_3))) % 127.57/17.84 | % 127.57/17.84 | ALPHA: (116) implies: % 127.57/17.84 | (117) ( ~ (all_52_0 = e0) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e0) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e0) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e0) & op(e0, e0) = all_52_3 & $i(all_52_3)) % 127.57/17.84 | (118) ( ~ (all_52_0 = e1) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e1) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e1) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e1) & op(e0, e0) = all_52_3 & $i(all_52_3)) % 127.57/17.84 | (119) ( ~ (all_52_0 = e2) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e2) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e2) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e2) & op(e0, e0) = all_52_3 & $i(all_52_3)) % 127.57/17.84 | (120) ( ~ (all_52_0 = e3) & op(e3, e3) = all_52_0 & $i(all_52_0)) | ( ~ % 127.57/17.84 | (all_52_1 = e3) & op(e2, e2) = all_52_1 & $i(all_52_1)) | ( ~ % 127.57/17.84 | (all_52_2 = e3) & op(e1, e1) = all_52_2 & $i(all_52_2)) | ( ~ % 127.57/17.84 | (all_52_3 = e3) & op(e0, e0) = all_52_3 & $i(all_52_3)) % 127.57/17.84 | % 127.57/17.84 | DELTA: instantiating (12) with fresh symbols all_53_0, all_53_1, all_53_2, % 127.57/17.84 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8, all_53_9, % 127.57/17.84 | all_53_10, all_53_11, all_53_12, all_53_13, all_53_14, all_53_15 gives: % 127.57/17.84 | (121) ~ (all_53_0 = all_53_1) & ~ (all_53_0 = all_53_2) & ~ (all_53_0 = % 127.57/17.84 | all_53_3) & ~ (all_53_0 = all_53_4) & ~ (all_53_0 = all_53_8) & % 127.57/17.84 | ~ (all_53_0 = all_53_12) & ~ (all_53_1 = all_53_2) & ~ (all_53_1 = % 127.57/17.84 | all_53_3) & ~ (all_53_1 = all_53_5) & ~ (all_53_1 = all_53_9) & % 127.57/17.84 | ~ (all_53_1 = all_53_13) & ~ (all_53_2 = all_53_3) & ~ (all_53_2 = % 127.57/17.84 | all_53_6) & ~ (all_53_2 = all_53_10) & ~ (all_53_2 = all_53_14) & % 127.57/17.84 | ~ (all_53_3 = all_53_7) & ~ (all_53_3 = all_53_11) & ~ (all_53_3 = % 127.57/17.84 | all_53_15) & ~ (all_53_4 = all_53_5) & ~ (all_53_4 = all_53_6) & % 127.57/17.84 | ~ (all_53_4 = all_53_7) & ~ (all_53_4 = all_53_8) & ~ (all_53_4 = % 127.57/17.84 | all_53_12) & ~ (all_53_5 = all_53_6) & ~ (all_53_5 = all_53_7) & % 127.57/17.84 | ~ (all_53_5 = all_53_9) & ~ (all_53_5 = all_53_13) & ~ (all_53_6 = % 127.57/17.84 | all_53_7) & ~ (all_53_6 = all_53_10) & ~ (all_53_6 = all_53_14) & % 127.57/17.84 | ~ (all_53_7 = all_53_11) & ~ (all_53_7 = all_53_15) & ~ (all_53_8 % 127.57/17.84 | = all_53_9) & ~ (all_53_8 = all_53_10) & ~ (all_53_8 = all_53_11) % 127.57/17.84 | & ~ (all_53_8 = all_53_12) & ~ (all_53_9 = all_53_10) & ~ % 127.57/17.84 | (all_53_9 = all_53_11) & ~ (all_53_9 = all_53_13) & ~ (all_53_10 = % 127.57/17.84 | all_53_11) & ~ (all_53_10 = all_53_14) & ~ (all_53_11 = % 127.57/17.84 | all_53_15) & ~ (all_53_12 = all_53_13) & ~ (all_53_12 = % 127.57/17.84 | all_53_14) & ~ (all_53_12 = all_53_15) & ~ (all_53_13 = % 127.57/17.84 | all_53_14) & ~ (all_53_13 = all_53_15) & ~ (all_53_14 = % 127.57/17.84 | all_53_15) & op(e3, e3) = all_53_0 & op(e3, e2) = all_53_4 & op(e3, % 127.57/17.84 | e1) = all_53_8 & op(e3, e0) = all_53_12 & op(e2, e3) = all_53_1 & % 127.57/17.84 | op(e2, e2) = all_53_5 & op(e2, e1) = all_53_9 & op(e2, e0) = % 127.57/17.84 | all_53_13 & op(e1, e3) = all_53_2 & op(e1, e2) = all_53_6 & op(e1, % 127.57/17.84 | e1) = all_53_10 & op(e1, e0) = all_53_14 & op(e0, e3) = all_53_3 & % 127.57/17.84 | op(e0, e2) = all_53_7 & op(e0, e1) = all_53_11 & op(e0, e0) = % 127.57/17.84 | all_53_15 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) % 127.57/17.84 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) & % 127.57/17.84 | $i(all_53_8) & $i(all_53_9) & $i(all_53_10) & $i(all_53_11) & % 127.57/17.84 | $i(all_53_12) & $i(all_53_13) & $i(all_53_14) & $i(all_53_15) % 127.57/17.84 | % 127.57/17.84 | ALPHA: (121) implies: % 127.57/17.84 | (122) ~ (all_53_14 = all_53_15) % 127.57/17.84 | (123) ~ (all_53_13 = all_53_15) % 127.57/17.84 | (124) ~ (all_53_13 = all_53_14) % 127.57/17.84 | (125) ~ (all_53_12 = all_53_15) % 127.57/17.84 | (126) ~ (all_53_12 = all_53_14) % 127.57/17.84 | (127) ~ (all_53_12 = all_53_13) % 127.57/17.84 | (128) ~ (all_53_11 = all_53_15) % 127.57/17.84 | (129) ~ (all_53_10 = all_53_14) % 127.57/17.84 | (130) ~ (all_53_10 = all_53_11) % 127.57/17.84 | (131) ~ (all_53_9 = all_53_13) % 127.57/17.84 | (132) ~ (all_53_9 = all_53_11) % 127.57/17.84 | (133) ~ (all_53_9 = all_53_10) % 127.57/17.85 | (134) ~ (all_53_8 = all_53_12) % 127.57/17.85 | (135) ~ (all_53_8 = all_53_11) % 127.57/17.85 | (136) ~ (all_53_8 = all_53_10) % 127.57/17.85 | (137) ~ (all_53_8 = all_53_9) % 127.57/17.85 | (138) ~ (all_53_7 = all_53_15) % 127.57/17.85 | (139) ~ (all_53_7 = all_53_11) % 127.57/17.85 | (140) ~ (all_53_6 = all_53_14) % 127.57/17.85 | (141) ~ (all_53_6 = all_53_10) % 127.57/17.85 | (142) ~ (all_53_6 = all_53_7) % 127.57/17.85 | (143) ~ (all_53_5 = all_53_13) % 127.57/17.85 | (144) ~ (all_53_5 = all_53_9) % 127.57/17.85 | (145) ~ (all_53_5 = all_53_7) % 127.57/17.85 | (146) ~ (all_53_5 = all_53_6) % 127.57/17.85 | (147) ~ (all_53_4 = all_53_12) % 127.57/17.85 | (148) ~ (all_53_4 = all_53_8) % 127.57/17.85 | (149) ~ (all_53_4 = all_53_7) % 127.57/17.85 | (150) ~ (all_53_4 = all_53_6) % 127.57/17.85 | (151) ~ (all_53_4 = all_53_5) % 127.57/17.85 | (152) ~ (all_53_3 = all_53_15) % 127.57/17.85 | (153) ~ (all_53_3 = all_53_11) % 127.57/17.85 | (154) ~ (all_53_3 = all_53_7) % 127.57/17.85 | (155) ~ (all_53_2 = all_53_14) % 127.57/17.85 | (156) ~ (all_53_2 = all_53_10) % 127.57/17.85 | (157) ~ (all_53_2 = all_53_6) % 127.57/17.85 | (158) ~ (all_53_2 = all_53_3) % 127.57/17.85 | (159) ~ (all_53_1 = all_53_13) % 127.57/17.85 | (160) ~ (all_53_1 = all_53_9) % 127.57/17.85 | (161) ~ (all_53_1 = all_53_5) % 127.57/17.85 | (162) ~ (all_53_1 = all_53_3) % 127.57/17.85 | (163) ~ (all_53_1 = all_53_2) % 127.57/17.85 | (164) ~ (all_53_0 = all_53_12) % 127.57/17.85 | (165) ~ (all_53_0 = all_53_8) % 127.57/17.85 | (166) ~ (all_53_0 = all_53_4) % 127.57/17.85 | (167) ~ (all_53_0 = all_53_3) % 127.57/17.85 | (168) ~ (all_53_0 = all_53_2) % 127.57/17.85 | (169) ~ (all_53_0 = all_53_1) % 127.57/17.85 | (170) op(e0, e0) = all_53_15 % 127.57/17.85 | (171) op(e0, e1) = all_53_11 % 127.57/17.85 | (172) op(e0, e2) = all_53_7 % 127.57/17.85 | (173) op(e0, e3) = all_53_3 % 127.57/17.85 | (174) op(e1, e0) = all_53_14 % 127.57/17.85 | (175) op(e1, e1) = all_53_10 % 127.57/17.85 | (176) op(e1, e2) = all_53_6 % 127.57/17.85 | (177) op(e1, e3) = all_53_2 % 127.57/17.85 | (178) op(e2, e0) = all_53_13 % 127.57/17.85 | (179) op(e2, e1) = all_53_9 % 127.57/17.85 | (180) op(e2, e2) = all_53_5 % 127.57/17.85 | (181) op(e2, e3) = all_53_1 % 127.57/17.85 | (182) op(e3, e0) = all_53_12 % 127.57/17.85 | (183) op(e3, e1) = all_53_8 % 127.57/17.85 | (184) op(e3, e2) = all_53_4 % 127.57/17.85 | (185) op(e3, e3) = all_53_0 % 127.57/17.85 | % 127.57/17.85 | DELTA: instantiating (1) with fresh symbols all_55_0, all_55_1, all_55_2, % 127.57/17.85 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, all_55_8, all_55_9, % 127.57/17.85 | all_55_10, all_55_11, all_55_12, all_55_13, all_55_14, all_55_15 gives: % 127.57/17.85 | (186) op(e3, e3) = all_55_0 & op(e3, e2) = all_55_1 & op(e3, e1) = all_55_2 % 127.57/17.85 | & op(e3, e0) = all_55_3 & op(e2, e3) = all_55_4 & op(e2, e2) = % 127.57/17.85 | all_55_5 & op(e2, e1) = all_55_6 & op(e2, e0) = all_55_7 & op(e1, e3) % 127.57/17.85 | = all_55_8 & op(e1, e2) = all_55_9 & op(e1, e1) = all_55_10 & op(e1, % 127.57/17.85 | e0) = all_55_11 & op(e0, e3) = all_55_12 & op(e0, e2) = all_55_13 & % 127.57/17.85 | op(e0, e1) = all_55_14 & op(e0, e0) = all_55_15 & $i(all_55_0) & % 127.57/17.85 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) & % 127.57/17.85 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7) & $i(all_55_8) & % 127.57/17.85 | $i(all_55_9) & $i(all_55_10) & $i(all_55_11) & $i(all_55_12) & % 127.57/17.85 | $i(all_55_13) & $i(all_55_14) & $i(all_55_15) & (all_55_0 = e3 | % 127.57/17.85 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0) & (all_55_1 = e3 | % 127.57/17.85 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0) & (all_55_2 = e3 | % 127.57/17.85 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0) & (all_55_3 = e3 | % 127.57/17.85 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0) & (all_55_4 = e3 | % 127.57/17.85 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0) & (all_55_5 = e3 | % 127.57/17.85 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0) & (all_55_6 = e3 | % 127.57/17.85 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0) & (all_55_7 = e3 | % 127.57/17.85 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0) & (all_55_8 = e3 | % 127.57/17.85 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0) & (all_55_9 = e3 | % 127.57/17.85 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0) & (all_55_10 = e3 | % 127.57/17.85 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0) & (all_55_11 = e3 % 127.57/17.85 | | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0) & (all_55_12 = % 127.57/17.85 | e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0) & (all_55_13 % 127.57/17.85 | = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0) & % 127.57/17.85 | (all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0) & % 127.57/17.85 | (all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0) % 127.57/17.85 | % 127.57/17.85 | ALPHA: (186) implies: % 127.57/17.85 | (187) op(e0, e0) = all_55_15 % 127.57/17.85 | (188) op(e0, e1) = all_55_14 % 127.57/17.85 | (189) op(e0, e2) = all_55_13 % 127.57/17.85 | (190) op(e0, e3) = all_55_12 % 127.57/17.85 | (191) op(e1, e0) = all_55_11 % 127.57/17.85 | (192) op(e1, e1) = all_55_10 % 127.57/17.85 | (193) op(e1, e2) = all_55_9 % 127.57/17.85 | (194) op(e1, e3) = all_55_8 % 127.57/17.85 | (195) op(e2, e0) = all_55_7 % 127.57/17.85 | (196) op(e2, e1) = all_55_6 % 127.57/17.85 | (197) op(e2, e2) = all_55_5 % 127.57/17.85 | (198) op(e2, e3) = all_55_4 % 127.57/17.85 | (199) op(e3, e0) = all_55_3 % 127.57/17.85 | (200) op(e3, e1) = all_55_2 % 127.57/17.85 | (201) op(e3, e2) = all_55_1 % 127.57/17.85 | (202) op(e3, e3) = all_55_0 % 127.57/17.85 | (203) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 127.57/17.85 | (204) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 127.57/17.85 | (205) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 127.57/17.85 | (206) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 127.57/17.85 | (207) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 127.57/17.85 | (208) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 127.57/17.86 | (209) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 127.57/17.86 | (210) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 127.57/17.86 | (211) all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0 % 127.57/17.86 | (212) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 127.57/17.86 | (213) all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0 % 127.57/17.86 | (214) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 127.57/17.86 | (215) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 127.57/17.86 | (216) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 127.57/17.86 | (217) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 127.57/17.86 | % 127.57/17.86 | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1, all_57_2, % 127.57/17.86 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9, % 127.57/17.86 | all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives: % 127.57/17.86 | (218) ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 127.57/17.86 | e3) | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, % 127.57/17.86 | e0) = e3)) & ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = % 127.57/17.86 | e3 & op(e2, e3) = e3) | (all_57_6 = e3 & op(e1, e3) = e3) | % 127.57/17.86 | (all_57_12 = e3 & op(e0, e3) = e3)) & ((all_57_0 = e2 & op(e3, e3) % 127.57/17.86 | = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_4 = e2 & % 127.57/17.86 | op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)) & % 127.57/17.86 | ((all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 127.57/17.86 | e2) | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & % 127.57/17.86 | op(e0, e3) = e2)) & ((all_57_0 = e1 & op(e3, e3) = e1) | % 127.57/17.86 | (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_4 = e1 & op(e3, e1) = % 127.57/17.86 | e1) | (all_57_9 = e1 & op(e3, e0) = e1)) & ((all_57_0 = e1 & % 127.57/17.86 | op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_6 % 127.57/17.86 | = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)) & % 127.57/17.86 | ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 127.57/17.86 | e0) | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, % 127.57/17.86 | e0) = e0)) & ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = % 127.57/17.86 | e0 & op(e2, e3) = e0) | (all_57_6 = e0 & op(e1, e3) = e0) | % 127.57/17.86 | (all_57_12 = e0 & op(e0, e3) = e0)) & ((all_57_1 = e3 & op(e3, e2) % 127.57/17.86 | = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | (all_57_7 = e3 & % 127.57/17.86 | op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)) & % 127.57/17.86 | ((all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = % 127.57/17.86 | e2) | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & % 127.57/17.86 | op(e0, e2) = e2)) & ((all_57_1 = e1 & op(e3, e2) = e1) | % 127.57/17.86 | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_7 = e1 & op(e1, e2) = % 127.57/17.86 | e1) | (all_57_13 = e1 & op(e0, e2) = e1)) & ((all_57_1 = e0 & % 127.57/17.86 | op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | (all_57_7 % 127.57/17.86 | = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)) & % 127.57/17.86 | ((all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = % 127.57/17.86 | e3) | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & % 127.57/17.86 | op(e2, e0) = e3)) & ((all_57_2 = e2 & op(e2, e3) = e2) | % 127.57/17.86 | (all_57_3 = e2 & op(e2, e2) = e2) | (all_57_5 = e2 & op(e2, e1) = % 127.57/17.86 | e2) | (all_57_10 = e2 & op(e2, e0) = e2)) & ((all_57_2 = e1 & % 127.57/17.86 | op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_5 % 127.57/17.86 | = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)) & % 127.57/17.86 | ((all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 127.57/17.86 | e0) | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & % 127.57/17.86 | op(e2, e0) = e0)) & ((all_57_4 = e3 & op(e3, e1) = e3) | % 127.57/17.86 | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_8 = e3 & op(e1, e1) = % 127.57/17.86 | e3) | (all_57_14 = e3 & op(e0, e1) = e3)) & ((all_57_4 = e2 & % 127.57/17.86 | op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_8 % 127.57/17.86 | = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)) & % 127.57/17.86 | ((all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = % 127.57/17.86 | e1) | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & % 127.57/17.86 | op(e0, e1) = e1)) & ((all_57_4 = e0 & op(e3, e1) = e0) | % 127.57/17.86 | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_8 = e0 & op(e1, e1) = % 127.57/17.86 | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) & ((all_57_6 = e3 & % 127.57/17.86 | op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_8 % 127.57/17.86 | = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)) & % 127.57/17.86 | ((all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 127.57/17.86 | e2) | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & % 127.57/17.86 | op(e1, e0) = e2)) & ((all_57_6 = e1 & op(e1, e3) = e1) | % 127.57/17.86 | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_8 = e1 & op(e1, e1) = % 127.57/17.86 | e1) | (all_57_11 = e1 & op(e1, e0) = e1)) & ((all_57_6 = e0 & % 127.57/17.86 | op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_8 % 127.57/17.86 | = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 127.57/17.86 | ((all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 127.57/17.86 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & % 127.57/17.86 | op(e0, e0) = e3)) & ((all_57_9 = e2 & op(e3, e0) = e2) | % 127.57/17.86 | (all_57_10 = e2 & op(e2, e0) = e2) | (all_57_11 = e2 & op(e1, e0) = % 127.57/17.86 | e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & ((all_57_9 = e1 & % 127.57/17.86 | op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 127.57/17.86 | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = % 127.57/17.86 | e1)) & ((all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & % 127.57/17.86 | op(e0, e2) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) | % 127.57/17.86 | (all_57_15 = e3 & op(e0, e0) = e3)) & ((all_57_12 = e2 & op(e0, e3) % 127.57/17.86 | = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | (all_57_14 = e2 & % 127.57/17.86 | op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & % 127.57/17.86 | ((all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 127.57/17.86 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & % 127.57/17.86 | op(e0, e0) = e1)) & ((all_57_15 = e0 & op(e0, e0) = e0) | % 127.57/17.86 | (((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) % 127.57/17.86 | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = % 127.57/17.86 | e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 127.57/17.86 | (all_57_14 = e0 & op(e0, e1) = e0)))) % 127.57/17.86 | % 127.57/17.86 | ALPHA: (218) implies: % 127.57/17.87 | (219) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = % 127.57/17.87 | e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 127.57/17.87 | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | % 127.57/17.87 | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) % 127.57/17.87 | = e0))) % 127.57/17.87 | (220) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 127.57/17.87 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, % 127.57/17.87 | e0) = e1) % 127.57/17.87 | (221) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = % 127.57/17.87 | e2) | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 127.57/17.87 | e0) = e2) % 127.57/17.87 | (222) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 127.57/17.87 | e3) | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, % 127.57/17.87 | e0) = e3) % 127.57/17.87 | (223) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = % 127.57/17.87 | e1) | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, % 127.57/17.87 | e0) = e1) % 127.57/17.87 | (224) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = % 127.57/17.87 | e2) | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, % 127.57/17.87 | e0) = e2) % 127.57/17.87 | (225) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 127.57/17.87 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, % 127.57/17.87 | e0) = e3) % 127.57/17.87 | (226) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) % 127.57/17.87 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = % 127.57/17.87 | e0) % 127.57/17.87 | (227) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) % 127.57/17.87 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = % 127.57/17.87 | e1) % 127.57/17.87 | (228) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) % 127.57/17.87 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 127.57/17.87 | e2) % 127.57/17.87 | (229) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) % 127.57/17.87 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 127.57/17.87 | e3) % 127.57/17.87 | (230) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) % 127.57/17.87 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 127.57/17.87 | e0) % 127.57/17.87 | (231) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 127.57/17.87 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 127.57/17.87 | e1) % 127.57/17.87 | (232) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) % 127.57/17.87 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = % 127.57/17.87 | e2) % 127.57/17.87 | (233) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) % 127.57/17.87 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = % 127.57/17.87 | e3) % 127.57/17.87 | (234) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 127.57/17.87 | | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 127.57/17.87 | e0) % 127.57/17.87 | (235) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 127.57/17.87 | | (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 127.57/17.87 | e1) % 127.57/17.87 | (236) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 127.57/17.87 | | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 127.57/17.87 | e2) % 127.57/17.87 | (237) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 127.57/17.87 | | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = % 127.57/17.87 | e3) % 127.57/17.87 | (238) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 127.57/17.87 | | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = % 127.57/17.87 | e0) % 127.57/17.87 | (239) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 127.57/17.87 | | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = % 127.57/17.87 | e1) % 127.57/17.87 | (240) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 127.57/17.87 | | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = % 127.57/17.87 | e2) % 127.57/17.87 | (241) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 127.57/17.87 | | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = % 127.57/17.87 | e3) % 127.57/17.87 | (242) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) % 127.57/17.87 | | (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 127.57/17.87 | e0) % 127.57/17.87 | (243) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 127.57/17.87 | | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 127.57/17.87 | e0) % 127.57/17.88 | (244) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 127.57/17.88 | | (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 127.57/17.88 | e1) % 127.57/17.88 | (245) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 127.57/17.88 | | (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 127.57/17.88 | e1) % 127.57/17.88 | (246) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) % 127.57/17.88 | | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 127.57/17.88 | e2) % 127.57/17.88 | (247) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) % 127.57/17.88 | | (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 127.57/17.88 | e2) % 127.57/17.88 | (248) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 127.57/17.88 | | (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 127.57/17.88 | e3) % 127.57/17.88 | (249) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 127.57/17.88 | | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 127.57/17.88 | e3) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_28_2, e0, e0, % 127.57/17.88 | simplifying with (69), (81) gives: % 127.57/17.88 | (250) all_28_2 = all_20_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_28_2, e0, e0, % 127.57/17.88 | simplifying with (63), (81) gives: % 127.57/17.88 | (251) all_28_2 = all_16_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_36_2, e0, e0, % 127.57/17.88 | simplifying with (69), (93) gives: % 127.57/17.88 | (252) all_36_2 = all_20_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_36_2, e0, e0, % 127.57/17.88 | simplifying with (54), (93) gives: % 127.57/17.88 | (253) all_36_2 = all_10_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_53_15, e0, e0, % 127.57/17.88 | simplifying with (81), (170) gives: % 127.57/17.88 | (254) all_53_15 = all_28_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_15, all_55_15, e0, % 127.57/17.88 | e0, simplifying with (170), (187) gives: % 127.57/17.88 | (255) all_55_15 = all_53_15 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_55_15, e0, e0, % 127.57/17.88 | simplifying with (51), (187) gives: % 127.57/17.88 | (256) all_55_15 = all_8_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_11, all_55_14, e1, % 127.57/17.88 | e0, simplifying with (171), (188) gives: % 127.57/17.88 | (257) all_55_14 = all_53_11 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_7, all_55_13, e2, e0, % 127.57/17.88 | simplifying with (172), (189) gives: % 127.57/17.88 | (258) all_55_13 = all_53_7 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_3, all_55_12, e3, e0, % 127.57/17.88 | simplifying with (173), (190) gives: % 127.57/17.88 | (259) all_55_12 = all_53_3 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_55_12, e0, e3, e0, % 127.57/17.88 | simplifying with (190) gives: % 127.57/17.88 | (260) all_55_12 = e0 | ~ (op(e0, e3) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_3, e0, e3, e0, % 127.57/17.88 | simplifying with (173) gives: % 127.57/17.88 | (261) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_55_13, e0, e2, e0, % 127.57/17.88 | simplifying with (189) gives: % 127.57/17.88 | (262) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_7, e0, e2, e0, % 127.57/17.88 | simplifying with (172) gives: % 127.57/17.88 | (263) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_55_14, e0, e1, e0, % 127.57/17.88 | simplifying with (188) gives: % 127.57/17.88 | (264) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_11, e0, e1, e0, % 127.57/17.88 | simplifying with (171) gives: % 127.57/17.88 | (265) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_55_15, e0, e0, e0, % 127.57/17.88 | simplifying with (187) gives: % 127.57/17.88 | (266) all_55_15 = e0 | ~ (op(e0, e0) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_15, e0, e0, e0, % 127.57/17.88 | simplifying with (170) gives: % 127.57/17.88 | (267) all_53_15 = e0 | ~ (op(e0, e0) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_36_2, e0, e0, e0, % 127.57/17.88 | simplifying with (93) gives: % 127.57/17.88 | (268) all_36_2 = e0 | ~ (op(e0, e0) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_16_2, e0, e0, e0, % 127.57/17.88 | simplifying with (63) gives: % 127.57/17.88 | (269) all_16_2 = e0 | ~ (op(e0, e0) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, e0, e0, % 127.57/17.88 | simplifying with (54) gives: % 127.57/17.88 | (270) all_10_2 = e0 | ~ (op(e0, e0) = e0) % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_53_14, all_55_11, e0, % 127.57/17.88 | e1, simplifying with (174), (191) gives: % 127.57/17.88 | (271) all_55_11 = all_53_14 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_22_2, e1, e1, % 127.57/17.88 | simplifying with (66), (72) gives: % 127.57/17.88 | (272) all_22_2 = all_18_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_24_2, e1, e1, % 127.57/17.88 | simplifying with (72), (75) gives: % 127.57/17.88 | (273) all_24_2 = all_22_2 % 127.57/17.88 | % 127.57/17.88 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_30_2, e1, e1, % 127.57/17.88 | simplifying with (75), (84) gives: % 127.57/17.88 | (274) all_30_2 = all_24_2 % 127.57/17.88 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_38_2, e1, e1, % 127.57/17.89 | simplifying with (84), (96) gives: % 127.57/17.89 | (275) all_38_2 = all_30_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_53_10, e1, e1, % 127.57/17.89 | simplifying with (96), (175) gives: % 127.57/17.89 | (276) all_53_10 = all_38_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_10, all_55_10, e1, % 127.57/17.89 | e1, simplifying with (175), (192) gives: % 127.57/17.89 | (277) all_55_10 = all_53_10 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_55_10, e1, e1, % 127.57/17.89 | simplifying with (57), (192) gives: % 127.57/17.89 | (278) all_55_10 = all_12_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_6, all_55_9, e2, e1, % 127.57/17.89 | simplifying with (176), (193) gives: % 127.57/17.89 | (279) all_55_9 = all_53_6 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_2, all_55_8, e3, e1, % 127.57/17.89 | simplifying with (177), (194) gives: % 127.57/17.89 | (280) all_55_8 = all_53_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_2, e1, e3, e1, % 127.57/17.89 | simplifying with (177) gives: % 127.57/17.89 | (281) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_55_9, e1, e2, e1, % 127.57/17.89 | simplifying with (193) gives: % 127.57/17.89 | (282) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_6, e1, e2, e1, % 127.57/17.89 | simplifying with (176) gives: % 127.57/17.89 | (283) all_53_6 = e1 | ~ (op(e1, e2) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_22_2, e1, e1, e1, % 127.57/17.89 | simplifying with (72) gives: % 127.57/17.89 | (284) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_12_2, e1, e1, e1, % 127.57/17.89 | simplifying with (57) gives: % 127.57/17.89 | (285) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_14, e1, e0, e1, % 127.57/17.89 | simplifying with (174) gives: % 127.57/17.89 | (286) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_13, all_55_7, e0, e2, % 127.57/17.89 | simplifying with (178), (195) gives: % 127.57/17.89 | (287) all_55_7 = all_53_13 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_9, all_55_6, e1, e2, % 127.57/17.89 | simplifying with (179), (196) gives: % 127.57/17.89 | (288) all_55_6 = all_53_9 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_44_2, e2, e2, % 127.57/17.89 | simplifying with (102), (105) gives: % 127.57/17.89 | (289) all_44_2 = all_42_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_44_2, e2, e2, % 127.57/17.89 | simplifying with (99), (105) gives: % 127.57/17.89 | (290) all_44_2 = all_40_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_50_2, e2, e2, % 127.57/17.89 | simplifying with (102), (114) gives: % 127.57/17.89 | (291) all_50_2 = all_42_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_53_5, e2, e2, % 127.57/17.89 | simplifying with (114), (180) gives: % 127.57/17.89 | (292) all_53_5 = all_50_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_53_5, e2, e2, % 127.57/17.89 | simplifying with (78), (180) gives: % 127.57/17.89 | (293) all_53_5 = all_26_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_55_5, e2, e2, % 127.57/17.89 | simplifying with (105), (197) gives: % 127.57/17.89 | (294) all_55_5 = all_44_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_55_5, e2, e2, % 127.57/17.89 | simplifying with (48), (197) gives: % 127.57/17.89 | (295) all_55_5 = all_6_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_1, all_55_4, e3, e2, % 127.57/17.89 | simplifying with (181), (198) gives: % 127.57/17.89 | (296) all_55_4 = all_53_1 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_55_4, e2, e3, e2, % 127.57/17.89 | simplifying with (198) gives: % 127.57/17.89 | (297) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_1, e2, e3, e2, % 127.57/17.89 | simplifying with (181) gives: % 127.57/17.89 | (298) all_53_1 = e2 | ~ (op(e2, e3) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_5, e2, e2, e2, % 127.57/17.89 | simplifying with (180) gives: % 127.57/17.89 | (299) all_53_5 = e2 | ~ (op(e2, e2) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_50_2, e2, e2, e2, % 127.57/17.89 | simplifying with (114) gives: % 127.57/17.89 | (300) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_42_2, e2, e2, e2, % 127.57/17.89 | simplifying with (102) gives: % 127.57/17.89 | (301) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_26_2, e2, e2, e2, % 127.57/17.89 | simplifying with (78) gives: % 127.57/17.89 | (302) all_26_2 = e2 | ~ (op(e2, e2) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_55_6, e2, e1, e2, % 127.57/17.89 | simplifying with (196) gives: % 127.57/17.89 | (303) all_55_6 = e2 | ~ (op(e2, e1) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_9, e2, e1, e2, % 127.57/17.89 | simplifying with (179) gives: % 127.57/17.89 | (304) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_55_7, e2, e0, e2, % 127.57/17.89 | simplifying with (195) gives: % 127.57/17.89 | (305) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_13, e2, e0, e2, % 127.57/17.89 | simplifying with (178) gives: % 127.57/17.89 | (306) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_12, all_55_3, e0, e3, % 127.57/17.89 | simplifying with (182), (199) gives: % 127.57/17.89 | (307) all_55_3 = all_53_12 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_8, all_55_2, e1, e3, % 127.57/17.89 | simplifying with (183), (200) gives: % 127.57/17.89 | (308) all_55_2 = all_53_8 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_4, all_55_1, e2, e3, % 127.57/17.89 | simplifying with (184), (201) gives: % 127.57/17.89 | (309) all_55_1 = all_53_4 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_32_2, e3, e3, % 127.57/17.89 | simplifying with (60), (87) gives: % 127.57/17.89 | (310) all_32_2 = all_14_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_48_2, e3, e3, % 127.57/17.89 | simplifying with (108), (111) gives: % 127.57/17.89 | (311) all_48_2 = all_46_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_53_0, e3, e3, % 127.57/17.89 | simplifying with (111), (185) gives: % 127.57/17.89 | (312) all_53_0 = all_48_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_53_0, e3, e3, % 127.57/17.89 | simplifying with (90), (185) gives: % 127.57/17.89 | (313) all_53_0 = all_34_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_53_0, e3, e3, % 127.57/17.89 | simplifying with (87), (185) gives: % 127.57/17.89 | (314) all_53_0 = all_32_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_55_0, e3, e3, % 127.57/17.89 | simplifying with (111), (202) gives: % 127.57/17.89 | (315) all_55_0 = all_48_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_55_0, e3, e3, % 127.57/17.89 | simplifying with (45), (202) gives: % 127.57/17.89 | (316) all_55_0 = all_4_2 % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_53_0, e3, e3, e3, % 127.57/17.89 | simplifying with (185) gives: % 127.57/17.89 | (317) all_53_0 = e3 | ~ (op(e3, e3) = e3) % 127.57/17.89 | % 127.57/17.89 | GROUND_INST: instantiating (function-axioms) with all_32_2, e3, e3, e3, % 127.57/17.89 | simplifying with (87) gives: % 127.57/17.90 | (318) all_32_2 = e3 | ~ (op(e3, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_14_2, e3, e3, e3, % 127.57/17.90 | simplifying with (60) gives: % 127.57/17.90 | (319) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, e3, e3, % 127.57/17.90 | simplifying with (45) gives: % 127.57/17.90 | (320) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_1, e3, e2, e3, % 127.57/17.90 | simplifying with (201) gives: % 127.57/17.90 | (321) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_4, e3, e2, e3, % 127.57/17.90 | simplifying with (184) gives: % 127.57/17.90 | (322) all_53_4 = e3 | ~ (op(e3, e2) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_8, e3, e1, e3, % 127.57/17.90 | simplifying with (183) gives: % 127.57/17.90 | (323) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_12, e3, e0, e3, % 127.57/17.90 | simplifying with (182) gives: % 127.57/17.90 | (324) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_3, e0, e0, e3, % 127.57/17.90 | simplifying with (199) gives: % 127.57/17.90 | (325) all_55_3 = e0 | ~ (op(e3, e0) = e0) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_12, e0, e0, e3, % 127.57/17.90 | simplifying with (182) gives: % 127.57/17.90 | (326) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_7, e0, e0, e2, % 127.57/17.90 | simplifying with (195) gives: % 127.57/17.90 | (327) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_13, e0, e0, e2, % 127.57/17.90 | simplifying with (178) gives: % 127.57/17.90 | (328) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_14, e0, e0, e1, % 127.57/17.90 | simplifying with (174) gives: % 127.57/17.90 | (329) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_8, e1, e1, e3, % 127.57/17.90 | simplifying with (183) gives: % 127.57/17.90 | (330) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_6, e1, e1, e2, % 127.57/17.90 | simplifying with (196) gives: % 127.57/17.90 | (331) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_9, e1, e1, e2, % 127.57/17.90 | simplifying with (179) gives: % 127.57/17.90 | (332) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_14, e1, e1, e0, % 127.57/17.90 | simplifying with (188) gives: % 127.57/17.90 | (333) all_55_14 = e1 | ~ (op(e0, e1) = e1) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_11, e1, e1, e0, % 127.57/17.90 | simplifying with (171) gives: % 127.57/17.90 | (334) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_4, e2, e2, e3, % 127.57/17.90 | simplifying with (184) gives: % 127.57/17.90 | (335) all_53_4 = e2 | ~ (op(e3, e2) = e2) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_9, e2, e2, e1, % 127.57/17.90 | simplifying with (193) gives: % 127.57/17.90 | (336) all_55_9 = e2 | ~ (op(e1, e2) = e2) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_6, e2, e2, e1, % 127.57/17.90 | simplifying with (176) gives: % 127.57/17.90 | (337) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_13, e2, e2, e0, % 127.57/17.90 | simplifying with (189) gives: % 127.57/17.90 | (338) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_7, e2, e2, e0, % 127.57/17.90 | simplifying with (172) gives: % 127.57/17.90 | (339) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_1, e3, e3, e2, % 127.57/17.90 | simplifying with (181) gives: % 127.57/17.90 | (340) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_8, e3, e3, e1, % 127.57/17.90 | simplifying with (194) gives: % 127.57/17.90 | (341) all_55_8 = e3 | ~ (op(e1, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_2, e3, e3, e1, % 127.57/17.90 | simplifying with (177) gives: % 127.57/17.90 | (342) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_55_12, e3, e3, e0, % 127.57/17.90 | simplifying with (190) gives: % 127.57/17.90 | (343) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | GROUND_INST: instantiating (function-axioms) with all_53_3, e3, e3, e0, % 127.57/17.90 | simplifying with (173) gives: % 127.57/17.90 | (344) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (315), (316) imply: % 127.57/17.90 | (345) all_48_2 = all_4_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (345) implies: % 127.57/17.90 | (346) all_48_2 = all_4_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (294), (295) imply: % 127.57/17.90 | (347) all_44_2 = all_6_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (347) implies: % 127.57/17.90 | (348) all_44_2 = all_6_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (277), (278) imply: % 127.57/17.90 | (349) all_53_10 = all_12_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (349) implies: % 127.57/17.90 | (350) all_53_10 = all_12_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (255), (256) imply: % 127.57/17.90 | (351) all_53_15 = all_8_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (351) implies: % 127.57/17.90 | (352) all_53_15 = all_8_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (313), (314) imply: % 127.57/17.90 | (353) all_34_2 = all_32_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (312), (313) imply: % 127.57/17.90 | (354) all_48_2 = all_34_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (354) implies: % 127.57/17.90 | (355) all_48_2 = all_34_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (292), (293) imply: % 127.57/17.90 | (356) all_50_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (356) implies: % 127.57/17.90 | (357) all_50_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (276), (350) imply: % 127.57/17.90 | (358) all_38_2 = all_12_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (358) implies: % 127.57/17.90 | (359) all_38_2 = all_12_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (254), (352) imply: % 127.57/17.90 | (360) all_28_2 = all_8_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (360) implies: % 127.57/17.90 | (361) all_28_2 = all_8_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (291), (357) imply: % 127.57/17.90 | (362) all_42_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (362) implies: % 127.57/17.90 | (363) all_42_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (311), (346) imply: % 127.57/17.90 | (364) all_46_2 = all_4_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (311), (355) imply: % 127.57/17.90 | (365) all_46_2 = all_34_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (364), (365) imply: % 127.57/17.90 | (366) all_34_2 = all_4_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (366) implies: % 127.57/17.90 | (367) all_34_2 = all_4_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (289), (290) imply: % 127.57/17.90 | (368) all_42_2 = all_40_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (368) implies: % 127.57/17.90 | (369) all_42_2 = all_40_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (290), (348) imply: % 127.57/17.90 | (370) all_40_2 = all_6_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (363), (369) imply: % 127.57/17.90 | (371) all_40_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (371) implies: % 127.57/17.90 | (372) all_40_2 = all_26_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (370), (372) imply: % 127.57/17.90 | (373) all_26_2 = all_6_2 % 127.57/17.90 | % 127.57/17.90 | SIMP: (373) implies: % 127.57/17.90 | (374) all_26_2 = all_6_2 % 127.57/17.90 | % 127.57/17.90 | COMBINE_EQS: (275), (359) imply: % 127.57/17.90 | (375) all_30_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (375) implies: % 127.57/17.91 | (376) all_30_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (252), (253) imply: % 127.57/17.91 | (377) all_20_2 = all_10_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (377) implies: % 127.57/17.91 | (378) all_20_2 = all_10_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (353), (367) imply: % 127.57/17.91 | (379) all_32_2 = all_4_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (379) implies: % 127.57/17.91 | (380) all_32_2 = all_4_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (310), (380) imply: % 127.57/17.91 | (381) all_14_2 = all_4_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (381) implies: % 127.57/17.91 | (382) all_14_2 = all_4_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (274), (376) imply: % 127.57/17.91 | (383) all_24_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (383) implies: % 127.57/17.91 | (384) all_24_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (250), (251) imply: % 127.57/17.91 | (385) all_20_2 = all_16_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (385) implies: % 127.57/17.91 | (386) all_20_2 = all_16_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (251), (361) imply: % 127.57/17.91 | (387) all_16_2 = all_8_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (273), (384) imply: % 127.57/17.91 | (388) all_22_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (388) implies: % 127.57/17.91 | (389) all_22_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (272), (389) imply: % 127.57/17.91 | (390) all_18_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (390) implies: % 127.57/17.91 | (391) all_18_2 = all_12_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (378), (386) imply: % 127.57/17.91 | (392) all_16_2 = all_10_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (392) implies: % 127.57/17.91 | (393) all_16_2 = all_10_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (387), (393) imply: % 127.57/17.91 | (394) all_10_2 = all_8_2 % 127.57/17.91 | % 127.57/17.91 | SIMP: (394) implies: % 127.57/17.91 | (395) all_10_2 = all_8_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (378), (395) imply: % 127.57/17.91 | (396) all_20_2 = all_8_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (253), (395) imply: % 127.57/17.91 | (397) all_36_2 = all_8_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (363), (374) imply: % 127.57/17.91 | (398) all_42_2 = all_6_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (357), (374) imply: % 127.57/17.91 | (399) all_50_2 = all_6_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (293), (374) imply: % 127.57/17.91 | (400) all_53_5 = all_6_2 % 127.57/17.91 | % 127.57/17.91 | COMBINE_EQS: (313), (367) imply: % 127.57/17.91 | (401) all_53_0 = all_4_2 % 127.57/17.91 | % 127.57/17.91 | REDUCE: (169), (401) imply: % 127.57/17.91 | (402) ~ (all_53_1 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (402) implies: % 127.57/17.91 | (403) ~ (all_53_1 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (168), (401) imply: % 127.57/17.91 | (404) ~ (all_53_2 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (404) implies: % 127.57/17.91 | (405) ~ (all_53_2 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (167), (401) imply: % 127.57/17.91 | (406) ~ (all_53_3 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (406) implies: % 127.57/17.91 | (407) ~ (all_53_3 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (166), (401) imply: % 127.57/17.91 | (408) ~ (all_53_4 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (408) implies: % 127.57/17.91 | (409) ~ (all_53_4 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (165), (401) imply: % 127.57/17.91 | (410) ~ (all_53_8 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (410) implies: % 127.57/17.91 | (411) ~ (all_53_8 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (164), (401) imply: % 127.57/17.91 | (412) ~ (all_53_12 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (412) implies: % 127.57/17.91 | (413) ~ (all_53_12 = all_4_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (161), (400) imply: % 127.57/17.91 | (414) ~ (all_53_1 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (156), (350) imply: % 127.57/17.91 | (415) ~ (all_53_2 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (152), (352) imply: % 127.57/17.91 | (416) ~ (all_53_3 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (151), (400) imply: % 127.57/17.91 | (417) ~ (all_53_4 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (146), (400) imply: % 127.57/17.91 | (418) ~ (all_53_6 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (418) implies: % 127.57/17.91 | (419) ~ (all_53_6 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (145), (400) imply: % 127.57/17.91 | (420) ~ (all_53_7 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (420) implies: % 127.57/17.91 | (421) ~ (all_53_7 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (144), (400) imply: % 127.57/17.91 | (422) ~ (all_53_9 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (422) implies: % 127.57/17.91 | (423) ~ (all_53_9 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (143), (400) imply: % 127.57/17.91 | (424) ~ (all_53_13 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (424) implies: % 127.57/17.91 | (425) ~ (all_53_13 = all_6_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (141), (350) imply: % 127.57/17.91 | (426) ~ (all_53_6 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (138), (352) imply: % 127.57/17.91 | (427) ~ (all_53_7 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (136), (350) imply: % 127.57/17.91 | (428) ~ (all_53_8 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (133), (350) imply: % 127.57/17.91 | (429) ~ (all_53_9 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (130), (350) imply: % 127.57/17.91 | (430) ~ (all_53_11 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (430) implies: % 127.57/17.91 | (431) ~ (all_53_11 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (129), (350) imply: % 127.57/17.91 | (432) ~ (all_53_14 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | SIMP: (432) implies: % 127.57/17.91 | (433) ~ (all_53_14 = all_12_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (128), (352) imply: % 127.57/17.91 | (434) ~ (all_53_11 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (125), (352) imply: % 127.57/17.91 | (435) ~ (all_53_12 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (123), (352) imply: % 127.57/17.91 | (436) ~ (all_53_13 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | REDUCE: (122), (352) imply: % 127.57/17.91 | (437) ~ (all_53_14 = all_8_2) % 127.57/17.91 | % 127.57/17.91 | BETA: splitting (46) gives: % 127.57/17.91 | % 127.57/17.91 | Case 1: % 127.57/17.91 | | % 127.57/17.91 | | (438) ~ (all_4_2 = e0) % 127.57/17.91 | | % 127.57/17.91 | | BETA: splitting (49) gives: % 127.57/17.91 | | % 127.57/17.91 | | Case 1: % 127.57/17.91 | | | % 127.57/17.91 | | | (439) ~ (all_6_2 = e3) % 127.57/17.91 | | | % 127.57/17.91 | | | BETA: splitting (52) gives: % 127.57/17.91 | | | % 127.57/17.91 | | | Case 1: % 127.57/17.91 | | | | % 127.57/17.91 | | | | (440) ~ (all_8_2 = e1) % 127.57/17.91 | | | | % 127.57/17.91 | | | | BETA: splitting (10) gives: % 127.57/17.91 | | | | % 127.57/17.91 | | | | Case 1: % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | (441) unit = e3 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (8), (441) imply: % 127.57/17.91 | | | | | (442) op(e3, e2) = e2 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (7), (441) imply: % 127.57/17.91 | | | | | (443) op(e3, e1) = e1 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (6), (441) imply: % 127.57/17.91 | | | | | (444) op(e3, e0) = e0 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (5), (441) imply: % 127.57/17.91 | | | | | (445) op(e3, e3) = e3 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (4), (441) imply: % 127.57/17.91 | | | | | (446) op(e2, e3) = e2 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (3), (441) imply: % 127.57/17.91 | | | | | (447) op(e1, e3) = e1 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | REDUCE: (2), (441) imply: % 127.57/17.91 | | | | | (448) op(e0, e3) = e0 % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | BETA: splitting (318) gives: % 127.57/17.91 | | | | | % 127.57/17.91 | | | | | Case 1: % 127.57/17.91 | | | | | | % 127.57/17.91 | | | | | | (449) ~ (op(e3, e3) = e3) % 127.57/17.91 | | | | | | % 127.57/17.91 | | | | | | PRED_UNIFY: (445), (449) imply: % 127.57/17.91 | | | | | | (450) $false % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | CLOSE: (450) is inconsistent. % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | Case 2: % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | (451) all_32_2 = e3 % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | COMBINE_EQS: (380), (451) imply: % 127.57/17.92 | | | | | | (452) all_4_2 = e3 % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | SIMP: (452) implies: % 127.57/17.92 | | | | | | (453) all_4_2 = e3 % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (403), (453) imply: % 127.57/17.92 | | | | | | (454) ~ (all_53_1 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (405), (453) imply: % 127.57/17.92 | | | | | | (455) ~ (all_53_2 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (407), (453) imply: % 127.57/17.92 | | | | | | (456) ~ (all_53_3 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (409), (453) imply: % 127.57/17.92 | | | | | | (457) ~ (all_53_4 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (411), (453) imply: % 127.57/17.92 | | | | | | (458) ~ (all_53_8 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | REDUCE: (413), (453) imply: % 127.57/17.92 | | | | | | (459) ~ (all_53_12 = e3) % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | BETA: splitting (335) gives: % 127.57/17.92 | | | | | | % 127.57/17.92 | | | | | | Case 1: % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | (460) ~ (op(e3, e2) = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | PRED_UNIFY: (442), (460) imply: % 127.57/17.92 | | | | | | | (461) $false % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | CLOSE: (461) is inconsistent. % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | Case 2: % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | (462) all_53_4 = e2 % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | REDUCE: (150), (462) imply: % 127.57/17.92 | | | | | | | (463) ~ (all_53_6 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | SIMP: (463) implies: % 127.57/17.92 | | | | | | | (464) ~ (all_53_6 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | REDUCE: (148), (462) imply: % 127.57/17.92 | | | | | | | (465) ~ (all_53_8 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | SIMP: (465) implies: % 127.57/17.92 | | | | | | | (466) ~ (all_53_8 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | REDUCE: (147), (462) imply: % 127.57/17.92 | | | | | | | (467) ~ (all_53_12 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | SIMP: (467) implies: % 127.57/17.92 | | | | | | | (468) ~ (all_53_12 = e2) % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | BETA: splitting (260) gives: % 127.57/17.92 | | | | | | | % 127.57/17.92 | | | | | | | Case 1: % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | (469) ~ (op(e0, e3) = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | PRED_UNIFY: (448), (469) imply: % 127.57/17.92 | | | | | | | | (470) $false % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | CLOSE: (470) is inconsistent. % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | Case 2: % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | (471) all_55_12 = e0 % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | COMBINE_EQS: (259), (471) imply: % 127.57/17.92 | | | | | | | | (472) all_53_3 = e0 % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | SIMP: (472) implies: % 127.57/17.92 | | | | | | | | (473) all_53_3 = e0 % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | REDUCE: (158), (473) imply: % 127.57/17.92 | | | | | | | | (474) ~ (all_53_2 = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | REDUCE: (154), (473) imply: % 127.57/17.92 | | | | | | | | (475) ~ (all_53_7 = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | SIMP: (475) implies: % 127.57/17.92 | | | | | | | | (476) ~ (all_53_7 = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | REDUCE: (153), (473) imply: % 127.57/17.92 | | | | | | | | (477) ~ (all_53_11 = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | SIMP: (477) implies: % 127.57/17.92 | | | | | | | | (478) ~ (all_53_11 = e0) % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | BETA: splitting (298) gives: % 127.57/17.92 | | | | | | | | % 127.57/17.92 | | | | | | | | Case 1: % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | (479) ~ (op(e2, e3) = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | PRED_UNIFY: (446), (479) imply: % 127.57/17.92 | | | | | | | | | (480) $false % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | CLOSE: (480) is inconsistent. % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | Case 2: % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | (481) all_53_1 = e2 % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | REDUCE: (163), (481) imply: % 127.57/17.92 | | | | | | | | | (482) ~ (all_53_2 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | SIMP: (482) implies: % 127.57/17.92 | | | | | | | | | (483) ~ (all_53_2 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | REDUCE: (160), (481) imply: % 127.57/17.92 | | | | | | | | | (484) ~ (all_53_9 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | SIMP: (484) implies: % 127.57/17.92 | | | | | | | | | (485) ~ (all_53_9 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | REDUCE: (414), (481) imply: % 127.57/17.92 | | | | | | | | | (486) ~ (all_6_2 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | SIMP: (486) implies: % 127.57/17.92 | | | | | | | | | (487) ~ (all_6_2 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | REDUCE: (454), (481) imply: % 127.57/17.92 | | | | | | | | | (488) ~ (e3 = e2) % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | BETA: splitting (281) gives: % 127.57/17.92 | | | | | | | | | % 127.57/17.92 | | | | | | | | | Case 1: % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | (489) ~ (op(e1, e3) = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | PRED_UNIFY: (447), (489) imply: % 127.57/17.92 | | | | | | | | | | (490) $false % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | CLOSE: (490) is inconsistent. % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | Case 2: % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | (491) all_53_2 = e1 % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | REDUCE: (157), (491) imply: % 127.57/17.92 | | | | | | | | | | (492) ~ (all_53_6 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | SIMP: (492) implies: % 127.57/17.92 | | | | | | | | | | (493) ~ (all_53_6 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | REDUCE: (155), (491) imply: % 127.57/17.92 | | | | | | | | | | (494) ~ (all_53_14 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | SIMP: (494) implies: % 127.57/17.92 | | | | | | | | | | (495) ~ (all_53_14 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | REDUCE: (455), (491) imply: % 127.57/17.92 | | | | | | | | | | (496) ~ (e3 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | REDUCE: (483), (491) imply: % 127.57/17.92 | | | | | | | | | | (497) ~ (e2 = e1) % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | BETA: splitting (326) gives: % 127.57/17.92 | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | Case 1: % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | (498) ~ (op(e3, e0) = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | PRED_UNIFY: (444), (498) imply: % 127.57/17.92 | | | | | | | | | | | (499) $false % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | CLOSE: (499) is inconsistent. % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | Case 2: % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | (500) all_53_12 = e0 % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (134), (500) imply: % 127.57/17.92 | | | | | | | | | | | (501) ~ (all_53_8 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (127), (500) imply: % 127.57/17.92 | | | | | | | | | | | (502) ~ (all_53_13 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | SIMP: (502) implies: % 127.57/17.92 | | | | | | | | | | | (503) ~ (all_53_13 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (126), (500) imply: % 127.57/17.92 | | | | | | | | | | | (504) ~ (all_53_14 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | SIMP: (504) implies: % 127.57/17.92 | | | | | | | | | | | (505) ~ (all_53_14 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (435), (500) imply: % 127.57/17.92 | | | | | | | | | | | (506) ~ (all_8_2 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | SIMP: (506) implies: % 127.57/17.92 | | | | | | | | | | | (507) ~ (all_8_2 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (459), (500) imply: % 127.57/17.92 | | | | | | | | | | | (508) ~ (e3 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | REDUCE: (468), (500) imply: % 127.57/17.92 | | | | | | | | | | | (509) ~ (e2 = e0) % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | BETA: splitting (219) gives: % 127.57/17.92 | | | | | | | | | | | % 127.57/17.92 | | | | | | | | | | | Case 1: % 127.57/17.92 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | (510) all_57_15 = e0 & op(e0, e0) = e0 % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | ALPHA: (510) implies: % 127.57/17.93 | | | | | | | | | | | | (511) op(e0, e0) = e0 % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | BETA: splitting (270) gives: % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | (512) ~ (op(e0, e0) = e0) % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | PRED_UNIFY: (511), (512) imply: % 127.57/17.93 | | | | | | | | | | | | | (513) $false % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | CLOSE: (513) is inconsistent. % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | Case 2: % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | (514) all_10_2 = e0 % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | COMBINE_EQS: (395), (514) imply: % 127.57/17.93 | | | | | | | | | | | | | (515) all_8_2 = e0 % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | SIMP: (515) implies: % 127.57/17.93 | | | | | | | | | | | | | (516) all_8_2 = e0 % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | REDUCE: (507), (516) imply: % 127.57/17.93 | | | | | | | | | | | | | (517) $false % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | CLOSE: (517) is inconsistent. % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | End of split % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | Case 2: % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | (518) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 127.57/17.93 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 127.57/17.93 | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 127.57/17.93 | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 127.57/17.93 | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | ALPHA: (518) implies: % 127.57/17.93 | | | | | | | | | | | | (519) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 127.57/17.93 | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 127.57/17.93 | | | | | | | | | | | | e1) = e0) % 127.57/17.93 | | | | | | | | | | | | (520) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 127.57/17.93 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 127.57/17.93 | | | | | | | | | | | | e0) = e0) % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | BETA: splitting (223) gives: % 127.57/17.93 | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | (521) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 127.57/17.93 | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | BETA: splitting (521) gives: % 127.57/17.93 | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | (522) all_57_9 = e1 & op(e3, e0) = e1 % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | REF_CLOSE: (13), (328), (329), (503), (505), (520), (522) are % 127.57/17.93 | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | Case 2: % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | (523) all_57_10 = e1 & op(e2, e0) = e1 % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | ALPHA: (523) implies: % 127.57/17.93 | | | | | | | | | | | | | | (524) all_57_10 = e1 % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | BETA: splitting (237) gives: % 127.57/17.93 | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | (525) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 127.57/17.93 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | REF_CLOSE: (48), (340), (439), (454), (525), % 127.57/17.93 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.93 | | | | | | | | | | | | | | | #351. % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | Case 2: % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | (526) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 127.57/17.93 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 127.57/17.93 | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | (527) all_57_5 = e3 & op(e2, e1) = e3 % 127.57/17.93 | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | ALPHA: (527) implies: % 127.57/17.93 | | | | | | | | | | | | | | | | (528) all_57_5 = e3 % 127.57/17.93 | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 127.57/17.93 | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | (529) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 127.57/17.93 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 127.57/17.93 | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | BETA: splitting (529) gives: % 127.57/17.93 | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | (530) all_57_0 = e2 & op(e3, e3) = e2 % 127.57/17.93 | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | ALPHA: (530) implies: % 127.57/17.93 | | | | | | | | | | | | | | | | | | (531) op(e3, e3) = e2 % 127.57/17.93 | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 127.57/17.93 | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (532) ~ (op(e3, e1) = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (443), (532) imply: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (533) $false % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | CLOSE: (533) is inconsistent. % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (534) all_53_8 = e1 % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | REDUCE: (137), (534) imply: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (535) ~ (all_53_9 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | SIMP: (535) implies: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (536) ~ (all_53_9 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | REDUCE: (135), (534) imply: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (537) ~ (all_53_11 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | SIMP: (537) implies: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (538) ~ (all_53_11 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | REDUCE: (428), (534) imply: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (539) ~ (all_12_2 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | SIMP: (539) implies: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | (540) ~ (all_12_2 = e1) % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | % 127.57/17.93 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.93 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | (541) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (541) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (542) all_57_0 = e0 & op(e3, e3) = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (543) op(e3, e3) = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (531), (543), (function-axioms) are % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (544) all_57_2 = e0 & op(e2, e3) = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (159), (236), (287), (296), (297), (301), % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (304), (305), (398), (446), (485), (487), (544) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #344. % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | (545) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (546) all_57_6 = e0 & op(e1, e3) = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (227), (279), (282), (285), (286), (493), % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (495), (540), (546) are inconsistent by sub-proof % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | #337. % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (547) all_57_12 = e0 & op(e0, e3) = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | (548) all_57_12 = e0 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | (549) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | (550) all_57_12 = e1 & op(e0, e3) = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (548), (550) are inconsistent by sub-proof % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | #336. % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | (551) all_57_13 = e1 & op(e0, e2) = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | (552) all_57_13 = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_57_6 = e1 & op(e1, e3) = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_57_6 = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (556) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_57_4 = e1 & op(e3, e1) = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (557) implies: % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_57_4 = e1 % 127.57/17.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (57), (97), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (174), (176), (226), (227), (228), (229), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (234), (236), (241), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (259), (265), (279), (282), (285), (286), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (287), (296), (297), (301), (304), (305), (309), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (321), (328), (332), (334), (337), (340), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (343), (344), (359), (398), (445), (446), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (453), (454), (455), (456), (457), (464), (473), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (478), (485), (487), (493), (495), (503), (528), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (536), (538), (540), (552), (555), (558), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #295. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_57_5 = e1 & op(e2, e1) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (559) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) op(e2, e1) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (536), (560) are inconsistent by sub-proof % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | #334. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (561) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (334), (538), (540), (561) are inconsistent % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #332. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_57_7 = e1 & op(e1, e2) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | (563) op(e1, e2) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (493), (563) are inconsistent by % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #341. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | (564) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (286), (495), (540), (564) are inconsistent % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #338. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | (565) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (440), (538), (565), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | #293. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | (566) all_57_1 = e2 & op(e3, e2) = e2 % 127.57/17.97 | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | (567) all_57_1 = e2 % 127.57/17.97 | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 127.57/17.97 | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | (568) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (568) gives: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (569) all_57_0 = e1 & op(e3, e3) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (569) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (570) all_57_0 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (248), (259), (340), (342), (343), (454), % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (455), (456), (570) are inconsistent by sub-proof % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | #310. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (571) all_57_1 = e1 & op(e3, e2) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (572) all_57_1 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (572) imply: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (573) e2 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (573) imply: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (574) $false % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | CLOSE: (574) is inconsistent. % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | (575) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (575) gives: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (576) all_57_4 = e1 & op(e3, e1) = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies: % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | (577) all_57_4 = e1 % 127.57/17.97 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (51), (57), (97), (135), (137), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (159), (174), (176), (220), (226), (227), (228), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (234), (236), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (241), (248), (258), (259), (262), (265), (279), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (282), (285), (286), (287), (296), (297), (301), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (304), (305), (309), (320), (321), (328), (330), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (332), (334), (337), (340), (342), (343), (344), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (359), (398), (428), (440), (443), (445), (446), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (453), (454), (455), (456), (457), (458), (464), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (466), (473), (476), (478), (485), (487), (493), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (495), (501), (503), (519), (528), (577), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | #289. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (578) all_57_9 = e1 & op(e3, e0) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (328), (329), (503), (505), (520), (578) are % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | (579) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 127.57/17.98 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 127.57/17.98 | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | BETA: splitting (579) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | (580) all_57_4 = e2 & op(e3, e1) = e2 % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | ALPHA: (580) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | (581) all_57_4 = e2 % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (582) ~ (op(e3, e1) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (443), (582) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (583) $false % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | CLOSE: (583) is inconsistent. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (584) all_53_8 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | REDUCE: (137), (584) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (585) ~ (all_53_9 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | SIMP: (585) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (586) ~ (all_53_9 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | REDUCE: (135), (584) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (587) ~ (all_53_11 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | SIMP: (587) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (588) ~ (all_53_11 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | REDUCE: (428), (584) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (589) ~ (all_12_2 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | SIMP: (589) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (590) ~ (all_12_2 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (231), (285), (332), (334), (581), (586), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (588), (590) are inconsistent by sub-proof #287. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | (591) all_57_9 = e2 & op(e3, e0) = e2 % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | ALPHA: (591) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | (592) all_57_9 = e2 % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | (593) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (594) all_57_0 = e1 & op(e3, e3) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (595) all_57_0 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (248), (259), (340), (342), (343), (454), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (455), (456), (595) are inconsistent by sub-proof % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | #310. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (596) all_57_1 = e1 & op(e3, e2) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | (597) all_57_1 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (598) ~ (op(e3, e1) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (443), (598) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (599) $false % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (599) is inconsistent. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (600) all_53_8 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (600) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (601) ~ (all_53_9 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (601) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (602) ~ (all_53_9 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (600) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (603) ~ (all_53_11 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (603) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (604) ~ (all_53_11 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (428), (600) imply: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (605) ~ (all_12_2 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (605) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | (606) ~ (all_12_2 = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | (607) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (607) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | (608) all_57_0 = e0 & op(e3, e3) = e0 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | (609) all_57_0 = e0 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | (610) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (610) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_57_12 = e1 & op(e0, e3) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (611) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_57_12 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (613) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (613) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_57_4 = e1 & op(e3, e1) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (614) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) all_57_4 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (231), (258), (262), (265), (285), (332), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (476), (478), (519), (602), (604), (606), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (612), (615) are inconsistent by sub-proof #290. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_57_5 = e1 & op(e2, e1) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) op(e2, e1) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (602), (617) are inconsistent by sub-proof % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | #334. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (334), (604), (606), (618) are inconsistent % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #332. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_57_13 = e1 & op(e0, e2) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (619) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_57_13 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (621) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (621) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_57_6 = e1 & op(e1, e3) = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_57_6 = e1 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (231), (285), (332), (334), (528), % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602), (604), (606), (624) are inconsistent by % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #329. % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (625) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_57_8 = e0 & op(e1, e1) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (626) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_57_8 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) op(e1, e1) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_57_1 = e3 & op(e3, e2) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (321), (457), (630) are inconsistent by % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #328. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_57_3 = e3 & op(e2, e2) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_57_3 = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (18), (159), (227), (228), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (234), (236), (279), (282), (285), (286), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287), (296), (297), (301), (304), (305), (320), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328), (337), (342), (398), (445), (446), (453), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455), (464), (485), (487), (493), (495), (503), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528), (606), (623), (627), (628), (632), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #313. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_57_7 = e3 & op(e1, e2) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_57_7 = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_57_0 = e3 & op(e3, e3) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (637) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) all_57_0 = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (609), (638) imply: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) e3 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (639) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) e3 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (640) imply: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) all_57_7 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (18), (228), (229), (623), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627), (628), (641), (function-axioms) are % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_57_2 = e3 & op(e2, e3) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) op(e2, e3) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (340), (454), (643) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (342), (344), (455), (473), (644) are % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_57_13 = e3 & op(e0, e2) = e3 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (620), (645) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_57_14 = e0 & op(e0, e1) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) op(e0, e1) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (478), (647) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_57_7 = e1 & op(e1, e2) = e1 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) op(e1, e2) = e1 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (493), (649) are inconsistent by % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #341. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (650) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (286), (495), (606), (650) are inconsistent % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #338. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | (651) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (440), (604), (651), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | #293. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | (652) all_57_1 = e0 & op(e3, e2) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (597), (652) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | #286. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | (653) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | (654) all_57_4 = e0 & op(e3, e1) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (654) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | (655) all_57_4 = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (231), (285), (332), (334), (602), (604), % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | (606), (655) are inconsistent by sub-proof #331. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | (656) all_57_9 = e0 & op(e3, e0) = e0 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (592), (656) are inconsistent by sub-proof % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | #285. % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | End of split % 127.57/17.99 | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | Case 2: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | (657) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 127.57/17.99 | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (657) gives: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | (658) all_57_4 = e1 & op(e3, e1) = e1 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (658) implies: % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | (659) all_57_4 = e1 % 127.57/17.99 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (51), (57), (97), (135), (137), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (159), (174), (176), (220), (226), (227), (228), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (234), (236), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (241), (248), (258), (259), (262), (265), (279), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (282), (285), (286), (287), (296), (297), (301), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (304), (305), (309), (320), (321), (328), (330), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (332), (334), (337), (340), (342), (343), (344), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (359), (398), (428), (440), (443), (445), (446), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (453), (454), (455), (456), (457), (458), (464), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (466), (473), (476), (478), (485), (487), (493), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (495), (501), (503), (519), (528), (659), % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | #289. % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (660) all_57_9 = e1 & op(e3, e0) = e1 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (328), (329), (503), (505), (520), (660) are % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | (661) all_57_10 = e3 & op(e2, e0) = e3 % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (524), (661) are inconsistent by sub-proof % 127.57/18.00 | | | | | | | | | | | | | | | | #284. % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | (662) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 127.57/18.00 | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (495), (662), % 127.57/18.00 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 127.57/18.00 | | | | | | | | | | | | | #283. % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | | % 127.57/18.00 | | | | | | | | | End of split % 127.57/18.00 | | | | | | | | | % 127.57/18.00 | | | | | | | | End of split % 127.57/18.00 | | | | | | | | % 127.57/18.00 | | | | | | | End of split % 127.57/18.00 | | | | | | | % 127.57/18.00 | | | | | | End of split % 127.57/18.00 | | | | | | % 127.57/18.00 | | | | | End of split % 127.57/18.00 | | | | | % 127.57/18.00 | | | | Case 2: % 127.57/18.00 | | | | | % 127.57/18.00 | | | | | (663) unit = e2 | unit = e1 | unit = e0 % 127.57/18.00 | | | | | % 127.57/18.00 | | | | | BETA: splitting (55) gives: % 127.57/18.00 | | | | | % 127.57/18.00 | | | | | Case 1: % 127.57/18.00 | | | | | | % 127.57/18.00 | | | | | | (664) ~ (all_10_2 = e3) % 127.57/18.00 | | | | | | % 127.57/18.00 | | | | | | REDUCE: (395), (664) imply: % 127.57/18.00 | | | | | | (665) ~ (all_8_2 = e3) % 127.57/18.00 | | | | | | % 127.57/18.00 | | | | | | BETA: splitting (58) gives: % 127.57/18.00 | | | | | | % 127.57/18.00 | | | | | | Case 1: % 127.57/18.00 | | | | | | | % 127.57/18.00 | | | | | | | (666) ~ (all_12_2 = e2) % 127.57/18.00 | | | | | | | % 127.57/18.00 | | | | | | | BETA: splitting (61) gives: % 127.57/18.00 | | | | | | | % 127.57/18.00 | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | % 127.57/18.00 | | | | | | | | (667) ~ (all_14_2 = e2) % 127.57/18.00 | | | | | | | | % 127.57/18.00 | | | | | | | | REDUCE: (382), (667) imply: % 127.57/18.00 | | | | | | | | (668) ~ (all_4_2 = e2) % 127.57/18.00 | | | | | | | | % 127.57/18.00 | | | | | | | | BETA: splitting (67) gives: % 127.57/18.00 | | | | | | | | % 127.57/18.00 | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | % 127.57/18.00 | | | | | | | | | (669) ~ (all_18_2 = e3) % 127.57/18.00 | | | | | | | | | % 127.57/18.00 | | | | | | | | | REDUCE: (391), (669) imply: % 127.57/18.00 | | | | | | | | | (670) ~ (all_12_2 = e3) % 127.57/18.00 | | | | | | | | | % 127.57/18.00 | | | | | | | | | BETA: splitting (73) gives: % 127.57/18.00 | | | | | | | | | % 127.57/18.00 | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | (671) ~ (all_22_2 = e0) % 127.57/18.00 | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | REDUCE: (389), (671) imply: % 127.57/18.00 | | | | | | | | | | (672) ~ (all_12_2 = e0) % 127.57/18.00 | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | BETA: splitting (208) gives: % 127.57/18.00 | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | (673) all_55_10 = e3 % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | REF_CLOSE: (278), (670), (673) are inconsistent by sub-proof % 127.57/18.00 | | | | | | | | | | | #282. % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | (674) ~ (all_55_10 = e3) % 127.57/18.00 | | | | | | | | | | | (675) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | BETA: splitting (675) gives: % 127.57/18.00 | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | (676) all_55_10 = e2 % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | REF_CLOSE: (278), (666), (676) are inconsistent by sub-proof % 127.57/18.00 | | | | | | | | | | | | #281. % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | (677) all_55_10 = e1 | all_55_10 = e0 % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | BETA: splitting (677) gives: % 127.57/18.00 | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | (678) all_55_10 = e1 % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | COMBINE_EQS: (278), (678) imply: % 127.57/18.00 | | | | | | | | | | | | | (679) all_12_2 = e1 % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | SIMP: (679) implies: % 127.57/18.00 | | | | | | | | | | | | | (680) all_12_2 = e1 % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | COMBINE_EQS: (389), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (681) all_22_2 = e1 % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REDUCE: (415), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (682) ~ (all_53_2 = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REDUCE: (426), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (683) ~ (all_53_6 = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REDUCE: (431), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (684) ~ (all_53_11 = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REDUCE: (433), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (685) ~ (all_53_14 = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | REDUCE: (670), (680) imply: % 127.57/18.00 | | | | | | | | | | | | | (686) ~ (e3 = e1) % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | BETA: splitting (227) gives: % 127.57/18.00 | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | (687) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 127.57/18.00 | | | | | | | | | | | | | | & op(e1, e2) = e1) % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | REF_CLOSE: (279), (281), (282), (682), (683), (687) are % 127.57/18.00 | | | | | | | | | | | | | | inconsistent by sub-proof #279. % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | (688) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 127.57/18.00 | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | BETA: splitting (688) gives: % 127.57/18.00 | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | (689) all_57_8 = e1 & op(e1, e1) = e1 % 127.57/18.00 | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | ALPHA: (689) implies: % 127.57/18.00 | | | | | | | | | | | | | | | (690) all_57_8 = e1 % 127.57/18.00 | | | | | | | | | | | | | | | (691) op(e1, e1) = e1 % 127.57/18.00 | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 127.57/18.00 | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | (692) ~ (all_26_2 = e1) % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | REDUCE: (374), (692) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | (693) ~ (all_6_2 = e1) % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 127.57/18.00 | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | (694) ~ (all_28_2 = e2) % 127.57/18.00 | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | REDUCE: (361), (694) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | (695) ~ (all_8_2 = e2) % 127.57/18.00 | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 127.57/18.00 | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | (696) all_55_15 = e3 % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (696) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | | (697) all_8_2 = e3 % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | REDUCE: (665), (697) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | | (698) $false % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | CLOSE: (698) is inconsistent. % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | (699) ~ (all_55_15 = e3) % 127.57/18.00 | | | | | | | | | | | | | | | | | | (700) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives: % 127.57/18.00 | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | (701) all_55_15 = e2 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (701) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | (702) all_8_2 = e2 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | REDUCE: (695), (702) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | (703) $false % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | CLOSE: (703) is inconsistent. % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | Case 2: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | (704) ~ (all_55_15 = e2) % 127.57/18.00 | | | | | | | | | | | | | | | | | | | (705) all_55_15 = e1 | all_55_15 = e0 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | BETA: splitting (705) gives: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | Case 1: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (706) all_55_15 = e1 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (706) imply: % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | (707) all_8_2 = e1 % 127.57/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | REDUCE: (440), (707) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (708) $false % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent. % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (709) all_55_15 = e0 % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (709) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (710) all_8_2 = e0 % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (710) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (711) ~ (all_53_3 = e0) % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (710) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (712) ~ (all_53_7 = e0) % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (710) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (713) ~ (all_53_11 = e0) % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | REDUCE: (435), (710) imply: % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | (714) ~ (all_53_12 = e0) % 128.14/18.00 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (710) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | (715) ~ (all_53_13 = e0) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (710) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | (716) ~ (all_53_14 = e0) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (665), (710) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | (717) ~ (e3 = e0) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (695), (710) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | (718) ~ (e2 = e0) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | (719) all_57_15 = e0 & op(e0, e0) = e0 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | ALPHA: (719) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | (720) all_57_15 = e0 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (721) ~ (all_34_2 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (721) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (722) ~ (all_4_2 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (723) all_55_0 = e3 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (723) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (724) all_4_2 = e3 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (724) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (725) all_4_2 = e3 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (725) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (726) ~ (all_53_2 = e3) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (286), (327), (328), (342), (663), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (685), (715), (726) are inconsistent by sub-proof % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | #275. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (727) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (316), (438), (668), (722), (727) are inconsistent % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #274. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (728) all_34_2 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (729) op(e3, e1) = all_34_1 & $i(all_34_1) & ( ~ % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e3, % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | e2) = all_34_0 & $i(all_34_0))) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (729) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (730) op(e3, e1) = all_34_1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (728) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (731) all_4_2 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | SIMP: (731) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (732) all_4_2 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (733) all_46_2 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (734) ~ (all_53_3 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (411), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (735) ~ (all_53_8 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (413), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (736) ~ (all_53_12 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (668), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (737) ~ (e2 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (732) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | (738) op(e3, e3) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | (739) ~ (op(e3, e1) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (740) ~ (all_46_2 = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (733), (740) imply: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (741) $false % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (741) is inconsistent. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (742) op(e3, e1) = all_46_1 & $i(all_46_1) & ( ~ % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (all_46_1 = e0) | ( ~ (all_46_0 = e2) & op(e3, % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_46_0 & $i(all_46_0))) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (742) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (743) op(e3, e1) = all_46_1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (744) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_57_1 = e1 & op(e3, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (745) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_57_1 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_57_9 = e1 & op(e3, e0) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (736), (748), (function-axioms) are % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_57_10 = e1 & op(e2, e0) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (749) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_57_10 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_57_12 = e1 & op(e0, e3) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (734), (752), (function-axioms) are % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #272. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_57_13 = e1 & op(e0, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_57_13 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (45), (48), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (228), (241), (243), (247), (284), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326), (329), (438), (439), (681), (690), (691), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714), (716), (720), (738), (746), (750), (754), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #255. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (440), (684), (755), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #293. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (685), (756), % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | #283. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_57_3 = e1 & op(e2, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (693), (757), (function-axioms) are % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #254. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (758) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_57_7 = e1 & op(e1, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (759) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (760) op(e1, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (683), (760) are inconsistent by % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #341. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_57_13 = e1 & op(e0, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_57_13 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (763) op(e0, e2) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_57_9 = e1 & op(e3, e0) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (736), (765), (function-axioms) are % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_57_10 = e1 & op(e2, e0) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_57_10 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) op(e2, e0) = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_57_0 = e1 & op(e3, e3) = e1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (770) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_57_0 = e1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (172), (763) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_53_7 = e1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e2, simplifying with (178), (768) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_53_13 = e1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e0, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (768) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) e2 = e1 | ~ (op(e2, e0) = e2) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_1, e1, e3, simplifying with (183), (730) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_53_8 = all_34_1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_46_1, e1, e3, simplifying with (183), (743) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_53_8 = all_46_1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (775), (776) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_46_1 = all_34_1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (772) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) ~ (all_53_11 = e1) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (775) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) ~ (all_53_11 = all_34_1) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (779) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) ~ (all_53_11 = all_34_1) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (773) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) ~ (all_53_9 = e1) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (773) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) ~ (all_6_2 = e1) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) ~ (all_42_2 = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (783) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) ~ (all_6_2 = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (212), (279), (282), (295), (304), % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (423), (439), (663), (683), (684), (693), % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) are inconsistent by sub-proof #249. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_42_2 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (785) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_6_2 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (786) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_6_2 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (787) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (all_53_9 = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (693), (787) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ (e1 = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) ~ (op(e2, e0) = e2) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_57_4 = e0 & op(e3, e1) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_57_4 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_57_0 = e0 & op(e3, e3) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (438), (795), (function-axioms) are % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #270. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_57_1 = e0 & op(e3, e2) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (796) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_57_1 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (18), (247), (249), (738), % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771), (793), (797), (function-axioms) are % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (798) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) op(e3, e1) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1, e0, % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (730), (799) gives: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_34_1 = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4), (790) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) ~ (unit = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (265), (331), (332), (663), (713), % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (801) are inconsistent by sub-proof #242. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_57_9 = e0 & op(e3, e0) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) op(e3, e0) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (326), (714), (803) are inconsistent by sub-proof % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #256. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_57_5 = e0 & op(e2, e1) = e0 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (788), (804), (function-axioms) are % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #241. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (265), (284), (681), (690), (691), (713), % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) are inconsistent by sub-proof #240. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) e2 = e1 % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (806) imply: % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) $false % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (807) is inconsistent. % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.14/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_57_1 = e1 & op(e3, e2) = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (808) implies: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_57_1 = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (45), (48), % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (228), (241), (243), (247), (284), % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326), (329), (438), (439), (681), (690), (691), % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714), (716), (720), (738), (762), (767), (809), % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #255. % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_57_4 = e1 & op(e3, e1) = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (739), (811) are inconsistent by sub-proof #239. % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_57_9 = e1 & op(e3, e0) = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (736), (812), (function-axioms) are % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (685), (813), % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | #283. % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | (814) op(e3, e1) = e1 % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (735), (814) are inconsistent by sub-proof % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | #238. % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.02 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | (815) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (261), (262), (265), (711), (712), (713), % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | (815) are inconsistent by sub-proof #236. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.03 | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | End of split % 128.70/18.03 | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | End of split % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | (816) all_28_2 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | (817) op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 128.70/18.03 | | | | | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | e1) = all_28_0 & $i(all_28_0))) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | ALPHA: (817) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | (818) op(e0, e2) = all_28_1 % 128.70/18.03 | | | | | | | | | | | | | | | | | (819) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | e1) = all_28_0 & $i(all_28_0)) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (816) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (820) all_8_2 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | SIMP: (820) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | (821) all_8_2 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (822) all_10_2 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (823) all_36_2 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (427), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (824) ~ (all_53_7 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (434), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (825) ~ (all_53_11 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (436), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (826) ~ (all_53_13 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (437), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (827) ~ (all_53_14 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (665), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (828) ~ (e3 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | REDUCE: (51), (821) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | (829) op(e0, e0) = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | (830) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | BETA: splitting (830) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | (831) all_57_9 = e2 & op(e3, e0) = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | ALPHA: (831) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | (832) all_57_9 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | (833) ~ (all_36_2 = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | REDUCE: (823), (833) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | (834) $false % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | CLOSE: (834) is inconsistent. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | (835) op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0))) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (835) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | (836) op(e0, e2) = all_36_1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | (837) ~ (op(e0, e2) = e2) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | (838) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (838) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (839) all_57_9 = e1 & op(e3, e0) = e1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (839) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (840) all_57_9 = e1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (832), (840) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (841) e2 = e1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (841) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (842) $false % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (842) is inconsistent. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (843) all_57_10 = e1 & op(e2, e0) = e1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (843) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | (844) all_57_10 = e1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | (845) all_57_15 = e0 & op(e0, e0) = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | (846) op(e0, e0) = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (270), (822), (846) are inconsistent by % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #235. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | (847) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | (848) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (848) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_57_9 = e0 & op(e3, e0) = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (832), (849) are inconsistent by sub-proof % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | #285. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | (850) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (850) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_57_10 = e0 & op(e2, e0) = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (851) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_57_10 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (844), (852) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (853) e1 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (853) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (854) e1 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (681), (854) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_22_2 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (691), (855) are inconsistent by % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_57_11 = e0 & op(e1, e0) = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (856) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_57_11 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (832), (844), (858) are inconsistent % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #261. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_57_11 = e3 & op(e1, e0) = e3 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (860) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_57_11 = e3 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (857), (861) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) e3 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (862) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) e3 = e0 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (863) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) $false % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (864) is inconsistent. % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_57_15 = e3 & op(e0, e0) = e3 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (865) implies: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_57_15 = e3 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) op(e0, e0) = e3 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e0, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (829), (867) gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) e3 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (866), (868) imply: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_57_15 = e2 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_28_1, e2, e0, simplifying with (172), (818) % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_53_7 = all_28_1 % 128.70/18.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (9), (14), (16), (17), (18), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (91), (103), (139), (142), (153), (158), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171), (172), (173), (204), (212), (217), (219), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (222), (257), (259), (260), (279), (282), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284), (295), (304), (316), (328), (334), (342), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344), (367), (398), (405), (407), (421), (423), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425), (438), (439), (440), (663), (668), (681), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683), (684), (691), (693), (819), (825), (836), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837), (869), (870), (function-axioms) are % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | (871) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (685), (871), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | #283. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (872) all_53_7 = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | REDUCE: (824), (872) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (873) $false % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | CLOSE: (873) is inconsistent. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (874) all_57_10 = e2 & op(e2, e0) = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | ALPHA: (874) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (875) op(e2, e0) = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (826), (875) are inconsistent by sub-proof % 128.70/18.04 | | | | | | | | | | | | | | | | | | | #225. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | (876) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 128.70/18.04 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | BETA: splitting (876) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (877) all_57_11 = e2 & op(e1, e0) = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (827), (877), (function-axioms) are % 128.70/18.04 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (878) all_57_15 = e2 & op(e0, e0) = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | ALPHA: (878) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (879) all_57_15 = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (880) ~ (all_36_2 = e2) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | REDUCE: (823), (880) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (881) $false % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | CLOSE: (881) is inconsistent. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (882) op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0))) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | ALPHA: (882) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (883) op(e0, e2) = all_36_1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (884) ~ (op(e0, e2) = e2) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | all_28_1, e2, e0, simplifying with (172), (818) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (885) all_53_7 = all_28_1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (9), (14), (16), (17), (18), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (51), (91), (103), (139), (142), (153), (158), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (171), (172), (173), (204), (212), (217), (219), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (220), (222), (257), (259), (260), (279), (282), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (284), (295), (304), (316), (328), (334), (342), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (344), (367), (398), (405), (407), (421), (423), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (425), (438), (439), (440), (663), (668), (681), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (683), (684), (691), (693), (819), (825), (879), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (883), (884), (885), (function-axioms) are % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #226. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (886) all_53_7 = e2 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | REDUCE: (824), (886) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | (887) $false % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | CLOSE: (887) is inconsistent. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | (888) all_26_2 = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (888) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | (889) all_6_2 = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | SIMP: (889) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | (890) all_6_2 = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | REDUCE: (423), (890) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | (891) ~ (all_53_9 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | REDUCE: (425), (890) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | (892) ~ (all_53_13 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | (893) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 128.70/18.04 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | BETA: splitting (893) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | (894) all_57_9 = e1 & op(e3, e0) = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | ALPHA: (894) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | | | (895) op(e3, e0) = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (896) ~ (op(e2, e1) = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 128.70/18.04 | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (182), (895) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (897) all_53_12 = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (896) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (898) ~ (unit = e2) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (897) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (899) ~ (all_53_14 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REDUCE: (435), (897) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (900) ~ (all_8_2 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REDUCE: (413), (897) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (901) ~ (all_4_2 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | SIMP: (901) implies: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (902) ~ (all_4_2 = e1) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (903) all_55_0 = e3 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (903) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (904) all_4_2 = e3 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (904) imply: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (905) ~ (all_53_2 = e3) % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (82), (203), (256), (286), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (327), (328), (339), (342), (361), (427), (436), % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (440), (663), (665), (685), (898), (905) are % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #221. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | (906) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (316), (438), (668), (902), (906) are inconsistent % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | by sub-proof #274. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | (907) op(e2, e1) = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (891), (907) are inconsistent by sub-proof % 128.70/18.04 | | | | | | | | | | | | | | | | | | | #334. % 128.70/18.04 | | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | End of split % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | (908) all_57_10 = e1 & op(e2, e0) = e1 % 128.70/18.04 | | | | | | | | | | | | | | | | | | % 128.70/18.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (892), (908), (function-axioms) are % 128.70/18.05 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 128.70/18.05 | | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | (909) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 128.70/18.05 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (685), (909), % 128.70/18.05 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.05 | | | | | | | | | | | | | | | | | #283. % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | (910) all_57_11 = e1 & op(e1, e0) = e1 % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | ALPHA: (910) implies: % 128.70/18.05 | | | | | | | | | | | | | | | (911) op(e1, e0) = e1 % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | REF_CLOSE: (286), (685), (911) are inconsistent by sub-proof % 128.70/18.05 | | | | | | | | | | | | | | | #339. % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | (912) all_55_10 = e0 % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | REF_CLOSE: (278), (672), (912) are inconsistent by sub-proof % 128.70/18.05 | | | | | | | | | | | | | #219. % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | (913) all_22_2 = e0 % 128.70/18.05 | | | | | | | | | | (914) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 128.70/18.05 | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 128.70/18.05 | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | ALPHA: (914) implies: % 128.70/18.05 | | | | | | | | | | (915) op(e1, e0) = all_22_1 % 128.70/18.05 | | | | | | | | | | (916) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 128.70/18.05 | | | | | | | | | | e3) = all_22_0 & $i(all_22_0)) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | COMBINE_EQS: (389), (913) imply: % 128.70/18.05 | | | | | | | | | | (917) all_12_2 = e0 % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | SIMP: (917) implies: % 128.70/18.05 | | | | | | | | | | (918) all_12_2 = e0 % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | COMBINE_EQS: (359), (918) imply: % 128.70/18.05 | | | | | | | | | | (919) all_38_2 = e0 % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | REDUCE: (415), (918) imply: % 128.70/18.05 | | | | | | | | | | (920) ~ (all_53_2 = e0) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | REDUCE: (428), (918) imply: % 128.70/18.05 | | | | | | | | | | (921) ~ (all_53_8 = e0) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | REDUCE: (429), (918) imply: % 128.70/18.05 | | | | | | | | | | (922) ~ (all_53_9 = e0) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | REDUCE: (433), (918) imply: % 128.70/18.05 | | | | | | | | | | (923) ~ (all_53_14 = e0) % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | REDUCE: (57), (918) imply: % 128.70/18.05 | | | | | | | | | | (924) op(e1, e1) = e0 % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | BETA: splitting (97) gives: % 128.70/18.05 | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | (925) ~ (all_38_2 = e0) % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | REDUCE: (919), (925) imply: % 128.70/18.05 | | | | | | | | | | | (926) $false % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | CLOSE: (926) is inconsistent. % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | (927) op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 128.70/18.05 | | | | | | | | | | | (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, % 128.70/18.05 | | | | | | | | | | | e2) = all_38_0 & $i(all_38_0))) % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | ALPHA: (927) implies: % 128.70/18.05 | | | | | | | | | | | (928) op(e1, e0) = all_38_1 % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | BETA: splitting (329) gives: % 128.70/18.05 | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | (929) ~ (op(e1, e0) = e0) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 128.70/18.05 | | | | | | | | | | | | all_22_1, e0, e1, simplifying with (174), (915) % 128.70/18.05 | | | | | | | | | | | | gives: % 128.70/18.05 | | | | | | | | | | | | (930) all_53_14 = all_22_1 % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 128.70/18.05 | | | | | | | | | | | | all_38_1, e0, e1, simplifying with (174), (928) % 128.70/18.05 | | | | | | | | | | | | gives: % 128.70/18.05 | | | | | | | | | | | | (931) all_53_14 = all_38_1 % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_1, % 128.70/18.05 | | | | | | | | | | | | e0, e1, simplifying with (928) gives: % 128.70/18.05 | | | | | | | | | | | | (932) all_38_1 = e1 | ~ (op(e1, e0) = e1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | PRED_UNIFY: (6), (929) imply: % 128.70/18.05 | | | | | | | | | | | | (933) ~ (unit = e1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | COMBINE_EQS: (930), (931) imply: % 128.70/18.05 | | | | | | | | | | | | (934) all_38_1 = all_22_1 % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | SIMP: (934) implies: % 128.70/18.05 | | | | | | | | | | | | (935) all_38_1 = all_22_1 % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | COMBINE_EQS: (271), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (936) all_55_11 = all_22_1 % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | REDUCE: (155), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (937) ~ (all_53_2 = all_22_1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | REDUCE: (140), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (938) ~ (all_53_6 = all_22_1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | REDUCE: (126), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (939) ~ (all_53_12 = all_22_1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | REDUCE: (124), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (940) ~ (all_53_13 = all_22_1) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | REDUCE: (437), (930) imply: % 128.70/18.05 | | | | | | | | | | | | (941) ~ (all_22_1 = all_8_2) % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | BETA: splitting (79) gives: % 128.70/18.05 | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | (942) ~ (all_26_2 = e1) % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | REDUCE: (374), (942) imply: % 128.70/18.05 | | | | | | | | | | | | | (943) ~ (all_6_2 = e1) % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | BETA: splitting (82) gives: % 128.70/18.05 | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | (944) ~ (all_28_2 = e2) % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | REDUCE: (361), (944) imply: % 128.70/18.05 | | | | | | | | | | | | | | (945) ~ (all_8_2 = e2) % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | BETA: splitting (203) gives: % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | (946) all_55_15 = e3 % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | COMBINE_EQS: (256), (946) imply: % 128.70/18.05 | | | | | | | | | | | | | | | (947) all_8_2 = e3 % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | REDUCE: (665), (947) imply: % 128.70/18.05 | | | | | | | | | | | | | | | (948) $false % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | CLOSE: (948) is inconsistent. % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | (949) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | BETA: splitting (949) gives: % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | (950) all_55_15 = e2 % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (950) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | (951) all_8_2 = e2 % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | REDUCE: (945), (951) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | (952) $false % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | CLOSE: (952) is inconsistent. % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | (953) all_55_15 = e1 | all_55_15 = e0 % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | BETA: splitting (953) gives: % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | Case 1: % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | (954) all_55_15 = e1 % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (954) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (955) all_8_2 = e1 % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REDUCE: (440), (955) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (956) $false % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | CLOSE: (956) is inconsistent. % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | (957) all_55_15 = e0 % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (957) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (958) all_8_2 = e0 % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REDUCE: (416), (958) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (959) ~ (all_53_3 = e0) % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REDUCE: (435), (958) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (960) ~ (all_53_12 = e0) % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REDUCE: (941), (958) imply: % 128.70/18.05 | | | | | | | | | | | | | | | | | (961) ~ (all_22_1 = e0) % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (45), (91), (134), (147), (148), % 128.70/18.05 | | | | | | | | | | | | | | | | | (157), (163), (177), (181), (183), (184), (207), % 128.70/18.05 | | | | | | | | | | | | | | | | | (210), (212), (214), (215), (217), (242), (243), % 128.70/18.05 | | | | | | | | | | | | | | | | | (261), (279), (280), (282), (295), (306), (307), % 128.70/18.05 | | | | | | | | | | | | | | | | | (308), (316), (322), (326), (367), (405), (409), % 128.70/18.05 | | | | | | | | | | | | | | | | | (411), (413), (417), (425), (438), (439), (663), % 128.70/18.05 | | | | | | | | | | | | | | | | | (668), (916), (920), (921), (933), (936), (937), % 128.70/18.05 | | | | | | | | | | | | | | | | | (938), (943), (959), (960), (961), % 128.70/18.05 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.05 | | | | | | | | | | | | | | | | | #208. % 128.70/18.05 | | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | End of split % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | Case 2: % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | (962) all_28_2 = e2 % 128.70/18.05 | | | | | | | | | | | | | | (963) op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 128.70/18.05 | | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, % 128.70/18.05 | | | | | | | | | | | | | | e1) = all_28_0 & $i(all_28_0))) % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | ALPHA: (963) implies: % 128.70/18.05 | | | | | | | | | | | | | | (964) op(e0, e2) = all_28_1 % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | COMBINE_EQS: (361), (962) imply: % 128.70/18.05 | | | | | | | | | | | | | | (965) all_8_2 = e2 % 128.70/18.05 | | | | | | | | | | | | | | % 128.70/18.05 | | | | | | | | | | | | | | COMBINE_EQS: (397), (965) imply: % 128.70/18.06 | | | | | | | | | | | | | | (966) all_36_2 = e2 % 128.70/18.06 | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | REDUCE: (427), (965) imply: % 128.70/18.06 | | | | | | | | | | | | | | (967) ~ (all_53_7 = e2) % 128.70/18.06 | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | BETA: splitting (94) gives: % 128.70/18.06 | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | Case 1: % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | (968) ~ (all_36_2 = e2) % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | REDUCE: (966), (968) imply: % 128.70/18.06 | | | | | | | | | | | | | | | (969) $false % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | CLOSE: (969) is inconsistent. % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | (970) op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 128.70/18.06 | | | | | | | | | | | | | | | (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, % 128.70/18.06 | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0))) % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | ALPHA: (970) implies: % 128.70/18.06 | | | | | | | | | | | | | | | (971) op(e0, e2) = all_36_1 % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | Case 1: % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | (972) ~ (op(e0, e2) = e2) % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, % 128.70/18.06 | | | | | | | | | | | | | | | | all_28_1, e2, e0, simplifying with (172), (964) % 128.70/18.06 | | | | | | | | | | | | | | | | gives: % 128.70/18.06 | | | | | | | | | | | | | | | | (973) all_53_7 = all_28_1 % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, % 128.70/18.06 | | | | | | | | | | | | | | | | all_36_1, e2, e0, simplifying with (172), (971) % 128.70/18.06 | | | | | | | | | | | | | | | | gives: % 128.70/18.06 | | | | | | | | | | | | | | | | (974) all_53_7 = all_36_1 % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1, % 128.70/18.06 | | | | | | | | | | | | | | | | e2, e0, simplifying with (971) gives: % 128.70/18.06 | | | | | | | | | | | | | | | | (975) all_36_1 = e0 | ~ (op(e0, e2) = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | PRED_UNIFY: (8), (972) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | (976) ~ (unit = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | COMBINE_EQS: (973), (974) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | (977) all_36_1 = all_28_1 % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | SIMP: (977) implies: % 128.70/18.06 | | | | | | | | | | | | | | | | (978) all_36_1 = all_28_1 % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | REDUCE: (154), (973) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | (979) ~ (all_53_3 = all_28_1) % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | Case 1: % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | (980) unit = e2 % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | REDUCE: (6), (980) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | (981) op(e2, e0) = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | REDUCE: (2), (980) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | (982) op(e0, e2) = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | BETA: splitting (975) gives: % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | (983) ~ (op(e0, e2) = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (982), (983) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | (984) $false % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | CLOSE: (984) is inconsistent. % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | (985) all_36_1 = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (978), (985) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | (986) all_28_1 = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | SIMP: (986) implies: % 128.70/18.06 | | | | | | | | | | | | | | | | | | (987) all_28_1 = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | REDUCE: (979), (987) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | (988) ~ (all_53_3 = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | Case 1: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (989) ~ (op(e2, e0) = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (981), (989) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (990) $false % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | CLOSE: (990) is inconsistent. % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (991) all_53_13 = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | REDUCE: (127), (991) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (992) ~ (all_53_12 = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | REDUCE: (940), (991) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (993) ~ (all_22_1 = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | SIMP: (993) implies: % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (994) ~ (all_22_1 = e0) % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (45), (91), (134), (147), (148), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (157), (163), (177), (181), (183), (184), (207), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (210), (212), (214), (215), (217), (242), (243), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (261), (279), (280), (282), (295), (306), (307), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (308), (316), (322), (326), (367), (405), (409), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (411), (413), (417), (425), (438), (439), (663), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (668), (916), (920), (921), (933), (936), (937), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (938), (943), (988), (992), (994), % 128.70/18.06 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.70/18.06 | | | | | | | | | | | | | | | | | | | #208. % 128.70/18.06 | | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | (995) unit = e1 | unit = e0 % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (933), (976), (995) are inconsistent by sub-proof % 128.70/18.06 | | | | | | | | | | | | | | | | | #278. % 128.70/18.06 | | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | (996) all_53_7 = e2 % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | REDUCE: (967), (996) imply: % 128.70/18.06 | | | | | | | | | | | | | | | | (997) $false % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | | CLOSE: (997) is inconsistent. % 128.70/18.06 | | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | (998) all_26_2 = e1 % 128.70/18.06 | | | | | | | | | | | | | (999) op(e2, e1) = all_26_1 & $i(all_26_1) & ( ~ % 128.70/18.06 | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, % 128.70/18.06 | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | ALPHA: (999) implies: % 128.70/18.06 | | | | | | | | | | | | | (1000) op(e2, e1) = all_26_1 % 128.70/18.06 | | | | | | | | | | | | | (1001) ~ (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, % 128.70/18.06 | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0)) % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | COMBINE_EQS: (374), (998) imply: % 128.70/18.06 | | | | | | | | | | | | | (1002) all_6_2 = e1 % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (48), (100), % 128.70/18.06 | | | | | | | | | | | | | (127), (131), (134), (135), (142), (147), (153), % 128.70/18.06 | | | | | | | | | | | | | (154), (158), (159), (162), (172), (179), (211), % 128.70/18.06 | | | | | | | | | | | | | (215), (227), (228), (229), (231), (232), (233), % 128.70/18.06 | | | | | | | | | | | | | (234), (236), (237), (238), (242), (245), (248), % 128.70/18.06 | | | | | | | | | | | | | (249), (258), (261), (262), (268), (279), (281), % 128.70/18.06 | | | | | | | | | | | | | (282), (284), (288), (296), (297), (300), (306), % 128.70/18.06 | | | | | | | | | | | | | (308), (309), (319), (321), (323), (324), (330), % 128.70/18.06 | | | | | | | | | | | | | (332), (334), (337), (339), (340), (342), (344), % 128.70/18.06 | | | | | | | | | | | | | (370), (382), (397), (399), (407), (416), (419), % 128.70/18.06 | | | | | | | | | | | | | (421), (423), (425), (427), (434), (436), (439), % 128.70/18.06 | | | | | | | | | | | | | (440), (663), (913), (921), (922), (924), (932), % 128.70/18.06 | | | | | | | | | | | | | (933), (935), (937), (939), (941), (1000), (1001), % 128.70/18.06 | | | | | | | | | | | | | (1002), (function-axioms) are inconsistent by % 128.70/18.06 | | | | | | | | | | | | | sub-proof #187. % 128.70/18.06 | | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | Case 2: % 128.70/18.06 | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | (1003) op(e1, e0) = e0 % 128.70/18.06 | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | | REF_CLOSE: (329), (923), (1003) are inconsistent by sub-proof % 128.70/18.06 | | | | | | | | | | | | #355. % 128.70/18.06 | | | | | | | | | | | | % 128.70/18.06 | | | | | | | | | | | End of split % 128.70/18.06 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | End of split % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | End of split % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | Case 2: % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | (1004) all_18_2 = e3 % 128.70/18.07 | | | | | | | | | (1005) op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 % 128.70/18.07 | | | | | | | | | = e2) | ( ~ (all_18_0 = e0) & op(e1, e2) = % 128.70/18.07 | | | | | | | | | all_18_0 & $i(all_18_0))) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | ALPHA: (1005) implies: % 128.70/18.07 | | | | | | | | | (1006) op(e1, e3) = all_18_1 % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | COMBINE_EQS: (391), (1004) imply: % 128.70/18.07 | | | | | | | | | (1007) all_12_2 = e3 % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | SIMP: (1007) implies: % 128.70/18.07 | | | | | | | | | (1008) all_12_2 = e3 % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | COMBINE_EQS: (384), (1008) imply: % 128.70/18.07 | | | | | | | | | (1009) all_24_2 = e3 % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (415), (1008) imply: % 128.70/18.07 | | | | | | | | | (1010) ~ (all_53_2 = e3) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (426), (1008) imply: % 128.70/18.07 | | | | | | | | | (1011) ~ (all_53_6 = e3) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (428), (1008) imply: % 128.70/18.07 | | | | | | | | | (1012) ~ (all_53_8 = e3) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (429), (1008) imply: % 128.70/18.07 | | | | | | | | | (1013) ~ (all_53_9 = e3) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (433), (1008) imply: % 128.70/18.07 | | | | | | | | | (1014) ~ (all_53_14 = e3) % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | REDUCE: (57), (1008) imply: % 128.70/18.07 | | | | | | | | | (1015) op(e1, e1) = e3 % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | BETA: splitting (76) gives: % 128.70/18.07 | | | | | | | | | % 128.70/18.07 | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | (1016) ~ (all_24_2 = e3) % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | REDUCE: (1009), (1016) imply: % 128.70/18.07 | | | | | | | | | | (1017) $false % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | CLOSE: (1017) is inconsistent. % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | Case 2: % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | (1018) op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 128.70/18.07 | | | | | | | | | | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, % 128.70/18.07 | | | | | | | | | | e0) = all_24_0 & $i(all_24_0))) % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | ALPHA: (1018) implies: % 128.70/18.07 | | | | | | | | | | (1019) op(e1, e3) = all_24_1 % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | BETA: splitting (342) gives: % 128.70/18.07 | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | (1020) ~ (op(e1, e3) = e3) % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 128.70/18.07 | | | | | | | | | | | all_18_1, e3, e1, simplifying with (177), (1006) % 128.70/18.07 | | | | | | | | | | | gives: % 128.70/18.07 | | | | | | | | | | | (1021) all_53_2 = all_18_1 % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 128.70/18.07 | | | | | | | | | | | all_24_1, e3, e1, simplifying with (177), (1019) % 128.70/18.07 | | | | | | | | | | | gives: % 128.70/18.07 | | | | | | | | | | | (1022) all_53_2 = all_24_1 % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | PRED_UNIFY: (9), (1020) imply: % 128.70/18.07 | | | | | | | | | | | (1023) ~ (unit = e1) % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | COMBINE_EQS: (1021), (1022) imply: % 128.70/18.07 | | | | | | | | | | | (1024) all_24_1 = all_18_1 % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | SIMP: (1024) implies: % 128.70/18.07 | | | | | | | | | | | (1025) all_24_1 = all_18_1 % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | REDUCE: (157), (1021) imply: % 128.70/18.07 | | | | | | | | | | | (1026) ~ (all_53_6 = all_18_1) % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | SIMP: (1026) implies: % 128.70/18.07 | | | | | | | | | | | (1027) ~ (all_53_6 = all_18_1) % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | BETA: splitting (79) gives: % 128.70/18.07 | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | (1028) ~ (all_26_2 = e1) % 128.70/18.07 | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | REDUCE: (374), (1028) imply: % 128.70/18.07 | | | | | | | | | | | | (1029) ~ (all_6_2 = e1) % 128.70/18.07 | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | BETA: splitting (82) gives: % 128.70/18.07 | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | (1030) ~ (all_28_2 = e2) % 128.70/18.07 | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | REDUCE: (361), (1030) imply: % 128.70/18.07 | | | | | | | | | | | | | (1031) ~ (all_8_2 = e2) % 128.70/18.07 | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | BETA: splitting (203) gives: % 128.70/18.07 | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | (1032) all_55_15 = e3 % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | COMBINE_EQS: (256), (1032) imply: % 128.70/18.07 | | | | | | | | | | | | | | (1033) all_8_2 = e3 % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | REDUCE: (665), (1033) imply: % 128.70/18.07 | | | | | | | | | | | | | | (1034) $false % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | CLOSE: (1034) is inconsistent. % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | Case 2: % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | (1035) ~ (all_55_15 = e3) % 128.70/18.07 | | | | | | | | | | | | | | (1036) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | BETA: splitting (1036) gives: % 128.70/18.07 | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | (1037) all_55_15 = e2 % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1037) imply: % 128.70/18.07 | | | | | | | | | | | | | | | (1038) all_8_2 = e2 % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | REDUCE: (1031), (1038) imply: % 128.70/18.07 | | | | | | | | | | | | | | | (1039) $false % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | CLOSE: (1039) is inconsistent. % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | Case 2: % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | (1040) ~ (all_55_15 = e2) % 128.70/18.07 | | | | | | | | | | | | | | | (1041) all_55_15 = e1 | all_55_15 = e0 % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | BETA: splitting (1041) gives: % 128.70/18.07 | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | (1042) all_55_15 = e1 % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1042) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1043) all_8_2 = e1 % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (440), (1043) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1044) $false % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | CLOSE: (1044) is inconsistent. % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | Case 2: % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | (1045) all_55_15 = e0 % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1045) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1046) all_8_2 = e0 % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (416), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1047) ~ (all_53_3 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (427), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1048) ~ (all_53_7 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (435), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1049) ~ (all_53_12 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (436), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1050) ~ (all_53_13 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (437), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1051) ~ (all_53_14 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (665), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1052) ~ (e3 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | REDUCE: (1031), (1046) imply: % 128.70/18.07 | | | | | | | | | | | | | | | | (1053) ~ (e2 = e0) % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 128.70/18.07 | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | Case 1: % 128.70/18.07 | | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | | (1054) ~ (all_34_2 = e1) % 128.70/18.07 | | | | | | | | | | | | | | | | | % 128.70/18.07 | | | | | | | | | | | | | | | | | REDUCE: (367), (1054) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1055) ~ (all_4_2 = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1056) all_55_0 = e3 % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (1056) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1057) all_4_2 = e3 % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | SIMP: (1057) implies: % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1058) all_4_2 = e3 % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | REDUCE: (403), (1058) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1059) ~ (all_53_1 = e3) % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | REDUCE: (413), (1058) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1060) ~ (all_53_12 = e3) % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (324), (340), (663), (1023), (1059), % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1060) are inconsistent by sub-proof #184. % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1061) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (316), (438), (668), (1055), (1061) are % 128.94/18.07 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274. % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | End of split % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | Case 2: % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | (1062) all_34_2 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (1062) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1063) all_4_2 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | SIMP: (1063) implies: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1064) all_4_2 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1065) all_53_0 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | REDUCE: (407), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1066) ~ (all_53_3 = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | REDUCE: (411), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1067) ~ (all_53_8 = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | REDUCE: (413), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1068) ~ (all_53_12 = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | REDUCE: (668), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1069) ~ (e2 = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | REDUCE: (45), (1064) imply: % 128.94/18.07 | | | | | | | | | | | | | | | | | (1070) op(e3, e3) = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 128.94/18.07 | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | (1071) ~ (op(e3, e1) = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 128.94/18.07 | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | (1072) ~ (op(e3, e1) = e3) % 128.94/18.07 | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | (1073) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1073) gives: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | (1074) all_57_0 = e1 & op(e3, e3) = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies: % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | (1075) all_57_0 = e1 % 128.94/18.07 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (14), (15), (17), (18), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (45), (48), (51), (103), (140), (142), (162), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (179), (182), (209), (212), (223), (226), (227), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (228), (237), (242), (248), (258), (261), (262), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (263), (279), (285), (286), (295), (328), (329), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (339), (340), (342), (344), (398), (419), (421), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (425), (438), (439), (440), (663), (1006), (1008), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1010), (1011), (1013), (1015), (1020), (1023), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1027), (1029), (1047), (1048), (1051), (1066), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1068), (1075), (function-axioms) are inconsistent % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | by sub-proof #167. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1076) all_57_2 = e1 & op(e2, e3) = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (17), (18), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (45), (140), (142), (209), (226), (227), (228), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (242), (261), (279), (285), (286), (328), (329), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (339), (438), (663), (1006), (1008), (1011), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1015), (1023), (1027), (1047), (1050), (1051), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1076), (function-axioms) are inconsistent by % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | sub-proof #165. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | (1077) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1077) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1078) all_57_6 = e1 & op(e1, e3) = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1078) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | (1079) all_57_6 = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | (1080) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1080) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1081) all_57_0 = e1 & op(e3, e3) = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1081) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1082) all_57_0 = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (14), (15), (17), (18), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (51), (103), (140), (142), (162), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (209), (212), (223), (226), (227), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (228), (237), (242), (248), (258), (261), (262), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (263), (279), (285), (286), (295), (328), (329), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (339), (340), (342), (344), (398), (419), (421), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (425), (438), (439), (440), (663), (1006), (1008), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1010), (1011), (1013), (1015), (1020), (1023), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1027), (1029), (1047), (1048), (1051), (1066), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1068), (1082), (function-axioms) are inconsistent % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #167. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1083) all_57_1 = e1 & op(e3, e2) = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | (1084) all_57_1 = e1 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | (1085) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1085) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_57_0 = e3 & op(e3, e3) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1086) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_57_0 = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1088) op(e3, e3) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (14), (15), (17), (18), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (51), (103), (140), (142), (162), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (209), (212), (223), (226), (227), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (228), (237), (242), (248), (258), (261), (262), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (263), (279), (285), (286), (295), (317), (328), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (329), (339), (340), (342), (344), (398), (419), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (421), (425), (438), (439), (440), (663), (1006), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1008), (1010), (1011), (1013), (1015), (1020), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1023), (1027), (1029), (1047), (1048), (1051), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1065), (1066), (1068), (1087), (1088), % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | #164. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_57_1 = e3 & op(e3, e2) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1084), (1089) are inconsistent by sub-proof % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | #271. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | (1090) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1090) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_57_4 = e3 & op(e3, e1) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1091) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1092) op(e3, e1) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1072), (1092) imply: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1093) $false % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1093) is inconsistent. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_57_9 = e3 & op(e3, e0) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1094) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_57_9 = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1096) op(e3, e0) = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) ~ (op(e3, e0) = e3) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1096), (1097) imply: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) $false % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1098) is inconsistent. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_53_12 = e3 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1100) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_57_0 = e0 & op(e3, e3) = e0 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (438), (1101), (function-axioms) are % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #270. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_57_2 = e0 & op(e2, e3) = e0 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1102) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_57_2 = e0 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1070), (1084), (1104), (function-axioms) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #265. % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_57_4 = e2 & op(e3, e1) = e2 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1106) implies: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_57_4 = e2 % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1108) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_57_0 = e3 & op(e3, e3) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1109) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_57_0 = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) op(e3, e3) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (14), (15), (17), (18), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (48), (51), (103), (140), (142), (162), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (209), (212), (223), (226), (227), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (237), (242), (248), (258), (261), (262), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (279), (285), (286), (295), (317), (328), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (339), (340), (342), (344), (398), (419), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421), (425), (438), (439), (440), (663), (1006), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008), (1010), (1011), (1013), (1015), (1020), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023), (1027), (1029), (1047), (1048), (1051), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065), (1066), (1068), (1110), (1111), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #164. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_57_2 = e3 & op(e2, e3) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1112) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_57_2 = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1103), (1113) imply: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) e3 = e0 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1114) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) e3 = e0 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1115) imply: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_53_12 = e0 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (1096), (1116) are inconsistent by % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1117) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_57_6 = e3 & op(e1, e3) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1020), (1118) are inconsistent by sub-proof #181. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_57_12 = e3 & op(e0, e3) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1119) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_57_12 = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1121) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_57_0 = e2 & op(e3, e3) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1122) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) op(e3, e3) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (243), (324), (1084), (1095), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096), (1099), (1107), (1123), (function-axioms) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #161. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_57_2 = e2 & op(e2, e3) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1103), (1124) are inconsistent by sub-proof % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #349. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1125) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_57_6 = e2 & op(e1, e3) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1079), (1126) are inconsistent by sub-proof % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #319. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_57_12 = e2 & op(e0, e3) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1127) implies: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_57_12 = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1120), (1128) imply: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) e3 = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (1129) imply: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) $false % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1130) is inconsistent. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_57_9 = e2 & op(e3, e0) = e2 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1095), (1131) are inconsistent by sub-proof % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1132) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_57_6 = e0 & op(e1, e3) = e0 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (17), (18), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140), (142), (209), (226), (227), (228), (279), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285), (286), (328), (329), (339), (663), (1006), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008), (1011), (1015), (1023), (1027), (1050), % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051), (1133), (function-axioms) are inconsistent % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #168. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_57_12 = e0 & op(e0, e3) = e0 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1047), (1134) are inconsistent by % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #237. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | (1135) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | (1136) all_57_4 = e1 & op(e3, e1) = e1 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1071), (1136) are inconsistent by sub-proof #239. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | (1137) all_57_9 = e1 & op(e3, e0) = e1 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (1068), (1137), (function-axioms) are % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | (1138) all_57_12 = e1 & op(e0, e3) = e1 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1066), (1138), (function-axioms) are % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #272. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | (1139) op(e3, e1) = e3 % 128.94/18.09 | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (323), (1012), (1139) are inconsistent by % 128.94/18.09 | | | | | | | | | | | | | | | | | | | sub-proof #160. % 128.94/18.09 | | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | (1140) op(e3, e1) = e1 % 128.94/18.09 | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (1067), (1140) are inconsistent by % 128.94/18.09 | | | | | | | | | | | | | | | | | | sub-proof #238. % 128.94/18.09 | | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | (1141) all_28_2 = e2 % 128.94/18.09 | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | COMBINE_EQS: (361), (1141) imply: % 128.94/18.09 | | | | | | | | | | | | | (1142) all_8_2 = e2 % 128.94/18.09 | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (124), (132), (140), % 128.94/18.09 | | | | | | | | | | | | | (207), (212), (271), (279), (282), (288), (295), % 128.94/18.09 | | | | | | | | | | | | | (304), (328), (331), (334), (339), (342), (423), % 128.94/18.09 | | | | | | | | | | | | | (425), (427), (437), (439), (663), (1010), (1014), % 128.94/18.09 | | | | | | | | | | | | | (1023), (1029), (1142) are inconsistent by % 128.94/18.09 | | | | | | | | | | | | | sub-proof #158. % 128.94/18.09 | | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | End of split % 128.94/18.09 | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | Case 2: % 128.94/18.09 | | | | | | | | | | | | % 128.94/18.09 | | | | | | | | | | | | (1143) all_26_2 = e1 % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | COMBINE_EQS: (374), (1143) imply: % 128.94/18.10 | | | | | | | | | | | | (1144) all_6_2 = e1 % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | REDUCE: (417), (1144) imply: % 128.94/18.10 | | | | | | | | | | | | (1145) ~ (all_53_4 = e1) % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | REDUCE: (419), (1144) imply: % 128.94/18.10 | | | | | | | | | | | | (1146) ~ (all_53_6 = e1) % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | REDUCE: (423), (1144) imply: % 128.94/18.10 | | | | | | | | | | | | (1147) ~ (all_53_9 = e1) % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (142), (147), (149), (150), (209), % 128.94/18.10 | | | | | | | | | | | | (216), (279), (309), (324), (332), (339), (663), % 128.94/18.10 | | | | | | | | | | | | (1011), (1023), (1145), (1146), (1147) are % 128.94/18.10 | | | | | | | | | | | | inconsistent by sub-proof #155. % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | End of split % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | (1148) op(e1, e3) = e3 % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | REF_CLOSE: (342), (1010), (1148) are inconsistent by % 128.94/18.10 | | | | | | | | | | | sub-proof #323. % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | End of split % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | End of split % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | End of split % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | (1149) all_14_2 = e2 % 128.94/18.10 | | | | | | | | (1150) op(e3, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = % 128.94/18.10 | | | | | | | | e0) | ( ~ (all_14_0 = e1) & op(e3, e0) = all_14_0 % 128.94/18.10 | | | | | | | | & $i(all_14_0))) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | ALPHA: (1150) implies: % 128.94/18.10 | | | | | | | | (1151) op(e3, e2) = all_14_1 % 128.94/18.10 | | | | | | | | (1152) ~ (all_14_1 = e0) | ( ~ (all_14_0 = e1) & op(e3, e0) % 128.94/18.10 | | | | | | | | = all_14_0 & $i(all_14_0)) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | COMBINE_EQS: (382), (1149) imply: % 128.94/18.10 | | | | | | | | (1153) all_4_2 = e2 % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | SIMP: (1153) implies: % 128.94/18.10 | | | | | | | | (1154) all_4_2 = e2 % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | COMBINE_EQS: (380), (1154) imply: % 128.94/18.10 | | | | | | | | (1155) all_32_2 = e2 % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (403), (1154) imply: % 128.94/18.10 | | | | | | | | (1156) ~ (all_53_1 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (405), (1154) imply: % 128.94/18.10 | | | | | | | | (1157) ~ (all_53_2 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (407), (1154) imply: % 128.94/18.10 | | | | | | | | (1158) ~ (all_53_3 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (409), (1154) imply: % 128.94/18.10 | | | | | | | | (1159) ~ (all_53_4 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (411), (1154) imply: % 128.94/18.10 | | | | | | | | (1160) ~ (all_53_8 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (413), (1154) imply: % 128.94/18.10 | | | | | | | | (1161) ~ (all_53_12 = e2) % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | REDUCE: (45), (1154) imply: % 128.94/18.10 | | | | | | | | (1162) op(e3, e3) = e2 % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | BETA: splitting (88) gives: % 128.94/18.10 | | | | | | | | % 128.94/18.10 | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | (1163) ~ (all_32_2 = e2) % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | REDUCE: (1155), (1163) imply: % 128.94/18.10 | | | | | | | | | (1164) $false % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | CLOSE: (1164) is inconsistent. % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | (1165) op(e3, e2) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 % 128.94/18.10 | | | | | | | | | = e1) | ( ~ (all_32_0 = e0) & op(e3, e1) = % 128.94/18.10 | | | | | | | | | all_32_0 & $i(all_32_0))) % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | ALPHA: (1165) implies: % 128.94/18.10 | | | | | | | | | (1166) op(e3, e2) = all_32_1 % 128.94/18.10 | | | | | | | | | (1167) ~ (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 128.94/18.10 | | | | | | | | | e1) = all_32_0 & $i(all_32_0)) % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | BETA: splitting (335) gives: % 128.94/18.10 | | | | | | | | | % 128.94/18.10 | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | (1168) ~ (op(e3, e2) = e2) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 128.94/18.10 | | | | | | | | | | all_14_1, e2, e3, simplifying with (184), (1151) % 128.94/18.10 | | | | | | | | | | gives: % 128.94/18.10 | | | | | | | | | | (1169) all_53_4 = all_14_1 % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_14_1, % 128.94/18.10 | | | | | | | | | | e2, e3, simplifying with (1151) gives: % 128.94/18.10 | | | | | | | | | | (1170) all_14_1 = e3 | ~ (op(e3, e2) = e3) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 128.94/18.10 | | | | | | | | | | all_32_1, e2, e3, simplifying with (184), (1166) % 128.94/18.10 | | | | | | | | | | gives: % 128.94/18.10 | | | | | | | | | | (1171) all_53_4 = all_32_1 % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | PRED_UNIFY: (1166), (1168) imply: % 128.94/18.10 | | | | | | | | | | (1172) ~ (all_32_1 = e2) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | COMBINE_EQS: (1169), (1171) imply: % 128.94/18.10 | | | | | | | | | | (1173) all_32_1 = all_14_1 % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | SIMP: (1173) implies: % 128.94/18.10 | | | | | | | | | | (1174) all_32_1 = all_14_1 % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | COMBINE_EQS: (309), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1175) all_55_1 = all_14_1 % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (150), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1176) ~ (all_53_6 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | SIMP: (1176) implies: % 128.94/18.10 | | | | | | | | | | (1177) ~ (all_53_6 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (149), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1178) ~ (all_53_7 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | SIMP: (1178) implies: % 128.94/18.10 | | | | | | | | | | (1179) ~ (all_53_7 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (148), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1180) ~ (all_53_8 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | SIMP: (1180) implies: % 128.94/18.10 | | | | | | | | | | (1181) ~ (all_53_8 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (147), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1182) ~ (all_53_12 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | SIMP: (1182) implies: % 128.94/18.10 | | | | | | | | | | (1183) ~ (all_53_12 = all_14_1) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (417), (1169) imply: % 128.94/18.10 | | | | | | | | | | (1184) ~ (all_14_1 = all_6_2) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | REDUCE: (1172), (1174) imply: % 128.94/18.10 | | | | | | | | | | (1185) ~ (all_14_1 = e2) % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | BETA: splitting (67) gives: % 128.94/18.10 | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | (1186) ~ (all_18_2 = e3) % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | REDUCE: (391), (1186) imply: % 128.94/18.10 | | | | | | | | | | | (1187) ~ (all_12_2 = e3) % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | BETA: splitting (73) gives: % 128.94/18.10 | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | (1188) ~ (all_22_2 = e0) % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | REDUCE: (389), (1188) imply: % 128.94/18.10 | | | | | | | | | | | | (1189) ~ (all_12_2 = e0) % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | BETA: splitting (208) gives: % 128.94/18.10 | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | (1190) all_55_10 = e3 % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | REF_CLOSE: (278), (1187), (1190) are inconsistent by % 128.94/18.10 | | | | | | | | | | | | | sub-proof #282. % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | (1191) ~ (all_55_10 = e3) % 128.94/18.10 | | | | | | | | | | | | | (1192) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | BETA: splitting (1192) gives: % 128.94/18.10 | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | (1193) all_55_10 = e2 % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | REF_CLOSE: (278), (666), (1193) are inconsistent by sub-proof % 128.94/18.10 | | | | | | | | | | | | | | #281. % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | (1194) ~ (all_55_10 = e2) % 128.94/18.10 | | | | | | | | | | | | | | (1195) all_55_10 = e1 | all_55_10 = e0 % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | BETA: splitting (1195) gives: % 128.94/18.10 | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | (1196) all_55_10 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1196) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1197) all_12_2 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | SIMP: (1197) implies: % 128.94/18.10 | | | | | | | | | | | | | | | (1198) all_12_2 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | COMBINE_EQS: (389), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1199) all_22_2 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (415), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1200) ~ (all_53_2 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (426), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1201) ~ (all_53_6 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (428), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1202) ~ (all_53_8 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (429), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1203) ~ (all_53_9 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (431), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1204) ~ (all_53_11 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (433), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1205) ~ (all_53_14 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (1187), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1206) ~ (e3 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | REDUCE: (666), (1198) imply: % 128.94/18.10 | | | | | | | | | | | | | | | (1207) ~ (e2 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 128.94/18.10 | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | (1208) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | REF_CLOSE: (330), (332), (1202), (1203), (1208) are % 128.94/18.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #154. % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | Case 2: % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | (1209) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 128.94/18.10 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | BETA: splitting (1209) gives: % 128.94/18.10 | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | (1210) all_57_8 = e1 & op(e1, e1) = e1 % 128.94/18.10 | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | ALPHA: (1210) implies: % 128.94/18.10 | | | | | | | | | | | | | | | | | (1211) all_57_8 = e1 % 128.94/18.10 | | | | | | | | | | | | | | | | | (1212) op(e1, e1) = e1 % 128.94/18.10 | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 128.94/18.10 | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | | (1213) ~ (all_26_2 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | | REDUCE: (374), (1213) imply: % 128.94/18.10 | | | | | | | | | | | | | | | | | | (1214) ~ (all_6_2 = e1) % 128.94/18.10 | | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 128.94/18.10 | | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.10 | | | | | | | | | | | | | | | | | | | % 128.94/18.10 | | | | | | | | | | | | | | | | | | | (1215) ~ (all_28_2 = e2) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | REDUCE: (361), (1215) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | (1216) ~ (all_8_2 = e2) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | (1217) all_55_15 = e3 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1217) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | (1218) all_8_2 = e3 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (665), (1218) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | (1219) $false % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | CLOSE: (1219) is inconsistent. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | (1220) ~ (all_55_15 = e3) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | (1221) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1221) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | (1222) all_55_15 = e2 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1222) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | (1223) all_8_2 = e2 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1216), (1223) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | (1224) $false % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1224) is inconsistent. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | (1225) ~ (all_55_15 = e2) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | (1226) all_55_15 = e1 | all_55_15 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1226) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1227) all_55_15 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1227) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1228) all_8_2 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (440), (1228) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1229) $false % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1229) is inconsistent. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1230) all_55_15 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1230) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1231) all_8_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (1231) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1232) ~ (all_53_3 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (1231) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1233) ~ (all_53_7 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (1231) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1234) ~ (all_53_11 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (435), (1231) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1235) ~ (all_53_12 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1216), (1231) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | (1236) ~ (e2 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | (1237) all_57_15 = e0 & op(e0, e0) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1237) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | (1238) all_57_15 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1239) ~ (all_42_2 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (1239) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1240) ~ (all_6_2 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (212), (279), (282), (295), (304), % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (334), (423), (439), (663), (1201), (1204), % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1214), (1240) are inconsistent by sub-proof #249. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1241) all_42_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (1241) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1242) all_6_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1242) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_6_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_50_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1245) ~ (all_53_9 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1246) ~ (all_53_13 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1247) ~ (e3 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1214), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1248) ~ (e1 = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (1243) imply: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | (1249) op(e2, e2) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1250) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1250) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_57_0 = e0 & op(e3, e3) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1251) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) op(e3, e3) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1252), (function-axioms) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) all_57_1 = e0 & op(e3, e2) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1253) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) all_57_1 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1255) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) all_57_0 = e1 & op(e3, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1256) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) op(e3, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1162), (1257), (function-axioms) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) all_57_1 = e1 & op(e3, e2) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1254), (1258) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1259) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) all_57_4 = e1 & op(e3, e1) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1260) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) op(e3, e1) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (1202), (1261) are inconsistent by % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) all_57_9 = e1 & op(e3, e0) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1262) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) all_57_9 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1264) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) all_57_4 = e0 & op(e3, e1) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1265) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) all_57_4 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (1154), (1254), % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263), (1266) are inconsistent by sub-proof #150. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) all_57_5 = e0 & op(e2, e1) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (1245), (1267), (function-axioms) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #241. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (265), (284), (1199), (1211), (1212), % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234), (1268) are inconsistent by sub-proof #240. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1269) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1269) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) all_57_4 = e0 & op(e3, e1) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1270) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) op(e3, e1) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1272) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_57_0 = e0 & op(e3, e3) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1273) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) op(e3, e3) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1274), (function-axioms) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) all_57_2 = e0 & op(e2, e3) = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1275) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_57_2 = e0 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1277) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) all_57_0 = e1 & op(e3, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1278) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) op(e3, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1162), (1279), (function-axioms) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) all_57_2 = e1 & op(e2, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1276), (1280) are % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_57_6 = e1 & op(e1, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1282) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) op(e1, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (1200), (1283) are inconsistent by % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280. % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) all_57_12 = e1 & op(e0, e3) = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1284) implies: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) all_57_12 = e1 % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1286) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) all_57_2 = e1 & op(e2, e3) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1276), (1287) are % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) all_57_3 = e1 & op(e2, e2) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1288) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) op(e2, e2) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1249), (1289), (function-axioms) are % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1290) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) all_57_5 = e1 & op(e2, e1) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1291) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) op(e2, e1) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (1203), (1292) are inconsistent by % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) all_57_10 = e1 & op(e2, e0) = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1293) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) all_57_10 = e1 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1295) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_57_2 = e3 & op(e2, e3) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1276), (1296) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #192. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_57_3 = e3 & op(e2, e2) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (439), (1297), (function-axioms) are % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1298) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_57_5 = e3 & op(e2, e1) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1299) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_57_5 = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1301) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) all_57_9 = e2 & op(e3, e0) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1302) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) all_57_9 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (1294), (1303), (1304) are % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #261. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1305) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) all_57_11 = e3 & op(e1, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1306) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) all_57_11 = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1308) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) all_57_2 = e2 & op(e2, e3) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1309) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) op(e2, e3) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (1156), (1310) are inconsistent by % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) all_57_3 = e2 & op(e2, e2) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1311) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) op(e2, e2) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (300), (1244), (1312) are inconsistent by % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1313) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) all_57_5 = e2 & op(e2, e1) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1314) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) all_57_5 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1315) imply: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) e3 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1307), (1316) imply: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) all_57_11 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (225), (1238), (1294), (1303), % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) are inconsistent by sub-proof #258. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) all_57_10 = e2 & op(e2, e0) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1318) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) all_57_10 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1294), (1319) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_57_15 = e3 & op(e0, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1238), (1320) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) all_57_10 = e2 & op(e2, e0) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1321) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_57_10 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1294), (1322) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1323) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) all_57_11 = e2 & op(e1, e0) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1324) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) all_57_11 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1326) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) all_57_9 = e3 & op(e3, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1327) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_57_9 = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1329) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) all_57_2 = e2 & op(e2, e3) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1330) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) op(e2, e3) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (1156), (1331) are inconsistent by % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_57_3 = e2 & op(e2, e2) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1332) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) op(e2, e2) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (300), (1244), (1333) are inconsistent by % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) all_57_5 = e2 & op(e2, e1) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1335) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) all_57_5 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1336) imply: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) e3 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1328), (1337) imply: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) all_57_9 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (225), (1238), (1294), (1325), % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) are inconsistent by sub-proof #258. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_57_10 = e2 & op(e2, e0) = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1339) implies: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_57_10 = e2 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1294), (1340) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_57_10 = e3 & op(e2, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1294), (1341) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #284. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1342) gives: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_57_11 = e3 & op(e1, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1325), (1343) are inconsistent by sub-proof % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #260. % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) all_57_15 = e3 & op(e0, e0) = e3 % 128.94/18.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1238), (1344) are inconsistent by sub-proof % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) all_57_15 = e2 & op(e0, e0) = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1345) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) all_57_15 = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1237), (1346) are inconsistent by sub-proof % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #229. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1347) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1348) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) all_57_12 = e0 & op(e0, e3) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1285), (1349) are % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #146. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1350) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) all_57_13 = e0 & op(e0, e2) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1351) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) op(e0, e2) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (256), (263), (427), (440), (665), (1216), % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) are inconsistent by sub-proof #143. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) all_57_14 = e0 & op(e0, e1) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1353) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) op(e0, e1) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1234), (1354) are inconsistent by % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #296. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) all_57_10 = e3 & op(e2, e0) = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1294), (1355) are inconsistent by sub-proof % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #284. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1356) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_57_6 = e0 & op(e1, e3) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1357) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) op(e1, e3) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e0, % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (177), (1358) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) all_53_2 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e0, % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (183), (1271) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_53_8 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1359) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) ~ (all_53_3 = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (1359) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) ~ (all_53_6 = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1362) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) ~ (all_53_6 = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1181), (1360) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) ~ (all_14_1 = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1364) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) ~ (all_14_1 = e0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1167) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) ~ (all_32_1 = e1) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1174), (1366) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) ~ (all_14_1 = e1) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_55_1 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1175), (1368) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_14_1 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1177), (1369) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) ~ (all_53_6 = e3) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1179), (1369) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) ~ (all_53_7 = e3) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_55_9 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1372) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_53_6 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1370), (1373) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) $false % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1374) is inconsistent. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_55_9 = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1376) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_53_6 = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1377) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1378) ~ (all_53_7 = e2) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1379) ~ (all_53_7 = e2) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_55_13 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1380) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1381) all_53_7 = e3 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1371), (1381) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1382) $false % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1382) is inconsistent. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1383) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_55_13 = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1384) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1385) all_53_7 = e2 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1379), (1385) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386) $false % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1386) is inconsistent. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387) all_55_13 = e1 | all_55_13 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1388) all_55_13 = e1 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1388) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_53_7 = e1 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (1389) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) ~ (all_53_3 = e1) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (158), (173), (206), (259), (286), % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327), (328), (342), (343), (663), (1158), (1205), % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232), (1246), (1390) are inconsistent by % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #140. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) all_55_13 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1391) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) all_53_7 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1233), (1392) imply: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) $false % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1393) is inconsistent. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) all_55_9 = e1 | all_55_9 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (1201), (1363), (1394) are inconsistent by % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #178. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1175), (1185), (1365), (1367), (1395) are % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) ~ (all_32_0 = e0) & op(e3, e1) = all_32_0 & % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_0) % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1271), (1396), (function-axioms) are inconsistent % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #138. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) all_57_12 = e0 & op(e0, e3) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1232), (1397) are inconsistent by % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #237. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) all_57_9 = e0 & op(e3, e0) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1398) implies: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) op(e3, e0) = e0 % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (326), (1235), (1399) are inconsistent by % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.13 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1400) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (261), (262), (265), (1232), (1233), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1234), (1400) are inconsistent by sub-proof #236. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1401) all_28_2 = e2 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1401) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1402) all_8_2 = e2 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | REDUCE: (427), (1402) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1403) ~ (all_53_7 = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | REDUCE: (434), (1402) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1404) ~ (all_53_11 = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | REDUCE: (437), (1402) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1405) ~ (all_53_14 = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | REDUCE: (665), (1402) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1406) ~ (e3 = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (9), (13), (14), (15), (16), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (17), (18), (45), (48), (51), (135), (163), (171), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (174), (182), (183), (212), (223), (226), (228), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (229), (232), (233), (237), (239), (240), (241), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (243), (247), (249), (258), (262), (263), (279), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (282), (284), (286), (295), (301), (304), (320), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (323), (324), (337), (338), (339), (340), (342), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (398), (419), (421), (423), (438), (439), (440), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (663), (1154), (1160), (1162), (1168), (1170), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1181), (1199), (1201), (1202), (1205), (1211), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1212), (1214), (1403), (1404), (1405), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 128.94/18.14 | | | | | | | | | | | | | | | | | | | #117. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1407) all_26_2 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1408) op(e2, e1) = all_26_1 & $i(all_26_1) & ( ~ % 128.94/18.14 | | | | | | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, % 128.94/18.14 | | | | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | ALPHA: (1408) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1409) op(e2, e1) = all_26_1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1407) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1410) all_6_2 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | SIMP: (1410) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1411) all_6_2 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (1411) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1412) all_50_2 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | REDUCE: (421), (1411) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1413) ~ (all_53_7 = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | REDUCE: (425), (1411) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1414) ~ (all_53_13 = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | REDUCE: (48), (1411) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | (1415) op(e2, e2) = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | (1416) ~ (op(e2, e1) = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | (1417) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1417) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | (1418) all_57_12 = e1 & op(e0, e3) = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1418) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | (1419) all_57_12 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | (1420) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1420) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1421) all_57_9 = e1 & op(e3, e0) = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1421) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1422) all_57_9 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1423) op(e3, e0) = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | all_26_1, e1, e2, simplifying with (179), (1409) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1424) all_53_9 = all_26_1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1, % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (1409) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1425) all_26_1 = e2 | ~ (op(e2, e1) = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (182), (1423) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1426) all_53_12 = e1 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (1416) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1427) ~ (unit = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (1424) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1428) ~ (all_53_13 = all_26_1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1428) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1429) ~ (all_53_13 = all_26_1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (1426) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1430) ~ (all_14_1 = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1430) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1431) ~ (all_14_1 = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (435), (1426) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | (1432) ~ (all_8_2 = e1) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1152) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | (1433) ~ (all_14_1 = e0) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_55_1 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1175), (1434) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_14_1 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1435) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1436) all_14_1 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1181), (1436) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | (1437) ~ (all_53_8 = e3) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1438) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_57_0 = e0 & op(e3, e3) = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1439) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) op(e3, e3) = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1440), (function-axioms) are % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) all_57_1 = e0 & op(e3, e2) = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1441) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) all_57_1 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (323), (1154), % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422), (1437), (1442) are inconsistent by % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1443) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_57_4 = e0 & op(e3, e1) = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1444) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_57_4 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_55_2 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1446) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_53_8 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1437), (1447) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) $false % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1448) is inconsistent. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) ~ (all_55_2 = e3) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_55_2 = e2 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1451) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) all_53_8 = e2 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1160), (1452) imply: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) $false % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1453) is inconsistent. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_55_2 = e1 | all_55_2 = e0 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1455) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) all_57_12 = e3 & op(e0, e3) = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1419), (1456) are inconsistent by sub-proof % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_57_13 = e3 & op(e0, e2) = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1457) implies: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) all_57_13 = e3 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (300), (1168), (1412), (1459) are % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #113. % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1460) gives: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_57_7 = e2 & op(e1, e2) = e2 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1461) implies: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) all_57_7 = e2 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1463) gives: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) all_57_1 = e0 & op(e3, e2) = e0 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1464) implies: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_57_1 = e0 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (323), (1154), % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422), (1437), (1465) are inconsistent by % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) all_57_3 = e0 & op(e2, e2) = e0 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1466) implies: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) op(e2, e2) = e0 % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1415), (1467), (function-axioms) are % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1468) gives: % 128.94/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_57_7 = e0 & op(e1, e2) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1462), (1469) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #131. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_57_13 = e0 & op(e0, e2) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1458), (1470) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #112. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_57_13 = e2 & op(e0, e2) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1458), (1471) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #111. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_57_14 = e3 & op(e0, e1) = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_57_14 = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_57_4 = e2 & op(e3, e1) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1445), (1476) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_57_5 = e2 & op(e2, e1) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1477) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) op(e2, e1) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1425) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) ~ (op(e2, e1) = e2) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1478), (1479) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) $false % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1480) is inconsistent. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_26_1 = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1429), (1481) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) ~ (all_53_13 = e2) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1454) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) all_55_2 = e1 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1483) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_53_8 = e1 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1202), (1484) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) $false % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1485) is inconsistent. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) all_55_2 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1486) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) all_53_8 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1487) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) ~ (all_53_11 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1488) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) ~ (all_53_11 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (264), (265), (306), (663), (1427), % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482), (1489) are inconsistent by sub-proof #110. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1490) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_57_8 = e2 & op(e1, e1) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1211), (1491) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) all_57_14 = e2 & op(e0, e1) = e2 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1474), (1492) are inconsistent by sub-proof % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #300. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_57_15 = e3 & op(e0, e0) = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1493) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_57_15 = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1495) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) all_57_0 = e3 & op(e3, e3) = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1496) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) op(e3, e3) = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (1154), (1497) are inconsistent by % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_57_1 = e3 & op(e3, e2) = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1498) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_57_1 = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1454) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_55_2 = e1 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1500) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_53_8 = e1 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1202), (1501) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) $false % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1502) is inconsistent. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_55_2 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (1503) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) all_53_8 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1504) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) ~ (all_53_11 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1505) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) ~ (all_53_11 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1437), (1504) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) ~ (e3 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1202), (1504) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) ~ (e1 = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) all_57_15 = e0 & op(e0, e0) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1509) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_57_15 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1494), (1510) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) e3 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1499), (1511) imply: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) all_57_1 = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (323), (1154), % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422), (1437), (1512) are inconsistent by % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1513) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1514) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_57_12 = e0 & op(e0, e3) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1419), (1515) are % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #146. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1516) gives: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) all_57_13 = e0 & op(e0, e2) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (139), (203), (256), (263), (264), % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (306), (427), (436), (440), (663), (665), % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427), (1517) are inconsistent by sub-proof #108. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) all_57_14 = e0 & op(e0, e1) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1518) implies: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) op(e0, e1) = e0 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1506), (1519) are inconsistent by % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #296. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (323), (1422), (1437), (1520) are % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #116. % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_57_9 = e0 & op(e3, e0) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1199), (1212), (1422), (1521) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1175), (1185), (1431), (1433), (1522) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | (1523) ~ (all_14_0 = e1) & op(e3, e0) = all_14_0 & % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1523) implies: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | (1524) ~ (all_14_0 = e1) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | (1525) op(e3, e0) = all_14_0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1423), (1524), (1525), (function-axioms) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | (1526) all_57_10 = e1 & op(e2, e0) = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (1414), (1526), (function-axioms) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | (1527) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (1205), (1527), % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | #283. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1528) all_57_13 = e1 & op(e0, e2) = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (1413), (1528), (function-axioms) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | (1529) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (440), (1204), (1529), % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | #293. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1530) op(e2, e1) = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (1203), (1530) are inconsistent by % 129.30/18.16 | | | | | | | | | | | | | | | | | | | sub-proof #334. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | (1531) all_57_14 = e1 & op(e0, e1) = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | ALPHA: (1531) implies: % 129.30/18.16 | | | | | | | | | | | | | | | | | (1532) op(e0, e1) = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1204), (1532) are inconsistent by % 129.30/18.16 | | | | | | | | | | | | | | | | | sub-proof #333. % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | (1533) all_55_10 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | REF_CLOSE: (278), (1189), (1533) are inconsistent by % 129.30/18.16 | | | | | | | | | | | | | | | sub-proof #219. % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | End of split % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | (1534) all_22_2 = e0 % 129.30/18.16 | | | | | | | | | | | | (1535) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 129.30/18.16 | | | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 129.30/18.16 | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | ALPHA: (1535) implies: % 129.30/18.16 | | | | | | | | | | | | (1536) op(e1, e0) = all_22_1 % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | COMBINE_EQS: (389), (1534) imply: % 129.30/18.16 | | | | | | | | | | | | (1537) all_12_2 = e0 % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | SIMP: (1537) implies: % 129.30/18.16 | | | | | | | | | | | | (1538) all_12_2 = e0 % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | COMBINE_EQS: (359), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1539) all_38_2 = e0 % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (415), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1540) ~ (all_53_2 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (428), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1541) ~ (all_53_8 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (429), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1542) ~ (all_53_9 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (431), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1543) ~ (all_53_11 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (433), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1544) ~ (all_53_14 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (666), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1545) ~ (e2 = e0) % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | REDUCE: (57), (1538) imply: % 129.30/18.16 | | | | | | | | | | | | (1546) op(e1, e1) = e0 % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | BETA: splitting (97) gives: % 129.30/18.16 | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | (1547) ~ (all_38_2 = e0) % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | REDUCE: (1539), (1547) imply: % 129.30/18.16 | | | | | | | | | | | | | (1548) $false % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | CLOSE: (1548) is inconsistent. % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | (1549) op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 129.30/18.16 | | | | | | | | | | | | | (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, % 129.30/18.16 | | | | | | | | | | | | | e2) = all_38_0 & $i(all_38_0))) % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | ALPHA: (1549) implies: % 129.30/18.16 | | | | | | | | | | | | | (1550) op(e1, e0) = all_38_1 % 129.30/18.16 | | | | | | | | | | | | | (1551) ~ (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, % 129.30/18.16 | | | | | | | | | | | | | e2) = all_38_0 & $i(all_38_0)) % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | BETA: splitting (329) gives: % 129.30/18.16 | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | (1552) ~ (op(e1, e0) = e0) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 129.30/18.16 | | | | | | | | | | | | | | all_22_1, e0, e1, simplifying with (174), (1536) % 129.30/18.16 | | | | | | | | | | | | | | gives: % 129.30/18.16 | | | | | | | | | | | | | | (1553) all_53_14 = all_22_1 % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 129.30/18.16 | | | | | | | | | | | | | | all_38_1, e0, e1, simplifying with (174), (1550) % 129.30/18.16 | | | | | | | | | | | | | | gives: % 129.30/18.16 | | | | | | | | | | | | | | (1554) all_53_14 = all_38_1 % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_1, % 129.30/18.16 | | | | | | | | | | | | | | e0, e1, simplifying with (1550) gives: % 129.30/18.16 | | | | | | | | | | | | | | (1555) all_38_1 = e1 | ~ (op(e1, e0) = e1) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | PRED_UNIFY: (6), (1552) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1556) ~ (unit = e1) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | COMBINE_EQS: (1553), (1554) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1557) all_38_1 = all_22_1 % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | SIMP: (1557) implies: % 129.30/18.16 | | | | | | | | | | | | | | (1558) all_38_1 = all_22_1 % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | REDUCE: (155), (1553) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1559) ~ (all_53_2 = all_22_1) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | REDUCE: (126), (1553) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1560) ~ (all_53_12 = all_22_1) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | REDUCE: (124), (1553) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1561) ~ (all_53_13 = all_22_1) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | REDUCE: (437), (1553) imply: % 129.30/18.16 | | | | | | | | | | | | | | (1562) ~ (all_22_1 = all_8_2) % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 129.30/18.16 | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | (1563) ~ (all_26_2 = e1) % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | REDUCE: (374), (1563) imply: % 129.30/18.16 | | | | | | | | | | | | | | | (1564) ~ (all_6_2 = e1) % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 129.30/18.16 | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | (1565) ~ (all_28_2 = e2) % 129.30/18.16 | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | REDUCE: (361), (1565) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | (1566) ~ (all_8_2 = e2) % 129.30/18.16 | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | (1567) all_55_15 = e3 % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1567) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | (1568) all_8_2 = e3 % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | REDUCE: (665), (1568) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | (1569) $false % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | CLOSE: (1569) is inconsistent. % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | (1570) ~ (all_55_15 = e3) % 129.30/18.16 | | | | | | | | | | | | | | | | | (1571) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | BETA: splitting (1571) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | (1572) all_55_15 = e2 % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1572) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | (1573) all_8_2 = e2 % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | REDUCE: (1566), (1573) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | (1574) $false % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | CLOSE: (1574) is inconsistent. % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | (1575) ~ (all_55_15 = e2) % 129.30/18.16 | | | | | | | | | | | | | | | | | | (1576) all_55_15 = e1 | all_55_15 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | BETA: splitting (1576) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1577) all_55_15 = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1577) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1578) all_8_2 = e1 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REDUCE: (440), (1578) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1579) $false % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | CLOSE: (1579) is inconsistent. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1580) all_55_15 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1580) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1581) all_8_2 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REDUCE: (416), (1581) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1582) ~ (all_53_3 = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REDUCE: (435), (1581) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1583) ~ (all_53_12 = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REDUCE: (665), (1581) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1584) ~ (e3 = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | REDUCE: (440), (1581) imply: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | (1585) ~ (e1 = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | (1586) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1586) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1587) all_57_0 = e0 & op(e3, e3) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1587) implies: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1588) op(e3, e3) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1588), (function-axioms) are % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1589) all_57_1 = e0 & op(e3, e2) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1589) implies: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1590) all_57_1 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | (1591) op(e3, e2) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | (1592) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1592) gives: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | (1593) all_57_0 = e0 & op(e3, e3) = e0 % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1593) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1594) op(e3, e3) = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1594), (function-axioms) are % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1595) all_57_2 = e0 & op(e2, e3) = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1595) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1596) op(e2, e3) = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0, % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (181), (1596) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1597) all_53_1 = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1, e0, % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1151), (1591) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1598) all_14_1 = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (1597) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1599) ~ (all_53_2 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1597) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1600) ~ (all_53_9 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1179), (1598) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1601) ~ (all_53_7 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1184), (1598) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1602) ~ (all_6_2 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1602) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | (1603) ~ (all_6_2 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1152) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | (1604) ~ (all_14_1 = e0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1598), (1604) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | (1605) $false % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1605) is inconsistent. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | (1606) ~ (all_14_0 = e1) & op(e3, e0) = all_14_0 & % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_0) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1606) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | (1607) ~ (all_14_0 = e1) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | (1608) op(e3, e0) = all_14_0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_55_5 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1609) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_6_2 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1610) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1611) $false % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1611) is inconsistent. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1612) ~ (all_55_5 = e3) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1613) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1613) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) all_55_5 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1614) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) all_6_2 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (1615) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_50_2 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (1615) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) ~ (all_53_6 = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (1615) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) ~ (all_53_9 = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (1615) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) ~ (all_53_13 = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1615) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) ~ (e3 = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1621) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_57_4 = e2 & op(e3, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (1160), (1622), (function-axioms) are % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) all_57_5 = e2 & op(e2, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1623) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) op(e2, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (1618), (1624) are inconsistent by % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #347. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1625) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_57_8 = e2 & op(e1, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1626) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) op(e1, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1546), (1627), (function-axioms) are % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_57_14 = e2 & op(e0, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1628) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_57_14 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) op(e0, e1) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1631) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_57_6 = e2 & op(e1, e3) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1632) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_57_6 = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (155), (157), (163), (210), (227), (279), % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280), (282), (285), (286), (320), (340), (415), % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1157), (1540), (1633), (1634) are % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #104. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1635) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) all_57_6 = e3 & op(e1, e3) = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1636) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_57_6 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1633), (1637) are inconsistent by sub-proof % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #135. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_57_12 = e3 & op(e0, e3) = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1638) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) op(e0, e3) = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) ~ (op(e0, e3) = e3) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1639), (1640) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) $false % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1641) is inconsistent. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_55_12 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1642) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_53_3 = e3 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1643) imply: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) ~ (all_53_2 = e3) % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (212), (258), (262), (263), (295), % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339), (342), (421), (439), (663), (1564), (1601), % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603), (1644) are inconsistent by sub-proof #182. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) all_57_7 = e2 & op(e1, e2) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1645) implies: % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) op(e1, e2) = e2 % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (1617), (1646) are inconsistent by % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 129.30/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1647) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_57_8 = e2 & op(e1, e1) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1648) implies: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) op(e1, e1) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1546), (1649), (function-axioms) are % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) all_57_11 = e2 & op(e1, e0) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1651) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_57_2 = e2 & op(e2, e3) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1652) implies: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) op(e2, e3) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (1156), (1653) are inconsistent by % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_57_3 = e2 & op(e2, e2) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1654) implies: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) op(e2, e2) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1650) implies: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) op(e1, e0) = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11, % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (171), (1630) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) all_53_11 = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1, e2, % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (1536), (1656) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) all_22_1 = e2 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_14_0, e0, e3, simplifying with (182), (1608) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) all_53_12 = all_14_0 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (1659) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) all_55_3 = all_14_0 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1161), (1659) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1661) ~ (all_14_0 = e2) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1583), (1659) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1662) ~ (all_14_0 = e0) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663) all_55_3 = e3 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1660), (1663) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1664) all_14_0 = e3 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1659), (1664) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1665) all_53_12 = e3 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1608), (1664) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1666) op(e3, e0) = e3 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1667) ~ (op(e2, e3) = e3) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (1667) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1668) ~ (unit = e2) % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (264), (265), (306), (663), (1543), % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619), (1668) are inconsistent by sub-proof #110. % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1669) all_53_1 = e3 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1597), (1669) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670) e3 = e0 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1670) implies: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1671) e3 = e0 % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1665), (1671) imply: % 129.40/18.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1672) all_53_12 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (1666), (1672) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (320), (1154), (1590), (1674) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #152. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1675) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1675) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1676) all_57_4 = e3 & op(e3, e1) = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1676) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1677) all_57_4 = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1678) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1678) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1679) all_57_4 = e1 & op(e3, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1677), (1679) are inconsistent by sub-proof % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #103. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1680) all_57_5 = e1 & op(e2, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1680) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1681) op(e2, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1682) ~ (op(e2, e1) = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1681), (1682) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683) $false % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1683) is inconsistent. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1684) all_53_9 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (1684) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1685) ~ (all_53_8 = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (1684) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1686) ~ (e2 = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1687) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1687) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1688) all_57_0 = e1 & op(e3, e3) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1688) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1689) op(e3, e3) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1162), (1689), (function-axioms) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1690) all_57_1 = e1 & op(e3, e2) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1590), (1690) are inconsistent by sub-proof % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1691) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1691) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1692) all_57_4 = e1 & op(e3, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1692) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693) op(e3, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (1685), (1693) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1694) all_57_9 = e1 & op(e3, e0) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1694) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1695) op(e3, e0) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1607), (1608), (1695), (function-axioms) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1696) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1696) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1697) all_57_8 = e1 & op(e1, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1697) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1698) op(e1, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1534), (1698) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1699) all_57_14 = e1 & op(e0, e1) = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1699) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1700) all_57_14 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1629), (1700) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1701) e2 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1616), (1701) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1702) all_50_2 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (300), (1655), (1702) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1703) all_57_9 = e3 & op(e3, e0) = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1704) op(e3, e0) = e3 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1673) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1705) all_55_3 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1660), (1705) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706) all_14_0 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1706) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1707) all_14_0 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1661), (1707) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1708) $false % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1708) is inconsistent. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1709) all_55_3 = e1 | all_55_3 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1709) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1710) all_55_3 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1660), (1710) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1711) all_14_0 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1711) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1712) all_14_0 = e1 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1607), (1712) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) $false % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1713) is inconsistent. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) all_55_3 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1660), (1714) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) all_14_0 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1715) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) all_14_0 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1659), (1716) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) all_53_12 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (1704), (1717) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (306), (1618), (1619), (1718) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) all_55_5 = e1 | all_55_5 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (295), (1564), (1603), (1719) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | (1720) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1720) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | (1721) all_57_6 = e0 & op(e1, e3) = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (1540), (1721), (function-axioms) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #101. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | (1722) all_57_12 = e0 & op(e0, e3) = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1582), (1722) are inconsistent by % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #237. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | (1723) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (326), (1541), (1583), (1723), % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | #209. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | End of split % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | (1724) all_28_2 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1724) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | (1725) all_8_2 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | SIMP: (1725) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | (1726) all_8_2 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (1726) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | (1727) all_10_2 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | REDUCE: (427), (1726) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | (1728) ~ (all_53_7 = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | REDUCE: (434), (1726) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | (1729) ~ (all_53_11 = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | REDUCE: (665), (1726) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | (1730) ~ (e3 = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | (1731) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | BETA: splitting (1731) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | (1732) all_57_6 = e2 & op(e1, e3) = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | (1733) all_57_6 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | (1734) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (1734) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | (1735) all_57_4 = e2 & op(e3, e1) = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (1160), (1735), (function-axioms) are % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | (1736) all_57_5 = e2 & op(e2, e1) = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | (1737) op(e2, e1) = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | (1738) ~ (op(e2, e1) = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1737), (1738) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | (1739) $false % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1739) is inconsistent. % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | (1740) all_55_6 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1740) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | (1741) all_53_9 = e2 % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (1741) imply: % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | (1742) ~ (all_6_2 = e2) % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.18 | | | | | | | | | | | | | | | | | | | | | SIMP: (1742) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | (1743) ~ (all_6_2 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1744) all_55_5 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1744) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1745) all_6_2 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1745) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1746) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1746) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1747) ~ (all_55_5 = e3) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1748) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1748) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1749) all_55_5 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1749) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1750) all_6_2 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1743), (1750) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1751) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1751) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1752) ~ (all_55_5 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1753) all_55_5 = e1 | all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1753) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1754) all_55_5 = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1754) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1755) all_6_2 = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1755) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1756) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1756) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1757) all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1757) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1758) all_6_2 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (1758) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1759) ~ (all_53_7 = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1758) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1760) ~ (e3 = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1761) ~ (op(e0, e2) = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) all_57_15 = e0 & op(e0, e0) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1762) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) op(e0, e0) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (270), (1727), (1763) are inconsistent by % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #235. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1764) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1765) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) all_57_12 = e0 & op(e0, e3) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1766) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) all_57_12 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (155), (157), (163), (210), (227), (279), % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280), (282), (285), (286), (320), (340), (415), % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1157), (1540), (1733), (1768) are % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #104. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1769) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) all_57_6 = e3 & op(e1, e3) = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1770) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) all_57_6 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1733), (1771) are inconsistent by sub-proof % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #135. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) all_57_12 = e3 & op(e0, e3) = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1772) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) all_57_12 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1767), (1773) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) e3 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1774) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) e3 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (1775) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1776) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1777) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) all_57_13 = e0 & op(e0, e2) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1778) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) op(e0, e2) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1761), (1779) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1780) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) all_57_14 = e0 & op(e0, e1) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1781) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) op(e0, e1) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1543), (1782) are inconsistent by % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #296. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1783) op(e0, e2) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (1759), (1783) are inconsistent by % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1784) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.40/18.19 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (171), (1546), (1729), (1784), % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.40/18.19 | | | | | | | | | | | | | | | | | | | #100. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | End of split % 129.40/18.19 | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | (1785) all_57_7 = e2 & op(e1, e2) = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | ALPHA: (1785) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | (1786) all_57_7 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | (1787) op(e1, e2) = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1788) ~ (op(e1, e2) = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1787), (1788) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1789) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | CLOSE: (1789) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1790) all_55_9 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1790) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1791) all_53_6 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | SIMP: (1791) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1792) all_53_6 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1792) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1793) ~ (all_53_7 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | REDUCE: (419), (1792) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1794) ~ (all_6_2 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | SIMP: (1794) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | (1795) ~ (all_6_2 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | (1796) all_55_5 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1796) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | (1797) all_6_2 = e3 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1797) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | (1798) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | CLOSE: (1798) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | (1799) ~ (all_55_5 = e3) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | (1800) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | (1801) ~ (op(e0, e2) = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1800) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1802) all_55_5 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1802) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1803) all_6_2 = e2 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1795), (1803) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1804) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1804) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1805) ~ (all_55_5 = e2) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | (1806) all_55_5 = e1 | all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1806) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1807) all_55_5 = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1807) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1808) all_6_2 = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1808) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1809) $false % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1809) is inconsistent. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1810) all_55_5 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1810) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1811) all_6_2 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (1811) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1812) ~ (all_53_7 = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1811) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1813) ~ (e3 = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1811) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1814) ~ (e1 = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (1811) imply: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | (1815) op(e2, e2) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | (1816) ~ (op(e0, e2) = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1817) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1817) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) all_57_0 = e0 & op(e3, e3) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) op(e3, e3) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (1819), (function-axioms) are % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) all_57_1 = e0 & op(e3, e2) = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1820) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) all_57_1 = e0 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1822) gives: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_57_1 = e1 & op(e3, e2) = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1821), (1823) are inconsistent by sub-proof % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201. % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_57_3 = e1 & op(e2, e2) = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1824) implies: % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) op(e2, e2) = e1 % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1815), (1825), (function-axioms) are % 129.40/18.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1826) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_57_7 = e1 & op(e1, e2) = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1827) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) all_57_7 = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1786), (1828) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) e2 = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (1829) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1830) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) all_57_13 = e1 & op(e0, e2) = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1831) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) all_57_13 = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1833) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_57_1 = e3 & op(e3, e2) = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1821), (1834) are inconsistent by sub-proof % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) all_57_3 = e3 & op(e2, e2) = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (439), (1835), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1836) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) all_57_7 = e3 & op(e1, e2) = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (1786), (1837) are inconsistent by sub-proof % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #134. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) all_57_13 = e3 & op(e0, e2) = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1832), (1838) are inconsistent by sub-proof % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | (1839) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1839) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) all_57_4 = e0 & op(e3, e1) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (1541), (1840), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) all_57_9 = e0 & op(e3, e0) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1841) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) op(e3, e0) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) ~ (op(e3, e0) = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1842), (1843) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1844) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2), (1816) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) ~ (unit = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (8), (1801) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) ~ (unit = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (265), (663), (1543), (1845), (1846) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #243. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1847) op(e0, e2) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (1812), (1847) are inconsistent by % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | (1848) op(e0, e2) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (338), (1728), (1848) are inconsistent by % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #118. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | (1849) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 129.40/18.20 | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | BETA: splitting (1849) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | (1850) all_57_8 = e2 & op(e1, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | ALPHA: (1850) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | (1851) op(e1, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1546), (1851), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | (1852) all_57_11 = e2 & op(e1, e0) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | ALPHA: (1852) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | (1853) all_57_11 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | (1854) op(e1, e0) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | (1855) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (1855) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | (1856) all_57_4 = e2 & op(e3, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (1160), (1856), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | (1857) all_57_5 = e2 & op(e2, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (1857) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | (1858) op(e2, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | (1859) ~ (op(e0, e2) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1860) ~ (op(e2, e1) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1858), (1860) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1861) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1861) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1862) all_55_6 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1862) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1863) all_53_9 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1863) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1864) ~ (all_53_11 = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (1863) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1865) ~ (all_6_2 = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1865) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | (1866) ~ (all_6_2 = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | (1867) all_55_5 = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1867) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | (1868) all_6_2 = e3 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1868) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | (1869) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1869) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | (1870) ~ (all_55_5 = e3) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | (1871) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1871) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1872) all_55_5 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1872) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1873) all_6_2 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1866), (1873) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1874) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1874) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1875) ~ (all_55_5 = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | (1876) all_55_5 = e1 | all_55_5 = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | (1877) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1877) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1878) all_57_12 = e2 & op(e0, e3) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1878) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1879) op(e0, e3) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1158), (1879), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #99. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_57_13 = e2 & op(e0, e2) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1859), (1880) are inconsistent by sub-proof #129. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | (1881) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1881) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1882) all_57_14 = e2 & op(e0, e1) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (1729), (1882), (function-axioms) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #119. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1883) all_57_15 = e2 & op(e0, e0) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1883) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) all_57_15 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1885) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (301), (398), (1168), (1866), (1885) are % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1886) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1886) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_57_7 = e2 & op(e1, e2) = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1887) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_57_7 = e2 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) all_55_5 = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1889) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) all_6_2 = e1 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1890) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) $false % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1891) is inconsistent. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_55_5 = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1892) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_6_2 = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (1893) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) ~ (all_53_13 = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (1893) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) ~ (e3 = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1564), (1893) imply: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) ~ (e1 = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) all_57_15 = e0 & op(e0, e0) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1897) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) op(e0, e0) = e0 % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (270), (1727), (1898) are inconsistent by % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #235. % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1899) implies: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) ~ (op(e2, e0) = e0) % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1902) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) all_57_6 = e3 & op(e1, e3) = e3 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1903) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) all_57_6 = e3 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1900) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) all_57_9 = e0 & op(e3, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1905) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) op(e3, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) ~ (op(e3, e0) = e0) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1906), (1907) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) $false % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1908) is inconsistent. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) all_55_3 = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (1909) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) all_53_12 = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1910) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_53_12 = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (1911) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) ~ (all_53_13 = e0) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1913) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_57_9 = e1 & op(e3, e0) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (328), (329), (1544), (1894), (1900), (1914) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #354. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_57_10 = e1 & op(e2, e0) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1915) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) all_57_10 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1917) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_57_6 = e1 & op(e1, e3) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1918) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) all_57_6 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1904), (1919) are inconsistent by sub-proof % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #322. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) all_57_7 = e1 & op(e1, e2) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1920) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) all_57_7 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1888), (1921) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) e2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1922) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) e2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1884), (1923) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) all_57_15 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (225), (324), (1853), (1911), % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916), (1924) are inconsistent by sub-proof #98. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1925) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_57_8 = e1 & op(e1, e1) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1926) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) op(e1, e1) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (1534), (1927) are inconsistent by % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_57_11 = e1 & op(e1, e0) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1928) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) all_57_11 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1853), (1929) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) e2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1930) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) e2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1884), (1931) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_57_15 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (225), (324), (1853), (1911), % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916), (1932) are inconsistent by sub-proof #98. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1933) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) all_57_11 = e1 & op(e1, e0) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1934) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) all_57_11 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (1853), (1935) are inconsistent by sub-proof % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #172. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) all_57_15 = e1 & op(e0, e0) = e1 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (440), (1936), (function-axioms) are % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1937) gives: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) all_57_10 = e0 & op(e2, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1938) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) op(e2, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1901), (1939) imply: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) $false % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1940) is inconsistent. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_57_11 = e0 & op(e1, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1552), (1941) are inconsistent by sub-proof #97. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) all_57_7 = e3 & op(e1, e2) = e3 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1942) implies: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) op(e1, e2) = e3 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1550), (1551), (1854), (1943), (function-axioms) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #309. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (1546), (1853), (1944), % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) op(e2, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (328), (1894), (1945) are inconsistent by % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #356. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) all_57_13 = e2 & op(e0, e2) = e2 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1859), (1946) are inconsistent by sub-proof #129. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | (1947) op(e0, e2) = e2 % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (338), (1728), (1947) are inconsistent by % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | sub-proof #118. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | (1948) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.40/18.21 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.40/18.21 | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (171), (1546), (1729), (1948), % 129.40/18.21 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.40/18.21 | | | | | | | | | | | | | | | | | | | #100. % 129.40/18.21 | | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | (1949) all_26_2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | (1950) op(e2, e1) = all_26_1 & $i(all_26_1) & ( ~ % 129.40/18.21 | | | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, % 129.40/18.21 | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | ALPHA: (1950) implies: % 129.40/18.21 | | | | | | | | | | | | | | | (1951) op(e2, e1) = all_26_1 % 129.40/18.21 | | | | | | | | | | | | | | | (1952) ~ (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, % 129.40/18.21 | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0)) % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (1949) imply: % 129.40/18.21 | | | | | | | | | | | | | | | (1953) all_6_2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | SIMP: (1953) implies: % 129.40/18.21 | | | | | | | | | | | | | | | (1954) all_6_2 = e1 % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (48), (100), % 129.40/18.21 | | | | | | | | | | | | | | | (127), (131), (134), (135), (142), (147), (153), % 129.40/18.21 | | | | | | | | | | | | | | | (154), (158), (159), (162), (172), (179), (211), % 129.40/18.21 | | | | | | | | | | | | | | | (215), (227), (228), (229), (231), (232), (233), % 129.40/18.21 | | | | | | | | | | | | | | | (234), (236), (237), (238), (242), (245), (248), % 129.40/18.21 | | | | | | | | | | | | | | | (249), (258), (261), (262), (268), (279), (281), % 129.40/18.21 | | | | | | | | | | | | | | | (282), (284), (288), (296), (297), (300), (306), % 129.40/18.21 | | | | | | | | | | | | | | | (308), (309), (319), (321), (323), (324), (330), % 129.40/18.21 | | | | | | | | | | | | | | | (332), (334), (337), (339), (340), (342), (344), % 129.40/18.21 | | | | | | | | | | | | | | | (370), (382), (397), (399), (407), (416), (419), % 129.40/18.21 | | | | | | | | | | | | | | | (421), (423), (425), (427), (434), (436), (439), % 129.40/18.21 | | | | | | | | | | | | | | | (440), (663), (1534), (1541), (1542), (1546), % 129.40/18.21 | | | | | | | | | | | | | | | (1555), (1556), (1558), (1559), (1560), (1562), % 129.40/18.21 | | | | | | | | | | | | | | | (1951), (1952), (1954), (function-axioms) are % 129.40/18.21 | | | | | | | | | | | | | | | inconsistent by sub-proof #187. % 129.40/18.21 | | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | (1955) op(e1, e0) = e0 % 129.40/18.21 | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | | REF_CLOSE: (329), (1544), (1955) are inconsistent by % 129.40/18.21 | | | | | | | | | | | | | | sub-proof #355. % 129.40/18.21 | | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | End of split % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | Case 2: % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | (1956) all_18_2 = e3 % 129.40/18.21 | | | | | | | | | | | (1957) op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ % 129.40/18.21 | | | | | | | | | | | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, % 129.40/18.21 | | | | | | | | | | | e2) = all_18_0 & $i(all_18_0))) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | ALPHA: (1957) implies: % 129.40/18.21 | | | | | | | | | | | (1958) op(e1, e3) = all_18_1 % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | COMBINE_EQS: (391), (1956) imply: % 129.40/18.21 | | | | | | | | | | | (1959) all_12_2 = e3 % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | COMBINE_EQS: (384), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1960) all_24_2 = e3 % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (415), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1961) ~ (all_53_2 = e3) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (426), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1962) ~ (all_53_6 = e3) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (428), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1963) ~ (all_53_8 = e3) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (429), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1964) ~ (all_53_9 = e3) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (433), (1959) imply: % 129.40/18.21 | | | | | | | | | | | (1965) ~ (all_53_14 = e3) % 129.40/18.21 | | | | | | | | | | | % 129.40/18.21 | | | | | | | | | | | REDUCE: (57), (1959) imply: % 129.40/18.22 | | | | | | | | | | | (1966) op(e1, e1) = e3 % 129.40/18.22 | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | BETA: splitting (76) gives: % 129.40/18.22 | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | (1967) ~ (all_24_2 = e3) % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | REDUCE: (1960), (1967) imply: % 129.40/18.22 | | | | | | | | | | | | (1968) $false % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | CLOSE: (1968) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | (1969) op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 129.40/18.22 | | | | | | | | | | | | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, % 129.40/18.22 | | | | | | | | | | | | e0) = all_24_0 & $i(all_24_0))) % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | ALPHA: (1969) implies: % 129.40/18.22 | | | | | | | | | | | | (1970) op(e1, e3) = all_24_1 % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | BETA: splitting (342) gives: % 129.40/18.22 | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | (1971) ~ (op(e1, e3) = e3) % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 129.40/18.22 | | | | | | | | | | | | | all_18_1, e3, e1, simplifying with (177), (1958) % 129.40/18.22 | | | | | | | | | | | | | gives: % 129.40/18.22 | | | | | | | | | | | | | (1972) all_53_2 = all_18_1 % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 129.40/18.22 | | | | | | | | | | | | | all_24_1, e3, e1, simplifying with (177), (1970) % 129.40/18.22 | | | | | | | | | | | | | gives: % 129.40/18.22 | | | | | | | | | | | | | (1973) all_53_2 = all_24_1 % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | PRED_UNIFY: (9), (1971) imply: % 129.40/18.22 | | | | | | | | | | | | | (1974) ~ (unit = e1) % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | COMBINE_EQS: (1972), (1973) imply: % 129.40/18.22 | | | | | | | | | | | | | (1975) all_24_1 = all_18_1 % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | SIMP: (1975) implies: % 129.40/18.22 | | | | | | | | | | | | | (1976) all_24_1 = all_18_1 % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | REDUCE: (157), (1972) imply: % 129.40/18.22 | | | | | | | | | | | | | (1977) ~ (all_53_6 = all_18_1) % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | SIMP: (1977) implies: % 129.40/18.22 | | | | | | | | | | | | | (1978) ~ (all_53_6 = all_18_1) % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | BETA: splitting (79) gives: % 129.40/18.22 | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | (1979) ~ (all_26_2 = e1) % 129.40/18.22 | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | REDUCE: (374), (1979) imply: % 129.40/18.22 | | | | | | | | | | | | | | (1980) ~ (all_6_2 = e1) % 129.40/18.22 | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | BETA: splitting (82) gives: % 129.40/18.22 | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | (1981) ~ (all_28_2 = e2) % 129.40/18.22 | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | REDUCE: (361), (1981) imply: % 129.40/18.22 | | | | | | | | | | | | | | | (1982) ~ (all_8_2 = e2) % 129.40/18.22 | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 129.40/18.22 | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | (1983) all_55_15 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1983) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | (1984) all_8_2 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | REDUCE: (665), (1984) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | (1985) $false % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | CLOSE: (1985) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | (1986) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | BETA: splitting (1986) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | (1987) all_55_15 = e2 % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1987) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | (1988) all_8_2 = e2 % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | REDUCE: (1982), (1988) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | (1989) $false % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | CLOSE: (1989) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | (1990) ~ (all_55_15 = e2) % 129.40/18.22 | | | | | | | | | | | | | | | | | (1991) all_55_15 = e1 | all_55_15 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | BETA: splitting (1991) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1992) all_55_15 = e1 % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1992) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1993) all_8_2 = e1 % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | REDUCE: (440), (1993) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1994) $false % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | CLOSE: (1994) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1995) all_55_15 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1995) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1996) all_8_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | REDUCE: (416), (1996) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1997) ~ (all_53_3 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | REDUCE: (427), (1996) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1998) ~ (all_53_7 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | REDUCE: (437), (1996) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (1999) ~ (all_53_14 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | REDUCE: (1982), (1996) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | (2000) ~ (e2 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2001) ~ (all_42_2 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (398), (2001) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2002) ~ (all_6_2 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (212), (258), (262), (263), (295), % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (339), (342), (421), (439), (663), (1961), (1980), % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (1998), (2002) are inconsistent by sub-proof #182. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2003) all_42_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2003) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2004) all_6_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | SIMP: (2004) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2005) all_6_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (414), (2005) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2006) ~ (all_53_1 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (425), (2005) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2007) ~ (all_53_13 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (439), (2005) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2008) ~ (e3 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (1980), (2005) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2009) ~ (e1 = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | REDUCE: (48), (2005) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | (2010) op(e2, e2) = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | (2011) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2011) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | (2012) all_57_0 = e0 & op(e3, e3) = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2012) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | (2013) op(e3, e3) = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1162), (2013), (function-axioms) are % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | (2014) all_57_2 = e0 & op(e2, e3) = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2014) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | (2015) all_57_2 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | (2016) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2016) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2017) all_57_0 = e3 & op(e3, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2017) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2018) op(e3, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (1154), (2018) are inconsistent by % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2019) all_57_2 = e3 & op(e2, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (2015), (2019) are inconsistent by sub-proof % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | #192. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | (2020) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2020) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2021) all_57_6 = e3 & op(e1, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1971), (2021) are inconsistent by sub-proof #181. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2022) all_57_12 = e3 & op(e0, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2022) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | (2023) op(e0, e3) = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | (2024) ~ (op(e0, e3) = e3) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2023), (2024) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | (2025) $false % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2025) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | (2026) all_53_3 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (2026) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | (2027) ~ (all_53_1 = e3) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2028) all_55_4 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (2028) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2029) all_53_1 = e3 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2027), (2029) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2030) $false % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2030) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2031) ~ (all_55_4 = e3) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2032) all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2032) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2033) all_55_4 = e2 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (2033) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2034) all_53_1 = e2 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1156), (2034) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2035) $false % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2035) is inconsistent. % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2036) ~ (all_55_4 = e2) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_55_4 = e1 | all_55_4 = e0 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2037) gives: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2038) all_55_4 = e1 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (2038) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2039) all_53_1 = e1 % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (2039) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2040) ~ (all_53_9 = e1) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2040) implies: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2041) ~ (all_53_9 = e1) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (2039) imply: % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2042) ~ (all_53_13 = e1) % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.40/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2042) implies: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2043) ~ (all_53_13 = e1) % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2027), (2039) imply: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044) ~ (e3 = e1) % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1156), (2039) imply: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2045) ~ (e2 = e1) % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2046) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2046) gives: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047) all_57_2 = e1 & op(e2, e3) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (17), (18), % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (140), (142), (209), (226), (227), (228), % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (261), (279), (285), (286), (328), (329), % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339), (438), (663), (1958), (1959), (1962), % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966), (1974), (1978), (1997), (1999), (2007), % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047), (function-axioms) are inconsistent by % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #165. % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2048) all_57_3 = e1 & op(e2, e2) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2048) implies: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2049) op(e2, e2) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2010), (2049), (function-axioms) are % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2050) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2050) gives: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051) all_57_5 = e1 & op(e2, e1) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2051) implies: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2052) op(e2, e1) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (2041), (2052) are inconsistent by % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_57_10 = e1 & op(e2, e0) = e1 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (2043), (2053), (function-axioms) are % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) all_55_4 = e0 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (2054) imply: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) all_53_1 = e0 % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2006), (2055) imply: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2056) $false % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2056) is inconsistent. % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | % 129.60/18.22 | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.22 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | (2057) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2057) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (2058) all_57_6 = e0 & op(e1, e3) = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (17), (18), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (140), (142), (209), (226), (227), (228), (279), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (285), (286), (328), (329), (339), (663), (1958), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (1959), (1962), (1966), (1974), (1978), (1999), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (2007), (2058), (function-axioms) are inconsistent % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | by sub-proof #168. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (2059) all_57_12 = e0 & op(e0, e3) = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1997), (2059) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | sub-proof #237. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | (2060) all_28_2 = e2 % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | COMBINE_EQS: (361), (2060) imply: % 129.60/18.23 | | | | | | | | | | | | | | | (2061) all_8_2 = e2 % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | SIMP: (2061) implies: % 129.60/18.23 | | | | | | | | | | | | | | | (2062) all_8_2 = e2 % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (124), (132), (140), % 129.60/18.23 | | | | | | | | | | | | | | | (207), (212), (271), (279), (282), (288), (295), % 129.60/18.23 | | | | | | | | | | | | | | | (304), (328), (331), (334), (339), (342), (423), % 129.60/18.23 | | | | | | | | | | | | | | | (425), (427), (437), (439), (663), (1961), (1965), % 129.60/18.23 | | | | | | | | | | | | | | | (1974), (1980), (2062) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | sub-proof #158. % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | (2063) all_26_2 = e1 % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | COMBINE_EQS: (374), (2063) imply: % 129.60/18.23 | | | | | | | | | | | | | | (2064) all_6_2 = e1 % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | SIMP: (2064) implies: % 129.60/18.23 | | | | | | | | | | | | | | (2065) all_6_2 = e1 % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | COMBINE_EQS: (399), (2065) imply: % 129.60/18.23 | | | | | | | | | | | | | | (2066) all_50_2 = e1 % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | REDUCE: (421), (2065) imply: % 129.60/18.23 | | | | | | | | | | | | | | (2067) ~ (all_53_7 = e1) % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | REDUCE: (423), (2065) imply: % 129.60/18.23 | | | | | | | | | | | | | | (2068) ~ (all_53_9 = e1) % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | BETA: splitting (332) gives: % 129.60/18.23 | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | (2069) ~ (op(e2, e1) = e1) % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | PRED_UNIFY: (7), (2069) imply: % 129.60/18.23 | | | | | | | | | | | | | | | (2070) ~ (unit = e2) % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.60/18.23 | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | (2071) unit = e2 % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | REDUCE: (2070), (2071) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | (2072) $false % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | CLOSE: (2072) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | (2073) unit = e1 | unit = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | BETA: splitting (2073) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | (2074) unit = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (1974), (2074) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2075) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | CLOSE: (2075) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | (2076) unit = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (9), (2076) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2077) op(e0, e3) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (8), (2076) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2078) op(e0, e2) = e2 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (5), (2076) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2079) op(e3, e0) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (3), (2076) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2080) op(e1, e0) = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | REDUCE: (2), (2076) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | (2081) op(e0, e0) = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2082) ~ (op(e0, e0) = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2081), (2082) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2083) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | CLOSE: (2083) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2084) all_55_15 = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2084) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2085) all_8_2 = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | REDUCE: (416), (2085) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2086) ~ (all_53_3 = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | REDUCE: (427), (2085) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2087) ~ (all_53_7 = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | REDUCE: (434), (2085) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2088) ~ (all_53_11 = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | REDUCE: (435), (2085) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2089) ~ (all_53_12 = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | REDUCE: (437), (2085) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | (2090) ~ (all_53_14 = e0) % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | (2091) ~ (op(e0, e2) = e2) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2078), (2091) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | (2092) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | CLOSE: (2092) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | (2093) all_53_7 = e2 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2093) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | (2094) ~ (all_53_6 = e2) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | (2095) ~ (op(e0, e3) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2077), (2095) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | (2096) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | CLOSE: (2096) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | (2097) all_53_3 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (2097) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | (2098) ~ (all_53_1 = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (2099) all_57_15 = e0 & op(e0, e0) = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | (2100) all_57_15 = e0 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | (2101) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (340), (439), (2098), (2101), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | #351. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | (2102) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2102) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | (2103) all_57_5 = e3 & op(e2, e1) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (1964), (2103), (function-axioms) are % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | (2104) all_57_10 = e3 & op(e2, e0) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2104) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | (2105) all_57_10 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | (2106) ~ (op(e1, e0) = e1) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2080), (2106) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | (2107) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2107) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | (2108) all_53_14 = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2108) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | (2109) ~ (all_53_12 = e1) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2110) ~ (op(e3, e0) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2079), (2110) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2111) $false % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2111) is inconsistent. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2112) all_53_12 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1183), (2112) imply: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2113) ~ (all_14_1 = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2113) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2114) ~ (all_14_1 = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2115) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_57_0 = e3 & op(e3, e3) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2116) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) op(e3, e3) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (1154), (2117) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_57_1 = e3 & op(e3, e2) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1170), (2114), (2118) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #127. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_57_4 = e3 & op(e3, e1) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2120) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) op(e3, e1) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (323), (1963), (2121) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #160. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) all_57_9 = e3 & op(e3, e0) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2122) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) all_57_9 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2124) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) all_57_1 = e3 & op(e3, e2) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1170), (2114), (2125) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #127. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) all_57_3 = e3 & op(e2, e2) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (439), (2126), (function-axioms) are % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_57_7 = e3 & op(e1, e2) = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2128) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_57_7 = e3 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (226), (228), % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966), (2129), (2130), (function-axioms) are % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #95. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2131) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_57_8 = e1 & op(e1, e1) = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2132) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) op(e1, e1) = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (285), (1959), (2133) are inconsistent by % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #174. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_57_11 = e1 & op(e1, e0) = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_57_11 = e1 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2136) gives: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_57_9 = e2 & op(e3, e0) = e2 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2123), (2137) are inconsistent by sub-proof % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_57_10 = e2 & op(e2, e0) = e2 % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2105), (2138) are inconsistent by sub-proof % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #193. % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2139) gives: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_57_11 = e2 & op(e1, e0) = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_57_11 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (2135), (2141) are inconsistent by sub-proof % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #172. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_57_15 = e2 & op(e0, e0) = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2142) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_57_15 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2100), (2143) imply: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) e2 = e0 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2144) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) e2 = e0 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (2145) imply: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) $false % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2146) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_57_13 = e3 & op(e0, e2) = e3 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2147) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_57_13 = e3 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (300), (1168), (2066), (2149) are % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #113. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2150) gives: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) all_57_7 = e2 & op(e1, e2) = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2151) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) op(e1, e2) = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (2094), (2152) are inconsistent by % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_57_13 = e2 & op(e0, e2) = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2153) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_57_13 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2148), (2154) imply: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2155) e3 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2155) implies: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2156) e3 = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (2156) imply: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) $false % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2157) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | (2158) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (261), (262), (265), (2086), (2087), % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | (2088), (2158) are inconsistent by sub-proof #236. % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | (2159) op(e2, e1) = e1 % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | REF_CLOSE: (332), (2068), (2159) are inconsistent by % 129.60/18.24 | | | | | | | | | | | | | | | sub-proof #334. % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | (2160) op(e1, e3) = e3 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | REF_CLOSE: (342), (1961), (2160) are inconsistent by % 129.60/18.24 | | | | | | | | | | | | | sub-proof #323. % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | (2161) op(e3, e2) = e2 % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | REF_CLOSE: (335), (1159), (2161) are inconsistent by % 129.60/18.24 | | | | | | | | | | sub-proof #94. % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | End of split % 129.60/18.24 | | | | | | | | % 129.60/18.24 | | | | | | | End of split % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | Case 2: % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | (2162) all_12_2 = e2 % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | REDUCE: (415), (2162) imply: % 129.60/18.24 | | | | | | | (2163) ~ (all_53_2 = e2) % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | REDUCE: (426), (2162) imply: % 129.60/18.24 | | | | | | | (2164) ~ (all_53_6 = e2) % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | REDUCE: (429), (2162) imply: % 129.60/18.24 | | | | | | | (2165) ~ (all_53_9 = e2) % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | REDUCE: (431), (2162) imply: % 129.60/18.24 | | | | | | | (2166) ~ (all_53_11 = e2) % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | REDUCE: (57), (2162) imply: % 129.60/18.24 | | | | | | | (2167) op(e1, e1) = e2 % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | BETA: splitting (337) gives: % 129.60/18.24 | | | | | | | % 129.60/18.24 | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | % 129.60/18.24 | | | | | | | | (2168) ~ (op(e1, e2) = e2) % 129.60/18.24 | | | | | | | | % 129.60/18.24 | | | | | | | | PRED_UNIFY: (8), (2168) imply: % 129.60/18.24 | | | | | | | | (2169) ~ (unit = e1) % 129.60/18.24 | | | | | | | | % 129.60/18.24 | | | | | | | | BETA: splitting (61) gives: % 129.60/18.24 | | | | | | | | % 129.60/18.24 | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | (2170) ~ (all_14_2 = e2) % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | REDUCE: (382), (2170) imply: % 129.60/18.24 | | | | | | | | | (2171) ~ (all_4_2 = e2) % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | BETA: splitting (79) gives: % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | (2172) ~ (all_26_2 = e1) % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | REDUCE: (374), (2172) imply: % 129.60/18.24 | | | | | | | | | | (2173) ~ (all_6_2 = e1) % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | BETA: splitting (82) gives: % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | (2174) ~ (all_28_2 = e2) % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | REDUCE: (361), (2174) imply: % 129.60/18.24 | | | | | | | | | | | (2175) ~ (all_8_2 = e2) % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | BETA: splitting (203) gives: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2176) all_55_15 = e3 % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | COMBINE_EQS: (256), (2176) imply: % 129.60/18.24 | | | | | | | | | | | | (2177) all_8_2 = e3 % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | REDUCE: (665), (2177) imply: % 129.60/18.24 | | | | | | | | | | | | (2178) $false % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | CLOSE: (2178) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2179) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | BETA: splitting (2179) gives: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | (2180) all_55_15 = e2 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | COMBINE_EQS: (256), (2180) imply: % 129.60/18.24 | | | | | | | | | | | | | (2181) all_8_2 = e2 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | REDUCE: (2175), (2181) imply: % 129.60/18.24 | | | | | | | | | | | | | (2182) $false % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | CLOSE: (2182) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | (2183) all_55_15 = e1 | all_55_15 = e0 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | BETA: splitting (2183) gives: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | (2184) all_55_15 = e1 % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | COMBINE_EQS: (256), (2184) imply: % 129.60/18.24 | | | | | | | | | | | | | | (2185) all_8_2 = e1 % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | REDUCE: (440), (2185) imply: % 129.60/18.24 | | | | | | | | | | | | | | (2186) $false % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | CLOSE: (2186) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | (2187) all_55_15 = e0 % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | COMBINE_EQS: (256), (2187) imply: % 129.60/18.24 | | | | | | | | | | | | | | (2188) all_8_2 = e0 % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | REDUCE: (436), (2188) imply: % 129.60/18.24 | | | | | | | | | | | | | | (2189) ~ (all_53_13 = e0) % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | BETA: splitting (328) gives: % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | (2190) ~ (op(e2, e0) = e0) % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | PRED_UNIFY: (6), (2190) imply: % 129.60/18.24 | | | | | | | | | | | | | | | (2191) ~ (unit = e2) % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | (2192) unit = e2 % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | REDUCE: (2191), (2192) imply: % 129.60/18.24 | | | | | | | | | | | | | | | | (2193) $false % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | CLOSE: (2193) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | (2194) unit = e1 | unit = e0 % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (18), (45), (158), (159), (162), (177), % 129.60/18.24 | | | | | | | | | | | | | | | | (217), (246), (248), (259), (296), (297), (306), % 129.60/18.24 | | | | | | | | | | | | | | | | (316), (319), (340), (342), (343), (382), (407), % 129.60/18.24 | | | | | | | | | | | | | | | | (438), (2163), (2169), (2171), (2194), % 129.60/18.24 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.60/18.24 | | | | | | | | | | | | | | | | #92. % 129.60/18.24 | | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | (2195) op(e2, e0) = e0 % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | | REF_CLOSE: (328), (2189), (2195) are inconsistent by % 129.60/18.24 | | | | | | | | | | | | | | | sub-proof #356. % 129.60/18.24 | | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | (2196) all_28_2 = e2 % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | COMBINE_EQS: (361), (2196) imply: % 129.60/18.24 | | | | | | | | | | | (2197) all_8_2 = e2 % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | REDUCE: (416), (2197) imply: % 129.60/18.24 | | | | | | | | | | | (2198) ~ (all_53_3 = e2) % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | BETA: splitting (246) gives: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2199) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 129.60/18.24 | | | | | | | | | | | | & op(e2, e3) = e2) % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | BETA: splitting (2199) gives: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | (2200) all_57_0 = e2 & op(e3, e3) = e2 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | REF_CLOSE: (45), (2171), (2200), (function-axioms) are % 129.60/18.24 | | | | | | | | | | | | | inconsistent by sub-proof #91. % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | (2201) all_57_2 = e2 & op(e2, e3) = e2 % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (159), (212), (258), (262), (295), % 129.60/18.24 | | | | | | | | | | | | | (298), (306), (328), (414), (421), (425), (439), % 129.60/18.24 | | | | | | | | | | | | | (663), (2169), (2173), (2201) are inconsistent by % 129.60/18.24 | | | | | | | | | | | | | sub-proof #89. % 129.60/18.24 | | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2202) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 129.60/18.24 | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | REF_CLOSE: (173), (177), (2163), (2198), (2202), % 129.60/18.24 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.60/18.24 | | | | | | | | | | | | #88. % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | (2203) all_26_2 = e1 % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | COMBINE_EQS: (374), (2203) imply: % 129.60/18.24 | | | | | | | | | | (2204) all_6_2 = e1 % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | REDUCE: (423), (2204) imply: % 129.60/18.24 | | | | | | | | | | (2205) ~ (all_53_9 = e1) % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | BETA: splitting (332) gives: % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | (2206) ~ (op(e2, e1) = e1) % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | PRED_UNIFY: (7), (2206) imply: % 129.60/18.24 | | | | | | | | | | | (2207) ~ (unit = e2) % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | BETA: splitting (663) gives: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 1: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2208) unit = e2 % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | REDUCE: (2207), (2208) imply: % 129.60/18.24 | | | | | | | | | | | | (2209) $false % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | CLOSE: (2209) is inconsistent. % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | (2210) unit = e1 | unit = e0 % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | | REF_CLOSE: (4), (9), (18), (45), (158), (159), (162), (177), % 129.60/18.24 | | | | | | | | | | | | (217), (246), (248), (259), (296), (297), (306), % 129.60/18.24 | | | | | | | | | | | | (316), (319), (340), (342), (343), (382), (407), % 129.60/18.24 | | | | | | | | | | | | (438), (2163), (2169), (2171), (2210), % 129.60/18.24 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.60/18.24 | | | | | | | | | | | | #92. % 129.60/18.24 | | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | (2211) op(e2, e1) = e1 % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | | REF_CLOSE: (332), (2205), (2211) are inconsistent by % 129.60/18.24 | | | | | | | | | | | sub-proof #334. % 129.60/18.24 | | | | | | | | | | | % 129.60/18.24 | | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | | % 129.60/18.24 | | | | | | | | | End of split % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | Case 2: % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | (2212) all_14_2 = e2 % 129.60/18.24 | | | | | | | | | (2213) op(e3, e2) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 % 129.60/18.24 | | | | | | | | | = e0) | ( ~ (all_14_0 = e1) & op(e3, e0) = % 129.60/18.24 | | | | | | | | | all_14_0 & $i(all_14_0))) % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | ALPHA: (2213) implies: % 129.60/18.24 | | | | | | | | | (2214) op(e3, e2) = all_14_1 % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | COMBINE_EQS: (382), (2212) imply: % 129.60/18.24 | | | | | | | | | (2215) all_4_2 = e2 % 129.60/18.24 | | | | | | | | | % 129.60/18.24 | | | | | | | | | COMBINE_EQS: (380), (2215) imply: % 129.60/18.24 | | | | | | | | | (2216) all_32_2 = e2 % 129.60/18.25 | | | | | | | | | % 129.60/18.25 | | | | | | | | | REDUCE: (403), (2215) imply: % 129.60/18.25 | | | | | | | | | (2217) ~ (all_53_1 = e2) % 129.60/18.25 | | | | | | | | | % 129.60/18.25 | | | | | | | | | REDUCE: (407), (2215) imply: % 129.60/18.25 | | | | | | | | | (2218) ~ (all_53_3 = e2) % 129.60/18.25 | | | | | | | | | % 129.60/18.25 | | | | | | | | | REDUCE: (45), (2215) imply: % 129.60/18.25 | | | | | | | | | (2219) op(e3, e3) = e2 % 129.60/18.25 | | | | | | | | | % 129.60/18.25 | | | | | | | | | BETA: splitting (88) gives: % 129.60/18.25 | | | | | | | | | % 129.60/18.25 | | | | | | | | | Case 1: % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | (2220) ~ (all_32_2 = e2) % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | REDUCE: (2216), (2220) imply: % 129.60/18.25 | | | | | | | | | | (2221) $false % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | CLOSE: (2221) is inconsistent. % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | Case 2: % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | (2222) op(e3, e2) = all_32_1 & $i(all_32_1) & ( ~ % 129.60/18.25 | | | | | | | | | | (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 129.60/18.25 | | | | | | | | | | e1) = all_32_0 & $i(all_32_0))) % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | ALPHA: (2222) implies: % 129.60/18.25 | | | | | | | | | | (2223) op(e3, e2) = all_32_1 % 129.60/18.25 | | | | | | | | | | (2224) ~ (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 129.60/18.25 | | | | | | | | | | e1) = all_32_0 & $i(all_32_0)) % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 129.60/18.25 | | | | | | | | | | all_14_1, e2, e3, simplifying with (184), (2214) % 129.60/18.25 | | | | | | | | | | gives: % 129.60/18.25 | | | | | | | | | | (2225) all_53_4 = all_14_1 % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 129.60/18.25 | | | | | | | | | | all_32_1, e2, e3, simplifying with (184), (2223) % 129.60/18.25 | | | | | | | | | | gives: % 129.60/18.25 | | | | | | | | | | (2226) all_53_4 = all_32_1 % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | COMBINE_EQS: (2225), (2226) imply: % 129.60/18.25 | | | | | | | | | | (2227) all_32_1 = all_14_1 % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | SIMP: (2227) implies: % 129.60/18.25 | | | | | | | | | | (2228) all_32_1 = all_14_1 % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | COMBINE_EQS: (309), (2225) imply: % 129.60/18.25 | | | | | | | | | | (2229) all_55_1 = all_14_1 % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | REDUCE: (149), (2225) imply: % 129.60/18.25 | | | | | | | | | | (2230) ~ (all_53_7 = all_14_1) % 129.60/18.25 | | | | | | | | | | % 129.60/18.25 | | | | | | | | | | SIMP: (2230) implies: % 129.70/18.25 | | | | | | | | | | (2231) ~ (all_53_7 = all_14_1) % 129.70/18.25 | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | REDUCE: (147), (2225) imply: % 129.70/18.25 | | | | | | | | | | (2232) ~ (all_53_12 = all_14_1) % 129.70/18.25 | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | SIMP: (2232) implies: % 129.70/18.25 | | | | | | | | | | (2233) ~ (all_53_12 = all_14_1) % 129.70/18.25 | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | REDUCE: (417), (2225) imply: % 129.70/18.25 | | | | | | | | | | (2234) ~ (all_14_1 = all_6_2) % 129.70/18.25 | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | BETA: splitting (79) gives: % 129.70/18.25 | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | (2235) ~ (all_26_2 = e1) % 129.70/18.25 | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | REDUCE: (374), (2235) imply: % 129.70/18.25 | | | | | | | | | | | (2236) ~ (all_6_2 = e1) % 129.70/18.25 | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | BETA: splitting (82) gives: % 129.70/18.25 | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | (2237) ~ (all_28_2 = e2) % 129.70/18.25 | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | REDUCE: (361), (2237) imply: % 129.70/18.25 | | | | | | | | | | | | (2238) ~ (all_8_2 = e2) % 129.70/18.25 | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | BETA: splitting (203) gives: % 129.70/18.25 | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | (2239) all_55_15 = e3 % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | COMBINE_EQS: (256), (2239) imply: % 129.70/18.25 | | | | | | | | | | | | | (2240) all_8_2 = e3 % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | REDUCE: (665), (2240) imply: % 129.70/18.25 | | | | | | | | | | | | | (2241) $false % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | CLOSE: (2241) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | (2242) ~ (all_55_15 = e3) % 129.70/18.25 | | | | | | | | | | | | | (2243) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | BETA: splitting (221) gives: % 129.70/18.25 | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | (2244) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 129.70/18.25 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 129.70/18.25 | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | BETA: splitting (2244) gives: % 129.70/18.25 | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | (2245) all_57_12 = e2 & op(e0, e3) = e2 % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | ALPHA: (2245) implies: % 129.70/18.25 | | | | | | | | | | | | | | | (2246) op(e0, e3) = e2 % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | REF_CLOSE: (173), (2218), (2246), (function-axioms) are % 129.70/18.25 | | | | | | | | | | | | | | | inconsistent by sub-proof #99. % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | (2247) all_57_13 = e2 & op(e0, e2) = e2 % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | ALPHA: (2247) implies: % 129.70/18.25 | | | | | | | | | | | | | | | (2248) op(e0, e2) = e2 % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 129.70/18.25 | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | (2249) ~ (op(e0, e2) = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | PRED_UNIFY: (2248), (2249) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | (2250) $false % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | CLOSE: (2250) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | (2251) all_53_7 = e2 % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | REDUCE: (2231), (2251) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | (2252) ~ (all_14_1 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | SIMP: (2252) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | (2253) ~ (all_14_1 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | REDUCE: (427), (2251) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | (2254) ~ (all_8_2 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | REDUCE: (421), (2251) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | (2255) ~ (all_6_2 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | SIMP: (2255) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | (2256) ~ (all_6_2 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | BETA: splitting (2243) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | (2257) all_55_15 = e2 % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2257) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | (2258) all_8_2 = e2 % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | REDUCE: (2238), (2258) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | (2259) $false % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | CLOSE: (2259) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | (2260) ~ (all_55_15 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | | (2261) all_55_15 = e1 | all_55_15 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | BETA: splitting (2261) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2262) all_55_15 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2262) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2263) all_8_2 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | REDUCE: (440), (2263) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2264) $false % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | CLOSE: (2264) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2265) all_55_15 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2265) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2266) all_8_2 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | REDUCE: (434), (2266) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2267) ~ (all_53_11 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | REDUCE: (435), (2266) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | (2268) ~ (all_53_12 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | (2269) all_55_5 = e3 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (2269) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | (2270) all_6_2 = e3 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | REDUCE: (439), (2270) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | (2271) $false % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | CLOSE: (2271) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | (2272) ~ (all_55_5 = e3) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | (2273) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (2273) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | (2274) all_55_5 = e2 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (2274) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | (2275) all_6_2 = e2 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (2256), (2275) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | (2276) $false % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (2276) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | (2277) ~ (all_55_5 = e2) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | (2278) all_55_5 = e1 | all_55_5 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2278) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2279) all_55_5 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (2279) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2280) all_6_2 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2236), (2280) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2281) $false % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2281) is inconsistent. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2282) all_55_5 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (2282) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2283) all_6_2 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (2283) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2284) ~ (all_53_9 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2234), (2283) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2285) ~ (all_14_1 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (2283) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2286) ~ (e3 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2256), (2283) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2287) ~ (e2 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2236), (2283) imply: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | (2288) ~ (e1 = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | (2289) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2289) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | (2290) all_57_0 = e0 & op(e3, e3) = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2290) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | (2291) op(e3, e3) = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2219), (2291), (function-axioms) are % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | (2292) all_57_1 = e0 & op(e3, e2) = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2292) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | (2293) all_57_1 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | (2294) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2294) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | (2295) all_57_4 = e0 & op(e3, e1) = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2295) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | (2296) all_57_4 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2297) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2298) all_57_0 = e1 & op(e3, e3) = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2298) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299) all_57_0 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2300) op(e3, e3) = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (18), (247), (249), % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2293), (2296), (2299), (2300), (function-axioms) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #244. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_57_1 = e1 & op(e3, e2) = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2293), (2301) are inconsistent by sub-proof % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | #201. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (2302) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2302) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303) all_57_4 = e1 & op(e3, e1) = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2296), (2303) are inconsistent by sub-proof % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | #335. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2304) all_57_9 = e1 & op(e3, e0) = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2304) implies: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2305) all_57_9 = e1 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (2215), (2293), % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296), (2305) are inconsistent by sub-proof #150. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | (2306) all_57_5 = e0 & op(e2, e1) = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (2284), (2306), (function-axioms) are % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #241. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | (2307) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (265), (2167), (2267), (2307), % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | #87. % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | (2308) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2308) gives: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.25 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | (2309) all_57_4 = e0 & op(e3, e1) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2309) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | (2310) op(e3, e1) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2224) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | (2311) ~ (all_32_1 = e1) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2228), (2311) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | (2312) ~ (all_14_1 = e1) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2313) all_55_1 = e3 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2229), (2313) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2314) all_14_1 = e3 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2314) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2315) all_14_1 = e3 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2233), (2315) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2316) ~ (all_53_12 = e3) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) ~ (op(e3, e0) = e3) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5), (2317) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) ~ (unit = e0) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) unit = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (2319) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) op(e0, e2) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (256), (263), (427), (440), (665), (2238), % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) are inconsistent by sub-proof #143. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) unit = e1 | unit = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2169), (2318), (2321) are inconsistent by % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) op(e3, e0) = e3 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (324), (2316), (2322) are inconsistent by % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #186. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2323) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2229), (2253), (2285), (2312), (2323) are % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | (2324) ~ (all_32_0 = e0) & op(e3, e1) = all_32_0 & % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_0) % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2310), (2324), (function-axioms) are inconsistent % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #138. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | (2325) all_57_9 = e0 & op(e3, e0) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2325) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | (2326) op(e3, e0) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (326), (2268), (2326) are inconsistent by % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | (2327) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 129.70/18.26 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | BETA: splitting (2327) gives: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | (2328) all_57_14 = e2 & op(e0, e1) = e2 % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | REF_CLOSE: (171), (2166), (2328), (function-axioms) are % 129.70/18.26 | | | | | | | | | | | | | | | inconsistent by sub-proof #119. % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | (2329) all_57_15 = e2 & op(e0, e0) = e2 % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | ALPHA: (2329) implies: % 129.70/18.26 | | | | | | | | | | | | | | | (2330) all_57_15 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | BETA: splitting (2243) gives: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2331) all_55_15 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2331) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2332) all_8_2 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | REDUCE: (2238), (2332) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2333) $false % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | CLOSE: (2333) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2334) ~ (all_55_15 = e2) % 129.70/18.26 | | | | | | | | | | | | | | | | (2335) all_55_15 = e1 | all_55_15 = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | BETA: splitting (2335) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | (2336) all_55_15 = e1 % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2336) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2337) all_8_2 = e1 % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | REDUCE: (440), (2337) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2338) $false % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | CLOSE: (2338) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | (2339) all_55_15 = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2339) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2340) all_8_2 = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | REDUCE: (416), (2340) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2341) ~ (all_53_3 = e0) % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | REDUCE: (427), (2340) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2342) ~ (all_53_7 = e0) % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | REDUCE: (434), (2340) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2343) ~ (all_53_11 = e0) % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | REDUCE: (2238), (2340) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | | (2344) ~ (e2 = e0) % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | (2345) all_57_15 = e0 & op(e0, e0) = e0 % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2330), (2345) are inconsistent by sub-proof % 129.70/18.26 | | | | | | | | | | | | | | | | | | #229. % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | (2346) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.70/18.26 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.70/18.26 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.70/18.26 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.70/18.26 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (261), (262), (265), (2341), (2342), % 129.70/18.26 | | | | | | | | | | | | | | | | | | (2343), (2346) are inconsistent by sub-proof #236. % 129.70/18.26 | | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | (2347) all_28_2 = e2 % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | COMBINE_EQS: (361), (2347) imply: % 129.70/18.26 | | | | | | | | | | | | (2348) all_8_2 = e2 % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | SIMP: (2348) implies: % 129.70/18.26 | | | | | | | | | | | | (2349) all_8_2 = e2 % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | REDUCE: (436), (2349) imply: % 129.70/18.26 | | | | | | | | | | | | (2350) ~ (all_53_13 = e2) % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | REDUCE: (51), (2349) imply: % 129.70/18.26 | | | | | | | | | | | | (2351) op(e0, e0) = e2 % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | BETA: splitting (236) gives: % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | (2352) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.70/18.26 | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | BETA: splitting (2352) gives: % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | (2353) all_57_2 = e2 & op(e2, e3) = e2 % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | ALPHA: (2353) implies: % 129.70/18.26 | | | | | | | | | | | | | | (2354) op(e2, e3) = e2 % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (2217), (2354) are inconsistent by % 129.70/18.26 | | | | | | | | | | | | | | sub-proof #346. % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | (2355) all_57_3 = e2 & op(e2, e2) = e2 % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | ALPHA: (2355) implies: % 129.70/18.26 | | | | | | | | | | | | | | (2356) op(e2, e2) = e2 % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | BETA: splitting (119) gives: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | (2357) ( ~ (all_52_0 = e2) & op(e3, e3) = all_52_0 & % 129.70/18.26 | | | | | | | | | | | | | | | $i(all_52_0)) | ( ~ (all_52_1 = e2) & op(e2, e2) % 129.70/18.26 | | | | | | | | | | | | | | | = all_52_1 & $i(all_52_1)) % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | BETA: splitting (2357) gives: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2358) ~ (all_52_0 = e2) & op(e3, e3) = all_52_0 & % 129.70/18.26 | | | | | | | | | | | | | | | | $i(all_52_0) % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | ALPHA: (2358) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | (2359) ~ (all_52_0 = e2) % 129.70/18.26 | | | | | | | | | | | | | | | | (2360) op(e3, e3) = all_52_0 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_0, % 129.70/18.26 | | | | | | | | | | | | | | | | e3, e3, simplifying with (2219), (2360) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | (2361) all_52_0 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | REDUCE: (2359), (2361) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2362) $false % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | CLOSE: (2362) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2363) ~ (all_52_1 = e2) & op(e2, e2) = all_52_1 & % 129.70/18.26 | | | | | | | | | | | | | | | | $i(all_52_1) % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | ALPHA: (2363) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | (2364) ~ (all_52_1 = e2) % 129.70/18.26 | | | | | | | | | | | | | | | | (2365) op(e2, e2) = all_52_1 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1, % 129.70/18.26 | | | | | | | | | | | | | | | | e2, e2, simplifying with (2356), (2365) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | (2366) all_52_1 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | REDUCE: (2364), (2366) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2367) $false % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | CLOSE: (2367) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | (2368) ( ~ (all_52_2 = e2) & op(e1, e1) = all_52_2 & % 129.70/18.26 | | | | | | | | | | | | | | | $i(all_52_2)) | ( ~ (all_52_3 = e2) & op(e0, e0) % 129.70/18.26 | | | | | | | | | | | | | | | = all_52_3 & $i(all_52_3)) % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | BETA: splitting (2368) gives: % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2369) ~ (all_52_2 = e2) & op(e1, e1) = all_52_2 & % 129.70/18.26 | | | | | | | | | | | | | | | | $i(all_52_2) % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | ALPHA: (2369) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | (2370) ~ (all_52_2 = e2) % 129.70/18.26 | | | | | | | | | | | | | | | | (2371) op(e1, e1) = all_52_2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_2, % 129.70/18.26 | | | | | | | | | | | | | | | | e1, e1, simplifying with (2167), (2371) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | (2372) all_52_2 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | REDUCE: (2370), (2372) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2373) $false % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | CLOSE: (2373) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | (2374) ~ (all_52_3 = e2) & op(e0, e0) = all_52_3 & % 129.70/18.26 | | | | | | | | | | | | | | | | $i(all_52_3) % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | ALPHA: (2374) implies: % 129.70/18.26 | | | | | | | | | | | | | | | | (2375) ~ (all_52_3 = e2) % 129.70/18.26 | | | | | | | | | | | | | | | | (2376) op(e0, e0) = all_52_3 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_3, % 129.70/18.26 | | | | | | | | | | | | | | | | e0, e0, simplifying with (2351), (2376) gives: % 129.70/18.26 | | | | | | | | | | | | | | | | (2377) all_52_3 = e2 % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | REDUCE: (2375), (2377) imply: % 129.70/18.26 | | | | | | | | | | | | | | | | (2378) $false % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | | CLOSE: (2378) is inconsistent. % 129.70/18.26 | | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | (2379) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 129.70/18.26 | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | REF_CLOSE: (304), (306), (2165), (2350), (2379) are % 129.70/18.26 | | | | | | | | | | | | | inconsistent by sub-proof #102. % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | End of split % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | Case 2: % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | (2380) all_26_2 = e1 % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | COMBINE_EQS: (374), (2380) imply: % 129.70/18.26 | | | | | | | | | | | (2381) all_6_2 = e1 % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | SIMP: (2381) implies: % 129.70/18.26 | | | | | | | | | | | (2382) all_6_2 = e1 % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | COMBINE_EQS: (399), (2382) imply: % 129.70/18.26 | | | | | | | | | | | (2383) all_50_2 = e1 % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | REDUCE: (423), (2382) imply: % 129.70/18.26 | | | | | | | | | | | (2384) ~ (all_53_9 = e1) % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | REDUCE: (48), (2382) imply: % 129.70/18.26 | | | | | | | | | | | (2385) op(e2, e2) = e1 % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | BETA: splitting (304) gives: % 129.70/18.26 | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | (2386) ~ (op(e2, e1) = e2) % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | BETA: splitting (332) gives: % 129.70/18.26 | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | (2387) ~ (op(e2, e1) = e1) % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | BETA: splitting (236) gives: % 129.70/18.26 | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | Case 1: % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.26 | | | | | | | | | | | | | | (2388) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.70/18.26 | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.70/18.26 | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | REF_CLOSE: (15), (296), (297), (300), (2217), (2383), (2388) % 129.70/18.27 | | | | | | | | | | | | | | are inconsistent by sub-proof #195. % 129.70/18.27 | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | (2389) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 129.70/18.27 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.70/18.27 | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | BETA: splitting (2389) gives: % 129.70/18.27 | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | (2390) all_57_5 = e2 & op(e2, e1) = e2 % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | ALPHA: (2390) implies: % 129.70/18.27 | | | | | | | | | | | | | | | (2391) op(e2, e1) = e2 % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | PRED_UNIFY: (2386), (2391) imply: % 129.70/18.27 | | | | | | | | | | | | | | | (2392) $false % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | CLOSE: (2392) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | (2393) all_57_10 = e2 & op(e2, e0) = e2 % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | ALPHA: (2393) implies: % 129.70/18.27 | | | | | | | | | | | | | | | (2394) all_57_10 = e2 % 129.70/18.27 | | | | | | | | | | | | | | | (2395) op(e2, e0) = e2 % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 129.70/18.27 | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | (2396) ~ (op(e2, e0) = e2) % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | PRED_UNIFY: (2395), (2396) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | (2397) $false % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | CLOSE: (2397) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | (2398) all_55_7 = e2 % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (2398) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | (2399) all_53_13 = e2 % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | REDUCE: (436), (2399) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | (2400) ~ (all_8_2 = e2) % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | SIMP: (2400) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | (2401) ~ (all_8_2 = e2) % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | (2402) all_55_15 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2402) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | (2403) all_8_2 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | REDUCE: (665), (2403) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | (2404) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | CLOSE: (2404) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | (2405) ~ (all_55_15 = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | (2406) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | BETA: splitting (2406) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | (2407) all_55_15 = e2 % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2407) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | (2408) all_8_2 = e2 % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | REDUCE: (2401), (2408) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | (2409) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | CLOSE: (2409) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | (2410) ~ (all_55_15 = e2) % 129.70/18.27 | | | | | | | | | | | | | | | | | | (2411) all_55_15 = e1 | all_55_15 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | BETA: splitting (2411) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2412) all_55_15 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2412) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2413) all_8_2 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | REDUCE: (440), (2413) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2414) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | CLOSE: (2414) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2415) all_55_15 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2415) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2416) all_8_2 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | REDUCE: (416), (2416) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2417) ~ (all_53_3 = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | REDUCE: (427), (2416) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2418) ~ (all_53_7 = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | REDUCE: (434), (2416) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2419) ~ (all_53_11 = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (2387) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | (2420) ~ (unit = e2) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | (2421) unit = e2 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (2420), (2421) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | (2422) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | CLOSE: (2422) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | (2423) unit = e1 | unit = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2423) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2424) unit = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2169), (2424) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2425) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2425) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2426) unit = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2420), (2426) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2427) ~ (e2 = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2426) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2428) op(e0, e3) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2426) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2429) op(e0, e1) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2426) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2430) op(e3, e0) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (2426) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | (2431) op(e1, e0) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2432) ~ (op(e3, e0) = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2430), (2432) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2433) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2433) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2434) all_53_12 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2434) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2435) ~ (all_53_8 = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2434) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2436) ~ (all_53_14 = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2436) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | (2437) ~ (all_53_14 = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2438) ~ (op(e0, e1) = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2429), (2438) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2439) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2439) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2440) all_53_11 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (2440) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2441) ~ (all_53_3 = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2440) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2442) ~ (all_53_8 = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2166), (2440) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | (2443) ~ (e2 = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | (2444) ~ (op(e0, e3) = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2428), (2444) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | (2445) $false % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2445) is inconsistent. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_55_12 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (2446) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | (2447) all_53_3 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2447) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | (2448) ~ (all_53_2 = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | (2449) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2449) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (2450) all_57_0 = e1 & op(e3, e3) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2450) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (2451) op(e3, e3) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (2219), (2451), (function-axioms) are % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (2452) all_57_2 = e1 & op(e2, e3) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2452) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (2453) all_57_2 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2454) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2454) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2455) all_57_6 = e3 & op(e1, e3) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2455) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2456) op(e1, e3) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (2448), (2456) are inconsistent by % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #323. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_57_7 = e3 & op(e1, e2) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2457) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2458) all_57_7 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2459) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2459) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_57_9 = e3 & op(e3, e0) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2460) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_57_9 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2462) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2462) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2463) all_57_2 = e0 & op(e2, e3) = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2453), (2463) are inconsistent by sub-proof % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #166. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_57_3 = e0 & op(e2, e2) = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) op(e2, e2) = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2385), (2465), (function-axioms) are % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) all_57_5 = e0 & op(e2, e1) = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2467) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) all_57_5 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2469) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) all_57_1 = e0 & op(e3, e2) = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2470) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) all_57_1 = e0 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (2387), (2442), (2472) are inconsistent by % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #207. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) all_57_8 = e1 & op(e1, e1) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (285), (2162), (2474) are inconsistent by % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #86. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) all_57_14 = e1 & op(e0, e1) = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2475) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) all_57_14 = e1 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2477) gives: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_57_4 = e3 & op(e3, e1) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2478) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479) op(e3, e1) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (323), (2435), (2479) are inconsistent by % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #160. % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2480) all_57_5 = e3 & op(e2, e1) = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2480) implies: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2481) all_57_5 = e3 % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2468), (2481) imply: % 129.70/18.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2447), (2482) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) all_53_3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (344), (2428), (2483) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #299. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2484) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) all_57_8 = e3 & op(e1, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2485) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) op(e1, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2167), (2486), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) all_57_14 = e3 & op(e0, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2487) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) all_57_14 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2476), (2488) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) e3 = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2461), (2489) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_57_9 = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (249), (320), (323), (2215), % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435), (2471), (2490) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) all_57_3 = e0 & op(e2, e2) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2491) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) op(e2, e2) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2385), (2492), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2493) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) all_57_7 = e0 & op(e1, e2) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2494) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) all_57_7 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2458), (2495) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2496) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2447), (2497) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) all_53_3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (344), (2428), (2498) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #299. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) all_57_13 = e0 & op(e0, e2) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2499) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) op(e0, e2) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (256), (263), (427), (440), (665), (2401), % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) are inconsistent by sub-proof #143. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) all_57_10 = e0 & op(e2, e0) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2501) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_57_10 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2503) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_57_2 = e3 & op(e2, e3) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (2453), (2504) are inconsistent by sub-proof % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #85. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_57_3 = e3 & op(e2, e2) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (439), (2505), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2506) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) all_57_5 = e3 & op(e2, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2507) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_57_5 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2509) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) all_57_2 = e2 & op(e2, e3) = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2510) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) all_57_2 = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2453), (2511) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) e2 = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2512) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) e2 = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (2513) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) $false % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2514) is inconsistent. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) all_57_3 = e2 & op(e2, e2) = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2515) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) op(e2, e2) = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (300), (2383), (2516) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2389) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) all_57_5 = e2 & op(e2, e1) = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2508), (2517) are inconsistent by sub-proof % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #303. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2394), (2502) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) e2 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2518) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) e2 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (2519) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) $false % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2520) is inconsistent. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_57_10 = e3 & op(e2, e0) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2521) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_57_10 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2502), (2522) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2523) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (2524) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) $false % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2525) is inconsistent. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) all_57_10 = e3 & op(e2, e0) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2526) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) all_57_10 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2394), (2527) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) e3 = e2 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (2528) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) $false % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2529) is inconsistent. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2530) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) all_57_11 = e3 & op(e1, e0) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (2437), (2531), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) all_57_15 = e3 & op(e0, e0) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2532) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) all_57_15 = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) all_57_15 = e0 & op(e0, e0) = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2534) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_57_15 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2533), (2535) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2536) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) e3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2447), (2537) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_53_3 = e0 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (344), (2428), (2538) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #299. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (261), (262), (265), (2417), (2418), % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2419), (2539) are inconsistent by sub-proof #236. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2540) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) all_57_8 = e3 & op(e1, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2541) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) op(e1, e1) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2167), (2542), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) all_57_11 = e3 & op(e1, e0) = e3 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (2437), (2543), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | (2544) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2544) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) all_57_6 = e1 & op(e1, e3) = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2545) implies: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) op(e1, e3) = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) ~ (op(e1, e0) = e1) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2431), (2547) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) $false % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2548) is inconsistent. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) all_53_14 = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (2549) imply: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) ~ (all_53_2 = e1) % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (2546), (2550) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) all_57_12 = e1 & op(e0, e3) = e1 % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2441), (2551), (function-axioms) are % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #272. % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | (2552) op(e2, e1) = e1 % 129.70/18.28 | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | | REF_CLOSE: (332), (2384), (2552) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | | sub-proof #334. % 129.70/18.28 | | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | (2553) op(e2, e1) = e2 % 129.70/18.28 | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | | REF_CLOSE: (304), (2165), (2553) are inconsistent by % 129.70/18.28 | | | | | | | | | | | | sub-proof #347. % 129.70/18.28 | | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | | % 129.70/18.28 | | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | | % 129.70/18.28 | | | | | | | | | End of split % 129.70/18.28 | | | | | | | | | % 129.70/18.28 | | | | | | | | End of split % 129.70/18.28 | | | | | | | | % 129.70/18.28 | | | | | | | Case 2: % 129.70/18.28 | | | | | | | | % 129.70/18.28 | | | | | | | | (2554) op(e1, e2) = e2 % 129.70/18.28 | | | | | | | | % 129.70/18.28 | | | | | | | | REF_CLOSE: (337), (2164), (2554) are inconsistent by sub-proof % 129.70/18.28 | | | | | | | | #326. % 129.70/18.28 | | | | | | | | % 129.70/18.28 | | | | | | | End of split % 129.70/18.28 | | | | | | | % 129.70/18.28 | | | | | | End of split % 129.70/18.28 | | | | | | % 129.70/18.28 | | | | | Case 2: % 129.70/18.28 | | | | | | % 129.70/18.29 | | | | | | (2555) all_10_2 = e3 % 129.70/18.29 | | | | | | (2556) op(e0, e3) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e2) % 129.70/18.29 | | | | | | | ( ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & % 129.70/18.29 | | | | | | $i(all_10_0))) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | ALPHA: (2556) implies: % 129.70/18.29 | | | | | | (2557) op(e0, e3) = all_10_1 % 129.70/18.29 | | | | | | (2558) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, e2) = % 129.70/18.29 | | | | | | all_10_0 & $i(all_10_0)) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | COMBINE_EQS: (395), (2555) imply: % 129.70/18.29 | | | | | | (2559) all_8_2 = e3 % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | COMBINE_EQS: (387), (2559) imply: % 129.70/18.29 | | | | | | (2560) all_16_2 = e3 % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | REDUCE: (416), (2559) imply: % 129.70/18.29 | | | | | | (2561) ~ (all_53_3 = e3) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | REDUCE: (434), (2559) imply: % 129.70/18.29 | | | | | | (2562) ~ (all_53_11 = e3) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | REDUCE: (435), (2559) imply: % 129.70/18.29 | | | | | | (2563) ~ (all_53_12 = e3) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | REDUCE: (436), (2559) imply: % 129.70/18.29 | | | | | | (2564) ~ (all_53_13 = e3) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | REDUCE: (437), (2559) imply: % 129.70/18.29 | | | | | | (2565) ~ (all_53_14 = e3) % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | BETA: splitting (64) gives: % 129.70/18.29 | | | | | | % 129.70/18.29 | | | | | | Case 1: % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | (2566) ~ (all_16_2 = e3) % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | REDUCE: (2560), (2566) imply: % 129.70/18.29 | | | | | | | (2567) $false % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | CLOSE: (2567) is inconsistent. % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | Case 2: % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | (2568) op(e0, e3) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = % 129.70/18.29 | | | | | | | e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 129.70/18.29 | | | | | | | $i(all_16_0))) % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | ALPHA: (2568) implies: % 129.70/18.29 | | | | | | | (2569) op(e0, e3) = all_16_1 % 129.70/18.29 | | | | | | | (2570) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = % 129.70/18.29 | | | | | | | all_16_0 & $i(all_16_0)) % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | BETA: splitting (222) gives: % 129.70/18.29 | | | | | | | % 129.70/18.29 | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | (2571) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & % 129.70/18.29 | | | | | | | | op(e0, e2) = e3) % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | BETA: splitting (2571) gives: % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | (2572) all_57_12 = e3 & op(e0, e3) = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | ALPHA: (2572) implies: % 129.70/18.29 | | | | | | | | | (2573) op(e0, e3) = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | REF_CLOSE: (259), (343), (2561), (2573) are inconsistent by % 129.70/18.29 | | | | | | | | | sub-proof #311. % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | (2574) all_57_13 = e3 & op(e0, e2) = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | ALPHA: (2574) implies: % 129.70/18.29 | | | | | | | | | (2575) all_57_13 = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | BETA: splitting (225) gives: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | (2576) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 129.70/18.29 | | | | | | | | | | e3 & op(e2, e0) = e3) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REF_CLOSE: (178), (324), (2563), (2564), (2576), % 129.70/18.29 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.29 | | | | | | | | | | #82. % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | (2577) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 129.70/18.29 | | | | | | | | | | e3 & op(e0, e0) = e3) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (51), (174), % 129.70/18.29 | | | | | | | | | | (219), (220), (221), (440), (2565), (2575), % 129.70/18.29 | | | | | | | | | | (2577), (function-axioms) are inconsistent by % 129.70/18.29 | | | | | | | | | | sub-proof #76. % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | End of split % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | End of split % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | (2578) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & % 129.70/18.29 | | | | | | | | op(e0, e0) = e3) % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | BETA: splitting (2578) gives: % 129.70/18.29 | | | | | | | | % 129.70/18.29 | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | (2579) all_57_14 = e3 & op(e0, e1) = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | REF_CLOSE: (171), (2562), (2579), (function-axioms) are % 129.70/18.29 | | | | | | | | | inconsistent by sub-proof #121. % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | (2580) all_57_15 = e3 & op(e0, e0) = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | ALPHA: (2580) implies: % 129.70/18.29 | | | | | | | | | (2581) all_57_15 = e3 % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | BETA: splitting (344) gives: % 129.70/18.29 | | | | | | | | | % 129.70/18.29 | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | (2582) ~ (op(e0, e3) = e3) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 129.70/18.29 | | | | | | | | | | all_10_1, e3, e0, simplifying with (173), (2557) % 129.70/18.29 | | | | | | | | | | gives: % 129.70/18.29 | | | | | | | | | | (2583) all_53_3 = all_10_1 % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 129.70/18.29 | | | | | | | | | | all_16_1, e3, e0, simplifying with (173), (2569) % 129.70/18.29 | | | | | | | | | | gives: % 129.70/18.29 | | | | | | | | | | (2584) all_53_3 = all_16_1 % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | PRED_UNIFY: (9), (2582) imply: % 129.70/18.29 | | | | | | | | | | (2585) ~ (unit = e0) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | PRED_UNIFY: (2569), (2582) imply: % 129.70/18.29 | | | | | | | | | | (2586) ~ (all_16_1 = e3) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | COMBINE_EQS: (2583), (2584) imply: % 129.70/18.29 | | | | | | | | | | (2587) all_16_1 = all_10_1 % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | SIMP: (2587) implies: % 129.70/18.29 | | | | | | | | | | (2588) all_16_1 = all_10_1 % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | COMBINE_EQS: (259), (2583) imply: % 129.70/18.29 | | | | | | | | | | (2589) all_55_12 = all_10_1 % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REDUCE: (154), (2583) imply: % 129.70/18.29 | | | | | | | | | | (2590) ~ (all_53_7 = all_10_1) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | SIMP: (2590) implies: % 129.70/18.29 | | | | | | | | | | (2591) ~ (all_53_7 = all_10_1) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REDUCE: (153), (2583) imply: % 129.70/18.29 | | | | | | | | | | (2592) ~ (all_53_11 = all_10_1) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | SIMP: (2592) implies: % 129.70/18.29 | | | | | | | | | | (2593) ~ (all_53_11 = all_10_1) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REDUCE: (407), (2583) imply: % 129.70/18.29 | | | | | | | | | | (2594) ~ (all_10_1 = all_4_2) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | REDUCE: (2586), (2588) imply: % 129.70/18.29 | | | | | | | | | | (2595) ~ (all_10_1 = e3) % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | BETA: splitting (58) gives: % 129.70/18.29 | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | (2596) ~ (all_12_2 = e2) % 129.70/18.29 | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | BETA: splitting (61) gives: % 129.70/18.29 | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | (2597) ~ (all_14_2 = e2) % 129.70/18.29 | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | REDUCE: (382), (2597) imply: % 129.70/18.29 | | | | | | | | | | | | (2598) ~ (all_4_2 = e2) % 129.70/18.29 | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | BETA: splitting (67) gives: % 129.70/18.29 | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | (2599) ~ (all_18_2 = e3) % 129.70/18.29 | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | REDUCE: (391), (2599) imply: % 129.70/18.29 | | | | | | | | | | | | | (2600) ~ (all_12_2 = e3) % 129.70/18.29 | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | BETA: splitting (73) gives: % 129.70/18.29 | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | (2601) ~ (all_22_2 = e0) % 129.70/18.29 | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | REDUCE: (389), (2601) imply: % 129.70/18.29 | | | | | | | | | | | | | | (2602) ~ (all_12_2 = e0) % 129.70/18.29 | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | BETA: splitting (208) gives: % 129.70/18.29 | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | (2603) all_55_10 = e3 % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | REF_CLOSE: (278), (2600), (2603) are inconsistent by % 129.70/18.29 | | | | | | | | | | | | | | | sub-proof #282. % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | (2604) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | BETA: splitting (2604) gives: % 129.70/18.29 | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | (2605) all_55_10 = e2 % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2596), (2605) are inconsistent by % 129.70/18.29 | | | | | | | | | | | | | | | | sub-proof #281. % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | (2606) all_55_10 = e1 | all_55_10 = e0 % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | BETA: splitting (2606) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | (2607) all_55_10 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (2607) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2608) all_12_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | SIMP: (2608) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2609) all_12_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (2609) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2610) all_22_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | REDUCE: (426), (2609) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2611) ~ (all_53_6 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | REDUCE: (431), (2609) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2612) ~ (all_53_11 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | REDUCE: (433), (2609) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2613) ~ (all_53_14 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | REDUCE: (57), (2609) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | (2614) op(e1, e1) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | (2615) ~ (all_26_2 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | REDUCE: (374), (2615) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | | (2616) ~ (all_6_2 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2617) ~ (all_34_2 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2617) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2618) ~ (all_4_2 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (103), (212), (217), (279), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (282), (295), (304), (316), (328), (342), (398), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (405), (423), (425), (438), (439), (663), (2585), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2598), (2611), (2616), (2618) are inconsistent by % 129.70/18.29 | | | | | | | | | | | | | | | | | | | sub-proof #231. % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2619) all_34_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (367), (2619) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2620) all_4_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | SIMP: (2620) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2621) all_4_2 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | REDUCE: (413), (2621) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2622) ~ (all_53_12 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | REDUCE: (2598), (2621) imply: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | (2623) ~ (e2 = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | (2624) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2624) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2625) all_57_1 = e1 & op(e3, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2625) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2626) op(e3, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (103), (150), (184), (212), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (217), (279), (282), (295), (304), (316), (328), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (342), (398), (405), (409), (417), (423), (425), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (438), (439), (663), (2585), (2598), (2626), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | #75. % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2627) all_57_3 = e1 & op(e2, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (2616), (2627), (function-axioms) are % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #254. % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | (2628) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2628) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2629) all_57_7 = e1 & op(e1, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2629) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2630) op(e1, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (2611), (2630) are inconsistent by % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | sub-proof #341. % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2631) all_57_13 = e1 & op(e0, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2631) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2632) all_57_13 = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | (2633) op(e0, e2) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | (2634) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2634) gives: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (2635) all_57_9 = e1 & op(e3, e0) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (2622), (2635), (function-axioms) are % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (2636) all_57_10 = e1 & op(e2, e0) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2636) implies: % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (2637) op(e2, e0) = e1 % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (13), (14), (15), (16), (18), (131), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (172), (178), (206), (219), (221), (265), (284), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (331), (332), (663), (2558), (2570), (2581), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (2585), (2588), (2589), (2591), (2593), (2595), % 129.70/18.29 | | | | | | | | | | | | | | | | | | | | | | | (2610), (2614), (2632), (2633), (2637), % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | #72. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2638) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (2613), (2638), % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | #283. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2639) all_26_2 = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2639) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2640) all_6_2 = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | REDUCE: (421), (2640) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2641) ~ (all_53_7 = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | REDUCE: (423), (2640) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2642) ~ (all_53_9 = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2643) ~ (op(e2, e1) = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | (2644) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2644) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2645) all_57_12 = e1 & op(e0, e3) = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2645) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2646) op(e0, e3) = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, e1, % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (2557), (2646) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2647) all_10_1 = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (2643) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2648) ~ (unit = e2) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2594), (2647) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2649) ~ (all_4_2 = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (2649) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2650) ~ (all_4_2 = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2651) all_55_0 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2651) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2652) all_4_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (2652) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2653) ~ (all_53_2 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (342), (663), (2585), (2648), (2653) are % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2654) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (316), (438), (2598), (2650), (2654) are % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2655) all_57_13 = e1 & op(e0, e2) = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (2641), (2655), (function-axioms) are % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | (2656) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (440), (2612), (2656), % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | #293. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2657) op(e2, e1) = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (2642), (2657) are inconsistent by % 129.70/18.30 | | | | | | | | | | | | | | | | | | | sub-proof #334. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | (2658) all_55_10 = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2602), (2658) are inconsistent by % 129.70/18.30 | | | | | | | | | | | | | | | | | sub-proof #219. % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | (2659) all_22_2 = e0 % 129.70/18.30 | | | | | | | | | | | | | | (2660) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 129.70/18.30 | | | | | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 129.70/18.30 | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | ALPHA: (2660) implies: % 129.70/18.30 | | | | | | | | | | | | | | (2661) op(e1, e0) = all_22_1 % 129.70/18.30 | | | | | | | | | | | | | | (2662) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 129.70/18.30 | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0)) % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | COMBINE_EQS: (389), (2659) imply: % 129.70/18.30 | | | | | | | | | | | | | | (2663) all_12_2 = e0 % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | SIMP: (2663) implies: % 129.70/18.30 | | | | | | | | | | | | | | (2664) all_12_2 = e0 % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | COMBINE_EQS: (359), (2664) imply: % 129.70/18.30 | | | | | | | | | | | | | | (2665) all_38_2 = e0 % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | REDUCE: (415), (2664) imply: % 129.70/18.30 | | | | | | | | | | | | | | (2666) ~ (all_53_2 = e0) % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | REDUCE: (433), (2664) imply: % 129.70/18.30 | | | | | | | | | | | | | | (2667) ~ (all_53_14 = e0) % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | BETA: splitting (97) gives: % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | (2668) ~ (all_38_2 = e0) % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | REDUCE: (2665), (2668) imply: % 129.70/18.30 | | | | | | | | | | | | | | | (2669) $false % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | CLOSE: (2669) is inconsistent. % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | (2670) op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 129.70/18.30 | | | | | | | | | | | | | | | (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, % 129.70/18.30 | | | | | | | | | | | | | | | e2) = all_38_0 & $i(all_38_0))) % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | ALPHA: (2670) implies: % 129.70/18.30 | | | | | | | | | | | | | | | (2671) op(e1, e0) = all_38_1 % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | (2672) ~ (op(e1, e0) = e0) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 129.70/18.30 | | | | | | | | | | | | | | | | all_22_1, e0, e1, simplifying with (174), (2661) % 129.70/18.30 | | | | | | | | | | | | | | | | gives: % 129.70/18.30 | | | | | | | | | | | | | | | | (2673) all_53_14 = all_22_1 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 129.70/18.30 | | | | | | | | | | | | | | | | all_38_1, e0, e1, simplifying with (174), (2671) % 129.70/18.30 | | | | | | | | | | | | | | | | gives: % 129.70/18.30 | | | | | | | | | | | | | | | | (2674) all_53_14 = all_38_1 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (2672) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2675) ~ (unit = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | PRED_UNIFY: (2671), (2672) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2676) ~ (all_38_1 = e0) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | COMBINE_EQS: (2673), (2674) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2677) all_38_1 = all_22_1 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | SIMP: (2677) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | (2678) all_38_1 = all_22_1 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2673) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2679) all_55_11 = all_22_1 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | REDUCE: (155), (2673) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2680) ~ (all_53_2 = all_22_1) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | REDUCE: (140), (2673) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2681) ~ (all_53_6 = all_22_1) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | REDUCE: (2676), (2678) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | (2682) ~ (all_22_1 = e0) % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | (2683) unit = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (9), (2683) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2684) op(e2, e3) = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (4), (2683) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2685) op(e2, e2) = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (157), (163), (177), (207), (210), % 129.70/18.30 | | | | | | | | | | | | | | | | | (279), (280), (282), (302), (306), (340), (374), % 129.70/18.30 | | | | | | | | | | | | | | | | | (425), (663), (2662), (2666), (2675), (2679), % 129.70/18.30 | | | | | | | | | | | | | | | | | (2680), (2681), (2682), (2684), (2685), % 129.70/18.30 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.30 | | | | | | | | | | | | | | | | | #71. % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | (2686) unit = e1 | unit = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (324), (2563), (2675), (2686) are % 129.70/18.30 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #185. % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | (2687) op(e1, e0) = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | REF_CLOSE: (329), (2667), (2687) are inconsistent by % 129.70/18.30 | | | | | | | | | | | | | | | | sub-proof #355. % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | End of split % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | (2688) all_18_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | COMBINE_EQS: (391), (2688) imply: % 129.70/18.30 | | | | | | | | | | | | | (2689) all_12_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | SIMP: (2689) implies: % 129.70/18.30 | | | | | | | | | | | | | (2690) all_12_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | REDUCE: (415), (2690) imply: % 129.70/18.30 | | | | | | | | | | | | | (2691) ~ (all_53_2 = e3) % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | REDUCE: (429), (2690) imply: % 129.70/18.30 | | | | | | | | | | | | | (2692) ~ (all_53_9 = e3) % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | REDUCE: (57), (2690) imply: % 129.70/18.30 | | | | | | | | | | | | | (2693) op(e1, e1) = e3 % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | BETA: splitting (342) gives: % 129.70/18.30 | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | (2694) ~ (op(e1, e3) = e3) % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | BETA: splitting (241) gives: % 129.70/18.30 | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | (2695) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | BETA: splitting (2695) gives: % 129.70/18.30 | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | (2696) all_57_1 = e3 & op(e3, e2) = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | ALPHA: (2696) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | (2697) op(e3, e2) = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | (2698) ~ (op(e3, e2) = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | PRED_UNIFY: (2697), (2698) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2699) $false % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | CLOSE: (2699) is inconsistent. % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | (2700) all_55_1 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (2700) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2701) all_53_4 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (149), (2701) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2702) ~ (all_53_7 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | SIMP: (2702) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2703) ~ (all_53_7 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (147), (2701) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2704) ~ (all_53_12 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (417), (2701) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2705) ~ (all_6_2 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | REDUCE: (409), (2701) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2706) ~ (all_4_2 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | SIMP: (2706) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | | (2707) ~ (all_4_2 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2708) all_55_0 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2708) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2709) all_4_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | REDUCE: (2707), (2709) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2710) $false % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | CLOSE: (2710) is inconsistent. % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2711) ~ (all_55_0 = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | | (2712) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2713) all_55_0 = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2713) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2714) all_4_2 = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | REDUCE: (2598), (2714) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2715) $false % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | CLOSE: (2715) is inconsistent. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | (2716) all_55_0 = e1 | all_55_0 = e0 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | (2717) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2717) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2718) all_57_0 = e3 & op(e3, e3) = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (319), (382), (2707), (2718) are inconsistent by % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | sub-proof #206. % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2719) all_57_2 = e3 & op(e2, e3) = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2719) implies: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | (2720) all_57_2 = e3 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2716) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2721) all_55_0 = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2721) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2722) all_4_2 = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2594), (2722) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2723) ~ (all_10_1 = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (2694) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | (2724) ~ (unit = e1) % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | (2725) unit = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2725) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | (2726) op(e2, e1) = e1 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2725) imply: % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | (2727) op(e2, e2) = e2 % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.30 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (2725) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | (2728) op(e0, e2) = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2729) ~ (op(e2, e2) = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2727), (2729) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2730) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2730) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2731) all_26_2 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2731) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_6_2 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2732) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_6_2 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (2733) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2734) all_50_2 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (2733) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2735) ~ (all_53_9 = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (2733) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2736) ~ (all_53_13 = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (2733) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (2737) ~ (e3 = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2738) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2738) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) all_57_2 = e2 & op(e2, e3) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2739) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) all_57_2 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2720), (2740) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) e3 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (2741) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2742) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) all_57_3 = e2 & op(e2, e2) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2743) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) all_57_3 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) ~ (op(e2, e1) = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2726), (2745) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2746) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2746) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_53_9 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (2747) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2748) ~ (all_53_13 = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2748) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2749) ~ (all_53_13 = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2692), (2747) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (e3 = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2735), (2747) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2751) ~ (e2 = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2752) ~ (op(e0, e2) = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2728), (2752) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2753) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2753) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_55_13 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (2754) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_53_7 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2755) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756) ~ (all_53_11 = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2756) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757) ~ (all_53_11 = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2591), (2755) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2758) ~ (all_10_1 = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2758) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2759) ~ (all_10_1 = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2703), (2755) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) ~ (e3 = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2761) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2761) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2762) all_57_2 = e1 & op(e2, e3) = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2762) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2763) all_57_2 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2720), (2763) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) e3 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (2764) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2765) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_57_3 = e1 & op(e2, e2) = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2766) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) all_57_3 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2744), (2767) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) e2 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2734), (2768) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_50_2 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (300), (2727), (2769) are inconsistent by % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2770) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) all_57_5 = e1 & op(e2, e1) = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2771) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) all_57_5 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) all_55_12 = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2589), (2773) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_10_1 = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2595), (2774) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2775) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) ~ (all_55_12 = e3) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2777) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) all_55_12 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2589), (2778) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_10_1 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2593), (2779) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) ~ (all_53_11 = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2781) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_57_4 = e2 & op(e3, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2782) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_57_4 = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2784) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) all_57_4 = e0 & op(e3, e1) = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2785) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) all_57_4 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2783), (2786) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) e2 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2787) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) e2 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2734), (2788) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) all_50_2 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (300), (2727), (2789) are inconsistent by % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_57_5 = e0 & op(e2, e1) = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2790) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) all_57_5 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2772), (2791) are inconsistent by sub-proof % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (265), (2693), (2757), (2792), % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #69. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) all_57_5 = e2 & op(e2, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2793) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) op(e2, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (2735), (2794) are inconsistent by % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #347. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2795) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_57_8 = e2 & op(e1, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2796) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) op(e1, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2693), (2797), (function-axioms) are % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_57_14 = e2 & op(e0, e1) = e2 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (2780), (2798), (function-axioms) are % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #119. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) all_55_12 = e1 | all_55_12 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2589), (2723), (2759), (2799) are inconsistent by % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #74. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) all_57_10 = e1 & op(e2, e0) = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (2749), (2800), (function-axioms) are % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2801) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (306), (2735), (2736), (2801) are % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | (2802) unit = e1 | unit = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (324), (2563), (2724), (2802) are % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #185. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | (2803) all_55_0 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (2803) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | (2804) all_4_2 = e0 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (438), (2804) imply: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | (2805) $false % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2805) is inconsistent. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | (2806) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2806) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | (2807) all_57_6 = e3 & op(e1, e3) = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2694), (2807) are inconsistent by sub-proof #181. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | (2808) all_57_12 = e3 & op(e0, e3) = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2582), (2808) are inconsistent by sub-proof #68. % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | (2809) all_57_3 = e3 & op(e2, e2) = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | REF_CLOSE: (48), (439), (2809), (function-axioms) are % 129.70/18.31 | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | End of split % 129.70/18.31 | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | (2810) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 129.70/18.31 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 129.70/18.31 | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | BETA: splitting (2810) gives: % 129.70/18.31 | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | (2811) all_57_7 = e3 & op(e1, e2) = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | ALPHA: (2811) implies: % 129.70/18.31 | | | | | | | | | | | | | | | | (2812) all_57_7 = e3 % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 129.70/18.31 | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | Case 1: % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | (2813) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 129.70/18.31 | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (226), (228), % 129.70/18.31 | | | | | | | | | | | | | | | | | (2693), (2812), (2813), (function-axioms) are % 129.70/18.31 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #95. % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | Case 2: % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.31 | | | | | | | | | | | | | | | | | (2814) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 129.70/18.31 | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 129.70/18.31 | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | BETA: splitting (2814) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | (2815) all_57_8 = e1 & op(e1, e1) = e1 % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | ALPHA: (2815) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | | | (2816) op(e1, e1) = e1 % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (285), (2690), (2816) are inconsistent by % 129.70/18.32 | | | | | | | | | | | | | | | | | | sub-proof #174. % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | (2817) all_57_11 = e1 & op(e1, e0) = e1 % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | ALPHA: (2817) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | | | (2818) all_57_11 = e1 % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | (2819) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (2819) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | (2820) all_57_6 = e2 & op(e1, e3) = e2 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (2820) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | (2821) all_57_6 = e2 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | (2822) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2822) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2823) all_57_6 = e0 & op(e1, e3) = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2821), (2823) are inconsistent by sub-proof % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | #132. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2824) all_57_7 = e0 & op(e1, e2) = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (2812), (2824) are inconsistent by sub-proof % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | #307. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | (2825) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2825) gives: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2826) all_57_8 = e0 & op(e1, e1) = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2826) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2827) op(e1, e1) = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (2693), (2827), (function-axioms) are % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2828) all_57_11 = e0 & op(e1, e0) = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2829) all_57_11 = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2818), (2829) imply: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2830) e1 = e0 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (2830) imply: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | (2831) $false % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2831) is inconsistent. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | (2832) all_57_7 = e2 & op(e1, e2) = e2 % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (2812), (2832) are inconsistent by sub-proof % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | #306. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | (2833) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 129.70/18.32 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (2693), (2818), (2833), % 129.70/18.32 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.32 | | | | | | | | | | | | | | | | | | | #171. % 129.70/18.32 | | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | (2834) all_57_13 = e3 & op(e0, e2) = e3 % 129.70/18.32 | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | ALPHA: (2834) implies: % 129.70/18.32 | | | | | | | | | | | | | | | | (2835) all_57_13 = e3 % 129.70/18.32 | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (51), (219), % 129.70/18.32 | | | | | | | | | | | | | | | | (220), (221), (440), (2581), (2835), % 129.70/18.32 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.70/18.32 | | | | | | | | | | | | | | | | #77. % 129.70/18.32 | | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | (2836) op(e1, e3) = e3 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | REF_CLOSE: (342), (2691), (2836) are inconsistent by % 129.70/18.32 | | | | | | | | | | | | | | sub-proof #323. % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | End of split % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | (2837) all_14_2 = e2 % 129.70/18.32 | | | | | | | | | | | | (2838) op(e3, e2) = all_14_1 & $i(all_14_1) & ( ~ % 129.70/18.32 | | | | | | | | | | | | (all_14_1 = e0) | ( ~ (all_14_0 = e1) & op(e3, % 129.70/18.32 | | | | | | | | | | | | e0) = all_14_0 & $i(all_14_0))) % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | ALPHA: (2838) implies: % 129.70/18.32 | | | | | | | | | | | | (2839) op(e3, e2) = all_14_1 % 129.70/18.32 | | | | | | | | | | | | (2840) ~ (all_14_1 = e0) | ( ~ (all_14_0 = e1) & op(e3, % 129.70/18.32 | | | | | | | | | | | | e0) = all_14_0 & $i(all_14_0)) % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | COMBINE_EQS: (382), (2837) imply: % 129.70/18.32 | | | | | | | | | | | | (2841) all_4_2 = e2 % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | COMBINE_EQS: (380), (2841) imply: % 129.70/18.32 | | | | | | | | | | | | (2842) all_32_2 = e2 % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | REDUCE: (409), (2841) imply: % 129.70/18.32 | | | | | | | | | | | | (2843) ~ (all_53_4 = e2) % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | REDUCE: (411), (2841) imply: % 129.70/18.32 | | | | | | | | | | | | (2844) ~ (all_53_8 = e2) % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | REDUCE: (2594), (2841) imply: % 129.70/18.32 | | | | | | | | | | | | (2845) ~ (all_10_1 = e2) % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | REDUCE: (45), (2841) imply: % 129.70/18.32 | | | | | | | | | | | | (2846) op(e3, e3) = e2 % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | BETA: splitting (335) gives: % 129.70/18.32 | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | (2847) ~ (op(e3, e2) = e2) % 129.70/18.32 | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | BETA: splitting (88) gives: % 129.70/18.32 | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | Case 1: % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | (2848) ~ (all_32_2 = e2) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | REDUCE: (2842), (2848) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2849) $false % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | CLOSE: (2849) is inconsistent. % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | Case 2: % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | (2850) op(e3, e2) = all_32_1 & $i(all_32_1) & ( ~ % 129.70/18.32 | | | | | | | | | | | | | | (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 129.70/18.32 | | | | | | | | | | | | | | e1) = all_32_0 & $i(all_32_0))) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | ALPHA: (2850) implies: % 129.70/18.32 | | | | | | | | | | | | | | (2851) op(e3, e2) = all_32_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 129.70/18.32 | | | | | | | | | | | | | | all_14_1, e2, e3, simplifying with (184), (2839) % 129.70/18.32 | | | | | | | | | | | | | | gives: % 129.70/18.32 | | | | | | | | | | | | | | (2852) all_53_4 = all_14_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_14_1, % 129.70/18.32 | | | | | | | | | | | | | | e2, e3, simplifying with (2839) gives: % 129.70/18.32 | | | | | | | | | | | | | | (2853) all_14_1 = e3 | ~ (op(e3, e2) = e3) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 129.70/18.32 | | | | | | | | | | | | | | all_32_1, e2, e3, simplifying with (184), (2851) % 129.70/18.32 | | | | | | | | | | | | | | gives: % 129.70/18.32 | | | | | | | | | | | | | | (2854) all_53_4 = all_32_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | PRED_UNIFY: (2847), (2851) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2855) ~ (all_32_1 = e2) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | COMBINE_EQS: (2852), (2854) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2856) all_32_1 = all_14_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | SIMP: (2856) implies: % 129.70/18.32 | | | | | | | | | | | | | | (2857) all_32_1 = all_14_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | COMBINE_EQS: (309), (2852) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2858) all_55_1 = all_14_1 % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | REDUCE: (148), (2852) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2859) ~ (all_53_8 = all_14_1) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | SIMP: (2859) implies: % 129.70/18.32 | | | | | | | | | | | | | | (2860) ~ (all_53_8 = all_14_1) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | REDUCE: (147), (2852) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2861) ~ (all_53_12 = all_14_1) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | SIMP: (2861) implies: % 129.70/18.32 | | | | | | | | | | | | | | (2862) ~ (all_53_12 = all_14_1) % 129.70/18.32 | | | | | | | | | | | | | | % 129.70/18.32 | | | | | | | | | | | | | | REDUCE: (2855), (2857) imply: % 129.70/18.32 | | | | | | | | | | | | | | (2863) ~ (all_14_1 = e2) % 129.70/18.32 | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.00/18.32 | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | (2864) ~ (all_18_2 = e3) % 130.00/18.32 | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | REDUCE: (391), (2864) imply: % 130.00/18.32 | | | | | | | | | | | | | | | (2865) ~ (all_12_2 = e3) % 130.00/18.32 | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 130.00/18.32 | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | (2866) ~ (all_22_2 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | REDUCE: (389), (2866) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | (2867) ~ (all_12_2 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | (2868) all_55_10 = e3 % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2865), (2868) are inconsistent by % 130.00/18.32 | | | | | | | | | | | | | | | | | sub-proof #282. % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | Case 2: % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | (2869) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | BETA: splitting (2869) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | (2870) all_55_10 = e2 % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2596), (2870) are inconsistent by % 130.00/18.32 | | | | | | | | | | | | | | | | | | sub-proof #281. % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | (2871) all_55_10 = e1 | all_55_10 = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | BETA: splitting (2871) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2872) all_55_10 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (2872) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2873) all_12_2 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | SIMP: (2873) implies: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2874) all_12_2 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2875) all_22_2 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (415), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2876) ~ (all_53_2 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (426), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2877) ~ (all_53_6 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (428), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2878) ~ (all_53_8 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (429), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2879) ~ (all_53_9 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (431), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2880) ~ (all_53_11 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | REDUCE: (433), (2874) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | (2881) ~ (all_53_14 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | (2882) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (332), (2878), (2879), (2882) are % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #154. % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | (2883) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2883) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | (2884) all_57_8 = e1 & op(e1, e1) = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | (2885) all_57_8 = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | (2886) ~ (all_26_2 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2886) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | (2887) ~ (all_6_2 = e1) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2888) ~ (all_42_2 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (2888) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2889) ~ (all_6_2 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (212), (279), (282), (295), (304), % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (334), (423), (439), (663), (2877), (2880), % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2887), (2889) are inconsistent by sub-proof #249. % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2890) all_42_2 = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (2890) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2891) all_6_2 = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2891) implies: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2892) all_6_2 = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (2892) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2893) ~ (all_53_6 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (2892) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2894) ~ (all_53_13 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (2892) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | (2895) ~ (e3 = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | (2896) ~ (op(e2, e0) = e0) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (2896) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | (2897) ~ (unit = e2) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2898) unit = e2 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2897), (2898) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2899) $false % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2899) is inconsistent. % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | (2900) unit = e1 | unit = e0 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2900) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) unit = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2901) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) op(e1, e3) = e3 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2901) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) op(e1, e2) = e2 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (2901) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) op(e1, e1) = e1 % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) ~ (op(e1, e3) = e3) % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2902), (2905) imply: % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) $false % 130.00/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2906) is inconsistent. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) all_55_8 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (2907) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) all_53_2 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (2908) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) ~ (all_53_6 = e3) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2909) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) ~ (all_53_6 = e3) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) ~ (op(e2, e1) = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4), (2911) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (unit = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (279), (282), (663), (2585), (2877), (2912) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #253. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2913) all_55_6 = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2913) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2914) all_53_9 = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2914) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2915) ~ (all_53_11 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2915) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2916) ~ (all_53_11 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917) ~ (op(e1, e2) = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2903), (2917) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2918) $false % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2918) is inconsistent. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) all_55_9 = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2919) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) all_53_6 = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2920) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) ~ (all_53_7 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2921) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) ~ (all_53_7 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2920) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) ~ (all_53_14 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2923) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) ~ (all_53_14 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2910), (2920) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) ~ (e3 = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (9), (13), (14), (15), (16), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (17), (18), (45), (48), (51), (135), (163), (171), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (183), (212), (223), (226), (228), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (232), (233), (237), (239), (240), (241), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (247), (249), (258), (262), (263), (279), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282), (284), (286), (295), (301), (304), (320), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323), (324), (337), (338), (339), (340), (342), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (419), (421), (423), (438), (439), (440), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663), (2841), (2844), (2846), (2847), (2853), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2860), (2875), (2877), (2878), (2881), (2885), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887), (2904), (2916), (2922), (2924), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #117. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) ~ (unit = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2585), (2900), (2926) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | (2927) op(e2, e0) = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (328), (2894), (2927) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #356. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | (2928) all_26_2 = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (2928) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | (2929) all_6_2 = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2929) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | (2930) all_6_2 = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (2930) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | (2931) ~ (all_53_13 = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | (2932) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2932) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | (2933) all_57_9 = e1 & op(e3, e0) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2933) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | (2934) op(e3, e0) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2935) ~ (op(e2, e1) = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (182), (2934) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_53_12 = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (2935) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2937) ~ (unit = e2) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2862), (2936) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2938) ~ (all_14_1 = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2938) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2939) ~ (all_14_1 = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) unit = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2937), (2940) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) $false % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2941) is inconsistent. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) unit = e1 | unit = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2840) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_14_1 = e0) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2942) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) unit = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (2944) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) op(e0, e1) = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) ~ (op(e0, e1) = e0) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (2945), (2946) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2947) $false % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2947) is inconsistent. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2948) all_53_11 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2948) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2949) ~ (all_53_8 = e0) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2950) all_55_1 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2858), (2950) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2951) all_14_1 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2951) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2952) all_14_1 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2860), (2952) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) ~ (all_53_8 = e3) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (308), (2844), (2878), (2949), (2953) are % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2858), (2863), (2939), (2943), (2954) are % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) ~ (unit = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2585), (2942), (2955) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) ~ (all_14_0 = e1) & op(e3, e0) = all_14_0 & % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_0) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2956) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) ~ (all_14_0 = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) op(e3, e0) = all_14_0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2934), (2957), (2958), (function-axioms) are % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2959) op(e2, e1) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (2879), (2959) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | (2960) all_57_10 = e1 & op(e2, e0) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (2931), (2960), (function-axioms) are % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | (2961) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (286), (440), (2881), (2961), % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | #283. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | (2962) all_57_14 = e1 & op(e0, e1) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2962) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | (2963) op(e0, e1) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (2880), (2963) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | sub-proof #333. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | (2964) all_55_10 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2867), (2964) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | | | sub-proof #219. % 130.00/18.33 | | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | (2965) all_22_2 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (2965) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | (2966) all_12_2 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | SIMP: (2966) implies: % 130.00/18.33 | | | | | | | | | | | | | | | | (2967) all_12_2 = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | REDUCE: (433), (2967) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | (2968) ~ (all_53_14 = e0) % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | (2969) ~ (op(e1, e0) = e0) % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (2969) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | (2970) ~ (unit = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2971) unit = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REDUCE: (7), (2971) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2972) op(e2, e1) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REDUCE: (4), (2971) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2973) op(e2, e2) = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REDUCE: (3), (2971) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2974) op(e1, e2) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REDUCE: (2), (2971) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2975) op(e0, e2) = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (51), (132), (142), (172), (206), (220), % 130.00/18.33 | | | | | | | | | | | | | | | | | | (221), (258), (262), (283), (299), (300), (332), % 130.00/18.33 | | | | | | | | | | | | | | | | | | (334), (339), (399), (400), (419), (421), (439), % 130.00/18.33 | | | | | | | | | | | | | | | | | | (440), (2570), (2581), (2588), (2589), (2591), % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2595), (2845), (2972), (2973), (2974), (2975), % 130.00/18.33 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.33 | | | | | | | | | | | | | | | | | | #66. % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | (2976) unit = e1 | unit = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (324), (2563), (2970), (2976) are % 130.00/18.33 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #185. % 130.00/18.33 | | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | (2977) op(e1, e0) = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (329), (2968), (2977) are inconsistent by % 130.00/18.33 | | | | | | | | | | | | | | | | | sub-proof #355. % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | (2978) all_18_2 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2978) imply: % 130.00/18.33 | | | | | | | | | | | | | | | (2979) all_12_2 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | SIMP: (2979) implies: % 130.00/18.33 | | | | | | | | | | | | | | | (2980) all_12_2 = e3 % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | REDUCE: (415), (2980) imply: % 130.00/18.33 | | | | | | | | | | | | | | | (2981) ~ (all_53_2 = e3) % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.00/18.33 | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | (2982) ~ (op(e1, e3) = e3) % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (2982) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | (2983) ~ (unit = e1) % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | Case 1: % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | (2984) unit = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REDUCE: (7), (2984) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | (2985) op(e2, e1) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REDUCE: (4), (2984) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | (2986) op(e2, e2) = e2 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REDUCE: (3), (2984) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | (2987) op(e1, e2) = e1 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REDUCE: (2), (2984) imply: % 130.00/18.33 | | | | | | | | | | | | | | | | | (2988) op(e0, e2) = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (51), (132), (142), (172), (206), (220), % 130.00/18.33 | | | | | | | | | | | | | | | | | (221), (258), (262), (283), (299), (300), (332), % 130.00/18.33 | | | | | | | | | | | | | | | | | (334), (339), (399), (400), (419), (421), (439), % 130.00/18.33 | | | | | | | | | | | | | | | | | (440), (2570), (2581), (2588), (2589), (2591), % 130.00/18.33 | | | | | | | | | | | | | | | | | (2595), (2845), (2985), (2986), (2987), (2988), % 130.00/18.33 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.33 | | | | | | | | | | | | | | | | | #66. % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | (2989) unit = e1 | unit = e0 % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (324), (2563), (2983), (2989) are % 130.00/18.33 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #185. % 130.00/18.33 | | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | | End of split % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.33 | | | | | | | | | | | | | | | Case 2: % 130.00/18.33 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | (2990) op(e1, e3) = e3 % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | REF_CLOSE: (342), (2981), (2990) are inconsistent by % 130.00/18.34 | | | | | | | | | | | | | | | | sub-proof #323. % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | (2991) op(e3, e2) = e2 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | REF_CLOSE: (335), (2843), (2991) are inconsistent by % 130.00/18.34 | | | | | | | | | | | | | sub-proof #94. % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | (2992) all_12_2 = e2 % 130.00/18.34 | | | | | | | | | | | (2993) op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 130.00/18.34 | | | | | | | | | | | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, % 130.00/18.34 | | | | | | | | | | | e3) = all_12_0 & $i(all_12_0))) % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | ALPHA: (2993) implies: % 130.00/18.34 | | | | | | | | | | | (2994) op(e1, e2) = all_12_1 % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | COMBINE_EQS: (376), (2992) imply: % 130.00/18.34 | | | | | | | | | | | (2995) all_30_2 = e2 % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | REDUCE: (426), (2992) imply: % 130.00/18.34 | | | | | | | | | | | (2996) ~ (all_53_6 = e2) % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | REDUCE: (431), (2992) imply: % 130.00/18.34 | | | | | | | | | | | (2997) ~ (all_53_11 = e2) % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | BETA: splitting (85) gives: % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | (2998) ~ (all_30_2 = e2) % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | REDUCE: (2995), (2998) imply: % 130.00/18.34 | | | | | | | | | | | | (2999) $false % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | CLOSE: (2999) is inconsistent. % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | (3000) op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ % 130.00/18.34 | | | | | | | | | | | | (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e1, % 130.00/18.34 | | | | | | | | | | | | e0) = all_30_0 & $i(all_30_0))) % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | ALPHA: (3000) implies: % 130.00/18.34 | | | | | | | | | | | | (3001) op(e1, e2) = all_30_1 % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | BETA: splitting (337) gives: % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | (3002) ~ (op(e1, e2) = e2) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.00/18.34 | | | | | | | | | | | | | all_12_1, e2, e1, simplifying with (176), (2994) % 130.00/18.34 | | | | | | | | | | | | | gives: % 130.00/18.34 | | | | | | | | | | | | | (3003) all_53_6 = all_12_1 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.00/18.34 | | | | | | | | | | | | | all_30_1, e2, e1, simplifying with (176), (3001) % 130.00/18.34 | | | | | | | | | | | | | gives: % 130.00/18.34 | | | | | | | | | | | | | (3004) all_53_6 = all_30_1 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_30_1, % 130.00/18.34 | | | | | | | | | | | | | e2, e1, simplifying with (3001) gives: % 130.00/18.34 | | | | | | | | | | | | | (3005) all_30_1 = e1 | ~ (op(e1, e2) = e1) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | PRED_UNIFY: (8), (3002) imply: % 130.00/18.34 | | | | | | | | | | | | | (3006) ~ (unit = e1) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | COMBINE_EQS: (3003), (3004) imply: % 130.00/18.34 | | | | | | | | | | | | | (3007) all_30_1 = all_12_1 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | SIMP: (3007) implies: % 130.00/18.34 | | | | | | | | | | | | | (3008) all_30_1 = all_12_1 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | REDUCE: (142), (3003) imply: % 130.00/18.34 | | | | | | | | | | | | | (3009) ~ (all_53_7 = all_12_1) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | SIMP: (3009) implies: % 130.00/18.34 | | | | | | | | | | | | | (3010) ~ (all_53_7 = all_12_1) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | REDUCE: (419), (3003) imply: % 130.00/18.34 | | | | | | | | | | | | | (3011) ~ (all_12_1 = all_6_2) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | BETA: splitting (663) gives: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | (3012) unit = e2 % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (48), (51), (132), (171), (172), % 130.00/18.34 | | | | | | | | | | | | | | (220), (221), (258), (300), (302), (332), (334), % 130.00/18.34 | | | | | | | | | | | | | | (338), (374), (399), (421), (439), (440), (2581), % 130.00/18.34 | | | | | | | | | | | | | | (2997), (3005), (3008), (3010), (3011), (3012), % 130.00/18.34 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.34 | | | | | | | | | | | | | | #65. % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | (3013) unit = e1 | unit = e0 % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | REF_CLOSE: (5), (324), (2563), (3006), (3013) are % 130.00/18.34 | | | | | | | | | | | | | | inconsistent by sub-proof #185. % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | (3014) op(e1, e2) = e2 % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | REF_CLOSE: (337), (2996), (3014) are inconsistent by % 130.00/18.34 | | | | | | | | | | | | | sub-proof #326. % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | (3015) op(e0, e3) = e3 % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | REF_CLOSE: (259), (343), (2561), (3015) are inconsistent by % 130.00/18.34 | | | | | | | | | | sub-proof #311. % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | End of split % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | End of split % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | End of split % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | End of split % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | End of split % 130.00/18.34 | | | | | % 130.00/18.34 | | | | End of split % 130.00/18.34 | | | | % 130.00/18.34 | | | Case 2: % 130.00/18.34 | | | | % 130.00/18.34 | | | | (3016) all_8_2 = e1 % 130.00/18.34 | | | | (3017) op(e0, e1) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e2) | ( ~ % 130.00/18.34 | | | | (all_8_0 = e3) & op(e0, e2) = all_8_0 & $i(all_8_0))) % 130.00/18.34 | | | | % 130.00/18.34 | | | | ALPHA: (3017) implies: % 130.00/18.34 | | | | (3018) op(e0, e1) = all_8_1 % 130.00/18.34 | | | | (3019) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 % 130.00/18.34 | | | | & $i(all_8_0)) % 130.00/18.34 | | | | % 130.00/18.34 | | | | COMBINE_EQS: (396), (3016) imply: % 130.00/18.34 | | | | (3020) all_20_2 = e1 % 130.00/18.34 | | | | % 130.00/18.34 | | | | REDUCE: (416), (3016) imply: % 130.00/18.34 | | | | (3021) ~ (all_53_3 = e1) % 130.00/18.34 | | | | % 130.00/18.34 | | | | REDUCE: (427), (3016) imply: % 130.00/18.34 | | | | (3022) ~ (all_53_7 = e1) % 130.00/18.34 | | | | % 130.00/18.34 | | | | REDUCE: (434), (3016) imply: % 130.00/18.34 | | | | (3023) ~ (all_53_11 = e1) % 130.00/18.34 | | | | % 130.00/18.34 | | | | REDUCE: (435), (3016) imply: % 130.00/18.34 | | | | (3024) ~ (all_53_12 = e1) % 130.00/18.34 | | | | % 130.00/18.34 | | | | REDUCE: (437), (3016) imply: % 130.00/18.34 | | | | (3025) ~ (all_53_14 = e1) % 130.00/18.34 | | | | % 130.00/18.34 | | | | BETA: splitting (70) gives: % 130.00/18.34 | | | | % 130.00/18.34 | | | | Case 1: % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | (3026) ~ (all_20_2 = e1) % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | REDUCE: (3020), (3026) imply: % 130.00/18.34 | | | | | (3027) $false % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | CLOSE: (3027) is inconsistent. % 130.00/18.34 | | | | | % 130.00/18.34 | | | | Case 2: % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | (3028) op(e0, e1) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e3) | % 130.00/18.34 | | | | | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 & % 130.00/18.34 | | | | | $i(all_20_0))) % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | ALPHA: (3028) implies: % 130.00/18.34 | | | | | (3029) op(e0, e1) = all_20_1 % 130.00/18.34 | | | | | (3030) ~ (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, e3) = % 130.00/18.34 | | | | | all_20_0 & $i(all_20_0)) % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | BETA: splitting (220) gives: % 130.00/18.34 | | | | | % 130.00/18.34 | | | | | Case 1: % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | (3031) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & % 130.00/18.34 | | | | | | op(e0, e2) = e1) % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | BETA: splitting (3031) gives: % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | Case 1: % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | (3032) all_57_12 = e1 & op(e0, e3) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | REF_CLOSE: (173), (3021), (3032), (function-axioms) are % 130.00/18.34 | | | | | | | inconsistent by sub-proof #272. % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | Case 2: % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | (3033) all_57_13 = e1 & op(e0, e2) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | REF_CLOSE: (172), (3022), (3033), (function-axioms) are % 130.00/18.34 | | | | | | | inconsistent by sub-proof #106. % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | End of split % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | Case 2: % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | (3034) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & % 130.00/18.34 | | | | | | op(e0, e0) = e1) % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | BETA: splitting (3034) gives: % 130.00/18.34 | | | | | | % 130.00/18.34 | | | | | | Case 1: % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | (3035) all_57_14 = e1 & op(e0, e1) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | ALPHA: (3035) implies: % 130.00/18.34 | | | | | | | (3036) op(e0, e1) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | REF_CLOSE: (334), (3023), (3036) are inconsistent by sub-proof % 130.00/18.34 | | | | | | | #333. % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | Case 2: % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | (3037) all_57_15 = e1 & op(e0, e0) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | ALPHA: (3037) implies: % 130.00/18.34 | | | | | | | (3038) all_57_15 = e1 % 130.00/18.34 | | | | | | | (3039) op(e0, e0) = e1 % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | BETA: splitting (334) gives: % 130.00/18.34 | | | | | | | % 130.00/18.34 | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | (3040) ~ (op(e0, e1) = e1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11, % 130.00/18.34 | | | | | | | | all_8_1, e1, e0, simplifying with (171), (3018) % 130.00/18.34 | | | | | | | | gives: % 130.00/18.34 | | | | | | | | (3041) all_53_11 = all_8_1 % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11, % 130.00/18.34 | | | | | | | | all_20_1, e1, e0, simplifying with (171), (3029) % 130.00/18.34 | | | | | | | | gives: % 130.00/18.34 | | | | | | | | (3042) all_53_11 = all_20_1 % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_20_1, % 130.00/18.34 | | | | | | | | e1, e0, simplifying with (3029) gives: % 130.00/18.34 | | | | | | | | (3043) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | PRED_UNIFY: (7), (3040) imply: % 130.00/18.34 | | | | | | | | (3044) ~ (unit = e0) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | PRED_UNIFY: (3029), (3040) imply: % 130.00/18.34 | | | | | | | | (3045) ~ (all_20_1 = e1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | COMBINE_EQS: (3041), (3042) imply: % 130.00/18.34 | | | | | | | | (3046) all_20_1 = all_8_1 % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | SIMP: (3046) implies: % 130.00/18.34 | | | | | | | | (3047) all_20_1 = all_8_1 % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | COMBINE_EQS: (257), (3041) imply: % 130.00/18.34 | | | | | | | | (3048) all_55_14 = all_8_1 % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | REDUCE: (153), (3041) imply: % 130.00/18.34 | | | | | | | | (3049) ~ (all_53_3 = all_8_1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | REDUCE: (139), (3041) imply: % 130.00/18.34 | | | | | | | | (3050) ~ (all_53_7 = all_8_1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | REDUCE: (132), (3041) imply: % 130.00/18.34 | | | | | | | | (3051) ~ (all_53_9 = all_8_1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | REDUCE: (431), (3041) imply: % 130.00/18.34 | | | | | | | | (3052) ~ (all_12_2 = all_8_1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | SIMP: (3052) implies: % 130.00/18.34 | | | | | | | | (3053) ~ (all_12_2 = all_8_1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | REDUCE: (3045), (3047) imply: % 130.00/18.34 | | | | | | | | (3054) ~ (all_8_1 = e1) % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | BETA: splitting (10) gives: % 130.00/18.34 | | | | | | | | % 130.00/18.34 | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | (3055) unit = e3 % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | REDUCE: (8), (3055) imply: % 130.00/18.34 | | | | | | | | | (3056) op(e3, e2) = e2 % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | REDUCE: (2), (3055) imply: % 130.00/18.34 | | | | | | | | | (3057) op(e0, e3) = e0 % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | REF_CLOSE: (149), (154), (172), (204), (205), (258), (261), % 130.00/18.34 | | | | | | | | | (335), (3019), (3022), (3048), (3049), (3050), % 130.00/18.34 | | | | | | | | | (3054), (3056), (3057), (function-axioms) are % 130.00/18.34 | | | | | | | | | inconsistent by sub-proof #59. % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | (3058) unit = e2 | unit = e1 | unit = e0 % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | BETA: splitting (58) gives: % 130.00/18.34 | | | | | | | | | % 130.00/18.34 | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | (3059) ~ (all_12_2 = e2) % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | BETA: splitting (61) gives: % 130.00/18.34 | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | (3060) ~ (all_14_2 = e2) % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | REDUCE: (382), (3060) imply: % 130.00/18.34 | | | | | | | | | | | (3061) ~ (all_4_2 = e2) % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | BETA: splitting (67) gives: % 130.00/18.34 | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | (3062) ~ (all_18_2 = e3) % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | REDUCE: (391), (3062) imply: % 130.00/18.34 | | | | | | | | | | | | (3063) ~ (all_12_2 = e3) % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | BETA: splitting (73) gives: % 130.00/18.34 | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | (3064) ~ (all_22_2 = e0) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | REDUCE: (389), (3064) imply: % 130.00/18.34 | | | | | | | | | | | | | (3065) ~ (all_12_2 = e0) % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.00/18.34 | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | (3066) all_55_10 = e3 % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | REF_CLOSE: (278), (3063), (3066) are inconsistent by % 130.00/18.34 | | | | | | | | | | | | | | sub-proof #282. % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | (3067) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | BETA: splitting (3067) gives: % 130.00/18.34 | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | (3068) all_55_10 = e2 % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | REF_CLOSE: (278), (3059), (3068) are inconsistent by % 130.00/18.34 | | | | | | | | | | | | | | | sub-proof #281. % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | Case 2: % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | (3069) all_55_10 = e1 | all_55_10 = e0 % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | BETA: splitting (3069) gives: % 130.00/18.34 | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | (3070) all_55_10 = e1 % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3070) imply: % 130.00/18.34 | | | | | | | | | | | | | | | | (3071) all_12_2 = e1 % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | SIMP: (3071) implies: % 130.00/18.34 | | | | | | | | | | | | | | | | (3072) all_12_2 = e1 % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | REDUCE: (426), (3072) imply: % 130.00/18.34 | | | | | | | | | | | | | | | | (3073) ~ (all_53_6 = e1) % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | REDUCE: (428), (3072) imply: % 130.00/18.34 | | | | | | | | | | | | | | | | (3074) ~ (all_53_8 = e1) % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | REDUCE: (57), (3072) imply: % 130.00/18.34 | | | | | | | | | | | | | | | | (3075) op(e1, e1) = e1 % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.00/18.34 | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | | (3076) ~ (all_26_2 = e1) % 130.00/18.34 | | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | | REDUCE: (374), (3076) imply: % 130.00/18.34 | | | | | | | | | | | | | | | | | (3077) ~ (all_6_2 = e1) % 130.00/18.34 | | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 130.00/18.34 | | | | | | | | | | | | | | | | | % 130.00/18.34 | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.34 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | (3078) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | BETA: splitting (3078) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3079) all_57_1 = e1 & op(e3, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | ALPHA: (3079) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3080) op(e3, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (103), (150), (184), (212), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (217), (279), (282), (295), (304), (316), (328), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (342), (398), (405), (409), (417), (423), (425), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (438), (439), (3044), (3058), (3061), (3080), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.35 | | | | | | | | | | | | | | | | | | | #75. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3081) all_57_3 = e1 & op(e2, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (3077), (3081), (function-axioms) are % 130.00/18.35 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #254. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | (3082) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 130.00/18.35 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | BETA: splitting (3082) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3083) all_57_7 = e1 & op(e1, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | ALPHA: (3083) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3084) op(e1, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (3073), (3084) are inconsistent by % 130.00/18.35 | | | | | | | | | | | | | | | | | | | sub-proof #341. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3085) all_57_13 = e1 & op(e0, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | ALPHA: (3085) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3086) op(e0, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (172), (3086) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3087) all_53_7 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | REDUCE: (3022), (3087) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3088) $false % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | CLOSE: (3088) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | (3089) all_26_2 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3089) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | (3090) all_6_2 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | REDUCE: (48), (3090) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | (3091) op(e2, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | (3092) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | BETA: splitting (3092) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3093) all_57_0 = e1 & op(e3, e3) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | ALPHA: (3093) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3094) op(e3, e3) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | (3095) ( ~ (all_52_0 = e1) & op(e3, e3) = all_52_0 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_52_0)) | ( ~ (all_52_1 = e1) & op(e2, e2) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | = all_52_1 & $i(all_52_1)) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3095) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3096) ~ (all_52_0 = e1) & op(e3, e3) = all_52_0 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | $i(all_52_0) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3096) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3097) ~ (all_52_0 = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3098) op(e3, e3) = all_52_0 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | all_52_0, e3, e3, simplifying with (45), (3098) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3099) all_52_0 = all_4_2 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_0, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3094), (3098) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3100) all_52_0 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3099), (3100) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3101) all_4_2 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3097), (3100) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3102) $false % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3102) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3103) ~ (all_52_1 = e1) & op(e2, e2) = all_52_1 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | $i(all_52_1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3103) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3104) ~ (all_52_1 = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3105) op(e2, e2) = all_52_1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (3091), (3105) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3106) all_52_1 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3104), (3106) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3107) $false % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3107) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | (3108) ( ~ (all_52_2 = e1) & op(e1, e1) = all_52_2 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_52_2)) | ( ~ (all_52_3 = e1) & op(e0, e0) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | = all_52_3 & $i(all_52_3)) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3108) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3109) ~ (all_52_2 = e1) & op(e1, e1) = all_52_2 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | $i(all_52_2) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3109) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3110) ~ (all_52_2 = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3111) op(e1, e1) = all_52_2 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_2, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (3075), (3111) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3112) all_52_2 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3110), (3112) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3113) $false % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3113) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3114) ~ (all_52_3 = e1) & op(e0, e0) = all_52_3 & % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | $i(all_52_3) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3114) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3115) ~ (all_52_3 = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3116) op(e0, e0) = all_52_3 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_3, % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (3039), (3116) gives: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3117) all_52_3 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3115), (3117) imply: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | (3118) $false % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3118) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3119) all_57_1 = e1 & op(e3, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | ALPHA: (3119) implies: % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (3120) op(e3, e2) = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (103), (150), (184), (212), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (217), (279), (282), (295), (304), (316), (328), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (342), (398), (405), (409), (417), (423), (425), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (438), (439), (3044), (3058), (3061), (3120), % 130.00/18.35 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.35 | | | | | | | | | | | | | | | | | | | #75. % 130.00/18.35 | | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | (3121) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 130.00/18.35 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (330), (3024), (3074), (3121), % 130.00/18.35 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.35 | | | | | | | | | | | | | | | | | | #58. % 130.00/18.35 | | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | (3122) all_55_10 = e0 % 130.00/18.35 | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (3065), (3122) are inconsistent by % 130.00/18.35 | | | | | | | | | | | | | | | | sub-proof #219. % 130.00/18.35 | | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | (3123) all_22_2 = e0 % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (127), (134), (137), (147), (148), % 130.00/18.35 | | | | | | | | | | | | | (214), (215), (307), (308), (322), (328), (329), % 130.00/18.35 | | | | | | | | | | | | | (332), (389), (428), (433), (3024), (3044), % 130.00/18.35 | | | | | | | | | | | | | (3058), (3123) are inconsistent by sub-proof #57. % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | (3124) all_18_2 = e3 % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | COMBINE_EQS: (391), (3124) imply: % 130.00/18.35 | | | | | | | | | | | | (3125) all_12_2 = e3 % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (13), (14), (15), (16), (17), % 130.00/18.35 | | | | | | | | | | | | (57), (137), (154), (160), (162), (174), (204), % 130.00/18.35 | | | | | | | | | | | | (213), (219), (221), (222), (226), (227), (228), % 130.00/18.35 | | | | | | | | | | | | (229), (230), (231), (232), (258), (259), (261), % 130.00/18.35 | | | | | | | | | | | | (262), (285), (286), (296), (301), (304), (330), % 130.00/18.35 | | | | | | | | | | | | (332), (340), (342), (343), (398), (414), (415), % 130.00/18.35 | | | | | | | | | | | | (423), (429), (433), (3019), (3022), (3025), % 130.00/18.35 | | | | | | | | | | | | (3038), (3040), (3043), (3044), (3047), (3048), % 130.00/18.35 | | | | | | | | | | | | (3050), (3051), (3053), (3058), (3059), (3125), % 130.00/18.35 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.35 | | | | | | | | | | | | #51. % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | End of split % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | (3126) all_14_2 = e2 % 130.00/18.35 | | | | | | | | | | | (3127) op(e3, e2) = all_14_1 & $i(all_14_1) & ( ~ % 130.00/18.35 | | | | | | | | | | | (all_14_1 = e0) | ( ~ (all_14_0 = e1) & op(e3, % 130.00/18.35 | | | | | | | | | | | e0) = all_14_0 & $i(all_14_0))) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | ALPHA: (3127) implies: % 130.00/18.35 | | | | | | | | | | | (3128) op(e3, e2) = all_14_1 % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | COMBINE_EQS: (382), (3126) imply: % 130.00/18.35 | | | | | | | | | | | (3129) all_4_2 = e2 % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | COMBINE_EQS: (380), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3130) all_32_2 = e2 % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (403), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3131) ~ (all_53_1 = e2) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (407), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3132) ~ (all_53_3 = e2) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (409), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3133) ~ (all_53_4 = e2) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (411), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3134) ~ (all_53_8 = e2) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (413), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3135) ~ (all_53_12 = e2) % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | REDUCE: (45), (3129) imply: % 130.00/18.35 | | | | | | | | | | | (3136) op(e3, e3) = e2 % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | BETA: splitting (88) gives: % 130.00/18.35 | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | (3137) ~ (all_32_2 = e2) % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | REDUCE: (3130), (3137) imply: % 130.00/18.35 | | | | | | | | | | | | (3138) $false % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | CLOSE: (3138) is inconsistent. % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | Case 2: % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | (3139) op(e3, e2) = all_32_1 & $i(all_32_1) & ( ~ % 130.00/18.35 | | | | | | | | | | | | (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 130.00/18.35 | | | | | | | | | | | | e1) = all_32_0 & $i(all_32_0))) % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | ALPHA: (3139) implies: % 130.00/18.35 | | | | | | | | | | | | (3140) op(e3, e2) = all_32_1 % 130.00/18.35 | | | | | | | | | | | | (3141) ~ (all_32_1 = e1) | ( ~ (all_32_0 = e0) & op(e3, % 130.00/18.35 | | | | | | | | | | | | e1) = all_32_0 & $i(all_32_0)) % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | BETA: splitting (335) gives: % 130.00/18.35 | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | Case 1: % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | (3142) ~ (op(e3, e2) = e2) % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 130.00/18.35 | | | | | | | | | | | | | all_14_1, e2, e3, simplifying with (184), (3128) % 130.00/18.35 | | | | | | | | | | | | | gives: % 130.00/18.35 | | | | | | | | | | | | | (3143) all_53_4 = all_14_1 % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, % 130.00/18.35 | | | | | | | | | | | | | all_32_1, e2, e3, simplifying with (184), (3140) % 130.00/18.35 | | | | | | | | | | | | | gives: % 130.00/18.35 | | | | | | | | | | | | | (3144) all_53_4 = all_32_1 % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | PRED_UNIFY: (3140), (3142) imply: % 130.00/18.35 | | | | | | | | | | | | | (3145) ~ (all_32_1 = e2) % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | COMBINE_EQS: (3143), (3144) imply: % 130.00/18.35 | | | | | | | | | | | | | (3146) all_32_1 = all_14_1 % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.35 | | | | | | | | | | | | | SIMP: (3146) implies: % 130.00/18.35 | | | | | | | | | | | | | (3147) all_32_1 = all_14_1 % 130.00/18.35 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (150), (3143) imply: % 130.00/18.36 | | | | | | | | | | | | | (3148) ~ (all_53_6 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | SIMP: (3148) implies: % 130.00/18.36 | | | | | | | | | | | | | (3149) ~ (all_53_6 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (149), (3143) imply: % 130.00/18.36 | | | | | | | | | | | | | (3150) ~ (all_53_7 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | SIMP: (3150) implies: % 130.00/18.36 | | | | | | | | | | | | | (3151) ~ (all_53_7 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (148), (3143) imply: % 130.00/18.36 | | | | | | | | | | | | | (3152) ~ (all_53_8 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | SIMP: (3152) implies: % 130.00/18.36 | | | | | | | | | | | | | (3153) ~ (all_53_8 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (147), (3143) imply: % 130.00/18.36 | | | | | | | | | | | | | (3154) ~ (all_53_12 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | SIMP: (3154) implies: % 130.00/18.36 | | | | | | | | | | | | | (3155) ~ (all_53_12 = all_14_1) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (417), (3143) imply: % 130.00/18.36 | | | | | | | | | | | | | (3156) ~ (all_14_1 = all_6_2) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | REDUCE: (3145), (3147) imply: % 130.00/18.36 | | | | | | | | | | | | | (3157) ~ (all_14_1 = e2) % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.00/18.36 | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | (3158) ~ (all_18_2 = e3) % 130.00/18.36 | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | REDUCE: (391), (3158) imply: % 130.00/18.36 | | | | | | | | | | | | | | (3159) ~ (all_12_2 = e3) % 130.00/18.36 | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | BETA: splitting (73) gives: % 130.00/18.36 | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | (3160) ~ (all_22_2 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | REDUCE: (389), (3160) imply: % 130.00/18.36 | | | | | | | | | | | | | | | (3161) ~ (all_12_2 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.00/18.36 | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | (3162) all_55_10 = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (3159), (3162) are inconsistent by % 130.00/18.36 | | | | | | | | | | | | | | | | sub-proof #282. % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | (3163) ~ (all_55_10 = e3) % 130.00/18.36 | | | | | | | | | | | | | | | | (3164) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | BETA: splitting (3164) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | (3165) all_55_10 = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (3059), (3165) are inconsistent by % 130.00/18.36 | | | | | | | | | | | | | | | | | sub-proof #281. % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | (3166) ~ (all_55_10 = e2) % 130.00/18.36 | | | | | | | | | | | | | | | | | (3167) all_55_10 = e1 | all_55_10 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | BETA: splitting (3167) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3168) all_55_10 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3168) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3169) all_12_2 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | SIMP: (3169) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3170) all_12_2 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3171) all_22_2 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (415), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3172) ~ (all_53_2 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (426), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3173) ~ (all_53_6 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (428), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3174) ~ (all_53_8 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (3053), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3175) ~ (all_8_1 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (3159), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3176) ~ (e3 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | REDUCE: (3059), (3170) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | (3177) ~ (e2 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | (3178) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (281), (282), (3172), (3173), (3178) are % 130.00/18.36 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | (3179) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 130.00/18.36 | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (3179) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | (3180) all_57_8 = e1 & op(e1, e1) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | ALPHA: (3180) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | (3181) all_57_8 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | (3182) op(e1, e1) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | (3183) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3183) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | (3184) all_57_0 = e1 & op(e3, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3184) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | (3185) op(e3, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3136), (3185), (function-axioms) are % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | (3186) all_57_2 = e1 & op(e2, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3186) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | (3187) all_57_2 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | (3188) op(e2, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | (3189) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3189) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3190) all_57_0 = e1 & op(e3, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3190) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3191) op(e3, e3) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3136), (3191), (function-axioms) are % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3192) all_57_1 = e1 & op(e3, e2) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3192) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_57_1 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3194) op(e3, e2) = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1, % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (181), (3188) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_53_1 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1, e1, % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (3128), (3194) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3196) all_14_1 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3147), (3196) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3197) all_32_1 = e1 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (3195) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3198) ~ (all_53_2 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (3195) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3199) ~ (all_53_3 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (3195) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3200) ~ (all_53_13 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3200) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3201) ~ (all_53_13 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3156), (3196) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3202) ~ (all_6_2 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3202) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | (3203) ~ (all_6_2 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3141) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | (3204) ~ (all_32_1 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3197), (3204) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | (3205) $false % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3205) is inconsistent. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | (3206) ~ (all_32_0 = e0) & op(e3, e1) = all_32_0 & % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3206) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | (3207) ~ (all_32_0 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | (3208) op(e3, e1) = all_32_0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3209) ~ (op(e3, e1) = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_0, e1, e3, simplifying with (183), (3208) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3210) all_53_8 = all_32_0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (3210) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3211) all_55_2 = all_32_0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3210) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3212) ~ (all_53_12 = all_32_0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3212) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3213) ~ (all_53_12 = all_32_0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3134), (3210) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3214) ~ (all_32_0 = e2) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3174), (3210) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (3215) ~ (all_32_0 = e1) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3216) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (284), (3136), (3171), (3182), (3193), % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3216), (function-axioms) are inconsistent by % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #123. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3217) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3217) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3218) all_57_4 = e0 & op(e3, e1) = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3218) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3219) all_57_4 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (249), (320), (324), (3129), (3193), % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207), (3211), (3213), (3214), (3215), (3219) are % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #50. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3220) all_57_9 = e0 & op(e3, e0) = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3220) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3221) all_57_9 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3222) op(e3, e0) = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3223) ~ (op(e3, e0) = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3222), (3223) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3224) $false % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3224) is inconsistent. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3225) all_53_12 = e0 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (3225) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3226) ~ (all_53_13 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3226) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3227) ~ (all_53_13 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3225) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3228) ~ (all_53_14 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3228) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3229) ~ (all_53_14 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3213), (3225) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3230) ~ (all_32_0 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3135), (3225) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3231) ~ (e2 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3024), (3225) imply: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3232) ~ (e1 = e0) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3233) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3233) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234) all_57_2 = e3 & op(e2, e3) = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3187), (3234) are inconsistent by sub-proof % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #85. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3235) all_57_3 = e3 & op(e2, e2) = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3235) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3236) all_57_3 = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3237) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3237) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3238) all_57_4 = e3 & op(e3, e1) = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3238) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3239) all_57_4 = e3 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3240) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3240) gives: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3241) all_57_2 = e2 & op(e2, e3) = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3241) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3242) op(e2, e3) = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (3131), (3242) are inconsistent by % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3243) all_57_3 = e2 & op(e2, e2) = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3243) implies: % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3244) all_57_3 = e2 % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3236), (3244) imply: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3245) e3 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3239), (3245) imply: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3246) all_57_4 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3246), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3247) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) all_57_5 = e2 & op(e2, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3248) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) all_57_5 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (234), (328), (3187), (3227), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3236), (3249) are inconsistent by sub-proof #48. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_57_10 = e2 & op(e2, e0) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (131), (279), (282), (304), (306), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044), (3058), (3173), (3250) are inconsistent by % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #47. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_57_5 = e3 & op(e2, e1) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3251) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) all_57_5 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3253) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_57_2 = e2 & op(e2, e3) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3254) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) op(e2, e3) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (3131), (3255) are inconsistent by % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3256) all_57_3 = e2 & op(e2, e2) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (3236), (3256) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #46. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_57_5 = e2 & op(e2, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (3252), (3258) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #303. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) all_57_10 = e2 & op(e2, e0) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (131), (279), (282), (304), (306), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044), (3058), (3173), (3259) are inconsistent by % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #47. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3260) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3260) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_57_8 = e3 & op(e1, e1) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3181), (3261) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #133. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3262) all_57_14 = e3 & op(e0, e1) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3262) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3263) all_57_14 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (320), (3129), (3193), (3264) are % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3265) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3265) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3266) all_57_4 = e3 & op(e3, e1) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3266) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3267) all_57_4 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3268) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3268) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3269) all_57_4 = e2 & op(e3, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3269) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3270) all_57_4 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3270), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3271) all_57_5 = e2 & op(e2, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3271) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3272) all_57_5 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (234), (328), (3187), (3227), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3236), (3272) are inconsistent by sub-proof #48. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3273) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3273) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3274) all_57_8 = e2 & op(e1, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3181), (3274) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3275) all_57_14 = e2 & op(e0, e1) = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3275) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3276) all_57_14 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3263), (3276) imply: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3277) e3 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3267), (3277) imply: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3278) all_57_4 = e2 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3278), % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3279) all_57_9 = e3 & op(e3, e0) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3279) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3280) op(e3, e0) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (3225), (3280) are inconsistent by % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3281) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3281) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3282) all_57_5 = e3 & op(e2, e1) = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3282) implies: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3283) all_57_5 = e3 % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.00/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3284) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3284) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3285) all_57_4 = e0 & op(e3, e1) = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3285) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3286) all_57_4 = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (249), (320), (324), (3129), (3193), % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207), (3211), (3213), (3214), (3215), (3286) are % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #50. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287) all_57_5 = e0 & op(e2, e1) = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (3283), (3287) are inconsistent by sub-proof % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3288) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3288) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3289) all_57_8 = e0 & op(e1, e1) = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (3171), (3181), (3182), (3289) are % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #257. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3290) all_57_14 = e0 & op(e0, e1) = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3290) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3291) all_57_14 = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3292) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (320), (3129), (3193), (3292) are % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3293) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3293) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3294) all_57_4 = e3 & op(e3, e1) = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3294) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3295) all_57_4 = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3296) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3296) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3297) all_57_4 = e2 & op(e3, e1) = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3297) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3298) all_57_4 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3298), % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3299) all_57_5 = e2 & op(e2, e1) = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3299) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3300) all_57_5 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3283), (3300) imply: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3301) e3 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3295), (3301) imply: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3302) all_57_4 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3302), % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3303) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3303) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3304) all_57_8 = e2 & op(e1, e1) = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3181), (3304) are inconsistent by sub-proof % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3305) all_57_14 = e2 & op(e0, e1) = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3305) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3306) all_57_14 = e2 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3291), (3306) imply: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3307) e2 = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3307) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3308) e2 = e0 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3308) imply: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3309) $false % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3309) is inconsistent. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3310) all_57_9 = e3 & op(e3, e0) = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3310) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3311) op(e3, e0) = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (3225), (3311) are inconsistent by % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3312) all_57_10 = e3 & op(e2, e0) = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3313) all_57_10 = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3314) op(e2, e0) = e3 % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3315) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (320), (3129), (3193), (3315) are % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3316) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3316) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3317) all_57_4 = e3 & op(e3, e1) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3317) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3318) all_57_4 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3319) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3320) all_57_9 = e2 & op(e3, e0) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3320) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3321) all_57_9 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3221), (3321) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3322) e2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3322) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3323) e2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3323) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3324) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3324) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3325) all_57_10 = e2 & op(e2, e0) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (131), (279), (282), (304), (306), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044), (3058), (3173), (3325) are inconsistent by % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #47. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3326) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3326) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327) all_57_11 = e2 & op(e1, e0) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3327) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3328) all_57_11 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3329) op(e1, e0) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (174), (3329) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3330) all_53_14 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13, % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (178), (3314) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3331) all_53_13 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (3330) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3332) ~ (all_53_2 = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3330) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3333) ~ (all_53_6 = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (3331) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3334) ~ (all_6_2 = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3335) ~ (all_44_2 = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (3335) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3336) ~ (all_6_2 = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (212), (279), (282), (295), (304), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423), (439), (3044), (3058), (3173), (3203), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3336) are inconsistent by sub-proof #234. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337) all_44_2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (3337) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3338) all_6_2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3338) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3339) all_6_2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (3339) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3340) all_26_2 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (3339) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3341) ~ (all_53_7 = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (3339) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3342) ~ (e3 = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3343) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3343) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3344) all_57_4 = e0 & op(e3, e1) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3344) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3345) all_57_4 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (249), (320), (324), (3129), (3193), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207), (3211), (3213), (3214), (3215), (3345) are % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #50. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3346) all_57_5 = e0 & op(e2, e1) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3346) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3347) all_57_5 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3348) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3348) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3349) all_57_4 = e2 & op(e3, e1) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3349) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3350) all_57_4 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3350), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3351) all_57_5 = e2 & op(e2, e1) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3347), (3351) are inconsistent by sub-proof % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #45. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3352) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3352) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3353) all_57_8 = e2 & op(e1, e1) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3181), (3353) are inconsistent by sub-proof % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #44. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3354) all_57_14 = e2 & op(e0, e1) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3354) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3355) all_57_14 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3356) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3356) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3357) all_57_1 = e0 & op(e3, e2) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (3171), (3182), (3193), (3357) are % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #268. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3358) all_57_3 = e0 & op(e2, e2) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3358) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359) all_57_3 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (14), (131), (236), (279), (282), (296), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (304), (306), (3044), (3058), (3131), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173), (3347), (3359) are inconsistent by % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3360) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3361) all_57_7 = e0 & op(e1, e2) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3361) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3362) all_57_7 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3363) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3363) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3364) all_57_6 = e3 & op(e1, e3) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3364) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3365) op(e1, e3) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3366) ~ (op(e1, e3) = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3365), (3366) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3367) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3367) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3368) all_55_8 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (3368) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3369) all_53_2 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3369) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3370) all_53_2 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3370) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3371) ~ (all_53_3 = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3371) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372) ~ (all_53_3 = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3373) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3373) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3374) all_57_12 = e3 & op(e0, e3) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3374) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3375) op(e0, e3) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (343), (3372), (3375) are inconsistent by % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #311. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3376) all_57_13 = e3 & op(e0, e2) = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3376) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3377) all_57_13 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3378) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3378) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3379) all_57_1 = e2 & op(e3, e2) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3379) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380) op(e3, e2) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3381) all_55_12 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3381) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3382) all_53_3 = e3 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3372), (3382) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3383) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3383) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3384) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3384) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3385) all_55_12 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3385) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3386) all_53_3 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3132), (3386) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3387) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3387) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3388) all_55_12 = e1 | all_55_12 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3388) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3389) all_55_12 = e1 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3389) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3390) all_53_3 = e1 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3021), (3390) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3391) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3391) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3392) all_55_12 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3392) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3393) all_53_3 = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (3393) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3394) op(e0, e3) = e0 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (154), (172), (204), (205), (258), (261), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335), (3019), (3022), (3048), (3049), (3050), % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3054), (3380), (3394), (function-axioms) are % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #59. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) all_57_3 = e2 & op(e2, e2) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3395) implies: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) all_57_3 = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) op(e2, e2) = e2 % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) ~ (op(e2, e2) = e2) % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3397), (3398) imply: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) $false % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3399) is inconsistent. % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) all_26_2 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3340), (3400) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) e2 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3396), (3401) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) all_57_3 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (14), (131), (236), (279), (282), (296), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (304), (306), (3044), (3058), (3131), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173), (3347), (3402) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3403) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) all_57_7 = e2 & op(e1, e2) = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3404) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) op(e1, e2) = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (3333), (3405) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) all_57_13 = e2 & op(e0, e2) = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3406) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) all_57_13 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3377), (3407) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) e3 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3408) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) e3 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3318), (3409) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) all_57_4 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3410), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3411) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) all_57_14 = e3 & op(e0, e1) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3412) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) all_57_14 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3355), (3413) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) e3 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3318), (3414) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) all_57_4 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3415), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) all_57_15 = e3 & op(e0, e0) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3416) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) all_57_15 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3038), (3417) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) e3 = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3313), (3418) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) all_57_10 = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (225), (324), (3038), (3225), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3328), (3419) are inconsistent by sub-proof #98. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) all_57_7 = e3 & op(e1, e2) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3420) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) all_57_7 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3362), (3421) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) e3 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3318), (3422) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) all_57_4 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (249), (320), (324), (3129), (3193), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207), (3211), (3213), (3214), (3215), (3423) are % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #50. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3424) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) all_57_8 = e3 & op(e1, e1) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3425) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) all_57_8 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (231), (3040), (3209), (3347), (3426) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #52. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) all_57_11 = e3 & op(e1, e0) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3427) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_57_11 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3328), (3428) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) e3 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3318), (3429) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) all_57_4 = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (182), (243), (249), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320), (324), (3129), (3136), (3193), (3430), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) all_57_13 = e0 & op(e0, e2) = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3431) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) op(e0, e2) = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (3341), (3432) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3433) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) all_57_8 = e0 & op(e1, e1) = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3434) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_57_8 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3181), (3435) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) e1 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3436) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) e1 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3171), (3437) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) all_22_2 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (3182), (3438) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) all_57_14 = e0 & op(e0, e1) = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3439) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) op(e0, e1) = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3043) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) ~ (op(e0, e1) = e0) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3440), (3441) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) $false % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3442) is inconsistent. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_20_1 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3047), (3443) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) all_8_1 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3444) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) all_8_1 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3049), (3445) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) ~ (all_53_3 = e0) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_55_12 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3447) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) all_53_3 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3448) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) all_53_3 = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (3449) imply: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) ~ (all_53_2 = e3) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (328), (342), (3044), (3058), (3227), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) are inconsistent by sub-proof #233. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3021), (3132), (3446), (3451) are % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) all_57_15 = e2 & op(e0, e0) = e2 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3038), (3452) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #42. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) all_57_9 = e3 & op(e3, e0) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3453) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) op(e3, e0) = e3 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (324), (3225), (3454) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #163. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) op(e3, e1) = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (3174), (3455) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | (3456) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (330), (3024), (3174), (3456), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | #58. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | (3457) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (281), (3021), (3172), (3457), % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | #41. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | (3458) all_57_11 = e1 & op(e1, e0) = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (3458) implies: % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | (3459) op(e1, e0) = e1 % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (3025), (3459) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | sub-proof #339. % 130.20/18.39 | | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | (3460) all_55_10 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (3161), (3460) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | | | | | | sub-proof #219. % 130.20/18.39 | | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | (3461) all_22_2 = e0 % 130.20/18.39 | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (127), (134), (137), (147), (148), % 130.20/18.39 | | | | | | | | | | | | | | | (214), (215), (307), (308), (322), (328), (329), % 130.20/18.39 | | | | | | | | | | | | | | | (332), (389), (428), (433), (3024), (3044), % 130.20/18.39 | | | | | | | | | | | | | | | (3058), (3461) are inconsistent by sub-proof #57. % 130.20/18.39 | | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | (3462) all_18_2 = e3 % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | COMBINE_EQS: (391), (3462) imply: % 130.20/18.39 | | | | | | | | | | | | | | (3463) all_12_2 = e3 % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | SIMP: (3463) implies: % 130.20/18.39 | | | | | | | | | | | | | | (3464) all_12_2 = e3 % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (13), (14), (15), (16), (17), % 130.20/18.39 | | | | | | | | | | | | | | (57), (137), (154), (160), (162), (174), (204), % 130.20/18.39 | | | | | | | | | | | | | | (213), (219), (221), (222), (226), (227), (228), % 130.20/18.39 | | | | | | | | | | | | | | (229), (230), (231), (232), (258), (259), (261), % 130.20/18.39 | | | | | | | | | | | | | | (262), (285), (286), (296), (301), (304), (330), % 130.20/18.39 | | | | | | | | | | | | | | (332), (340), (342), (343), (398), (414), (415), % 130.20/18.39 | | | | | | | | | | | | | | (423), (429), (433), (3019), (3022), (3025), % 130.20/18.39 | | | | | | | | | | | | | | (3038), (3040), (3043), (3044), (3047), (3048), % 130.20/18.39 | | | | | | | | | | | | | | (3050), (3051), (3053), (3058), (3059), (3464), % 130.20/18.39 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.39 | | | | | | | | | | | | | | #51. % 130.20/18.39 | | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | (3465) op(e3, e2) = e2 % 130.20/18.39 | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | | REF_CLOSE: (335), (3133), (3465) are inconsistent by % 130.20/18.39 | | | | | | | | | | | | | sub-proof #94. % 130.20/18.39 | | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | End of split % 130.20/18.39 | | | | | | | | | | % 130.20/18.39 | | | | | | | | | Case 2: % 130.20/18.39 | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | (3466) all_12_2 = e2 % 130.20/18.39 | | | | | | | | | | (3467) op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 130.20/18.39 | | | | | | | | | | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, % 130.20/18.39 | | | | | | | | | | e3) = all_12_0 & $i(all_12_0))) % 130.20/18.39 | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | ALPHA: (3467) implies: % 130.20/18.39 | | | | | | | | | | (3468) op(e1, e2) = all_12_1 % 130.20/18.39 | | | | | | | | | | % 130.20/18.39 | | | | | | | | | | COMBINE_EQS: (376), (3466) imply: % 130.20/18.40 | | | | | | | | | | (3469) all_30_2 = e2 % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (426), (3466) imply: % 130.20/18.40 | | | | | | | | | | (3470) ~ (all_53_6 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (429), (3466) imply: % 130.20/18.40 | | | | | | | | | | (3471) ~ (all_53_9 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (3053), (3466) imply: % 130.20/18.40 | | | | | | | | | | (3472) ~ (all_8_1 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | SIMP: (3472) implies: % 130.20/18.40 | | | | | | | | | | (3473) ~ (all_8_1 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (57), (3466) imply: % 130.20/18.40 | | | | | | | | | | (3474) op(e1, e1) = e2 % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (13), (14), (15), % 130.20/18.40 | | | | | | | | | | (16), (17), (18), (85), (137), (140), (142), % 130.20/18.40 | | | | | | | | | | (157), (163), (176), (204), (221), (226), (227), % 130.20/18.40 | | | | | | | | | | (228), (229), (230), (231), (232), (233), (258), % 130.20/18.40 | | | | | | | | | | (262), (281), (285), (286), (299), (304), (330), % 130.20/18.40 | | | | | | | | | | (332), (337), (339), (340), (342), (400), (419), % 130.20/18.40 | | | | | | | | | | (421), (3018), (3030), (3038), (3040), (3043), % 130.20/18.40 | | | | | | | | | | (3044), (3047), (3048), (3050), (3051), (3058), % 130.20/18.40 | | | | | | | | | | (3466), (3468), (3469), (3470), (3471), (3473), % 130.20/18.40 | | | | | | | | | | (3474), (function-axioms) are inconsistent by % 130.20/18.40 | | | | | | | | | | sub-proof #35. % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | End of split % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | End of split % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | (3475) all_53_11 = e1 % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | REDUCE: (3023), (3475) imply: % 130.20/18.40 | | | | | | | | (3476) $false % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | CLOSE: (3476) is inconsistent. % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | End of split % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | End of split % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | End of split % 130.20/18.40 | | | | | % 130.20/18.40 | | | | End of split % 130.20/18.40 | | | | % 130.20/18.40 | | | End of split % 130.20/18.40 | | | % 130.20/18.40 | | Case 2: % 130.20/18.40 | | | % 130.20/18.40 | | | (3477) all_6_2 = e3 % 130.20/18.40 | | | (3478) op(e2, e3) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e0) | ( ~ % 130.20/18.40 | | | (all_6_0 = e1) & op(e2, e0) = all_6_0 & $i(all_6_0))) % 130.20/18.40 | | | % 130.20/18.40 | | | ALPHA: (3478) implies: % 130.20/18.40 | | | (3479) op(e2, e3) = all_6_1 % 130.20/18.40 | | | % 130.20/18.40 | | | COMBINE_EQS: (399), (3477) imply: % 130.20/18.40 | | | (3480) all_50_2 = e3 % 130.20/18.40 | | | % 130.20/18.40 | | | REDUCE: (414), (3477) imply: % 130.20/18.40 | | | (3481) ~ (all_53_1 = e3) % 130.20/18.40 | | | % 130.20/18.40 | | | REDUCE: (419), (3477) imply: % 130.20/18.40 | | | (3482) ~ (all_53_6 = e3) % 130.20/18.40 | | | % 130.20/18.40 | | | REDUCE: (421), (3477) imply: % 130.20/18.40 | | | (3483) ~ (all_53_7 = e3) % 130.20/18.40 | | | % 130.20/18.40 | | | REDUCE: (423), (3477) imply: % 130.20/18.40 | | | (3484) ~ (all_53_9 = e3) % 130.20/18.40 | | | % 130.20/18.40 | | | REDUCE: (425), (3477) imply: % 130.20/18.40 | | | (3485) ~ (all_53_13 = e3) % 130.20/18.40 | | | % 130.20/18.40 | | | BETA: splitting (237) gives: % 130.20/18.40 | | | % 130.20/18.40 | | | Case 1: % 130.20/18.40 | | | | % 130.20/18.40 | | | | (3486) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, % 130.20/18.40 | | | | e2) = e3) % 130.20/18.40 | | | | % 130.20/18.40 | | | | BETA: splitting (3486) gives: % 130.20/18.40 | | | | % 130.20/18.40 | | | | Case 1: % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | (3487) all_57_2 = e3 & op(e2, e3) = e3 % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | ALPHA: (3487) implies: % 130.20/18.40 | | | | | (3488) op(e2, e3) = e3 % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | REF_CLOSE: (340), (3481), (3488) are inconsistent by sub-proof #353. % 130.20/18.40 | | | | | % 130.20/18.40 | | | | Case 2: % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | (3489) all_57_3 = e3 & op(e2, e2) = e3 % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | ALPHA: (3489) implies: % 130.20/18.40 | | | | | (3490) all_57_3 = e3 % 130.20/18.40 | | | | | (3491) op(e2, e2) = e3 % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | BETA: splitting (115) gives: % 130.20/18.40 | | | | | % 130.20/18.40 | | | | | Case 1: % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | (3492) ~ (all_50_2 = e3) % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | REDUCE: (3480), (3492) imply: % 130.20/18.40 | | | | | | (3493) $false % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | CLOSE: (3493) is inconsistent. % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | Case 2: % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | (3494) op(e2, e3) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e1) % 130.20/18.40 | | | | | | | ( ~ (all_50_0 = e0) & op(e2, e1) = all_50_0 & % 130.20/18.40 | | | | | | $i(all_50_0))) % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | ALPHA: (3494) implies: % 130.20/18.40 | | | | | | (3495) op(e2, e3) = all_50_1 % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | BETA: splitting (340) gives: % 130.20/18.40 | | | | | | % 130.20/18.40 | | | | | | Case 1: % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | (3496) ~ (op(e2, e3) = e3) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, % 130.20/18.40 | | | | | | | all_6_1, e3, e2, simplifying with (181), (3479) % 130.20/18.40 | | | | | | | gives: % 130.20/18.40 | | | | | | | (3497) all_53_1 = all_6_1 % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, % 130.20/18.40 | | | | | | | all_50_1, e3, e2, simplifying with (181), (3495) % 130.20/18.40 | | | | | | | gives: % 130.20/18.40 | | | | | | | (3498) all_53_1 = all_50_1 % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1, % 130.20/18.40 | | | | | | | e3, e2, simplifying with (3495) gives: % 130.20/18.40 | | | | | | | (3499) all_50_1 = e2 | ~ (op(e2, e3) = e2) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | PRED_UNIFY: (9), (3496) imply: % 130.20/18.40 | | | | | | | (3500) ~ (unit = e2) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | COMBINE_EQS: (3497), (3498) imply: % 130.20/18.40 | | | | | | | (3501) all_50_1 = all_6_1 % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | SIMP: (3501) implies: % 130.20/18.40 | | | | | | | (3502) all_50_1 = all_6_1 % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | REDUCE: (163), (3497) imply: % 130.20/18.40 | | | | | | | (3503) ~ (all_53_2 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | SIMP: (3503) implies: % 130.20/18.40 | | | | | | | (3504) ~ (all_53_2 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | REDUCE: (162), (3497) imply: % 130.20/18.40 | | | | | | | (3505) ~ (all_53_3 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | SIMP: (3505) implies: % 130.20/18.40 | | | | | | | (3506) ~ (all_53_3 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | REDUCE: (160), (3497) imply: % 130.20/18.40 | | | | | | | (3507) ~ (all_53_9 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | SIMP: (3507) implies: % 130.20/18.40 | | | | | | | (3508) ~ (all_53_9 = all_6_1) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | REDUCE: (403), (3497) imply: % 130.20/18.40 | | | | | | | (3509) ~ (all_6_1 = all_4_2) % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | BETA: splitting (52) gives: % 130.20/18.40 | | | | | | | % 130.20/18.40 | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | (3510) ~ (all_8_2 = e1) % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | BETA: splitting (10) gives: % 130.20/18.40 | | | | | | | | % 130.20/18.40 | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | (3511) unit = e3 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (8), (3511) imply: % 130.20/18.40 | | | | | | | | | (3512) op(e3, e2) = e2 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (7), (3511) imply: % 130.20/18.40 | | | | | | | | | (3513) op(e3, e1) = e1 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (6), (3511) imply: % 130.20/18.40 | | | | | | | | | (3514) op(e3, e0) = e0 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (5), (3511) imply: % 130.20/18.40 | | | | | | | | | (3515) op(e3, e3) = e3 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (4), (3511) imply: % 130.20/18.40 | | | | | | | | | (3516) op(e2, e3) = e2 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (3), (3511) imply: % 130.20/18.40 | | | | | | | | | (3517) op(e1, e3) = e1 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | REDUCE: (2), (3511) imply: % 130.20/18.40 | | | | | | | | | (3518) op(e0, e3) = e0 % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | BETA: splitting (3499) gives: % 130.20/18.40 | | | | | | | | | % 130.20/18.40 | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | (3519) ~ (op(e2, e3) = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | PRED_UNIFY: (3516), (3519) imply: % 130.20/18.40 | | | | | | | | | | (3520) $false % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | CLOSE: (3520) is inconsistent. % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | (3521) all_50_1 = e2 % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | COMBINE_EQS: (3502), (3521) imply: % 130.20/18.40 | | | | | | | | | | (3522) all_6_1 = e2 % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | SIMP: (3522) implies: % 130.20/18.40 | | | | | | | | | | (3523) all_6_1 = e2 % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (3504), (3523) imply: % 130.20/18.40 | | | | | | | | | | (3524) ~ (all_53_2 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (3506), (3523) imply: % 130.20/18.40 | | | | | | | | | | (3525) ~ (all_53_3 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (3508), (3523) imply: % 130.20/18.40 | | | | | | | | | | (3526) ~ (all_53_9 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | REDUCE: (3509), (3523) imply: % 130.20/18.40 | | | | | | | | | | (3527) ~ (all_4_2 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | SIMP: (3527) implies: % 130.20/18.40 | | | | | | | | | | (3528) ~ (all_4_2 = e2) % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | BETA: splitting (246) gives: % 130.20/18.40 | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | (3529) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 130.20/18.40 | | | | | | | | | | | & op(e2, e3) = e2) % 130.20/18.40 | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | BETA: splitting (3529) gives: % 130.20/18.40 | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | (3530) all_57_0 = e2 & op(e3, e3) = e2 % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | REF_CLOSE: (45), (3528), (3530), (function-axioms) are % 130.20/18.40 | | | | | | | | | | | | inconsistent by sub-proof #91. % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | (3531) all_57_2 = e2 & op(e2, e3) = e2 % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | ALPHA: (3531) implies: % 130.20/18.40 | | | | | | | | | | | | (3532) all_57_2 = e2 % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | BETA: splitting (335) gives: % 130.20/18.40 | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | (3533) ~ (op(e3, e2) = e2) % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | PRED_UNIFY: (3512), (3533) imply: % 130.20/18.40 | | | | | | | | | | | | | (3534) $false % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | CLOSE: (3534) is inconsistent. % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | (3535) all_53_4 = e2 % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | REDUCE: (150), (3535) imply: % 130.20/18.40 | | | | | | | | | | | | | (3536) ~ (all_53_6 = e2) % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | SIMP: (3536) implies: % 130.20/18.40 | | | | | | | | | | | | | (3537) ~ (all_53_6 = e2) % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | REDUCE: (149), (3535) imply: % 130.20/18.40 | | | | | | | | | | | | | (3538) ~ (all_53_7 = e2) % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | SIMP: (3538) implies: % 130.20/18.40 | | | | | | | | | | | | | (3539) ~ (all_53_7 = e2) % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | BETA: splitting (326) gives: % 130.20/18.40 | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | (3540) ~ (op(e3, e0) = e0) % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | PRED_UNIFY: (3514), (3540) imply: % 130.20/18.40 | | | | | | | | | | | | | | (3541) $false % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | CLOSE: (3541) is inconsistent. % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | (3542) all_53_12 = e0 % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | REDUCE: (134), (3542) imply: % 130.20/18.40 | | | | | | | | | | | | | | (3543) ~ (all_53_8 = e0) % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | REDUCE: (126), (3542) imply: % 130.20/18.40 | | | | | | | | | | | | | | (3544) ~ (all_53_14 = e0) % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | SIMP: (3544) implies: % 130.20/18.40 | | | | | | | | | | | | | | (3545) ~ (all_53_14 = e0) % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | BETA: splitting (261) gives: % 130.20/18.40 | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | (3546) ~ (op(e0, e3) = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | PRED_UNIFY: (3518), (3546) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3547) $false % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | CLOSE: (3547) is inconsistent. % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | (3548) all_53_3 = e0 % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | REDUCE: (158), (3548) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3549) ~ (all_53_2 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | REDUCE: (154), (3548) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3550) ~ (all_53_7 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | SIMP: (3550) implies: % 130.20/18.40 | | | | | | | | | | | | | | | (3551) ~ (all_53_7 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | REDUCE: (416), (3548) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3552) ~ (all_8_2 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | SIMP: (3552) implies: % 130.20/18.40 | | | | | | | | | | | | | | | (3553) ~ (all_8_2 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | REDUCE: (407), (3548) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3554) ~ (all_4_2 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | REDUCE: (3525), (3548) imply: % 130.20/18.40 | | | | | | | | | | | | | | | (3555) ~ (e2 = e0) % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 130.20/18.40 | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | (3556) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | BETA: splitting (3556) gives: % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | (3557) all_57_0 = e0 & op(e3, e3) = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (438), (3557), (function-axioms) are % 130.20/18.40 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #270. % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | (3558) all_57_2 = e0 & op(e2, e3) = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | ALPHA: (3558) implies: % 130.20/18.40 | | | | | | | | | | | | | | | | | (3559) all_57_2 = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3532), (3559) imply: % 130.20/18.40 | | | | | | | | | | | | | | | | | (3560) e2 = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | REDUCE: (14), (3560) imply: % 130.20/18.40 | | | | | | | | | | | | | | | | | (3561) $false % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | CLOSE: (3561) is inconsistent. % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | End of split % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | (3562) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 130.20/18.40 | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | BETA: splitting (3562) gives: % 130.20/18.40 | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | (3563) all_57_6 = e0 & op(e1, e3) = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (3549), (3563), (function-axioms) are % 130.20/18.40 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #101. % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | (3564) all_57_12 = e0 & op(e0, e3) = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | ALPHA: (3564) implies: % 130.20/18.40 | | | | | | | | | | | | | | | | | (3565) all_57_12 = e0 % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 130.20/18.40 | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | | (3566) ~ (op(e3, e1) = e1) % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3513), (3566) imply: % 130.20/18.40 | | | | | | | | | | | | | | | | | | (3567) $false % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | | CLOSE: (3567) is inconsistent. % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | | (3568) all_53_8 = e1 % 130.20/18.40 | | | | | | | | | | | | | | | | | | % 130.20/18.40 | | | | | | | | | | | | | | | | | | REDUCE: (137), (3568) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3569) ~ (all_53_9 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | SIMP: (3569) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3570) ~ (all_53_9 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | REDUCE: (135), (3568) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3571) ~ (all_53_11 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | SIMP: (3571) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3572) ~ (all_53_11 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | REDUCE: (428), (3568) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3573) ~ (all_12_2 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | SIMP: (3573) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3574) ~ (all_12_2 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | REDUCE: (411), (3568) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3575) ~ (all_4_2 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | SIMP: (3575) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | (3576) ~ (all_4_2 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | (3577) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 130.20/18.41 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (3577) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | (3578) all_57_12 = e1 & op(e0, e3) = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3565), (3578) are inconsistent by sub-proof % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | #336. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | (3579) all_57_13 = e1 & op(e0, e2) = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | ALPHA: (3579) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | (3580) all_57_13 = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | (3581) op(e0, e2) = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | (3582) ~ (op(e3, e3) = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3515), (3582) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | (3583) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3583) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | (3584) all_4_2 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (3584) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | (3585) ~ (all_53_2 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | (3586) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3586) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3587) all_57_0 = e0 & op(e3, e3) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3587) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3588) all_57_0 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (248), (340), (342), (344), (3481), (3548), % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3585), (3588) are inconsistent by sub-proof #32. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3589) all_57_1 = e0 & op(e3, e2) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3589) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3590) all_57_1 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3591) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3591) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3592) all_57_1 = e2 & op(e3, e2) = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3590), (3592) are inconsistent by sub-proof % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | #246. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3593) all_57_3 = e2 & op(e2, e2) = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (3490), (3515), (3584), (3593) are % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3594) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (337), (338), (3537), (3539), (3594) are % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #30. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | (3595) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3595) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3596) all_57_4 = e0 & op(e3, e1) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3596) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3597) all_57_4 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (231), (285), (332), (334), (3570), (3572), % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3574), (3597) are inconsistent by sub-proof #331. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3598) all_57_9 = e0 & op(e3, e0) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3598) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | (3599) all_57_9 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3600) ~ (op(e1, e3) = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3517), (3600) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3601) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3601) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3602) all_53_2 = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (3602) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3603) ~ (all_53_6 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3603) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3604) ~ (all_53_6 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (3602) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3605) ~ (all_53_14 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3605) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3606) ~ (all_53_14 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3585), (3602) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3607) ~ (e3 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3524), (3602) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (3608) ~ (e2 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3609) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3609) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3610) all_57_6 = e0 & op(e1, e3) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (227), (279), (282), (285), (286), (3574), % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3604), (3606), (3610) are inconsistent by % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3611) all_57_7 = e0 & op(e1, e2) = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3611) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3612) all_57_7 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3613) ~ (all_10_2 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (3613) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3614) ~ (all_8_2 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3615) all_55_15 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3615) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3616) all_8_2 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3614), (3616) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3617) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3617) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3618) ~ (all_55_15 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3619) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3620) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3620) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3621) all_57_12 = e3 & op(e0, e3) = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3621) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3622) op(e0, e3) = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3623) ~ (op(e0, e3) = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3622), (3623) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3624) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3624) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3625) all_55_12 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3625) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3626) all_53_3 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (3626) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3627) ~ (all_4_2 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3627) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3628) ~ (all_4_2 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3629) all_55_0 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3629) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3630) all_4_2 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3584), (3628) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3631) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3631) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3632) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (316), (438), (3528), (3576), (3632) are % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3633) all_57_13 = e3 & op(e0, e2) = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3580), (3633) are inconsistent by sub-proof % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3634) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3634) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635) all_57_14 = e3 & op(e0, e1) = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3635) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3636) op(e0, e1) = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3619) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3637) all_55_15 = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3637) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3638) all_8_2 = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (3638) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3639) all_28_2 = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (3638) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3640) all_36_2 = e2 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3641) ~ (all_28_2 = e2) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3639), (3641) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3642) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3642) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3643) op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_28_0 & $i(all_28_0))) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3643) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3644) op(e0, e2) = all_28_1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3645) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_28_0 & $i(all_28_0)) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3646) ~ (all_36_2 = e2) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3640), (3646) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3647) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3647) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3648) op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_36_0 & $i(all_36_0))) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3648) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3649) op(e0, e2) = all_36_1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3645) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3650) ~ (all_28_1 = e1) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_36_1, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (3581), (3649) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3651) all_36_1 = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_1, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_36_1, e2, e0, simplifying with (3644), (3649) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3652) all_36_1 = all_28_1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3651), (3652) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3653) all_28_1 = e1 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3650), (3653) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3654) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3654) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3655) ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_0) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3655) implies: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3656) ~ (all_28_0 = e3) % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3657) op(e0, e1) = all_28_0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_0, % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (3636), (3657) gives: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3658) all_28_0 = e3 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3656), (3658) imply: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3659) $false % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3659) is inconsistent. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3660) all_55_15 = e1 | all_55_15 = e0 % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (3510), (3553), (3660) are inconsistent by % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #144. % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3661) all_57_15 = e3 & op(e0, e0) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3661) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3662) all_57_15 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3619) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3663) all_55_15 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3663) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3664) all_8_2 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (3664) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3665) ~ (all_53_14 = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3614), (3664) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3666) ~ (e3 = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3667) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3667) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3668) all_57_9 = e2 & op(e3, e0) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3668) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3669) all_57_9 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3599), (3669) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3670) e2 = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3670) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3671) $false % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3671) is inconsistent. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3672) all_57_10 = e2 & op(e2, e0) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3672) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3673) op(e2, e0) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (287), (296), (297), (305), (3516), (3673) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3674) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3674) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3675) all_57_11 = e2 & op(e1, e0) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (3665), (3675), (function-axioms) are % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3676) all_57_15 = e2 & op(e0, e0) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3676) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3677) all_57_15 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (3662), (3677) are inconsistent by sub-proof % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #227. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3678) all_55_15 = e1 | all_55_15 = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (3510), (3553), (3678) are inconsistent by % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #144. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3679) all_10_2 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (3679) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3680) all_8_2 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3680) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3681) all_8_2 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (3681) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3682) ~ (all_53_14 = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (3681) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3683) op(e0, e0) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3684) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3684) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3685) all_57_6 = e3 & op(e1, e3) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3685) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3686) op(e1, e3) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (3585), (3686) are inconsistent by % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #323. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3687) all_57_7 = e3 & op(e1, e2) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3687) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3688) all_57_7 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (3612), (3688) are inconsistent by sub-proof % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #321. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3689) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3689) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3690) all_57_8 = e3 & op(e1, e1) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3690) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3691) op(e1, e1) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3692) ( ~ (all_52_0 = e3) & op(e3, e3) = all_52_0 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_0)) | ( ~ (all_52_1 = e3) & op(e2, e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_1 & $i(all_52_1)) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3692) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3693) ~ (all_52_0 = e3) & op(e3, e3) = all_52_0 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_0) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3693) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3694) ~ (all_52_0 = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3695) op(e3, e3) = all_52_0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_0, % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3515), (3695) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696) all_52_0 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3694), (3696) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3697) $false % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3697) is inconsistent. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3698) ~ (all_52_1 = e3) & op(e2, e2) = all_52_1 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_1) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3698) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3699) ~ (all_52_1 = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3700) op(e2, e2) = all_52_1 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_1, % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (3491), (3700) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3701) all_52_1 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3699), (3701) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3702) $false % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3702) is inconsistent. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3703) ( ~ (all_52_2 = e3) & op(e1, e1) = all_52_2 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_2)) | ( ~ (all_52_3 = e3) & op(e0, e0) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_52_3 & $i(all_52_3)) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3703) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3704) ~ (all_52_2 = e3) & op(e1, e1) = all_52_2 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3704) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3705) ~ (all_52_2 = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3706) op(e1, e1) = all_52_2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_2, % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (3691), (3706) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3707) all_52_2 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3705), (3707) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3708) $false % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3708) is inconsistent. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3709) ~ (all_52_3 = e3) & op(e0, e0) = all_52_3 & % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3709) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3710) ~ (all_52_3 = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3711) op(e0, e0) = all_52_3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_3, % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (3683), (3711) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3712) all_52_3 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3710), (3712) imply: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3713) $false % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3713) is inconsistent. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3714) all_57_11 = e3 & op(e1, e0) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (3682), (3714), (function-axioms) are % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3715) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3715) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3716) all_57_8 = e0 & op(e1, e1) = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3717) all_57_8 = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3718) op(e1, e1) = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3719) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3719) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3720) all_57_4 = e2 & op(e3, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3720) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3721) all_57_4 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (231), (285), (332), (334), (3570), (3572), % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574), (3721) are inconsistent by sub-proof #287. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3722) all_57_5 = e2 & op(e2, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3722) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3723) op(e2, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (3526), (3723) are inconsistent by % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #347. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3724) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3724) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3725) all_57_8 = e2 & op(e1, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3725) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3726) op(e1, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3718), (3726), (function-axioms) are % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3727) all_57_14 = e2 & op(e0, e1) = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3727) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3728) all_57_14 = e2 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3729) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3729) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3730) all_57_4 = e3 & op(e3, e1) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3730) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3731) all_57_4 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3732) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3732) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3733) all_57_6 = e1 & op(e1, e3) = e1 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3733) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) all_57_6 = e1 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3735) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) all_57_1 = e0 & op(e3, e2) = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3736) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3737) all_57_1 = e0 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3738) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3738) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) all_57_6 = e3 & op(e1, e3) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3739) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) op(e1, e3) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (3585), (3740) are inconsistent by % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #323. % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) all_57_7 = e3 & op(e1, e2) = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3741) implies: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) all_57_7 = e3 % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (157), (210), (227), (279), (280), (282), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285), (286), (337), (415), (3524), (3537), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549), (3585), (3743) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3744) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) all_57_8 = e2 & op(e1, e1) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3745) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) op(e1, e1) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3718), (3746), (function-axioms) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) all_57_11 = e2 & op(e1, e0) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3747) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) all_57_11 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3749) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) all_57_1 = e2 & op(e3, e2) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) all_57_1 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3737), (3751) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) e2 = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (18), (228), (3717), (3734), (3742), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748), (3752) are inconsistent by sub-proof #301. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_57_3 = e2 & op(e2, e2) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (3490), (3515), (3584), (3753) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (337), (338), (3537), (3539), (3754) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #30. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3755) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) all_57_8 = e3 & op(e1, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3756) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) op(e1, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (3718), (3757), (function-axioms) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) all_57_11 = e3 & op(e1, e0) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3758) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3759) all_57_11 = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (157), (210), (227), (279), (280), (282), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285), (286), (337), (415), (3524), (3537), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549), (3585), (3760) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #29. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3761) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_57_8 = e2 & op(e1, e1) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3762) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) op(e1, e1) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3718), (3763), (function-axioms) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) all_57_11 = e2 & op(e1, e0) = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3764) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3765) all_57_11 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (3515), (3584), (3759), (3765) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #314. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3766) all_57_3 = e0 & op(e2, e2) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3766) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3767) all_57_3 = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3490), (3767) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3768) e3 = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3731), (3768) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3769) all_57_4 = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (231), (285), (332), (334), (3570), (3572), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574), (3769) are inconsistent by sub-proof #331. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3770) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3770) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3771) all_57_7 = e0 & op(e1, e2) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3771) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3772) all_57_7 = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (18), (228), (229), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3717), (3718), (3734), (3772), (function-axioms) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #316. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3773) all_57_13 = e0 & op(e0, e2) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3773) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3774) op(e0, e2) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (3551), (3774) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3775) all_57_7 = e1 & op(e1, e2) = e1 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3775) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3776) op(e1, e2) = e1 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (282), (3604), (3776) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #341. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3777) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (286), (3574), (3606), (3777) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #338. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3778) all_57_5 = e3 & op(e2, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (3484), (3778), (function-axioms) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3779) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3779) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3780) all_57_8 = e3 & op(e1, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3780) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3781) op(e1, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (3718), (3781), (function-axioms) are % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3782) all_57_14 = e3 & op(e0, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3782) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3783) all_57_14 = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3728), (3783) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3784) e3 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3584), (3784) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3785) all_4_2 = e2 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (3515), (3785) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (3786) all_57_11 = e0 & op(e1, e0) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3786) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (3787) op(e1, e0) = e0 % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (329), (3545), (3787) are inconsistent by % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #355. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | (3788) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 130.20/18.43 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.20/18.43 | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (3510), (3572), (3788), % 130.20/18.43 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.43 | | | | | | | | | | | | | | | | | | | #293. % 130.20/18.43 | | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | (3789) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 130.20/18.43 | | | | | | | | | | | e2 & op(e0, e3) = e2) % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | REF_CLOSE: (173), (177), (3524), (3525), (3789), % 130.20/18.43 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.43 | | | | | | | | | | | #88. % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | | % 130.20/18.43 | | | | | | | | | End of split % 130.20/18.43 | | | | | | | | | % 130.20/18.43 | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | % 130.20/18.43 | | | | | | | | | (3790) ~ (unit = e3) % 130.20/18.43 | | | | | | | | | (3791) unit = e2 | unit = e1 | unit = e0 % 130.20/18.43 | | | | | | | | | % 130.20/18.43 | | | | | | | | | BETA: splitting (55) gives: % 130.20/18.43 | | | | | | | | | % 130.20/18.43 | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | (3792) ~ (all_10_2 = e3) % 130.20/18.43 | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | REDUCE: (395), (3792) imply: % 130.20/18.43 | | | | | | | | | | (3793) ~ (all_8_2 = e3) % 130.20/18.43 | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | BETA: splitting (58) gives: % 130.20/18.43 | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | (3794) ~ (all_12_2 = e2) % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | BETA: splitting (61) gives: % 130.20/18.43 | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | (3795) ~ (all_14_2 = e2) % 130.20/18.43 | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | REDUCE: (382), (3795) imply: % 130.20/18.43 | | | | | | | | | | | | (3796) ~ (all_4_2 = e2) % 130.20/18.43 | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | BETA: splitting (67) gives: % 130.20/18.43 | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | (3797) ~ (all_18_2 = e3) % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REDUCE: (391), (3797) imply: % 130.20/18.43 | | | | | | | | | | | | | (3798) ~ (all_12_2 = e3) % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (73), (82), (94), % 130.20/18.43 | | | | | | | | | | | | | (124), (139), (140), (142), (153), (154), (155), % 130.20/18.43 | | | | | | | | | | | | | (158), (172), (173), (203), (205), (206), (207), % 130.20/18.43 | | | | | | | | | | | | | (208), (209), (256), (258), (259), (265), (271), % 130.20/18.43 | | | | | | | | | | | | | (278), (279), (280), (286), (327), (328), (329), % 130.20/18.43 | | | | | | | | | | | | | (331), (332), (334), (338), (339), (341), (342), % 130.20/18.43 | | | | | | | | | | | | | (343), (361), (389), (397), (416), (426), (427), % 130.20/18.43 | | | | | | | | | | | | | (429), (431), (433), (434), (437), (3482), (3483), % 130.20/18.43 | | | | | | | | | | | | | (3500), (3510), (3791), (3793), (3794), (3798), % 130.20/18.43 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.20/18.43 | | | | | | | | | | | | | #26. % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | (3799) all_18_2 = e3 % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | COMBINE_EQS: (391), (3799) imply: % 130.20/18.43 | | | | | | | | | | | | | (3800) all_12_2 = e3 % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REDUCE: (415), (3800) imply: % 130.20/18.43 | | | | | | | | | | | | | (3801) ~ (all_53_2 = e3) % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REDUCE: (431), (3800) imply: % 130.20/18.43 | | | | | | | | | | | | | (3802) ~ (all_53_11 = e3) % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REDUCE: (433), (3800) imply: % 130.20/18.43 | | | | | | | | | | | | | (3803) ~ (all_53_14 = e3) % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | REDUCE: (57), (3800) imply: % 130.20/18.43 | | | | | | | | | | | | | (3804) op(e1, e1) = e3 % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.20/18.43 | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | (3805) ~ (op(e1, e3) = e3) % 130.20/18.43 | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.20/18.43 | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | (3806) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.20/18.43 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.20/18.43 | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | BETA: splitting (3806) gives: % 130.20/18.43 | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | (3807) all_57_12 = e3 & op(e0, e3) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | ALPHA: (3807) implies: % 130.20/18.43 | | | | | | | | | | | | | | | | (3808) op(e0, e3) = e3 % 130.20/18.43 | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.20/18.43 | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | Case 1: % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | (3809) ~ (op(e0, e3) = e3) % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | PRED_UNIFY: (3808), (3809) imply: % 130.20/18.43 | | | | | | | | | | | | | | | | | (3810) $false % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | | CLOSE: (3810) is inconsistent. % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.43 | | | | | | | | | | | | | | | | Case 2: % 130.20/18.43 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | (3811) all_53_3 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | REDUCE: (407), (3811) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | (3812) ~ (all_4_2 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | SIMP: (3812) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | (3813) ~ (all_4_2 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3814) all_55_0 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3814) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3815) all_4_2 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | REDUCE: (3813), (3815) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3816) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | CLOSE: (3816) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3817) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (3817) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3818) all_55_0 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3818) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3819) all_4_2 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | REDUCE: (3796), (3819) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3820) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | CLOSE: (3820) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3821) all_55_0 = e1 | all_55_0 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (3821) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3822) all_55_0 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3822) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3823) all_4_2 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (3823) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3824) ~ (all_53_4 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (3805) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3825) ~ (unit = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3791) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3826) unit = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3500), (3826) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3827) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3827) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3828) unit = e1 | unit = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3828) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3829) unit = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3829) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3830) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3830) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3831) unit = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3831) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3832) op(e0, e1) = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3831) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3833) op(e2, e0) = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (3831) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3834) op(e1, e0) = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (3831) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3835) op(e0, e0) = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3836) ~ (op(e0, e0) = e0) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3835), (3836) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3837) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3837) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3838) all_36_2 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (3838) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3839) all_8_2 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3839) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3840) all_8_2 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (3840) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3841) ~ (all_53_11 = e0) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3842) ~ (op(e2, e0) = e2) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3833), (3842) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3843) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3843) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3844) all_55_7 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3844) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3845) all_53_13 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (3845) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3846) ~ (all_53_14 = e2) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3846) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3847) ~ (all_53_14 = e2) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3848) ~ (op(e0, e1) = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3832), (3848) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3849) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3849) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3850) all_55_14 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (3850) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3851) all_53_11 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (3851) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3852) ~ (all_53_9 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3853) all_55_11 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3853) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3854) all_53_14 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3803), (3854) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3855) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3855) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3856) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3856) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3857) all_55_11 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3857) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3858) all_53_14 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3847), (3858) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3859) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3859) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3860) all_55_11 = e1 | all_55_11 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3860) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3861) all_55_11 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3861) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3862) all_53_14 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3862) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3863) all_53_14 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3863) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3864) ~ (all_53_6 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (142), (147), (149), (150), (209), % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (279), (309), (324), (332), (339), (3482), % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3791), (3824), (3825), (3852), (3864) are % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #155. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3865) all_55_11 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3865) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3866) all_53_14 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3866) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_53_14 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (286), (3834), (3867) are inconsistent by % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3868) all_55_0 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3868) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3869) all_4_2 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (438), (3869) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3870) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | CLOSE: (3870) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | (3871) all_57_13 = e3 & op(e0, e2) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | ALPHA: (3871) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | (3872) all_57_13 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | (3873) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.20/18.44 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | BETA: splitting (3873) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3874) all_57_9 = e3 & op(e3, e0) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | ALPHA: (3874) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3875) all_57_9 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | (3876) op(e3, e0) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3877) ~ (op(e3, e0) = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3876), (3877) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3878) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | CLOSE: (3878) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3879) all_53_12 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | REDUCE: (147), (3879) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3880) ~ (all_53_4 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | REDUCE: (413), (3879) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3881) ~ (all_4_2 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | SIMP: (3881) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | (3882) ~ (all_4_2 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3883) all_55_0 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3883) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3884) all_4_2 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (3882), (3884) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3885) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | CLOSE: (3885) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3886) ~ (all_55_0 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | (3887) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3887) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3888) all_55_0 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3888) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3889) all_4_2 = e2 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3796), (3889) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3890) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3890) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | (3891) all_55_0 = e1 | all_55_0 = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3892) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3892) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3893) all_57_0 = e3 & op(e3, e3) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (319), (382), (3882), (3893) are inconsistent by % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #206. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3894) all_57_2 = e3 & op(e2, e3) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3496), (3894) are inconsistent by sub-proof #24. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | (3895) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3895) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3896) all_57_6 = e3 & op(e1, e3) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3805), (3896) are inconsistent by sub-proof #181. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3897) all_57_12 = e3 & op(e0, e3) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3897) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3898) all_57_12 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | (3899) op(e0, e3) = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3900) ~ (op(e0, e3) = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3899), (3900) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3901) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3901) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3902) all_55_12 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3902) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3903) all_53_3 = e3 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (3903) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3904) ~ (all_53_7 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (3903) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (3905) ~ (all_8_2 = e3) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3906) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3872), (3898), (3906) are inconsistent by % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3907) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3907) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_57_14 = e1 & op(e0, e1) = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3908) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_57_14 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3910) op(e0, e1) = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3911) ~ (op(e0, e1) = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3910), (3911) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3912) $false % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3912) is inconsistent. % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3913) all_53_11 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (3913) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3914) ~ (all_53_7 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (3913) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3915) ~ (all_8_2 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3891) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916) all_55_0 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3916) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3917) all_4_2 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3917) implies: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3918) all_4_2 = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (3918) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3919) ~ (all_53_2 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (3918) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3920) ~ (all_53_4 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3882), (3918) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) ~ (e3 = e1) % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (3918) imply: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) op(e3, e3) = e1 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) all_57_15 = e0 & op(e0, e0) = e0 % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3923) implies: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924) all_57_15 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3925) op(e0, e0) = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3926) ~ (op(e0, e0) = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3925), (3926) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3927) $false % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3927) is inconsistent. % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3928) all_53_15 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (3928) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3929) all_8_2 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3929) implies: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3930) all_8_2 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (3930) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931) ~ (all_53_7 = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (3930) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3932) ~ (all_53_13 = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3793), (3930) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3933) ~ (e3 = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3510), (3930) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3934) ~ (e1 = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3935) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3935) gives: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3936) all_57_1 = e1 & op(e3, e2) = e1 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3936) implies: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3937) all_57_1 = e1 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3938) gives: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3939) all_57_1 = e0 & op(e3, e2) = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3937), (3939) are inconsistent by sub-proof % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #286. % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3940) all_57_3 = e0 & op(e2, e2) = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3940) implies: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3941) all_57_3 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3490), (3941) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) e3 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3903), (3942) imply: % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) all_53_3 = e0 % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.20/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (344), (3899), (3943) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #299. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3944) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) all_57_7 = e0 & op(e1, e2) = e0 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) all_57_7 = e0 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) all_55_13 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3947) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) all_53_7 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3483), (3948) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) $false % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3949) is inconsistent. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) ~ (all_55_13 = e3) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3951) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) all_55_13 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3952) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) all_53_7 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (3953) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) ~ (all_53_6 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3483), (3953) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) ~ (e3 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3956) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) all_57_6 = e1 & op(e1, e3) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3957) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) op(e1, e3) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (3919), (3958) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_57_7 = e1 & op(e1, e2) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) all_57_7 = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3946), (3960) are inconsistent by sub-proof % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3961) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) all_57_8 = e1 & op(e1, e1) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3962) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) op(e1, e1) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (285), (3800), (3963) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #174. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) all_57_11 = e1 & op(e1, e0) = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3964) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_57_11 = e1 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3966) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) all_57_6 = e2 & op(e1, e3) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3967) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) all_57_6 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3969) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) all_57_0 = e2 & op(e3, e3) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3970) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) op(e3, e3) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3922), (3971), (function-axioms) are % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) all_57_1 = e2 & op(e3, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3972) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) op(e3, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) ~ (op(e3, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3973), (3974) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) $false % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3975) is inconsistent. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) all_53_4 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (3976) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) ~ (all_53_6 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (3976) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) ~ (all_53_7 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3978) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) ~ (all_53_7 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (3976) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) ~ (all_6_2 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3980) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) ~ (all_6_2 = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_55_13 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3982) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) all_53_7 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3984) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (3937), (3972) are inconsistent by sub-proof % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #266. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_57_3 = e2 & op(e2, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3985) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) op(e2, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (301), (398), (3981), (3986) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #348. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3987) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) all_57_7 = e2 & op(e1, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3988) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) op(e1, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (3954), (3989) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) all_57_13 = e2 & op(e0, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) op(e0, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) ~ (op(e0, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (3991), (3992) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) $false % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3993) is inconsistent. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3953), (3983) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) e3 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3994) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) e3 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (3995) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) $false % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3996) is inconsistent. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3914), (3931), (3951), (3979) are % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3997) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_57_4 = e2 & op(e3, e1) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3998) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) all_57_4 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4000) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_57_12 = e2 & op(e0, e3) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4001) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_57_12 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (248), (319), (340), (342), (382), (3481), % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3801), (3882), (4002) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #203. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) all_57_13 = e2 & op(e0, e2) = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4003) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_57_13 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3872), (4004) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) e3 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4005) implies: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) e3 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3875), (4006) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) all_57_9 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4008) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4008) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4009) all_57_0 = e3 & op(e3, e3) = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (319), (382), (3882), (4009) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #206. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010) all_57_1 = e3 & op(e3, e2) = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (321), (3880), (4010) are inconsistent by % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #328. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4011) gives: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012) all_57_4 = e3 & op(e3, e1) = e3 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (248), (319), (340), (342), (382), (3481), % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3801), (3882), (3898), (3999), (4012) are % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #202. % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3898), (4006) imply: % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4013) all_57_12 = e2 % 130.50/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (248), (319), (340), (342), (382), (3481), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3801), (3882), (4013) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #203. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4014) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4014) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4015) all_57_14 = e2 & op(e0, e1) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4015) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4016) all_57_14 = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3909), (4016) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017) e2 = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (4017) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4018) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4018) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4019) all_57_15 = e2 & op(e0, e0) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4019) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4020) all_57_15 = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3924), (4020) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4021) e2 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3968), (4021) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022) all_57_6 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (18), (228), (3804), (3946), (3965), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022), (function-axioms) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #170. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4023) all_57_9 = e2 & op(e3, e0) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4023) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4024) all_57_9 = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3875), (4024) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4025) e3 = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3898), (4025) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4026) all_57_12 = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (248), (319), (340), (342), (382), (3481), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3801), (3882), (4026) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #203. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4027) all_57_7 = e2 & op(e1, e2) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4027) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4028) op(e1, e2) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (3954), (4028) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4029) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (3804), (3965), (4029), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #171. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4030) all_55_13 = e1 | all_55_13 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3914), (3931), (4030) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #61. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031) all_57_13 = e0 & op(e0, e2) = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4031) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4032) op(e0, e2) = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (3931), (4032) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_57_3 = e1 & op(e2, e2) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3490), (4033) are inconsistent by sub-proof % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #22. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4034) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4034) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_57_7 = e1 & op(e1, e2) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4035) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4036) op(e1, e2) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4037) ~ (op(e1, e2) = e1) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4036), (4037) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4038) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4038) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4039) all_53_6 = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (4039) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4040) ~ (all_53_14 = e1) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4040) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4041) ~ (all_53_14 = e1) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (158), (259), (286), (327), (328), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342), (343), (3791), (3899), (3932), (4041) are % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4042) all_57_13 = e1 & op(e0, e2) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (3914), (4042), (function-axioms) are % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4043) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (13), (16), (139), (203), (256), (263), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (265), (306), (344), (427), (436), (3500), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3510), (3791), (3793), (3898), (3899), (3903), % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3909), (4043) are inconsistent by sub-proof #20. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4044) all_55_0 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (4044) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4045) all_4_2 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4045) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4046) all_4_2 = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (438), (4046) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4047) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4047) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (4048) all_57_15 = e1 & op(e0, e0) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3510), (4048), (function-axioms) are % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | (4049) all_57_10 = e3 & op(e2, e0) = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (3485), (4049), (function-axioms) are % 130.50/18.46 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | (4050) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.50/18.46 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (51), (174), % 130.50/18.46 | | | | | | | | | | | | | | | | | (219), (220), (221), (3510), (3803), (3872), % 130.50/18.46 | | | | | | | | | | | | | | | | | (4050), (function-axioms) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | | | | sub-proof #76. % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | (4051) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.50/18.46 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | BETA: splitting (4051) gives: % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | (4052) all_57_14 = e3 & op(e0, e1) = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | REF_CLOSE: (171), (3802), (4052), (function-axioms) are % 130.50/18.46 | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | (4053) all_57_15 = e3 & op(e0, e0) = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3793), (4053), (function-axioms) are % 130.50/18.46 | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | (4054) op(e1, e3) = e3 % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REF_CLOSE: (342), (3801), (4054) are inconsistent by % 130.50/18.46 | | | | | | | | | | | | | | sub-proof #323. % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | End of split % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | (4055) all_14_2 = e2 % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | COMBINE_EQS: (382), (4055) imply: % 130.50/18.46 | | | | | | | | | | | | (4056) all_4_2 = e2 % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | REDUCE: (409), (4056) imply: % 130.50/18.46 | | | | | | | | | | | | (4057) ~ (all_53_4 = e2) % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | REDUCE: (45), (4056) imply: % 130.50/18.46 | | | | | | | | | | | | (4058) op(e3, e3) = e2 % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | BETA: splitting (335) gives: % 130.50/18.46 | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | (4059) ~ (op(e3, e2) = e2) % 130.50/18.46 | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.50/18.46 | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | (4060) ~ (all_18_2 = e3) % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REDUCE: (391), (4060) imply: % 130.50/18.46 | | | | | | | | | | | | | | (4061) ~ (all_12_2 = e3) % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (73), (82), (94), % 130.50/18.46 | | | | | | | | | | | | | | (124), (139), (140), (142), (153), (154), (155), % 130.50/18.46 | | | | | | | | | | | | | | (158), (172), (173), (203), (205), (206), (207), % 130.50/18.46 | | | | | | | | | | | | | | (208), (209), (256), (258), (259), (265), (271), % 130.50/18.46 | | | | | | | | | | | | | | (278), (279), (280), (286), (327), (328), (329), % 130.50/18.46 | | | | | | | | | | | | | | (331), (332), (334), (338), (339), (341), (342), % 130.50/18.46 | | | | | | | | | | | | | | (343), (361), (389), (397), (416), (426), (427), % 130.50/18.46 | | | | | | | | | | | | | | (429), (431), (433), (434), (437), (3482), (3483), % 130.50/18.46 | | | | | | | | | | | | | | (3500), (3510), (3791), (3793), (3794), (4061), % 130.50/18.46 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.50/18.46 | | | | | | | | | | | | | | #26. % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | (4062) all_18_2 = e3 % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | COMBINE_EQS: (391), (4062) imply: % 130.50/18.46 | | | | | | | | | | | | | | (4063) all_12_2 = e3 % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REDUCE: (415), (4063) imply: % 130.50/18.46 | | | | | | | | | | | | | | (4064) ~ (all_53_2 = e3) % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REDUCE: (431), (4063) imply: % 130.50/18.46 | | | | | | | | | | | | | | (4065) ~ (all_53_11 = e3) % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | REDUCE: (57), (4063) imply: % 130.50/18.46 | | | | | | | | | | | | | | (4066) op(e1, e1) = e3 % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.50/18.46 | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | (4067) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.50/18.46 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | BETA: splitting (4067) gives: % 130.50/18.46 | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | (4068) all_57_12 = e3 & op(e0, e3) = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | ALPHA: (4068) implies: % 130.50/18.46 | | | | | | | | | | | | | | | | (4069) all_57_12 = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | (4070) op(e0, e3) = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | (4071) ~ (op(e0, e3) = e3) % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | PRED_UNIFY: (4070), (4071) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | (4072) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | CLOSE: (4072) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | (4073) all_53_3 = e3 % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | REDUCE: (153), (4073) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | (4074) ~ (all_53_11 = e3) % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | REDUCE: (416), (4073) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | (4075) ~ (all_8_2 = e3) % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | (4076) ~ (op(e1, e3) = e3) % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (4076) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | (4077) ~ (unit = e1) % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | BETA: splitting (3791) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | (4078) unit = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | REDUCE: (3500), (4078) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | (4079) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | CLOSE: (4079) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | (4080) unit = e1 | unit = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (4080) gives: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4081) unit = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (4077), (4081) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4082) $false % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | CLOSE: (4082) is inconsistent. % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4083) unit = e0 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4083) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4084) op(e0, e2) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (4083) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4085) op(e0, e1) = e1 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (4083) imply: % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | (4086) op(e2, e0) = e2 % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | % 130.50/18.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (4083) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | (4087) op(e0, e0) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4088) ~ (op(e0, e2) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4084), (4088) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4089) $false % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4089) is inconsistent. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4090) all_53_7 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4090) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4091) ~ (all_53_6 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4090) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4092) ~ (all_53_11 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | SIMP: (4092) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | (4093) ~ (all_53_11 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4094) ~ (op(e2, e0) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4086), (4094) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4095) $false % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4095) is inconsistent. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4096) all_55_7 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4096) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4097) all_53_13 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (4097) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4098) ~ (all_53_9 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (4097) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4099) ~ (all_53_14 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4099) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4100) ~ (all_53_14 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (4097) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4101) ~ (all_8_2 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4101) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4102) ~ (all_8_2 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3485), (4097) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | (4103) ~ (e3 = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4104) ~ (op(e0, e0) = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4087), (4104) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4105) $false % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4105) is inconsistent. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4106) all_55_15 = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4106) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4107) all_8_2 = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (4107) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4108) ~ (all_53_11 = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3793), (4107) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4109) ~ (e3 = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4102), (4107) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | (4110) ~ (e2 = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4111) ~ (op(e0, e1) = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4085), (4111) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4112) $false % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4112) is inconsistent. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4113) all_53_11 = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (4113) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4114) ~ (all_53_9 = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4065), (4113) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4115) ~ (e3 = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4093), (4113) imply: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (4116) ~ (e2 = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4117) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4117) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4118) all_57_2 = e2 & op(e2, e3) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4118) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4119) op(e2, e3) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (287), (296), (297), (305), (4086), (4119) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4120) all_57_3 = e2 & op(e2, e2) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (3490), (4120) are inconsistent by sub-proof % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | #46. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4121) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4121) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4122) all_57_5 = e2 & op(e2, e1) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4122) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4123) op(e2, e1) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4098), (4123) are inconsistent by % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #347. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4124) all_57_10 = e2 & op(e2, e0) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4124) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (4125) all_57_10 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4126) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4126) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4127) all_57_2 = e1 & op(e2, e3) = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4127) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4128) all_57_2 = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4129) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4129) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4130) all_57_6 = e2 & op(e1, e3) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4130) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4131) all_57_6 = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4132) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4132) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4133) all_57_0 = e0 & op(e3, e3) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4133) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4134) op(e3, e3) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4058), (4134), (function-axioms) are % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4135) all_57_2 = e0 & op(e2, e3) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4128), (4135) are inconsistent by sub-proof % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #166. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4136) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4136) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4137) all_57_6 = e0 & op(e1, e3) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4131), (4137) are inconsistent by sub-proof % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #132. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4138) all_57_12 = e0 & op(e0, e3) = e0 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (344), (4069), (4070), (4073), (4138) are % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4139) all_57_7 = e2 & op(e1, e2) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4139) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4140) op(e1, e2) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (4091), (4140) are inconsistent by % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4141) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4141) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4142) all_57_8 = e2 & op(e1, e1) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4142) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4143) op(e1, e1) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (4066), (4143), (function-axioms) are % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4144) all_57_11 = e2 & op(e1, e0) = e2 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (4100), (4144), (function-axioms) are % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4145) all_57_3 = e1 & op(e2, e2) = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (3490), (4145) are inconsistent by sub-proof % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #22. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4146) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4146) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4147) all_57_5 = e1 & op(e2, e1) = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4147) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4148) op(e2, e1) = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (4114), (4148) are inconsistent by % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4149) all_57_10 = e1 & op(e2, e0) = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4149) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4150) all_57_10 = e1 % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (4125), (4150) are inconsistent by sub-proof % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | (4151) op(e1, e3) = e3 % 130.50/18.47 | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (4064), (4151) are inconsistent by % 130.50/18.47 | | | | | | | | | | | | | | | | | | sub-proof #323. % 130.50/18.47 | | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | End of split % 130.50/18.47 | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | Case 2: % 130.50/18.47 | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | (4152) all_57_13 = e3 & op(e0, e2) = e3 % 130.50/18.47 | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | ALPHA: (4152) implies: % 130.50/18.47 | | | | | | | | | | | | | | | | (4153) all_57_13 = e3 % 130.50/18.47 | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 130.50/18.47 | | | | | | | | | | | | | | | | % 130.50/18.47 | | | | | | | | | | | | | | | | Case 1: % 130.50/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | (4154) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | BETA: splitting (4154) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4155) all_57_0 = e3 & op(e3, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | ALPHA: (4155) implies: % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4156) op(e3, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (320), (4056), (4156) are inconsistent by % 130.61/18.47 | | | | | | | | | | | | | | | | | | sub-proof #315. % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4157) all_57_2 = e3 & op(e2, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3496), (4157) are inconsistent by sub-proof #24. % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | End of split % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | (4158) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 130.61/18.47 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | BETA: splitting (4158) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4159) all_57_6 = e3 & op(e1, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | ALPHA: (4159) implies: % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4160) op(e1, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (4064), (4160) are inconsistent by % 130.61/18.47 | | | | | | | | | | | | | | | | | | sub-proof #323. % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4161) all_57_12 = e3 & op(e0, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | ALPHA: (4161) implies: % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4162) all_57_12 = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | (4163) op(e0, e3) = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4164) ~ (op(e0, e3) = e3) % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4163), (4164) imply: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4165) $false % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | CLOSE: (4165) is inconsistent. % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4166) all_55_12 = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4166) imply: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4167) all_53_3 = e3 % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | REDUCE: (154), (4167) imply: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4168) ~ (all_53_7 = e3) % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | REDUCE: (416), (4167) imply: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | (4169) ~ (all_8_2 = e3) % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | (4170) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (4153), (4162), (4170) are inconsistent by % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | sub-proof #23. % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | (4171) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4171) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | (4172) all_57_14 = e1 & op(e0, e1) = e1 % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4172) implies: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | (4173) all_57_14 = e1 % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | (4174) op(e0, e1) = e1 % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.47 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | (4175) ~ (op(e0, e1) = e1) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4174), (4175) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | (4176) $false % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4176) is inconsistent. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | (4177) all_53_11 = e1 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4177) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | (4178) ~ (all_53_7 = e1) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (4177) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | (4179) ~ (all_8_2 = e1) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (4180) all_57_15 = e0 & op(e0, e0) = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4180) implies: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (4181) op(e0, e0) = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4182) ~ (op(e0, e0) = e0) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4181), (4182) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4183) $false % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4183) is inconsistent. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4184) all_36_2 = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (4184) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4185) all_8_2 = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4185) implies: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4186) all_8_2 = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (4186) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | (4187) ~ (all_53_7 = e0) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4188) all_55_13 = e3 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4188) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4189) all_53_7 = e3 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3483), (4189) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4190) $false % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4190) is inconsistent. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4191) ~ (all_55_13 = e3) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4192) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4192) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4193) all_55_13 = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4193) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4194) all_53_7 = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4194) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4195) ~ (all_53_6 = e2) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3483), (4194) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4196) ~ (e3 = e2) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4197) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4197) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4198) all_57_1 = e2 & op(e3, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4059), (4198) are inconsistent by sub-proof #137. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4199) all_57_3 = e2 & op(e2, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (3490), (4199) are inconsistent by sub-proof % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #46. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4200) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4200) gives: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4201) all_57_7 = e2 & op(e1, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4201) implies: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4202) op(e1, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (4195), (4202) are inconsistent by % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_57_13 = e2 & op(e0, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (4153), (4203) are inconsistent by sub-proof % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #111. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4204) all_55_13 = e1 | all_55_13 = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (4178), (4187), (4204) are inconsistent by % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #61. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (4205) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (13), (16), (139), (203), (256), (263), % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (264), (265), (306), (344), (427), (436), (3500), % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (3510), (3791), (3793), (4162), (4163), (4167), % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | (4173), (4205) are inconsistent by sub-proof #20. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | (4206) all_57_15 = e1 & op(e0, e0) = e1 % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3510), (4206), (function-axioms) are % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294. % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | (4207) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.61/18.48 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | BETA: splitting (4207) gives: % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | (4208) all_57_14 = e3 & op(e0, e1) = e3 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REF_CLOSE: (171), (4065), (4208), (function-axioms) are % 130.61/18.48 | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | (4209) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3793), (4209), (function-axioms) are % 130.61/18.48 | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | (4210) op(e3, e2) = e2 % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | REF_CLOSE: (335), (4057), (4210) are inconsistent by % 130.61/18.48 | | | | | | | | | | | | | sub-proof #94. % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | (4211) all_12_2 = e2 % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | REDUCE: (426), (4211) imply: % 130.61/18.48 | | | | | | | | | | | (4212) ~ (all_53_6 = e2) % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | REDUCE: (57), (4211) imply: % 130.61/18.48 | | | | | | | | | | | (4213) op(e1, e1) = e2 % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (18), (134), (153), (171), (179), % 130.61/18.48 | | | | | | | | | | | (233), (323), (324), (337), (344), (3484), (3500), % 130.61/18.48 | | | | | | | | | | | (3791), (4212), (4213), (function-axioms) are % 130.61/18.48 | | | | | | | | | | | inconsistent by sub-proof #18. % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | End of split % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | (4214) all_10_2 = e3 % 130.61/18.48 | | | | | | | | | | (4215) op(e0, e3) = all_10_1 & $i(all_10_1) & ( ~ % 130.61/18.48 | | | | | | | | | | (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, % 130.61/18.48 | | | | | | | | | | e2) = all_10_0 & $i(all_10_0))) % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | ALPHA: (4215) implies: % 130.61/18.48 | | | | | | | | | | (4216) op(e0, e3) = all_10_1 % 130.61/18.48 | | | | | | | | | | (4217) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, % 130.61/18.48 | | | | | | | | | | e2) = all_10_0 & $i(all_10_0)) % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | COMBINE_EQS: (395), (4214) imply: % 130.61/18.48 | | | | | | | | | | (4218) all_8_2 = e3 % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | SIMP: (4218) implies: % 130.61/18.48 | | | | | | | | | | (4219) all_8_2 = e3 % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | COMBINE_EQS: (387), (4219) imply: % 130.61/18.48 | | | | | | | | | | (4220) all_16_2 = e3 % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | REDUCE: (416), (4219) imply: % 130.61/18.48 | | | | | | | | | | (4221) ~ (all_53_3 = e3) % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | REDUCE: (435), (4219) imply: % 130.61/18.48 | | | | | | | | | | (4222) ~ (all_53_12 = e3) % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | REDUCE: (437), (4219) imply: % 130.61/18.48 | | | | | | | | | | (4223) ~ (all_53_14 = e3) % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | BETA: splitting (344) gives: % 130.61/18.48 | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | (4224) ~ (op(e0, e3) = e3) % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | BETA: splitting (64) gives: % 130.61/18.48 | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | (4225) ~ (all_16_2 = e3) % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | REDUCE: (4220), (4225) imply: % 130.61/18.48 | | | | | | | | | | | | (4226) $false % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | CLOSE: (4226) is inconsistent. % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | (4227) op(e0, e3) = all_16_1 & $i(all_16_1) & ( ~ % 130.61/18.48 | | | | | | | | | | | | (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.48 | | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0))) % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | ALPHA: (4227) implies: % 130.61/18.48 | | | | | | | | | | | | (4228) op(e0, e3) = all_16_1 % 130.61/18.48 | | | | | | | | | | | | (4229) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.48 | | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0)) % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | BETA: splitting (225) gives: % 130.61/18.48 | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | (4230) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.61/18.48 | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | REF_CLOSE: (178), (324), (3485), (4222), (4230), % 130.61/18.48 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.48 | | | | | | | | | | | | | #82. % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | (4231) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.61/18.48 | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | BETA: splitting (4231) gives: % 130.61/18.48 | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | (4232) all_57_11 = e3 & op(e1, e0) = e3 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | REF_CLOSE: (174), (4223), (4232), (function-axioms) are % 130.61/18.48 | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | (4233) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | ALPHA: (4233) implies: % 130.61/18.48 | | | | | | | | | | | | | | (4234) all_57_15 = e3 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.48 | | | | | | | | | | | | | | all_10_1, e3, e0, simplifying with (173), (4216) % 130.61/18.48 | | | | | | | | | | | | | | gives: % 130.61/18.48 | | | | | | | | | | | | | | (4235) all_53_3 = all_10_1 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.48 | | | | | | | | | | | | | | all_16_1, e3, e0, simplifying with (173), (4228) % 130.61/18.48 | | | | | | | | | | | | | | gives: % 130.61/18.48 | | | | | | | | | | | | | | (4236) all_53_3 = all_16_1 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | PRED_UNIFY: (9), (4224) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4237) ~ (unit = e0) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | PRED_UNIFY: (4224), (4228) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4238) ~ (all_16_1 = e3) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | COMBINE_EQS: (4235), (4236) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4239) all_16_1 = all_10_1 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | SIMP: (4239) implies: % 130.61/18.48 | | | | | | | | | | | | | | (4240) all_16_1 = all_10_1 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | COMBINE_EQS: (259), (4235) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4241) all_55_12 = all_10_1 % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | REDUCE: (154), (4235) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4242) ~ (all_53_7 = all_10_1) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | SIMP: (4242) implies: % 130.61/18.48 | | | | | | | | | | | | | | (4243) ~ (all_53_7 = all_10_1) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | REDUCE: (153), (4235) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4244) ~ (all_53_11 = all_10_1) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | SIMP: (4244) implies: % 130.61/18.48 | | | | | | | | | | | | | | (4245) ~ (all_53_11 = all_10_1) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | REDUCE: (4238), (4240) imply: % 130.61/18.48 | | | | | | | | | | | | | | (4246) ~ (all_10_1 = e3) % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | BETA: splitting (3791) gives: % 130.61/18.48 | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | (4247) unit = e2 % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | REDUCE: (3500), (4247) imply: % 130.61/18.48 | | | | | | | | | | | | | | | (4248) $false % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | CLOSE: (4248) is inconsistent. % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | Case 2: % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | (4249) unit = e1 | unit = e0 % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | BETA: splitting (4249) gives: % 130.61/18.48 | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | Case 1: % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | (4250) unit = e1 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (3790), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4251) ~ (e3 = e1) % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (3500), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4252) ~ (e2 = e1) % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (6), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4253) op(e1, e0) = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (5), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4254) op(e3, e1) = e3 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (4), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4255) op(e2, e1) = e2 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (3), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4256) op(e1, e1) = e1 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.48 | | | | | | | | | | | | | | | | REDUCE: (2), (4250) imply: % 130.61/18.48 | | | | | | | | | | | | | | | | (4257) op(e0, e1) = e0 % 130.61/18.48 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (13), (15), (17), (57), (124), (126), % 130.61/18.49 | | | | | | | | | | | | | | | | (131), (132), (134), (135), (137), (139), (148), % 130.61/18.49 | | | | | | | | | | | | | | | | (172), (174), (178), (179), (183), (206), (208), % 130.61/18.49 | | | | | | | | | | | | | | | | (219), (221), (227), (228), (229), (230), (231), % 130.61/18.49 | | | | | | | | | | | | | | | | (234), (235), (236), (238), (239), (248), (249), % 130.61/18.49 | | | | | | | | | | | | | | | | (257), (258), (262), (264), (265), (278), (279), % 130.61/18.49 | | | | | | | | | | | | | | | | (282), (283), (284), (285), (286), (288), (303), % 130.61/18.49 | | | | | | | | | | | | | | | | (306), (309), (319), (321), (323), (324), (326), % 130.61/18.49 | | | | | | | | | | | | | | | | (328), (329), (331), (332), (382), (389), (411), % 130.61/18.49 | | | | | | | | | | | | | | | | (426), (428), (429), (433), (3490), (3496), % 130.61/18.49 | | | | | | | | | | | | | | | | (3791), (4217), (4223), (4224), (4229), (4234), % 130.61/18.49 | | | | | | | | | | | | | | | | (4237), (4240), (4241), (4243), (4245), (4246), % 130.61/18.49 | | | | | | | | | | | | | | | | (4253), (4254), (4255), (4256), (4257), % 130.61/18.49 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.49 | | | | | | | | | | | | | | | | #14. % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | (4258) ~ (unit = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (324), (340), (3481), (3791), (4222), % 130.61/18.49 | | | | | | | | | | | | | | | | (4258) are inconsistent by sub-proof #184. % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | (4259) op(e0, e3) = e3 % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | REF_CLOSE: (259), (343), (4221), (4259) are inconsistent by % 130.61/18.49 | | | | | | | | | | | sub-proof #311. % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | | % 130.61/18.49 | | | | | | | | | End of split % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | End of split % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | (4260) all_8_2 = e1 % 130.61/18.49 | | | | | | | | (4261) op(e0, e1) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = % 130.61/18.49 | | | | | | | | e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 130.61/18.49 | | | | | | | | $i(all_8_0))) % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | ALPHA: (4261) implies: % 130.61/18.49 | | | | | | | | (4262) op(e0, e1) = all_8_1 % 130.61/18.49 | | | | | | | | (4263) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = % 130.61/18.49 | | | | | | | | all_8_0 & $i(all_8_0)) % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | COMBINE_EQS: (396), (4260) imply: % 130.61/18.49 | | | | | | | | (4264) all_20_2 = e1 % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | REDUCE: (427), (4260) imply: % 130.61/18.49 | | | | | | | | (4265) ~ (all_53_7 = e1) % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | REDUCE: (434), (4260) imply: % 130.61/18.49 | | | | | | | | (4266) ~ (all_53_11 = e1) % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | REF_CLOSE: (2), (7), (8), (10), (70), (139), (142), (149), % 130.61/18.49 | | | | | | | | (153), (154), (171), (172), (204), (205), (257), % 130.61/18.49 | | | | | | | | (258), (261), (334), (335), (337), (3483), (3500), % 130.61/18.49 | | | | | | | | (4262), (4263), (4264), (4265), (4266), % 130.61/18.49 | | | | | | | | (function-axioms) are inconsistent by sub-proof #13. % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | End of split % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | Case 2: % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | | (4267) op(e2, e3) = e3 % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | | REF_CLOSE: (340), (3481), (4267) are inconsistent by sub-proof % 130.61/18.49 | | | | | | | #353. % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | End of split % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | End of split % 130.61/18.49 | | | | | % 130.61/18.49 | | | | End of split % 130.61/18.49 | | | | % 130.61/18.49 | | | Case 2: % 130.61/18.49 | | | | % 130.61/18.49 | | | | (4268) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, % 130.61/18.49 | | | | e0) = e3) % 130.61/18.49 | | | | % 130.61/18.49 | | | | BETA: splitting (4268) gives: % 130.61/18.49 | | | | % 130.61/18.49 | | | | Case 1: % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | (4269) all_57_5 = e3 & op(e2, e1) = e3 % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | REF_CLOSE: (179), (3484), (4269), (function-axioms) are inconsistent % 130.61/18.49 | | | | | by sub-proof #180. % 130.61/18.49 | | | | | % 130.61/18.49 | | | | Case 2: % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | (4270) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | REF_CLOSE: (178), (3485), (4270), (function-axioms) are inconsistent % 130.61/18.49 | | | | | by sub-proof #83. % 130.61/18.49 | | | | | % 130.61/18.49 | | | | End of split % 130.61/18.49 | | | | % 130.61/18.49 | | | End of split % 130.61/18.49 | | | % 130.61/18.49 | | End of split % 130.61/18.49 | | % 130.61/18.49 | Case 2: % 130.61/18.49 | | % 130.61/18.49 | | (4271) all_4_2 = e0 % 130.61/18.49 | | (4272) op(e3, e0) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e1) | ( ~ % 130.61/18.49 | | (all_4_0 = e2) & op(e3, e1) = all_4_0 & $i(all_4_0))) % 130.61/18.49 | | % 130.61/18.49 | | ALPHA: (4272) implies: % 130.61/18.49 | | (4273) op(e3, e0) = all_4_1 % 130.61/18.49 | | (4274) ~ (all_4_1 = e1) | ( ~ (all_4_0 = e2) & op(e3, e1) = all_4_0 & % 130.61/18.49 | | $i(all_4_0)) % 130.61/18.49 | | % 130.61/18.49 | | COMBINE_EQS: (346), (4271) imply: % 130.61/18.49 | | (4275) all_48_2 = e0 % 130.61/18.49 | | % 130.61/18.49 | | REDUCE: (405), (4271) imply: % 130.61/18.49 | | (4276) ~ (all_53_2 = e0) % 130.61/18.49 | | % 130.61/18.49 | | REDUCE: (409), (4271) imply: % 130.61/18.49 | | (4277) ~ (all_53_4 = e0) % 130.61/18.49 | | % 130.61/18.49 | | REDUCE: (411), (4271) imply: % 130.61/18.49 | | (4278) ~ (all_53_8 = e0) % 130.61/18.49 | | % 130.61/18.49 | | REDUCE: (413), (4271) imply: % 130.61/18.49 | | (4279) ~ (all_53_12 = e0) % 130.61/18.49 | | % 130.61/18.49 | | BETA: splitting (112) gives: % 130.61/18.49 | | % 130.61/18.49 | | Case 1: % 130.61/18.49 | | | % 130.61/18.49 | | | (4280) ~ (all_48_2 = e0) % 130.61/18.49 | | | % 130.61/18.49 | | | REDUCE: (4275), (4280) imply: % 130.61/18.49 | | | (4281) $false % 130.61/18.49 | | | % 130.61/18.49 | | | CLOSE: (4281) is inconsistent. % 130.61/18.49 | | | % 130.61/18.49 | | Case 2: % 130.61/18.49 | | | % 130.61/18.49 | | | (4282) op(e3, e0) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e2) | ( ~ % 130.61/18.49 | | | (all_48_0 = e1) & op(e3, e2) = all_48_0 & $i(all_48_0))) % 130.61/18.49 | | | % 130.61/18.49 | | | ALPHA: (4282) implies: % 130.61/18.49 | | | (4283) op(e3, e0) = all_48_1 % 130.61/18.49 | | | % 130.61/18.49 | | | BETA: splitting (243) gives: % 130.61/18.49 | | | % 130.61/18.49 | | | Case 1: % 130.61/18.49 | | | | % 130.61/18.49 | | | | (4284) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, % 130.61/18.49 | | | | e2) = e0) % 130.61/18.49 | | | | % 130.61/18.49 | | | | BETA: splitting (4284) gives: % 130.61/18.49 | | | | % 130.61/18.49 | | | | Case 1: % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | (4285) all_57_0 = e0 & op(e3, e3) = e0 % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | ALPHA: (4285) implies: % 130.61/18.49 | | | | | (4286) all_57_0 = e0 % 130.61/18.49 | | | | | (4287) op(e3, e3) = e0 % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | BETA: splitting (326) gives: % 130.61/18.49 | | | | | % 130.61/18.49 | | | | | Case 1: % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | (4288) ~ (op(e3, e0) = e0) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 130.61/18.49 | | | | | | all_4_1, e0, e3, simplifying with (182), (4273) gives: % 130.61/18.49 | | | | | | (4289) all_53_12 = all_4_1 % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12, % 130.61/18.49 | | | | | | all_48_1, e0, e3, simplifying with (182), (4283) gives: % 130.61/18.49 | | | | | | (4290) all_53_12 = all_48_1 % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1, e0, % 130.61/18.49 | | | | | | e3, simplifying with (4283) gives: % 130.61/18.49 | | | | | | (4291) all_48_1 = e3 | ~ (op(e3, e0) = e3) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | PRED_UNIFY: (6), (4288) imply: % 130.61/18.49 | | | | | | (4292) ~ (unit = e3) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | PRED_UNIFY: (4283), (4288) imply: % 130.61/18.49 | | | | | | (4293) ~ (all_48_1 = e0) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | COMBINE_EQS: (4289), (4290) imply: % 130.61/18.49 | | | | | | (4294) all_48_1 = all_4_1 % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | SIMP: (4294) implies: % 130.61/18.49 | | | | | | (4295) all_48_1 = all_4_1 % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | COMBINE_EQS: (307), (4289) imply: % 130.61/18.49 | | | | | | (4296) all_55_3 = all_4_1 % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | REDUCE: (147), (4289) imply: % 130.61/18.49 | | | | | | (4297) ~ (all_53_4 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | REDUCE: (134), (4289) imply: % 130.61/18.49 | | | | | | (4298) ~ (all_53_8 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | REDUCE: (126), (4289) imply: % 130.61/18.49 | | | | | | (4299) ~ (all_53_14 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | SIMP: (4299) implies: % 130.61/18.49 | | | | | | (4300) ~ (all_53_14 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | REDUCE: (435), (4289) imply: % 130.61/18.49 | | | | | | (4301) ~ (all_8_2 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | SIMP: (4301) implies: % 130.61/18.49 | | | | | | (4302) ~ (all_8_2 = all_4_1) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | REDUCE: (4293), (4295) imply: % 130.61/18.49 | | | | | | (4303) ~ (all_4_1 = e0) % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | BETA: splitting (49) gives: % 130.61/18.49 | | | | | | % 130.61/18.49 | | | | | | Case 1: % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | | (4304) ~ (all_6_2 = e3) % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | | BETA: splitting (52) gives: % 130.61/18.49 | | | | | | | % 130.61/18.49 | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | (4305) ~ (all_8_2 = e1) % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | BETA: splitting (10) gives: % 130.61/18.49 | | | | | | | | % 130.61/18.49 | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | (4306) unit = e3 % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | REDUCE: (4292), (4306) imply: % 130.61/18.49 | | | | | | | | | (4307) $false % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | CLOSE: (4307) is inconsistent. % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | (4308) unit = e2 | unit = e1 | unit = e0 % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | BETA: splitting (55) gives: % 130.61/18.49 | | | | | | | | | % 130.61/18.49 | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | (4309) ~ (all_10_2 = e3) % 130.61/18.49 | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | REDUCE: (395), (4309) imply: % 130.61/18.49 | | | | | | | | | | (4310) ~ (all_8_2 = e3) % 130.61/18.49 | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | BETA: splitting (58) gives: % 130.61/18.49 | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | (4311) ~ (all_12_2 = e2) % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | BETA: splitting (67) gives: % 130.61/18.49 | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | (4312) ~ (all_18_2 = e3) % 130.61/18.49 | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | REDUCE: (391), (4312) imply: % 130.61/18.49 | | | | | | | | | | | | (4313) ~ (all_12_2 = e3) % 130.61/18.49 | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | BETA: splitting (73) gives: % 130.61/18.49 | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | (4314) ~ (all_22_2 = e0) % 130.61/18.49 | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | REDUCE: (389), (4314) imply: % 130.61/18.49 | | | | | | | | | | | | | (4315) ~ (all_12_2 = e0) % 130.61/18.49 | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.61/18.49 | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | (4316) all_55_10 = e3 % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | REF_CLOSE: (278), (4313), (4316) are inconsistent by % 130.61/18.49 | | | | | | | | | | | | | | sub-proof #282. % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | (4317) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | BETA: splitting (4317) gives: % 130.61/18.49 | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | (4318) all_55_10 = e2 % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | REF_CLOSE: (278), (4311), (4318) are inconsistent by % 130.61/18.49 | | | | | | | | | | | | | | | sub-proof #281. % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | (4319) ~ (all_55_10 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | (4320) all_55_10 = e1 | all_55_10 = e0 % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | BETA: splitting (4320) gives: % 130.61/18.49 | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | (4321) all_55_10 = e1 % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (4321) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4322) all_12_2 = e1 % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | SIMP: (4322) implies: % 130.61/18.49 | | | | | | | | | | | | | | | | (4323) all_12_2 = e1 % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4324) all_22_2 = e1 % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (426), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4325) ~ (all_53_6 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (428), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4326) ~ (all_53_8 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (429), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4327) ~ (all_53_9 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (431), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4328) ~ (all_53_11 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (4311), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4329) ~ (e2 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | REDUCE: (57), (4323) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | (4330) op(e1, e1) = e1 % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.61/18.49 | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | (4331) ~ (all_26_2 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | REDUCE: (374), (4331) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | (4332) ~ (all_6_2 = e1) % 130.61/18.49 | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.61/18.49 | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4333) ~ (all_28_2 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | REDUCE: (361), (4333) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4334) ~ (all_8_2 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (203), (256), (265), (331), (332), % 130.61/18.49 | | | | | | | | | | | | | | | | | | (334), (434), (4305), (4308), (4310), (4327), % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4328), (4334) are inconsistent by sub-proof #28. % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4335) all_28_2 = e2 % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4335) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4336) all_8_2 = e2 % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | REDUCE: (436), (4336) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4337) ~ (all_53_13 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | REDUCE: (4302), (4336) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4338) ~ (all_4_1 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | SIMP: (4338) implies: % 130.61/18.49 | | | | | | | | | | | | | | | | | | (4339) ~ (all_4_1 = e2) % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 130.61/18.49 | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4340) ~ (all_42_2 = e0) % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | REDUCE: (398), (4340) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4341) ~ (all_6_2 = e0) % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (212), (279), (282), (295), (304), % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (334), (423), (4304), (4308), (4325), (4328), % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4332), (4341) are inconsistent by sub-proof #249. % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4342) all_42_2 = e0 % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (4342) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4343) all_6_2 = e0 % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | SIMP: (4343) implies: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4344) all_6_2 = e0 % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | REDUCE: (425), (4344) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | (4345) ~ (all_53_13 = e0) % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | | (4346) ~ (op(e2, e0) = e0) % 130.61/18.49 | | | | | | | | | | | | | | | | | | | | % 130.61/18.49 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (4346) imply: % 130.61/18.49 | | | | | | | | | | | | | | | | | | | | (4347) ~ (unit = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4348) unit = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4347), (4348) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4349) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4349) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4350) unit = e1 | unit = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4350) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4351) unit = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4351) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4352) op(e1, e2) = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (4351) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4353) op(e3, e1) = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4354) ~ (op(e3, e1) = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4353), (4354) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4355) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4355) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4356) all_53_8 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4356) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4357) ~ (all_53_4 = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4298), (4356) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4358) ~ (all_4_1 = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4358) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4359) ~ (all_4_1 = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4360) ~ (op(e1, e2) = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4352), (4360) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4361) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4361) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4362) all_53_6 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (4362) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4363) ~ (all_53_4 = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4364) all_55_1 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4364) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4365) all_53_4 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4357), (4365) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4366) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4366) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4367) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4368) all_55_3 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4296), (4368) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4369) all_4_1 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4369) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4370) all_4_1 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4359), (4370) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4371) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4371) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4372) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4372) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4373) all_55_3 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4296), (4373) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4374) all_4_1 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4374) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4375) all_4_1 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4339), (4375) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4376) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4376) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4377) all_55_3 = e1 | all_55_3 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4377) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4378) all_55_3 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4296), (4378) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4379) all_4_1 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4379) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4380) all_4_1 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4297), (4380) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4381) ~ (all_53_4 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (4277), (4363), (4367), (4381) are % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4382) all_55_3 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4296), (4382) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4383) all_4_1 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4383) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4384) all_4_1 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4303), (4384) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4385) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4385) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4386) ~ (unit = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (306), (4337), (4350), (4386) are % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | (4387) op(e2, e0) = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (328), (4345), (4387) are inconsistent by % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | sub-proof #356. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | End of split % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | (4388) all_26_2 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4388) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4389) all_6_2 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | SIMP: (4389) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4390) all_6_2 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (4390) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4391) all_50_2 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | REDUCE: (421), (4390) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4392) ~ (all_53_7 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | REDUCE: (4304), (4390) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4393) ~ (e3 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | REDUCE: (48), (4390) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | (4394) op(e2, e2) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | (4395) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 130.61/18.50 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | BETA: splitting (4395) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | (4396) all_57_12 = e1 & op(e0, e3) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | ALPHA: (4396) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | (4397) all_57_12 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | (4398) op(e0, e3) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | (4399) ~ (op(e2, e1) = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4400) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (48), (172), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (238), (240), (241), (284), (300), (339), (4286), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4304), (4324), (4330), (4391), (4394), (4400), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | #9. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | (4401) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4401) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4402) all_57_4 = e1 & op(e3, e1) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4402) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4403) op(e3, e1) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (4326), (4403) are inconsistent by % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4404) all_57_9 = e1 & op(e3, e0) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4404) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4405) op(e3, e0) = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e1, % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (173), (4398) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4406) all_53_3 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (4273), (4405) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4407) all_4_1 = e1 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (4399) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4408) ~ (unit = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (4406) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4409) ~ (all_53_11 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4300), (4407) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | (4410) ~ (all_53_14 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4274) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4411) ~ (all_4_1 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4407), (4411) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4412) $false % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4412) is inconsistent. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4413) ~ (all_4_0 = e2) & op(e3, e1) = all_4_0 & % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_4_0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4413) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4414) ~ (all_4_0 = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4415) op(e3, e1) = all_4_0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | all_4_0, e1, e3, simplifying with (183), (4415) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4416) all_53_8 = all_4_0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (4416) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4417) all_55_2 = all_4_0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (4416) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4418) ~ (all_53_11 = all_4_0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4418) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4419) ~ (all_53_11 = all_4_0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4326), (4416) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | (4420) ~ (all_4_0 = e1) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4421) all_55_2 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4417), (4421) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4422) all_4_0 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4419), (4422) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | (4423) ~ (all_53_11 = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4424) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4424) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4425) all_57_12 = e3 & op(e0, e3) = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (4397), (4425) are inconsistent by sub-proof % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4426) all_57_13 = e3 & op(e0, e2) = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4426) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4427) op(e0, e2) = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4428) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (184), (4277), (4394), (4428), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4429) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4429) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4430) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4430) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4431) op(e1, e2) = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3, % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (172), (4427) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4432) all_53_7 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e0, % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (176), (4431) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4433) all_53_6 = e0 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (4433) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4434) ~ (all_53_14 = e0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4434) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4435) ~ (all_53_14 = e0) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (4432) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4436) ~ (all_8_2 = e3) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4437) ~ (all_36_2 = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (4437) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4438) ~ (all_8_2 = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (203), (256), (265), (331), (332), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (434), (4305), (4308), (4310), (4327), % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4328), (4438) are inconsistent by sub-proof #28. % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4439) all_36_2 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (4439) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4440) all_8_2 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4440) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4441) all_8_2 = e2 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (4441) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4442) ~ (all_53_14 = e2) % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4443) all_55_11 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (4443) imply: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4444) all_53_14 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4444) implies: % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4445) all_53_14 = e3 % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (4445) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4446) ~ (all_53_2 = e3) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (82), (203), (256), (286), % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327), (328), (339), (342), (361), (427), (436), % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4305), (4308), (4310), (4408), (4410), (4446) are % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #221. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4447) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4447) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4448) all_55_11 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (4448) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4449) all_53_14 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4449) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4450) all_53_14 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4442), (4450) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4451) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4451) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4452) all_55_11 = e1 | all_55_11 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4452) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4453) all_55_11 = e1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (4410), (4453) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #27. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4454) all_55_11 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (4435), (4454) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4455) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (94), (139), (203), (256), (263), % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (265), (306), (397), (427), (436), (4305), % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4308), (4310), (4399), (4455) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | (4456) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4456) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (4457) all_57_14 = e3 & op(e0, e1) = e3 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (4423), (4457), (function-axioms) are % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #121. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (4458) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (4310), (4458), (function-axioms) are % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | (4459) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4459) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | (4460) all_55_2 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4417), (4460) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | (4461) all_4_0 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4414), (4461) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | (4462) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4462) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | (4463) all_55_2 = e1 | all_55_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (308), (4278), (4326), (4463) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #213. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | (4464) op(e2, e1) = e1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (4327), (4464) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4465) all_57_13 = e1 & op(e0, e2) = e1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (4392), (4465), (function-axioms) are % 130.61/18.51 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | (4466) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 130.61/18.51 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (334), (4305), (4328), (4466), % 130.61/18.51 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.51 | | | | | | | | | | | | | | | | | | #293. % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | (4467) all_55_10 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (4315), (4467) are inconsistent by % 130.61/18.51 | | | | | | | | | | | | | | | | sub-proof #219. % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | (4468) all_22_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | (4469) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 130.61/18.51 | | | | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.51 | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | ALPHA: (4469) implies: % 130.61/18.51 | | | | | | | | | | | | | (4470) op(e1, e0) = all_22_1 % 130.61/18.51 | | | | | | | | | | | | | (4471) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.51 | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0)) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | COMBINE_EQS: (389), (4468) imply: % 130.61/18.51 | | | | | | | | | | | | | (4472) all_12_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | SIMP: (4472) implies: % 130.61/18.51 | | | | | | | | | | | | | (4473) all_12_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | COMBINE_EQS: (359), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4474) all_38_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | REDUCE: (426), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4475) ~ (all_53_6 = e0) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | REDUCE: (433), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4476) ~ (all_53_14 = e0) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | REDUCE: (4313), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4477) ~ (e3 = e0) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | REDUCE: (4311), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4478) ~ (e2 = e0) % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | REDUCE: (57), (4473) imply: % 130.61/18.51 | | | | | | | | | | | | | (4479) op(e1, e1) = e0 % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | BETA: splitting (329) gives: % 130.61/18.51 | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | (4480) ~ (op(e1, e0) = e0) % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14, % 130.61/18.51 | | | | | | | | | | | | | | all_22_1, e0, e1, simplifying with (174), (4470) % 130.61/18.51 | | | | | | | | | | | | | | gives: % 130.61/18.51 | | | | | | | | | | | | | | (4481) all_53_14 = all_22_1 % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | PRED_UNIFY: (6), (4480) imply: % 130.61/18.51 | | | | | | | | | | | | | | (4482) ~ (unit = e1) % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | COMBINE_EQS: (271), (4481) imply: % 130.61/18.51 | | | | | | | | | | | | | | (4483) all_55_11 = all_22_1 % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | REDUCE: (155), (4481) imply: % 130.61/18.51 | | | | | | | | | | | | | | (4484) ~ (all_53_2 = all_22_1) % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | REDUCE: (140), (4481) imply: % 130.61/18.51 | | | | | | | | | | | | | | (4485) ~ (all_53_6 = all_22_1) % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | REDUCE: (124), (4481) imply: % 130.61/18.51 | | | | | | | | | | | | | | (4486) ~ (all_53_13 = all_22_1) % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.61/18.51 | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | (4487) ~ (all_26_2 = e1) % 130.61/18.51 | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | REDUCE: (374), (4487) imply: % 130.61/18.51 | | | | | | | | | | | | | | | (4488) ~ (all_6_2 = e1) % 130.61/18.51 | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.61/18.51 | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | (4489) ~ (all_28_2 = e2) % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | REDUCE: (361), (4489) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | (4490) ~ (all_8_2 = e2) % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | (4491) all_55_15 = e3 % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4491) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | (4492) all_8_2 = e3 % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | REDUCE: (4310), (4492) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | (4493) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | CLOSE: (4493) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | (4494) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | BETA: splitting (4494) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | (4495) all_55_15 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4495) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | (4496) all_8_2 = e2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | REDUCE: (4490), (4496) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | (4497) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | CLOSE: (4497) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | (4498) all_55_15 = e1 | all_55_15 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | BETA: splitting (4498) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4499) all_55_15 = e1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4499) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4500) all_8_2 = e1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | REDUCE: (4305), (4500) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4501) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | CLOSE: (4501) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4502) all_55_15 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4502) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4503) all_8_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | REDUCE: (427), (4503) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4504) ~ (all_53_7 = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | REDUCE: (51), (4503) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | (4505) op(e0, e0) = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | (4506) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4506) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | (4507) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (4277), (4507), (function-axioms) are % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | (4508) all_57_3 = e0 & op(e2, e2) = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4508) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | (4509) op(e2, e2) = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | (4510) ( ~ (all_52_0 = e0) & op(e3, e3) = all_52_0 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | $i(all_52_0)) | ( ~ (all_52_1 = e0) & op(e2, e2) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | = all_52_1 & $i(all_52_1)) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4510) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4511) ~ (all_52_0 = e0) & op(e3, e3) = all_52_0 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4511) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4512) ~ (all_52_0 = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4513) op(e3, e3) = all_52_0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_0, % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (4287), (4513) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4514) all_52_0 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4512), (4514) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4515) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4515) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4516) ~ (all_52_1 = e0) & op(e2, e2) = all_52_1 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_1) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4516) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4517) ~ (all_52_1 = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4518) op(e2, e2) = all_52_1 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_1, % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (4509), (4518) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4519) all_52_1 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4517), (4519) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4520) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4520) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | (4521) ( ~ (all_52_2 = e0) & op(e1, e1) = all_52_2 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | $i(all_52_2)) | ( ~ (all_52_3 = e0) & op(e0, e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | = all_52_3 & $i(all_52_3)) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4521) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4522) ~ (all_52_2 = e0) & op(e1, e1) = all_52_2 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_2) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4522) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4523) ~ (all_52_2 = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4524) op(e1, e1) = all_52_2 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_2, % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (4479), (4524) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4525) all_52_2 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4523), (4525) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4526) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4526) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4527) ~ (all_52_3 = e0) & op(e0, e0) = all_52_3 & % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_3) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4527) implies: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4528) ~ (all_52_3 = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4529) op(e0, e0) = all_52_3 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_3, % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (4505), (4529) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4530) all_52_3 = e0 % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4528), (4530) imply: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | (4531) $false % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4531) is inconsistent. % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | (4532) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4532) gives: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.51 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4533) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (4475), (4533), (function-axioms) are % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4534) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4534) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4535) op(e0, e2) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (262), (4504), (4535) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | (4536) all_28_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4536) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | (4537) all_8_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | SIMP: (4537) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | (4538) all_8_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (4538) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | (4539) all_10_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | REDUCE: (427), (4538) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | (4540) ~ (all_53_7 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | REDUCE: (434), (4538) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | (4541) ~ (all_53_11 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | (4542) all_57_15 = e0 & op(e0, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | ALPHA: (4542) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | (4543) op(e0, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (270), (4539), (4543) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | sub-proof #235. % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | (4544) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 130.61/18.52 | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 130.61/18.52 | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 130.61/18.52 | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 130.61/18.52 | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | ALPHA: (4544) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | (4545) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 130.61/18.52 | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 130.61/18.52 | | | | | | | | | | | | | | | | | e0) = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | (4546) ~ (op(e0, e2) = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | BETA: splitting (4545) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | (4547) all_57_9 = e0 & op(e3, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | ALPHA: (4547) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | (4548) op(e3, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4288), (4548) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | (4549) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | CLOSE: (4549) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | (4550) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 130.61/18.52 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (4550) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | (4551) all_57_10 = e0 & op(e2, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | ALPHA: (4551) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | (4552) op(e2, e0) = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4553) ~ (op(e2, e0) = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4552), (4553) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4554) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4554) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4555) all_55_7 = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4555) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4556) all_53_13 = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4486), (4556) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4557) ~ (all_22_1 = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | SIMP: (4557) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4558) ~ (all_22_1 = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (4556) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4559) ~ (all_6_2 = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | SIMP: (4559) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | (4560) ~ (all_6_2 = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | (4561) all_55_5 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (4561) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | (4562) all_6_2 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4562) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | (4563) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4563) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | (4564) ~ (all_55_5 = e3) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | (4565) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4565) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | (4566) all_55_5 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (4566) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | (4567) all_6_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (4567) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | (4568) ~ (all_53_6 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (4567) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | (4569) ~ (all_53_9 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4567) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | (4570) ~ (e3 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | (4571) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4571) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4572) all_57_6 = e2 & op(e1, e3) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4572) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4573) op(e1, e3) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (4574) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4574) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e2, % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (177), (4573) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4575) all_53_2 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (8), (4546) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4576) ~ (unit = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4484), (4575) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4577) ~ (all_22_1 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4577) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4578) ~ (all_22_1 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4579) unit = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (4579) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4580) op(e1, e2) = e1 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4581) ~ (op(e1, e2) = e1) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4580), (4581) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4582) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4582) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4583) all_53_6 = e1 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4485), (4583) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4584) ~ (all_22_1 = e1) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4584) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4585) ~ (all_22_1 = e1) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (207), (4471), (4483), (4558), (4573), (4578), % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4585), (function-axioms) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4586) unit = e1 | unit = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4482), (4576), (4586) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4587) all_57_5 = e2 & op(e2, e1) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4587) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4588) op(e2, e1) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (304), (4569), (4588) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #347. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (4589) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (171), (4479), (4541), (4589), % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | #100. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4590) all_57_7 = e2 & op(e1, e2) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4590) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4591) op(e1, e2) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (337), (4568), (4591) are inconsistent by % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | (4592) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4592) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4593) all_57_8 = e2 & op(e1, e1) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4593) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4594) op(e1, e1) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4479), (4594), (function-axioms) are % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4595) all_57_11 = e2 & op(e1, e0) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4595) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4596) all_57_11 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | (4597) op(e1, e0) = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (4598) ~ (op(e2, e0) = e0) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4552), (4598) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (4599) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4599) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4600) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4600) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4601) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4601) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4602) op(e3, e0) = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4291) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4603) ~ (op(e3, e0) = e3) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4602), (4603) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4604) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4604) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4605) all_48_1 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4295), (4605) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4606) all_4_1 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4606) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4607) all_4_1 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4297), (4607) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4608) ~ (all_53_4 = e3) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4609) all_55_5 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (4609) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4610) all_6_2 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4610) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4611) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4611) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4565) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (4567) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4612) ~ (all_53_4 = e2) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4613) all_55_1 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4613) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4614) all_53_4 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4608), (4614) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4615) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4615) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4616) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4616) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4617) all_55_1 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4617) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4618) all_53_4 = e2 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4612), (4618) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4619) $false % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4619) is inconsistent. % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4620) all_55_1 = e1 | all_55_1 = e0 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4620) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4621) all_55_1 = e1 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4621) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4622) all_53_4 = e1 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (4622) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4623) ~ (all_53_6 = e1) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4623) implies: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4624) ~ (all_53_6 = e1) % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4625) all_55_9 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (4625) imply: % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4626) all_53_6 = e3 % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (4626) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4627) op(e1, e2) = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (4474), (4597), (4627), (function-axioms) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #308. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4628) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (4475), (4568), (4624), (4628) are % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #177. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4629) all_55_1 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4629) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630) all_53_4 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4277), (4630) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4631) $false % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4631) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4632) all_55_5 = e1 | all_55_5 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (295), (4488), (4560), (4632) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4633) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4633) implies: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4634) all_57_10 = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4545) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4635) all_57_9 = e0 & op(e3, e0) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4635) implies: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4636) op(e3, e0) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (326), (4279), (4636) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4550) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4551) implies: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4637) all_57_10 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4634), (4637) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4638) e3 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (4638) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4639) $false % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4639) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4640) all_57_11 = e0 & op(e1, e0) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4480), (4640) are inconsistent by sub-proof #97. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4641) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4642) all_57_11 = e3 & op(e1, e0) = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (4596), (4642) are inconsistent by sub-proof % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #260. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4643) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (4310), (4643), (function-axioms) are % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | (4644) all_55_5 = e1 | all_55_5 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (295), (4488), (4560), (4644) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | (4645) all_57_11 = e0 & op(e1, e0) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4480), (4645) are inconsistent by sub-proof #97. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4646) op(e0, e2) = e2 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (338), (4540), (4646) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | | | sub-proof #118. % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | (4647) all_26_2 = e1 % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4647) imply: % 130.61/18.53 | | | | | | | | | | | | | | | (4648) all_6_2 = e1 % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | SIMP: (4648) implies: % 130.61/18.53 | | | | | | | | | | | | | | | (4649) all_6_2 = e1 % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | REDUCE: (423), (4649) imply: % 130.61/18.53 | | | | | | | | | | | | | | | (4650) ~ (all_53_9 = e1) % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | REDUCE: (48), (4649) imply: % 130.61/18.53 | | | | | | | | | | | | | | | (4651) op(e2, e2) = e1 % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | (4652) ~ (op(e2, e1) = e1) % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | (4653) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (184), (4277), (4651), (4653), % 130.61/18.53 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.53 | | | | | | | | | | | | | | | | | #7. % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | (4654) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.61/18.53 | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | BETA: splitting (4654) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4655) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (4475), (4655), (function-axioms) are % 130.61/18.53 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4656) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (94), (139), (203), (256), (263), % 130.61/18.53 | | | | | | | | | | | | | | | | | | (264), (265), (306), (397), (427), (436), (4305), % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4308), (4310), (4652), (4656) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | | | sub-proof #6. % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | (4657) op(e2, e1) = e1 % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | REF_CLOSE: (332), (4650), (4657) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | | | sub-proof #334. % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | (4658) op(e1, e0) = e0 % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | REF_CLOSE: (329), (4476), (4658) are inconsistent by % 130.61/18.53 | | | | | | | | | | | | | | sub-proof #355. % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | End of split % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | (4659) all_18_2 = e3 % 130.61/18.53 | | | | | | | | | | | | (4660) op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ % 130.61/18.53 | | | | | | | | | | | | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, % 130.61/18.53 | | | | | | | | | | | | e2) = all_18_0 & $i(all_18_0))) % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | ALPHA: (4660) implies: % 130.61/18.53 | | | | | | | | | | | | (4661) op(e1, e3) = all_18_1 % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | COMBINE_EQS: (391), (4659) imply: % 130.61/18.53 | | | | | | | | | | | | (4662) all_12_2 = e3 % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | COMBINE_EQS: (384), (4662) imply: % 130.61/18.53 | | | | | | | | | | | | (4663) all_24_2 = e3 % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | REDUCE: (415), (4662) imply: % 130.61/18.53 | | | | | | | | | | | | (4664) ~ (all_53_2 = e3) % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | REDUCE: (426), (4662) imply: % 130.61/18.53 | | | | | | | | | | | | (4665) ~ (all_53_6 = e3) % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | REDUCE: (433), (4662) imply: % 130.61/18.53 | | | | | | | | | | | | (4666) ~ (all_53_14 = e3) % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | REDUCE: (57), (4662) imply: % 130.61/18.53 | | | | | | | | | | | | (4667) op(e1, e1) = e3 % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | BETA: splitting (76) gives: % 130.61/18.53 | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | (4668) ~ (all_24_2 = e3) % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | REDUCE: (4663), (4668) imply: % 130.61/18.53 | | | | | | | | | | | | | (4669) $false % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | CLOSE: (4669) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | (4670) op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 130.61/18.53 | | | | | | | | | | | | | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, % 130.61/18.53 | | | | | | | | | | | | | e0) = all_24_0 & $i(all_24_0))) % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | ALPHA: (4670) implies: % 130.61/18.53 | | | | | | | | | | | | | (4671) op(e1, e3) = all_24_1 % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.61/18.53 | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | (4672) ~ (op(e1, e3) = e3) % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.53 | | | | | | | | | | | | | | all_18_1, e3, e1, simplifying with (177), (4661) % 130.61/18.53 | | | | | | | | | | | | | | gives: % 130.61/18.53 | | | | | | | | | | | | | | (4673) all_53_2 = all_18_1 % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.53 | | | | | | | | | | | | | | all_24_1, e3, e1, simplifying with (177), (4671) % 130.61/18.53 | | | | | | | | | | | | | | gives: % 130.61/18.53 | | | | | | | | | | | | | | (4674) all_53_2 = all_24_1 % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | PRED_UNIFY: (9), (4672) imply: % 130.61/18.53 | | | | | | | | | | | | | | (4675) ~ (unit = e1) % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | COMBINE_EQS: (4673), (4674) imply: % 130.61/18.53 | | | | | | | | | | | | | | (4676) all_24_1 = all_18_1 % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | SIMP: (4676) implies: % 130.61/18.53 | | | | | | | | | | | | | | (4677) all_24_1 = all_18_1 % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | REDUCE: (157), (4673) imply: % 130.61/18.53 | | | | | | | | | | | | | | (4678) ~ (all_53_6 = all_18_1) % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | SIMP: (4678) implies: % 130.61/18.53 | | | | | | | | | | | | | | (4679) ~ (all_53_6 = all_18_1) % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.61/18.53 | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | (4680) ~ (all_26_2 = e1) % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | REDUCE: (374), (4680) imply: % 130.61/18.53 | | | | | | | | | | | | | | | (4681) ~ (all_6_2 = e1) % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.61/18.53 | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | (4682) ~ (all_28_2 = e2) % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | REDUCE: (361), (4682) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | (4683) ~ (all_8_2 = e2) % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | (4684) all_55_15 = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4684) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | (4685) all_8_2 = e3 % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | REDUCE: (4310), (4685) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | (4686) $false % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | CLOSE: (4686) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | (4687) ~ (all_55_15 = e3) % 130.61/18.53 | | | | | | | | | | | | | | | | | (4688) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | BETA: splitting (4688) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4689) all_55_15 = e2 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4689) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4690) all_8_2 = e2 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | REDUCE: (4683), (4690) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4691) $false % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | CLOSE: (4691) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4692) ~ (all_55_15 = e2) % 130.61/18.53 | | | | | | | | | | | | | | | | | | (4693) all_55_15 = e1 | all_55_15 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | BETA: splitting (4693) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4694) all_55_15 = e1 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4694) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4695) all_8_2 = e1 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (4305), (4695) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4696) $false % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | CLOSE: (4696) is inconsistent. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4697) all_55_15 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4697) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4698) all_8_2 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (434), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4699) ~ (all_53_11 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (436), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4700) ~ (all_53_13 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (437), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4701) ~ (all_53_14 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (4310), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4702) ~ (e3 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (4683), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4703) ~ (e2 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (4305), (4698) imply: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | (4704) ~ (e1 = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | (4705) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4705) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (4706) all_57_6 = e0 & op(e1, e3) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (17), (18), % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (140), (142), (209), (226), (227), (228), (279), % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (285), (286), (328), (329), (339), (4308), (4661), % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (4662), (4665), (4667), (4675), (4679), (4700), % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (4701), (4706), (function-axioms) are inconsistent % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | by sub-proof #168. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (4707) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4707) implies: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | (4708) op(e1, e2) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | (4709) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4709) gives: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | (4710) all_57_4 = e0 & op(e3, e1) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (4278), (4710), (function-axioms) are % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210. % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | (4711) all_57_5 = e0 & op(e2, e1) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4711) implies: % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | (4712) op(e2, e1) = e0 % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.53 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e0, % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (176), (4708) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4713) all_53_6 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0, % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (179), (4712) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4714) all_53_9 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4713) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4715) ~ (all_53_7 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4715) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4716) ~ (all_53_7 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (4714) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4717) ~ (all_53_13 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (4714) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4718) ~ (all_6_2 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (212), (258), (262), (295), (306), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (328), (425), (4304), (4308), (4675), (4681), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | (4700), (4716), (4718) are inconsistent by % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4719) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (265), (4667), (4699), (4719), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | #69. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | (4720) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (329), (4667), (4701), (4720), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | #169. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | (4721) all_28_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4721) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | (4722) all_8_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | SIMP: (4722) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | (4723) all_8_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (124), (132), (140), % 130.61/18.54 | | | | | | | | | | | | | | | | (207), (212), (271), (279), (282), (288), (295), % 130.61/18.54 | | | | | | | | | | | | | | | | (304), (328), (331), (334), (339), (342), (423), % 130.61/18.54 | | | | | | | | | | | | | | | | (425), (427), (437), (4304), (4308), (4664), % 130.61/18.54 | | | | | | | | | | | | | | | | (4666), (4675), (4681), (4723) are inconsistent by % 130.61/18.54 | | | | | | | | | | | | | | | | sub-proof #158. % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | (4724) all_26_2 = e1 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4724) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4725) all_6_2 = e1 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | SIMP: (4725) implies: % 130.61/18.54 | | | | | | | | | | | | | | | (4726) all_6_2 = e1 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REDUCE: (417), (4726) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4727) ~ (all_53_4 = e1) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REDUCE: (419), (4726) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4728) ~ (all_53_6 = e1) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REDUCE: (423), (4726) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4729) ~ (all_53_9 = e1) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (142), (147), (149), (150), (209), % 130.61/18.54 | | | | | | | | | | | | | | | (216), (279), (309), (324), (332), (339), (4308), % 130.61/18.54 | | | | | | | | | | | | | | | (4665), (4675), (4727), (4728), (4729) are % 130.61/18.54 | | | | | | | | | | | | | | | inconsistent by sub-proof #155. % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | (4730) op(e1, e3) = e3 % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | REF_CLOSE: (342), (4664), (4730) are inconsistent by % 130.61/18.54 | | | | | | | | | | | | | | sub-proof #323. % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | (4731) all_12_2 = e2 % 130.61/18.54 | | | | | | | | | | | (4732) op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 130.61/18.54 | | | | | | | | | | | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, % 130.61/18.54 | | | | | | | | | | | e3) = all_12_0 & $i(all_12_0))) % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | ALPHA: (4732) implies: % 130.61/18.54 | | | | | | | | | | | (4733) op(e1, e2) = all_12_1 % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | COMBINE_EQS: (376), (4731) imply: % 130.61/18.54 | | | | | | | | | | | (4734) all_30_2 = e2 % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | REDUCE: (415), (4731) imply: % 130.61/18.54 | | | | | | | | | | | (4735) ~ (all_53_2 = e2) % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | REDUCE: (426), (4731) imply: % 130.61/18.54 | | | | | | | | | | | (4736) ~ (all_53_6 = e2) % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | REDUCE: (57), (4731) imply: % 130.61/18.54 | | | | | | | | | | | (4737) op(e1, e1) = e2 % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | BETA: splitting (337) gives: % 130.61/18.54 | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | (4738) ~ (op(e1, e2) = e2) % 130.61/18.54 | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | BETA: splitting (85) gives: % 130.61/18.54 | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | (4739) ~ (all_30_2 = e2) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | REDUCE: (4734), (4739) imply: % 130.61/18.54 | | | | | | | | | | | | | (4740) $false % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | CLOSE: (4740) is inconsistent. % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | (4741) op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ % 130.61/18.54 | | | | | | | | | | | | | (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e1, % 130.61/18.54 | | | | | | | | | | | | | e0) = all_30_0 & $i(all_30_0))) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | ALPHA: (4741) implies: % 130.61/18.54 | | | | | | | | | | | | | (4742) op(e1, e2) = all_30_1 % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.61/18.54 | | | | | | | | | | | | | all_12_1, e2, e1, simplifying with (176), (4733) % 130.61/18.54 | | | | | | | | | | | | | gives: % 130.61/18.54 | | | | | | | | | | | | | (4743) all_53_6 = all_12_1 % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.61/18.54 | | | | | | | | | | | | | all_30_1, e2, e1, simplifying with (176), (4742) % 130.61/18.54 | | | | | | | | | | | | | gives: % 130.61/18.54 | | | | | | | | | | | | | (4744) all_53_6 = all_30_1 % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | PRED_UNIFY: (8), (4738) imply: % 130.61/18.54 | | | | | | | | | | | | | (4745) ~ (unit = e1) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | COMBINE_EQS: (4743), (4744) imply: % 130.61/18.54 | | | | | | | | | | | | | (4746) all_30_1 = all_12_1 % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | SIMP: (4746) implies: % 130.61/18.54 | | | | | | | | | | | | | (4747) all_30_1 = all_12_1 % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | REDUCE: (142), (4743) imply: % 130.61/18.54 | | | | | | | | | | | | | (4748) ~ (all_53_7 = all_12_1) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | SIMP: (4748) implies: % 130.61/18.54 | | | | | | | | | | | | | (4749) ~ (all_53_7 = all_12_1) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | REDUCE: (419), (4743) imply: % 130.61/18.54 | | | | | | | | | | | | | (4750) ~ (all_12_1 = all_6_2) % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.61/18.54 | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | (4751) ~ (all_26_2 = e1) % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | REDUCE: (374), (4751) imply: % 130.61/18.54 | | | | | | | | | | | | | | (4752) ~ (all_6_2 = e1) % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.61/18.54 | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | (4753) ~ (all_28_2 = e2) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REDUCE: (361), (4753) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4754) ~ (all_8_2 = e2) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | (4755) all_55_15 = e3 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4755) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | (4756) all_8_2 = e3 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | REDUCE: (4310), (4756) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | (4757) $false % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | CLOSE: (4757) is inconsistent. % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | (4758) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | BETA: splitting (4758) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | (4759) all_55_15 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4759) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | (4760) all_8_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | REDUCE: (4754), (4760) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | (4761) $false % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | CLOSE: (4761) is inconsistent. % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | (4762) ~ (all_55_15 = e2) % 130.61/18.54 | | | | | | | | | | | | | | | | | (4763) all_55_15 = e1 | all_55_15 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | BETA: splitting (4763) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4764) all_55_15 = e1 % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4764) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4765) all_8_2 = e1 % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | REDUCE: (4305), (4765) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4766) $false % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | CLOSE: (4766) is inconsistent. % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4767) all_55_15 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4767) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4768) all_8_2 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | REDUCE: (434), (4768) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4769) ~ (all_53_11 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | REDUCE: (437), (4768) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4770) ~ (all_53_14 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | REDUCE: (4754), (4768) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | (4771) ~ (e2 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | (4772) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | (4773) all_57_4 = e0 & op(e3, e1) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (183), (4278), (4773), (function-axioms) are % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #210. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | (4774) all_57_5 = e0 & op(e2, e1) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (4774) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | (4775) op(e2, e1) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | (4776) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4776) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4777) all_57_6 = e0 & op(e1, e3) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (4276), (4777), (function-axioms) are % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #101. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4778) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4778) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4779) op(e1, e2) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1, e0, % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (4733), (4779) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4780) all_12_1 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0, % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (179), (4775) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4781) all_53_9 = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4749), (4780) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4782) ~ (all_53_7 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (4781) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4783) ~ (all_53_13 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4783) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4784) ~ (all_53_13 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4750), (4780) imply: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4785) ~ (all_6_2 = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (212), (258), (262), (295), (306), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (328), (425), (4304), (4308), (4745), (4752), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4782), (4784), (4785) are inconsistent by % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | (4786) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4786) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4787) all_57_8 = e0 & op(e1, e1) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4787) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4788) op(e1, e1) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4737), (4788), (function-axioms) are % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4789) all_57_11 = e0 & op(e1, e0) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4789) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | (4790) op(e1, e0) = e0 % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (329), (4770), (4790) are inconsistent by % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #355. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | (4791) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 130.61/18.54 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (265), (4737), (4769), (4791), % 130.61/18.54 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.54 | | | | | | | | | | | | | | | | | | | #87. % 130.61/18.54 | | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | End of split % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | (4792) all_28_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | COMBINE_EQS: (361), (4792) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4793) all_8_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | SIMP: (4793) implies: % 130.61/18.54 | | | | | | | | | | | | | | | (4794) all_8_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | REDUCE: (416), (4794) imply: % 130.61/18.54 | | | | | | | | | | | | | | | (4795) ~ (all_53_3 = e2) % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 130.61/18.54 | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | (4796) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | BETA: splitting (4796) gives: % 130.61/18.54 | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | (4797) all_57_0 = e2 & op(e3, e3) = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | ALPHA: (4797) implies: % 130.61/18.54 | | | | | | | | | | | | | | | | | (4798) op(e3, e3) = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4287), (4798), (function-axioms) are % 130.61/18.54 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.54 | | | | | | | | | | | | | | | | | (4799) all_57_2 = e2 & op(e2, e3) = e2 % 130.61/18.54 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (159), (212), (258), (262), (295), % 130.61/18.55 | | | | | | | | | | | | | | | | | (298), (306), (328), (414), (421), (425), (4304), % 130.61/18.55 | | | | | | | | | | | | | | | | | (4308), (4745), (4752), (4799) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | | | sub-proof #89. % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | (4800) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 130.61/18.55 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | REF_CLOSE: (173), (177), (4735), (4795), (4800), % 130.61/18.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.55 | | | | | | | | | | | | | | | | #88. % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | (4801) all_26_2 = e1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | COMBINE_EQS: (374), (4801) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4802) all_6_2 = e1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | SIMP: (4802) implies: % 130.61/18.55 | | | | | | | | | | | | | | (4803) all_6_2 = e1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | REDUCE: (423), (4803) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4804) ~ (all_53_9 = e1) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | BETA: splitting (331) gives: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | (4805) ~ (op(e2, e1) = e1) % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | PRED_UNIFY: (7), (4805) imply: % 130.61/18.55 | | | | | | | | | | | | | | | (4806) ~ (unit = e2) % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | (4807) unit = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | REDUCE: (4806), (4807) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | (4808) $false % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | CLOSE: (4808) is inconsistent. % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | (4809) unit = e1 | unit = e0 % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | BETA: splitting (4809) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | (4810) unit = e1 % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (4745), (4810) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4811) $false % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | CLOSE: (4811) is inconsistent. % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | (4812) unit = e0 % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (4806), (4812) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4813) ~ (e2 = e0) % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (9), (4812) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4814) op(e0, e3) = e3 % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (8), (4812) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4815) op(e0, e2) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (4), (4812) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4816) op(e2, e0) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4817) ~ (op(e0, e3) = e3) % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4814), (4817) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4818) $false % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | CLOSE: (4818) is inconsistent. % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4819) all_53_3 = e3 % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | REDUCE: (158), (4819) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4820) ~ (all_53_2 = e3) % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4821) ~ (op(e2, e0) = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4816), (4821) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4822) $false % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | CLOSE: (4822) is inconsistent. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4823) all_55_7 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4823) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4824) all_53_13 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (4824) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4825) ~ (all_53_1 = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | (4826) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4826) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4827) all_57_0 = e2 & op(e3, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4827) implies: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4828) op(e3, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4287), (4828), (function-axioms) are % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4829) all_57_2 = e2 & op(e2, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4829) implies: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4830) op(e2, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (296), (297), (4825), (4830) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | sub-proof #346. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | (4831) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4831) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4832) all_57_6 = e2 & op(e1, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4832) implies: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4833) all_57_6 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (157), (210), (227), (279), (280), (282), % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (285), (286), (415), (4276), (4735), (4820), % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4833) are inconsistent by sub-proof #105. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4834) all_57_12 = e2 & op(e0, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4834) implies: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | (4835) op(e0, e3) = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | (4836) ~ (op(e0, e2) = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4815), (4836) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | (4837) $false % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4837) is inconsistent. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | (4838) all_53_7 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (4838) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | (4839) ~ (all_53_3 = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4835), (4839), (function-axioms) are % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #99. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | (4840) op(e2, e1) = e1 % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (332), (4804), (4840) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | sub-proof #334. % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | (4841) op(e1, e2) = e2 % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | REF_CLOSE: (337), (4736), (4841) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | sub-proof #326. % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | (4842) all_10_2 = e3 % 130.61/18.55 | | | | | | | | | | (4843) op(e0, e3) = all_10_1 & $i(all_10_1) & ( ~ % 130.61/18.55 | | | | | | | | | | (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, % 130.61/18.55 | | | | | | | | | | e2) = all_10_0 & $i(all_10_0))) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | ALPHA: (4843) implies: % 130.61/18.55 | | | | | | | | | | (4844) op(e0, e3) = all_10_1 % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | COMBINE_EQS: (395), (4842) imply: % 130.61/18.55 | | | | | | | | | | (4845) all_8_2 = e3 % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | SIMP: (4845) implies: % 130.61/18.55 | | | | | | | | | | (4846) all_8_2 = e3 % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | COMBINE_EQS: (387), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4847) all_16_2 = e3 % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | REDUCE: (416), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4848) ~ (all_53_3 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | REDUCE: (434), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4849) ~ (all_53_11 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | REDUCE: (436), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4850) ~ (all_53_13 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | REDUCE: (437), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4851) ~ (all_53_14 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | REDUCE: (4302), (4846) imply: % 130.61/18.55 | | | | | | | | | | (4852) ~ (all_4_1 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | SIMP: (4852) implies: % 130.61/18.55 | | | | | | | | | | (4853) ~ (all_4_1 = e3) % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | BETA: splitting (64) gives: % 130.61/18.55 | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | (4854) ~ (all_16_2 = e3) % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | REDUCE: (4847), (4854) imply: % 130.61/18.55 | | | | | | | | | | | (4855) $false % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | CLOSE: (4855) is inconsistent. % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | (4856) op(e0, e3) = all_16_1 & $i(all_16_1) & ( ~ % 130.61/18.55 | | | | | | | | | | | (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.55 | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0))) % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | ALPHA: (4856) implies: % 130.61/18.55 | | | | | | | | | | | (4857) op(e0, e3) = all_16_1 % 130.61/18.55 | | | | | | | | | | | (4858) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.55 | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0)) % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | BETA: splitting (222) gives: % 130.61/18.55 | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | (4859) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 130.61/18.55 | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | BETA: splitting (4859) gives: % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | (4860) all_57_12 = e3 & op(e0, e3) = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | ALPHA: (4860) implies: % 130.61/18.55 | | | | | | | | | | | | | (4861) op(e0, e3) = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | REF_CLOSE: (259), (343), (4848), (4861) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | sub-proof #311. % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | (4862) all_57_13 = e3 & op(e0, e2) = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | ALPHA: (4862) implies: % 130.61/18.55 | | | | | | | | | | | | | (4863) all_57_13 = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | BETA: splitting (225) gives: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | (4864) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.61/18.55 | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | BETA: splitting (4864) gives: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | (4865) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (4291), (4295), (4853), (4865) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | sub-proof #3. % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | (4866) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (178), (4850), (4866), (function-axioms) are % 130.61/18.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | (4867) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.61/18.55 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (51), (174), % 130.61/18.55 | | | | | | | | | | | | | | (219), (220), (221), (4305), (4851), (4863), % 130.61/18.55 | | | | | | | | | | | | | | (4867), (function-axioms) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | sub-proof #76. % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | End of split % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | (4868) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 130.61/18.55 | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | BETA: splitting (4868) gives: % 130.61/18.55 | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | (4869) all_57_14 = e3 & op(e0, e1) = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | REF_CLOSE: (171), (4849), (4869), (function-axioms) are % 130.61/18.55 | | | | | | | | | | | | | inconsistent by sub-proof #121. % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | (4870) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | ALPHA: (4870) implies: % 130.61/18.55 | | | | | | | | | | | | | (4871) all_57_15 = e3 % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.61/18.55 | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | (4872) ~ (op(e0, e3) = e3) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.55 | | | | | | | | | | | | | | all_10_1, e3, e0, simplifying with (173), (4844) % 130.61/18.55 | | | | | | | | | | | | | | gives: % 130.61/18.55 | | | | | | | | | | | | | | (4873) all_53_3 = all_10_1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.55 | | | | | | | | | | | | | | all_16_1, e3, e0, simplifying with (173), (4857) % 130.61/18.55 | | | | | | | | | | | | | | gives: % 130.61/18.55 | | | | | | | | | | | | | | (4874) all_53_3 = all_16_1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | PRED_UNIFY: (9), (4872) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4875) ~ (unit = e0) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | PRED_UNIFY: (4857), (4872) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4876) ~ (all_16_1 = e3) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | COMBINE_EQS: (4873), (4874) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4877) all_16_1 = all_10_1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | SIMP: (4877) implies: % 130.61/18.55 | | | | | | | | | | | | | | (4878) all_16_1 = all_10_1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | COMBINE_EQS: (259), (4873) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4879) all_55_12 = all_10_1 % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | REDUCE: (158), (4873) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4880) ~ (all_53_2 = all_10_1) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | REDUCE: (154), (4873) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4881) ~ (all_53_7 = all_10_1) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | SIMP: (4881) implies: % 130.61/18.55 | | | | | | | | | | | | | | (4882) ~ (all_53_7 = all_10_1) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | REDUCE: (4876), (4878) imply: % 130.61/18.55 | | | | | | | | | | | | | | (4883) ~ (all_10_1 = e3) % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | BETA: splitting (58) gives: % 130.61/18.55 | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | (4884) ~ (all_12_2 = e2) % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.61/18.55 | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | (4885) ~ (all_18_2 = e3) % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | REDUCE: (391), (4885) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | (4886) ~ (all_12_2 = e3) % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | (4887) ~ (all_22_2 = e0) % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | REDUCE: (389), (4887) imply: % 130.61/18.55 | | | | | | | | | | | | | | | | | (4888) ~ (all_12_2 = e0) % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4889) all_55_10 = e3 % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (4886), (4889) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | | | | sub-proof #282. % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | (4890) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | BETA: splitting (4890) gives: % 130.61/18.55 | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4891) all_55_10 = e2 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (4884), (4891) are inconsistent by % 130.61/18.55 | | | | | | | | | | | | | | | | | | | sub-proof #281. % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4892) ~ (all_55_10 = e2) % 130.61/18.55 | | | | | | | | | | | | | | | | | | | (4893) all_55_10 = e1 | all_55_10 = e0 % 130.61/18.55 | | | | | | | | | | | | | | | | | | | % 130.61/18.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (4893) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4894) all_55_10 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (4894) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4895) all_12_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | SIMP: (4895) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4896) all_12_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4897) all_22_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4898) ~ (all_53_2 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4899) ~ (all_53_6 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (428), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4900) ~ (all_53_8 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (431), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4901) ~ (all_53_11 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (433), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4902) ~ (all_53_14 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (4884), (4896) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | (4903) ~ (e2 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | (4904) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (281), (282), (4898), (4899), (4904) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | (4905) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4905) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | (4906) all_57_8 = e1 & op(e1, e1) = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4906) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | (4907) all_57_8 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | (4908) op(e1, e1) = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4909) ~ (all_26_2 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4909) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4910) ~ (all_6_2 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4911) ~ (all_42_2 = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (4911) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4912) ~ (all_6_2 = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (212), (279), (282), (295), (304), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (334), (423), (4304), (4308), (4899), (4901), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4910), (4912) are inconsistent by sub-proof #249. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4913) all_42_2 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (4913) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4914) all_6_2 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4914) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4915) all_6_2 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (4915) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4916) ~ (all_53_6 = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (4915) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4917) ~ (all_53_13 = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4910), (4915) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4918) ~ (e1 = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | (4919) ~ (op(e2, e0) = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (4920) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4920) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4921) all_57_6 = e0 & op(e1, e3) = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (4276), (4921), (function-axioms) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #101. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4922) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (4916), (4922), (function-axioms) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (4923) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4923) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4924) all_57_8 = e0 & op(e1, e1) = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (4897), (4907), (4908), (4924) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #257. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4925) all_57_11 = e0 & op(e1, e0) = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4925) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4926) all_57_11 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (6), (4919) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4927) ~ (unit = e2) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4928) unit = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4927), (4928) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4929) $false % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4929) is inconsistent. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4930) unit = e1 | unit = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4930) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4931) unit = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4931) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4932) op(e1, e2) = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (4931) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4933) op(e3, e1) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4934) ~ (op(e1, e2) = e2) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4932), (4934) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4935) $false % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4935) is inconsistent. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4936) all_53_6 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (4936) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4937) ~ (all_53_2 = e2) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) all_55_8 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (4938) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) all_53_2 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (4939) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) ~ (all_53_1 = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4941) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) all_57_6 = e2 & op(e1, e3) = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (4937), (4942), (function-axioms) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #93. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4943) all_57_7 = e2 & op(e1, e2) = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4943) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944) all_57_7 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4945) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (340), (4286), (4940), (4945) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #33. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4946) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4946) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4947) all_57_6 = e3 & op(e1, e3) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4947) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4948) all_57_6 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4949) ~ (op(e3, e1) = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4933), (4949) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4950) $false % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4950) is inconsistent. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4951) all_53_8 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4951) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4952) ~ (all_53_4 = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4953) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4954) all_57_1 = e3 & op(e3, e2) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (321), (4952), (4954) are inconsistent by % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #328. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4955) all_57_3 = e3 & op(e2, e2) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (4304), (4955), (function-axioms) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4956) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4957) all_57_7 = e3 & op(e1, e2) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4957) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4958) all_57_7 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4944), (4958) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4959) e3 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4948), (4959) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4960) all_57_6 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (17), (18), (226), (229), (284), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4897), (4907), (4908), (4944), (4960) are % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4961) all_57_13 = e3 & op(e0, e2) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4961) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4962) all_57_13 = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (51), (219), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (4305), (4871), (4962), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #77. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963) all_57_12 = e3 & op(e0, e3) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4963) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4964) op(e0, e3) = e3 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (103), (158), (212), (279), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282), (295), (304), (328), (342), (344), (398), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423), (425), (4304), (4308), (4875), (4899), % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4910), (4964) are inconsistent by sub-proof #230. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4965) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4965) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4966) all_57_8 = e2 & op(e1, e1) = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (4907), (4966) are inconsistent by sub-proof % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4967) all_57_11 = e2 & op(e1, e0) = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4926), (4967) are inconsistent by sub-proof % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #305. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4968) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4968) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4969) all_55_8 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (4969) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4970) all_53_2 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4970) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4971) all_53_2 = e2 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4937), (4971) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4972) $false % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4972) is inconsistent. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4973) all_55_8 = e1 | all_55_8 = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (4276), (4898), (4973) are inconsistent by % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #215. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4974) ~ (unit = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4875), (4930), (4974) are inconsistent by % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | (4975) op(e2, e0) = e0 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (328), (4917), (4975) are inconsistent by % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #356. % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4976) all_26_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (4976) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4977) all_6_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4977) implies: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4978) all_6_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (399), (4978) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4979) all_50_2 = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (4978) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4980) ~ (all_53_9 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4304), (4978) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4981) ~ (e3 = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (4978) imply: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | (4982) op(e2, e2) = e1 % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (4983) ~ (op(e2, e1) = e1) % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | (4984) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (17), (18), (48), (172), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | (238), (240), (241), (284), (300), (339), (4286), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | (4304), (4897), (4908), (4979), (4982), (4984), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | #9. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | (4985) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4985) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4986) all_57_4 = e1 & op(e3, e1) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4986) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4987) op(e3, e1) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (4900), (4987) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4988) all_57_9 = e1 & op(e3, e0) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4988) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4989) op(e3, e0) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (4273), (4989) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4990) all_4_1 = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (7), (4983) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4991) ~ (unit = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4297), (4990) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (4992) ~ (all_53_4 = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4993) unit = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4991), (4993) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4994) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4994) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4995) unit = e1 | unit = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4995) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4996) unit = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4996) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4997) op(e1, e2) = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (4996) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4998) op(e3, e1) = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4999) ~ (op(e1, e2) = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4997), (4999) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5000) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5000) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5001) all_53_6 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (5001) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5002) ~ (all_53_4 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5003) ~ (op(e3, e1) = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (4998), (5003) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5004) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5004) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5005) all_53_8 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5005) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5006) ~ (all_53_4 = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (216), (309), (4277), (4992), (5002), (5006) are % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #156. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5007) ~ (unit = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4875), (4995), (5007) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | (5008) op(e2, e1) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (4980), (5008) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #334. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5009) all_57_11 = e1 & op(e1, e0) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5009) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5010) op(e1, e0) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (286), (4902), (5010) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #339. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5011) all_55_10 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (4888), (5011) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | sub-proof #219. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | (5012) all_22_2 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | (5013) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 130.61/18.57 | | | | | | | | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | ALPHA: (5013) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5014) op(e1, e0) = all_22_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | (5015) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0)) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (5012) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5016) all_12_2 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | SIMP: (5016) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5017) all_12_2 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (5017) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5018) all_38_2 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | REDUCE: (433), (5017) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5019) ~ (all_53_14 = e0) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (97), (140), (155), (157), % 130.61/18.57 | | | | | | | | | | | | | | | | | (163), (174), (177), (207), (210), (271), (279), % 130.61/18.57 | | | | | | | | | | | | | | | | | (280), (282), (302), (306), (329), (340), (374), % 130.61/18.57 | | | | | | | | | | | | | | | | | (425), (4276), (4308), (4875), (5014), (5015), % 130.61/18.57 | | | | | | | | | | | | | | | | | (5018), (5019), (function-axioms) are inconsistent % 130.61/18.57 | | | | | | | | | | | | | | | | | by sub-proof #2. % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | (5020) all_18_2 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | (5021) op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ % 130.61/18.57 | | | | | | | | | | | | | | | | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | | e2) = all_18_0 & $i(all_18_0))) % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | ALPHA: (5021) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | (5022) op(e1, e3) = all_18_1 % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5020) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | (5023) all_12_2 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | SIMP: (5023) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | (5024) all_12_2 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | COMBINE_EQS: (384), (5024) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | (5025) all_24_2 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | REDUCE: (415), (5024) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | (5026) ~ (all_53_2 = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | (5027) ~ (all_24_2 = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | REDUCE: (5025), (5027) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5028) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | CLOSE: (5028) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | (5029) op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 130.61/18.57 | | | | | | | | | | | | | | | | | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | | | e0) = all_24_0 & $i(all_24_0))) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | ALPHA: (5029) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5030) op(e1, e3) = all_24_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5031) ~ (op(e1, e3) = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.57 | | | | | | | | | | | | | | | | | | all_18_1, e3, e1, simplifying with (177), (5022) % 130.61/18.57 | | | | | | | | | | | | | | | | | | gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5032) all_53_2 = all_18_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.57 | | | | | | | | | | | | | | | | | | all_24_1, e3, e1, simplifying with (177), (5030) % 130.61/18.57 | | | | | | | | | | | | | | | | | | gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5033) all_53_2 = all_24_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5030), (5031) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5034) ~ (all_24_1 = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5032), (5033) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5035) all_24_1 = all_18_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | SIMP: (5035) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5036) all_24_1 = all_18_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (5032) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5037) all_55_8 = all_18_1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | REDUCE: (157), (5032) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5038) ~ (all_53_6 = all_18_1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | SIMP: (5038) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5039) ~ (all_53_6 = all_18_1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | REDUCE: (4880), (5032) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5040) ~ (all_18_1 = all_10_1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | REDUCE: (4276), (5032) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5041) ~ (all_18_1 = e0) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | REDUCE: (5034), (5036) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5042) ~ (all_18_1 = e3) % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5043) unit = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5043) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5044) op(e2, e1) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5043) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5045) op(e2, e2) = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | REDUCE: (3), (5043) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5046) op(e1, e2) = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (5043) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5047) op(e0, e2) = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5048) ~ (op(e1, e2) = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5046), (5048) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5049) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (5049) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5050) all_53_6 = e1 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (5039), (5050) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5051) ~ (all_18_1 = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | SIMP: (5051) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | (5052) ~ (all_18_1 = e1) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | (5053) all_55_8 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5037), (5053) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | (5054) all_18_1 = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5042), (5054) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | (5055) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5055) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | (5056) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5056) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5057) all_55_8 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5037), (5057) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5058) all_18_1 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5058) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5059) all_18_1 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5040), (5059) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5060) ~ (all_10_1 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5060) implies: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5061) ~ (all_10_1 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (51), (132), (142), (172), (206), (220), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (221), (258), (262), (283), (299), (300), (332), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (334), (339), (399), (400), (419), (421), (4304), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (4305), (4858), (4871), (4878), (4879), (4882), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (4883), (5044), (5045), (5046), (5047), (5061), % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | #66. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | (5062) all_55_8 = e1 | all_55_8 = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5037), (5041), (5052), (5062) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | (5063) unit = e1 | unit = e0 % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (342), (4875), (5026), (5063) are % 130.61/18.57 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #277. % 130.61/18.57 | | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | (5064) op(e1, e3) = e3 % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (5026), (5064) are inconsistent by % 130.61/18.57 | | | | | | | | | | | | | | | | | | sub-proof #323. % 130.61/18.57 | | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | End of split % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | (5065) all_12_2 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | (5066) op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 130.61/18.57 | | | | | | | | | | | | | | | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | e3) = all_12_0 & $i(all_12_0))) % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | ALPHA: (5066) implies: % 130.61/18.57 | | | | | | | | | | | | | | | (5067) op(e1, e2) = all_12_1 % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | COMBINE_EQS: (376), (5065) imply: % 130.61/18.57 | | | | | | | | | | | | | | | (5068) all_30_2 = e2 % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | REDUCE: (426), (5065) imply: % 130.61/18.57 | | | | | | | | | | | | | | | (5069) ~ (all_53_6 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | REDUCE: (431), (5065) imply: % 130.61/18.57 | | | | | | | | | | | | | | | (5070) ~ (all_53_11 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 130.61/18.57 | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | (5071) ~ (op(e1, e2) = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 130.61/18.57 | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | (5072) ~ (all_30_2 = e2) % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | REDUCE: (5068), (5072) imply: % 130.61/18.57 | | | | | | | | | | | | | | | | | (5073) $false % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | CLOSE: (5073) is inconsistent. % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.57 | | | | | | | | | | | | | | | | | % 130.61/18.57 | | | | | | | | | | | | | | | | | (5074) op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ % 130.61/18.57 | | | | | | | | | | | | | | | | | (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e1, % 130.61/18.57 | | | | | | | | | | | | | | | | | e0) = all_30_0 & $i(all_30_0))) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | ALPHA: (5074) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5075) op(e1, e2) = all_30_1 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.61/18.58 | | | | | | | | | | | | | | | | | all_12_1, e2, e1, simplifying with (176), (5067) % 130.61/18.58 | | | | | | | | | | | | | | | | | gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5076) all_53_6 = all_12_1 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, % 130.61/18.58 | | | | | | | | | | | | | | | | | all_30_1, e2, e1, simplifying with (176), (5075) % 130.61/18.58 | | | | | | | | | | | | | | | | | gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5077) all_53_6 = all_30_1 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_30_1, % 130.61/18.58 | | | | | | | | | | | | | | | | | e2, e1, simplifying with (5075) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5078) all_30_1 = e1 | ~ (op(e1, e2) = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | PRED_UNIFY: (8), (5071) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5079) ~ (unit = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | COMBINE_EQS: (5076), (5077) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5080) all_30_1 = all_12_1 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | SIMP: (5080) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5081) all_30_1 = all_12_1 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | REDUCE: (142), (5076) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5082) ~ (all_53_7 = all_12_1) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | SIMP: (5082) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5083) ~ (all_53_7 = all_12_1) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | REDUCE: (419), (5076) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | (5084) ~ (all_12_1 = all_6_2) % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | (5085) unit = e2 % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (48), (51), (132), (171), (172), % 130.61/18.58 | | | | | | | | | | | | | | | | | | (220), (221), (258), (300), (302), (332), (334), % 130.61/18.58 | | | | | | | | | | | | | | | | | | (338), (374), (399), (421), (4304), (4305), % 130.61/18.58 | | | | | | | | | | | | | | | | | | (4871), (5070), (5078), (5081), (5083), (5084), % 130.61/18.58 | | | | | | | | | | | | | | | | | | (5085), (function-axioms) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | | | | | sub-proof #65. % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | (5086) unit = e1 | unit = e0 % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4875), (5079), (5086) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | (5087) op(e1, e2) = e2 % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | REF_CLOSE: (337), (5069), (5087) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | | | sub-proof #326. % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | (5088) op(e0, e3) = e3 % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | REF_CLOSE: (259), (343), (4848), (5088) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | sub-proof #311. % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | % 130.61/18.58 | | | | | | | | End of split % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | (5089) all_8_2 = e1 % 130.61/18.58 | | | | | | | | (5090) op(e0, e1) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = % 130.61/18.58 | | | | | | | | e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 130.61/18.58 | | | | | | | | $i(all_8_0))) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | ALPHA: (5090) implies: % 130.61/18.58 | | | | | | | | (5091) op(e0, e1) = all_8_1 % 130.61/18.58 | | | | | | | | (5092) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = % 130.61/18.58 | | | | | | | | all_8_0 & $i(all_8_0)) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | COMBINE_EQS: (396), (5089) imply: % 130.61/18.58 | | | | | | | | (5093) all_20_2 = e1 % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | REDUCE: (416), (5089) imply: % 130.61/18.58 | | | | | | | | (5094) ~ (all_53_3 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | REDUCE: (427), (5089) imply: % 130.61/18.58 | | | | | | | | (5095) ~ (all_53_7 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | REDUCE: (434), (5089) imply: % 130.61/18.58 | | | | | | | | (5096) ~ (all_53_11 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | REDUCE: (437), (5089) imply: % 130.61/18.58 | | | | | | | | (5097) ~ (all_53_14 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | REDUCE: (4302), (5089) imply: % 130.61/18.58 | | | | | | | | (5098) ~ (all_4_1 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | SIMP: (5098) implies: % 130.61/18.58 | | | | | | | | (5099) ~ (all_4_1 = e1) % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | BETA: splitting (333) gives: % 130.61/18.58 | | | | | | | | % 130.61/18.58 | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | % 130.61/18.58 | | | | | | | | | (5100) ~ (op(e0, e1) = e1) % 130.61/18.58 | | | | | | | | | % 130.61/18.58 | | | | | | | | | BETA: splitting (70) gives: % 130.61/18.58 | | | | | | | | | % 130.61/18.58 | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | (5101) ~ (all_20_2 = e1) % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | REDUCE: (5093), (5101) imply: % 130.61/18.58 | | | | | | | | | | (5102) $false % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | CLOSE: (5102) is inconsistent. % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | (5103) op(e0, e1) = all_20_1 & $i(all_20_1) & ( ~ % 130.61/18.58 | | | | | | | | | | (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, % 130.61/18.58 | | | | | | | | | | e3) = all_20_0 & $i(all_20_0))) % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | ALPHA: (5103) implies: % 130.61/18.58 | | | | | | | | | | (5104) op(e0, e1) = all_20_1 % 130.61/18.58 | | | | | | | | | | (5105) ~ (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, % 130.61/18.58 | | | | | | | | | | e3) = all_20_0 & $i(all_20_0)) % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | BETA: splitting (220) gives: % 130.61/18.58 | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | (5106) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 130.61/18.58 | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | BETA: splitting (5106) gives: % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | (5107) all_57_12 = e1 & op(e0, e3) = e1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REF_CLOSE: (173), (5094), (5107), (function-axioms) are % 130.61/18.58 | | | | | | | | | | | | inconsistent by sub-proof #272. % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | (5108) all_57_13 = e1 & op(e0, e2) = e1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REF_CLOSE: (172), (5095), (5108), (function-axioms) are % 130.61/18.58 | | | | | | | | | | | | inconsistent by sub-proof #106. % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | End of split % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | (5109) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 130.61/18.58 | | | | | | | | | | | e1 & op(e0, e0) = e1) % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | BETA: splitting (5109) gives: % 130.61/18.58 | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | (5110) all_57_14 = e1 & op(e0, e1) = e1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REF_CLOSE: (5100), (5110) are inconsistent by sub-proof #53. % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | (5111) all_57_15 = e1 & op(e0, e0) = e1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | ALPHA: (5111) implies: % 130.61/18.58 | | | | | | | | | | | | (5112) all_57_15 = e1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11, % 130.61/18.58 | | | | | | | | | | | | all_8_1, e1, e0, simplifying with (171), (5091) % 130.61/18.58 | | | | | | | | | | | | gives: % 130.61/18.58 | | | | | | | | | | | | (5113) all_53_11 = all_8_1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11, % 130.61/18.58 | | | | | | | | | | | | all_20_1, e1, e0, simplifying with (171), (5104) % 130.61/18.58 | | | | | | | | | | | | gives: % 130.61/18.58 | | | | | | | | | | | | (5114) all_53_11 = all_20_1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_20_1, % 130.61/18.58 | | | | | | | | | | | | e1, e0, simplifying with (5104) gives: % 130.61/18.58 | | | | | | | | | | | | (5115) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | PRED_UNIFY: (7), (5100) imply: % 130.61/18.58 | | | | | | | | | | | | (5116) ~ (unit = e0) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | COMBINE_EQS: (5113), (5114) imply: % 130.61/18.58 | | | | | | | | | | | | (5117) all_20_1 = all_8_1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | SIMP: (5117) implies: % 130.61/18.58 | | | | | | | | | | | | (5118) all_20_1 = all_8_1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | COMBINE_EQS: (257), (5113) imply: % 130.61/18.58 | | | | | | | | | | | | (5119) all_55_14 = all_8_1 % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REDUCE: (139), (5113) imply: % 130.61/18.58 | | | | | | | | | | | | (5120) ~ (all_53_7 = all_8_1) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REDUCE: (132), (5113) imply: % 130.61/18.58 | | | | | | | | | | | | (5121) ~ (all_53_9 = all_8_1) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | REDUCE: (431), (5113) imply: % 130.61/18.58 | | | | | | | | | | | | (5122) ~ (all_12_2 = all_8_1) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | SIMP: (5122) implies: % 130.61/18.58 | | | | | | | | | | | | (5123) ~ (all_12_2 = all_8_1) % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | BETA: splitting (10) gives: % 130.61/18.58 | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | (5124) unit = e3 % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | REDUCE: (4292), (5124) imply: % 130.61/18.58 | | | | | | | | | | | | | (5125) $false % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | CLOSE: (5125) is inconsistent. % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | (5126) unit = e2 | unit = e1 | unit = e0 % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | BETA: splitting (58) gives: % 130.61/18.58 | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | (5127) ~ (all_12_2 = e2) % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.61/18.58 | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | (5128) ~ (all_18_2 = e3) % 130.61/18.58 | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | REDUCE: (391), (5128) imply: % 130.61/18.58 | | | | | | | | | | | | | | | (5129) ~ (all_12_2 = e3) % 130.61/18.58 | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 130.61/18.58 | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | (5130) ~ (all_22_2 = e0) % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | REDUCE: (389), (5130) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | (5131) ~ (all_12_2 = e0) % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | (5132) all_55_10 = e3 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5129), (5132) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | | | | sub-proof #282. % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | (5133) ~ (all_55_10 = e3) % 130.61/18.58 | | | | | | | | | | | | | | | | | (5134) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (5134) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | (5135) all_55_10 = e2 % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5127), (5135) are inconsistent by % 130.61/18.58 | | | | | | | | | | | | | | | | | | sub-proof #281. % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | (5136) all_55_10 = e1 | all_55_10 = e0 % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (5136) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5137) all_55_10 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5137) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5138) all_12_2 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | SIMP: (5138) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5139) all_12_2 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (5139) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5140) all_22_2 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | REDUCE: (415), (5139) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5141) ~ (all_53_2 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | REDUCE: (428), (5139) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5142) ~ (all_53_8 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | REDUCE: (5129), (5139) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5143) ~ (e3 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | REDUCE: (57), (5139) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | (5144) op(e1, e1) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | (5145) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5145) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | (5146) all_57_0 = e1 & op(e3, e3) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (4286), (5140), (5144), (5146) are % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | (5147) all_57_1 = e1 & op(e3, e2) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5147) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | (5148) all_57_1 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | (5149) op(e3, e2) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | (5150) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5150) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5151) all_57_0 = e1 & op(e3, e3) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (284), (4286), (5140), (5144), (5151) are % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5152) all_57_2 = e1 & op(e2, e3) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5152) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5153) all_57_2 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5154) op(e2, e3) = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1, % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (181), (5154) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5155) all_53_1 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1, % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (184), (5149) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5156) all_53_4 = e1 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (5156) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5157) ~ (all_53_6 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5157) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5158) ~ (all_53_6 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5156) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5159) ~ (all_53_8 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (5156) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5160) ~ (all_6_2 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5160) implies: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | (5161) ~ (all_6_2 = e1) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | (5162) all_55_3 = e3 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4296), (5162) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | (5163) all_4_1 = e3 % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4298), (5163) imply: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | (5164) ~ (all_53_8 = e3) % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5165) all_55_2 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (5165) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5166) all_53_8 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5164), (5166) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5167) $false % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5167) is inconsistent. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5168) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5168) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5169) all_55_2 = e2 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (5169) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5170) all_53_8 = e2 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (5170) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5171) ~ (all_53_9 = e2) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5171) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5172) ~ (all_53_9 = e2) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (279), (282), (304), (5116), (5126), % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5158), (5172) are inconsistent by sub-proof #252. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5173) all_55_2 = e1 | all_55_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (308), (4278), (5142), (5173) are inconsistent by % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #213. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (5174) ~ (all_55_3 = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4296), (5174) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (5175) ~ (all_4_1 = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5176) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5176) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5177) all_57_0 = e3 & op(e3, e3) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (4286), (5177) are inconsistent by sub-proof % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5178) all_57_1 = e3 & op(e3, e2) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (5148), (5178) are inconsistent by sub-proof % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | #271. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5179) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5179) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5180) all_57_4 = e3 & op(e3, e1) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5180) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5181) op(e3, e1) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5182) ~ (op(e3, e1) = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5181), (5182) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5183) $false % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5183) is inconsistent. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5184) all_53_8 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (5184) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5185) ~ (all_53_9 = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5185) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5186) ~ (all_53_9 = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5187) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5187) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5188) all_57_2 = e3 & op(e2, e3) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (5153), (5188) are inconsistent by sub-proof % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #85. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5189) all_57_3 = e3 & op(e2, e2) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (4304), (5189), (function-axioms) are % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5190) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5190) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5191) all_57_5 = e3 & op(e2, e1) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (5186), (5191), (function-axioms) are % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5192) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5192) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5193) op(e2, e0) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5194) ~ (all_44_2 = e0) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (5194) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5195) ~ (all_6_2 = e0) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (212), (279), (282), (295), (304), % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423), (4304), (5116), (5126), (5158), (5161), % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5195) are inconsistent by sub-proof #234. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5196) op(e2, e0) = all_44_1 & $i(all_44_1) & ( ~ % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_44_1 = e3) | ( ~ (all_44_0 = e1) & op(e2, % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_44_0 & $i(all_44_0))) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5196) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5197) op(e2, e0) = all_44_1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5198) ~ (all_44_1 = e3) | ( ~ (all_44_0 = e1) & op(e2, % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_44_0 & $i(all_44_0)) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5198) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5199) ~ (all_44_1 = e3) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1, % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (5193), (5197) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5200) all_44_1 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5199), (5200) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5201) $false % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5201) is inconsistent. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5202) ~ (all_44_0 = e1) & op(e2, e3) = all_44_0 & % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5202) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5203) ~ (all_44_0 = e1) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5204) op(e2, e3) = all_44_0 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_44_0, % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (5154), (5204) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5205) all_44_0 = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5203), (5205) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5206) $false % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5206) is inconsistent. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5207) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4291), (4295), (5175), (5207) are inconsistent by % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | (5208) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (281), (5094), (5141), (5208), % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | #41. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | (5209) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5209) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5210) all_57_4 = e1 & op(e3, e1) = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5210) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5211) op(e3, e1) = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (5142), (5211) are inconsistent by % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | sub-proof #238. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5212) all_57_9 = e1 & op(e3, e0) = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5212) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5213) op(e3, e0) = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (4273), (5213) gives: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5214) all_4_1 = e1 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5099), (5214) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | (5215) $false % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5215) is inconsistent. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | (5216) all_55_10 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5131), (5216) are inconsistent by % 130.61/18.59 | | | | | | | | | | | | | | | | | | | sub-proof #219. % 130.61/18.59 | | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | (5217) all_22_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | (5218) op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 130.61/18.59 | | | | | | | | | | | | | | | | (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.59 | | | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0))) % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | ALPHA: (5218) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | (5219) op(e1, e0) = all_22_1 % 130.61/18.59 | | | | | | | | | | | | | | | | (5220) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, % 130.61/18.59 | | | | | | | | | | | | | | | | e3) = all_22_0 & $i(all_22_0)) % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (5217) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | (5221) all_12_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | SIMP: (5221) implies: % 130.61/18.59 | | | | | | | | | | | | | | | | (5222) all_12_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (5222) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | (5223) all_38_2 = e0 % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | REDUCE: (433), (5222) imply: % 130.61/18.59 | | | | | | | | | | | | | | | | (5224) ~ (all_53_14 = e0) % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (97), (140), (155), (157), % 130.61/18.59 | | | | | | | | | | | | | | | | (163), (174), (177), (207), (210), (271), (279), % 130.61/18.59 | | | | | | | | | | | | | | | | (280), (282), (302), (306), (329), (340), (374), % 130.61/18.59 | | | | | | | | | | | | | | | | (425), (4276), (5116), (5126), (5219), (5220), % 130.61/18.59 | | | | | | | | | | | | | | | | (5223), (5224), (function-axioms) are inconsistent % 130.61/18.59 | | | | | | | | | | | | | | | | by sub-proof #2. % 130.61/18.59 | | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | (5225) all_18_2 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5225) imply: % 130.61/18.59 | | | | | | | | | | | | | | | (5226) all_12_2 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | SIMP: (5226) implies: % 130.61/18.59 | | | | | | | | | | | | | | | (5227) all_12_2 = e3 % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (13), (14), (15), (16), (17), % 130.61/18.59 | | | | | | | | | | | | | | | (57), (137), (154), (160), (162), (174), (204), % 130.61/18.59 | | | | | | | | | | | | | | | (213), (219), (221), (222), (226), (227), (228), % 130.61/18.59 | | | | | | | | | | | | | | | (229), (230), (231), (232), (258), (259), (261), % 130.61/18.59 | | | | | | | | | | | | | | | (262), (285), (286), (296), (301), (304), (330), % 130.61/18.59 | | | | | | | | | | | | | | | (332), (340), (342), (343), (398), (414), (415), % 130.61/18.59 | | | | | | | | | | | | | | | (423), (429), (433), (5092), (5095), (5097), % 130.61/18.59 | | | | | | | | | | | | | | | (5100), (5112), (5115), (5116), (5118), (5119), % 130.61/18.59 | | | | | | | | | | | | | | | (5120), (5121), (5123), (5126), (5127), (5227), % 130.61/18.59 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.59 | | | | | | | | | | | | | | | #51. % 130.61/18.59 | | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | End of split % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | Case 2: % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | (5228) all_12_2 = e2 % 130.61/18.59 | | | | | | | | | | | | | | (5229) op(e1, e2) = all_12_1 & $i(all_12_1) & ( ~ % 130.61/18.59 | | | | | | | | | | | | | | (all_12_1 = e3) | ( ~ (all_12_0 = e0) & op(e1, % 130.61/18.59 | | | | | | | | | | | | | | e3) = all_12_0 & $i(all_12_0))) % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | ALPHA: (5229) implies: % 130.61/18.59 | | | | | | | | | | | | | | (5230) op(e1, e2) = all_12_1 % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | COMBINE_EQS: (376), (5228) imply: % 130.61/18.59 | | | | | | | | | | | | | | (5231) all_30_2 = e2 % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.59 | | | | | | | | | | | | | | REDUCE: (426), (5228) imply: % 130.61/18.59 | | | | | | | | | | | | | | (5232) ~ (all_53_6 = e2) % 130.61/18.59 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | REDUCE: (429), (5228) imply: % 130.61/18.60 | | | | | | | | | | | | | | (5233) ~ (all_53_9 = e2) % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | REDUCE: (5123), (5228) imply: % 130.61/18.60 | | | | | | | | | | | | | | (5234) ~ (all_8_1 = e2) % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | SIMP: (5234) implies: % 130.61/18.60 | | | | | | | | | | | | | | (5235) ~ (all_8_1 = e2) % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | REDUCE: (57), (5228) imply: % 130.61/18.60 | | | | | | | | | | | | | | (5236) op(e1, e1) = e2 % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (13), (14), (15), % 130.61/18.60 | | | | | | | | | | | | | | (16), (17), (18), (85), (137), (140), (142), % 130.61/18.60 | | | | | | | | | | | | | | (157), (163), (176), (204), (221), (226), (227), % 130.61/18.60 | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (258), % 130.61/18.60 | | | | | | | | | | | | | | (262), (281), (285), (286), (299), (304), (330), % 130.61/18.60 | | | | | | | | | | | | | | (332), (337), (339), (340), (342), (400), (419), % 130.61/18.60 | | | | | | | | | | | | | | (421), (5091), (5100), (5105), (5112), (5115), % 130.61/18.60 | | | | | | | | | | | | | | (5116), (5118), (5119), (5120), (5121), (5126), % 130.61/18.60 | | | | | | | | | | | | | | (5228), (5230), (5231), (5232), (5233), (5235), % 130.61/18.60 | | | | | | | | | | | | | | (5236), (function-axioms) are inconsistent by % 130.61/18.60 | | | | | | | | | | | | | | sub-proof #35. % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | | % 130.61/18.60 | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | (5237) op(e0, e1) = e1 % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | REF_CLOSE: (334), (5096), (5237) are inconsistent by sub-proof % 130.61/18.60 | | | | | | | | | #333. % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | End of split % 130.61/18.60 | | | | | | | | % 130.61/18.60 | | | | | | | End of split % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | Case 2: % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | (5238) all_6_2 = e3 % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | REDUCE: (414), (5238) imply: % 130.61/18.60 | | | | | | | (5239) ~ (all_53_1 = e3) % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | REDUCE: (419), (5238) imply: % 130.61/18.60 | | | | | | | (5240) ~ (all_53_6 = e3) % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | REDUCE: (421), (5238) imply: % 130.61/18.60 | | | | | | | (5241) ~ (all_53_7 = e3) % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | REDUCE: (423), (5238) imply: % 130.61/18.60 | | | | | | | (5242) ~ (all_53_9 = e3) % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | REDUCE: (425), (5238) imply: % 130.61/18.60 | | | | | | | (5243) ~ (all_53_13 = e3) % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | BETA: splitting (237) gives: % 130.61/18.60 | | | | | | | % 130.61/18.60 | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | % 130.61/18.60 | | | | | | | | (5244) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & % 130.61/18.60 | | | | | | | | op(e2, e2) = e3) % 130.61/18.60 | | | | | | | | % 130.61/18.60 | | | | | | | | BETA: splitting (5244) gives: % 130.61/18.60 | | | | | | | | % 130.61/18.60 | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | (5245) all_57_2 = e3 & op(e2, e3) = e3 % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | ALPHA: (5245) implies: % 130.61/18.60 | | | | | | | | | (5246) op(e2, e3) = e3 % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | REF_CLOSE: (340), (5239), (5246) are inconsistent by sub-proof % 130.61/18.60 | | | | | | | | | #353. % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | (5247) all_57_3 = e3 & op(e2, e2) = e3 % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | ALPHA: (5247) implies: % 130.61/18.60 | | | | | | | | | (5248) all_57_3 = e3 % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | BETA: splitting (340) gives: % 130.61/18.60 | | | | | | | | | % 130.61/18.60 | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | (5249) ~ (op(e2, e3) = e3) % 130.61/18.60 | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | PRED_UNIFY: (9), (5249) imply: % 130.61/18.60 | | | | | | | | | | (5250) ~ (unit = e2) % 130.61/18.60 | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | BETA: splitting (10) gives: % 130.61/18.60 | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | (5251) unit = e3 % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | REDUCE: (4292), (5251) imply: % 130.61/18.60 | | | | | | | | | | | (5252) $false % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | CLOSE: (5252) is inconsistent. % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | (5253) unit = e2 | unit = e1 | unit = e0 % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | BETA: splitting (52) gives: % 130.61/18.60 | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | (5254) ~ (all_8_2 = e1) % 130.61/18.60 | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | BETA: splitting (55) gives: % 130.61/18.60 | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | (5255) ~ (all_10_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | REDUCE: (395), (5255) imply: % 130.61/18.60 | | | | | | | | | | | | | (5256) ~ (all_8_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | BETA: splitting (58) gives: % 130.61/18.60 | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | (5257) ~ (all_12_2 = e2) % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | BETA: splitting (67) gives: % 130.61/18.60 | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | (5258) ~ (all_18_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | REDUCE: (391), (5258) imply: % 130.61/18.60 | | | | | | | | | | | | | | | (5259) ~ (all_12_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (73), (82), (94), % 130.61/18.60 | | | | | | | | | | | | | | | (124), (139), (140), (142), (153), (154), (155), % 130.61/18.60 | | | | | | | | | | | | | | | (158), (172), (173), (203), (205), (206), (207), % 130.61/18.60 | | | | | | | | | | | | | | | (208), (209), (256), (258), (259), (265), (271), % 130.61/18.60 | | | | | | | | | | | | | | | (278), (279), (280), (286), (327), (328), (329), % 130.61/18.60 | | | | | | | | | | | | | | | (331), (332), (334), (338), (339), (341), (342), % 130.61/18.60 | | | | | | | | | | | | | | | (343), (361), (389), (397), (416), (426), (427), % 130.61/18.60 | | | | | | | | | | | | | | | (429), (431), (433), (434), (437), (5240), (5241), % 130.61/18.60 | | | | | | | | | | | | | | | (5250), (5253), (5254), (5256), (5257), (5259), % 130.61/18.60 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.60 | | | | | | | | | | | | | | | #26. % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | (5260) all_18_2 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | (5261) op(e1, e3) = all_18_1 & $i(all_18_1) & ( ~ % 130.61/18.60 | | | | | | | | | | | | | | | (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, % 130.61/18.60 | | | | | | | | | | | | | | | e2) = all_18_0 & $i(all_18_0))) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | ALPHA: (5261) implies: % 130.61/18.60 | | | | | | | | | | | | | | | (5262) op(e1, e3) = all_18_1 % 130.61/18.60 | | | | | | | | | | | | | | | (5263) ~ (all_18_1 = e2) | ( ~ (all_18_0 = e0) & op(e1, % 130.61/18.60 | | | | | | | | | | | | | | | e2) = all_18_0 & $i(all_18_0)) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5260) imply: % 130.61/18.60 | | | | | | | | | | | | | | | (5264) all_12_2 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | SIMP: (5264) implies: % 130.61/18.60 | | | | | | | | | | | | | | | (5265) all_12_2 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | COMBINE_EQS: (384), (5265) imply: % 130.61/18.60 | | | | | | | | | | | | | | | (5266) all_24_2 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | REDUCE: (415), (5265) imply: % 130.61/18.60 | | | | | | | | | | | | | | | (5267) ~ (all_53_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | REDUCE: (433), (5265) imply: % 130.61/18.60 | | | | | | | | | | | | | | | (5268) ~ (all_53_14 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 130.61/18.60 | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | (5269) ~ (all_24_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | REDUCE: (5266), (5269) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | (5270) $false % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | CLOSE: (5270) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | (5271) op(e1, e3) = all_24_1 & $i(all_24_1) & ( ~ % 130.61/18.60 | | | | | | | | | | | | | | | | (all_24_1 = e0) | ( ~ (all_24_0 = e2) & op(e1, % 130.61/18.60 | | | | | | | | | | | | | | | | e0) = all_24_0 & $i(all_24_0))) % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | ALPHA: (5271) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | (5272) op(e1, e3) = all_24_1 % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | (5273) ~ (op(e1, e3) = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | (5274) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | BETA: splitting (5274) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | (5275) all_57_0 = e3 & op(e3, e3) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (4286), (5275) are inconsistent by sub-proof % 130.61/18.60 | | | | | | | | | | | | | | | | | | | #34. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | (5276) all_57_2 = e3 & op(e2, e3) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5249), (5276) are inconsistent by sub-proof #24. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | (5277) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 130.61/18.60 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | BETA: splitting (5277) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | (5278) all_57_6 = e3 & op(e1, e3) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5273), (5278) are inconsistent by sub-proof #181. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | (5279) all_57_12 = e3 & op(e0, e3) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | ALPHA: (5279) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | (5280) op(e0, e3) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | (5281) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5281) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | (5282) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5282) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | (5283) all_57_9 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5284) ~ (op(e0, e3) = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5280), (5284) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5285) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5285) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5286) all_53_3 = e3 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (5286) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5287) ~ (all_53_11 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5287) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5288) ~ (all_53_11 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (5286) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5289) ~ (all_8_2 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | all_18_1, e3, e1, simplifying with (177), (5262) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5290) all_53_2 = all_18_1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | all_24_1, e3, e1, simplifying with (177), (5272) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5291) all_53_2 = all_24_1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (5273) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5292) ~ (unit = e1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5272), (5273) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5293) ~ (all_24_1 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5290), (5291) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5294) all_24_1 = all_18_1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5294) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5295) all_24_1 = all_18_1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (5290) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5296) all_55_8 = all_18_1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (5290) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5297) ~ (all_53_14 = all_18_1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5297) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5298) ~ (all_53_14 = all_18_1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4276), (5290) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5299) ~ (all_18_1 = e0) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5293), (5295) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | (5300) ~ (all_18_1 = e3) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5253) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | (5301) unit = e2 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5250), (5301) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | (5302) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5302) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | (5303) unit = e1 | unit = e0 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5303) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5304) unit = e1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5292), (5304) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5305) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5305) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5306) unit = e0 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5306) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5307) op(e0, e1) = e1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (5306) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5308) op(e1, e0) = e1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (5306) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | (5309) op(e0, e0) = e0 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5310) ~ (op(e0, e0) = e0) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5309), (5310) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5311) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5311) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5312) all_16_2 = e0 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (5312) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5313) all_8_2 = e0 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (5313) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5314) ~ (all_53_11 = e0) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5256), (5313) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5315) ~ (e3 = e0) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5316) ~ (op(e1, e0) = e1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5308), (5316) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5317) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5317) is inconsistent. % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5318) all_53_14 = e1 % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5298), (5318) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5319) ~ (all_18_1 = e1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5319) implies: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5320) ~ (all_18_1 = e1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5321) ~ (op(e0, e1) = e1) % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5307), (5321) imply: % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5322) $false % 130.61/18.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5322) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5323) all_53_11 = e1 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5323) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324) ~ (all_53_8 = e1) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5288), (5323) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5325) ~ (e3 = e1) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5326) all_55_8 = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5296), (5326) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5327) all_18_1 = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5300), (5327) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5328) $false % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5328) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5329) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5329) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5330) all_55_8 = e2 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5296), (5330) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5331) all_18_1 = e2 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5331) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5332) all_18_1 = e2 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5333) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5333) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5334) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5334) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5335) all_57_1 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (245), (330), (4286), (5283), (5324), % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5335) are inconsistent by sub-proof #200. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5336) all_57_3 = e0 & op(e2, e2) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5336) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5337) all_57_3 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5248), (5337) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5338) e3 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5338) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5339) e3 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5286), (5339) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5340) all_53_3 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (248), (340), (342), (344), (4286), (5239), % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5267), (5340) are inconsistent by sub-proof #32. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5341) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5341) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5342) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5342) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5343) op(e1, e2) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5263) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5344) ~ (all_18_1 = e2) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5332), (5344) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5345) $false % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5345) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5346) ~ (all_18_0 = e0) & op(e1, e2) = all_18_0 & % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_18_0) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5346) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5347) ~ (all_18_0 = e0) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5348) op(e1, e2) = all_18_0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_18_0, % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (5343), (5348) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349) all_18_0 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5347), (5349) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5350) $false % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5350) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5351) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (139), (203), (256), (263), (264), % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (306), (427), (436), (5250), (5253), % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5254), (5256), (5351) are inconsistent by % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #108. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5352) all_55_8 = e1 | all_55_8 = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5296), (5299), (5320), (5352) are inconsistent by % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | (5353) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (5243), (5353), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | (5354) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5354) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | (5355) all_57_11 = e3 & op(e1, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (5268), (5355), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | (5356) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (5256), (5356), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | (5357) op(e1, e3) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (342), (5267), (5357) are inconsistent by % 130.61/18.61 | | | | | | | | | | | | | | | | | sub-proof #323. % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | (5358) all_12_2 = e2 % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | REDUCE: (426), (5358) imply: % 130.61/18.61 | | | | | | | | | | | | | | (5359) ~ (all_53_6 = e2) % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | REDUCE: (57), (5358) imply: % 130.61/18.61 | | | | | | | | | | | | | | (5360) op(e1, e1) = e2 % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (18), (134), (153), (171), (179), % 130.61/18.61 | | | | | | | | | | | | | | (233), (323), (324), (337), (344), (5242), (5250), % 130.61/18.61 | | | | | | | | | | | | | | (5253), (5359), (5360), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | inconsistent by sub-proof #18. % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | (5361) all_10_2 = e3 % 130.61/18.61 | | | | | | | | | | | | | (5362) op(e0, e3) = all_10_1 & $i(all_10_1) & ( ~ % 130.61/18.61 | | | | | | | | | | | | | (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, % 130.61/18.61 | | | | | | | | | | | | | e2) = all_10_0 & $i(all_10_0))) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | ALPHA: (5362) implies: % 130.61/18.61 | | | | | | | | | | | | | (5363) op(e0, e3) = all_10_1 % 130.61/18.61 | | | | | | | | | | | | | (5364) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, % 130.61/18.61 | | | | | | | | | | | | | e2) = all_10_0 & $i(all_10_0)) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | COMBINE_EQS: (395), (5361) imply: % 130.61/18.61 | | | | | | | | | | | | | (5365) all_8_2 = e3 % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | SIMP: (5365) implies: % 130.61/18.61 | | | | | | | | | | | | | (5366) all_8_2 = e3 % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | COMBINE_EQS: (387), (5366) imply: % 130.61/18.61 | | | | | | | | | | | | | (5367) all_16_2 = e3 % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | REDUCE: (416), (5366) imply: % 130.61/18.61 | | | | | | | | | | | | | (5368) ~ (all_53_3 = e3) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | REDUCE: (437), (5366) imply: % 130.61/18.61 | | | | | | | | | | | | | (5369) ~ (all_53_14 = e3) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | REDUCE: (4302), (5366) imply: % 130.61/18.61 | | | | | | | | | | | | | (5370) ~ (all_4_1 = e3) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | SIMP: (5370) implies: % 130.61/18.61 | | | | | | | | | | | | | (5371) ~ (all_4_1 = e3) % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | BETA: splitting (64) gives: % 130.61/18.61 | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | (5372) ~ (all_16_2 = e3) % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | REDUCE: (5367), (5372) imply: % 130.61/18.61 | | | | | | | | | | | | | | (5373) $false % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | CLOSE: (5373) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | (5374) op(e0, e3) = all_16_1 & $i(all_16_1) & ( ~ % 130.61/18.61 | | | | | | | | | | | | | | (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.61 | | | | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0))) % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | ALPHA: (5374) implies: % 130.61/18.61 | | | | | | | | | | | | | | (5375) op(e0, e3) = all_16_1 % 130.61/18.61 | | | | | | | | | | | | | | (5376) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, % 130.61/18.61 | | | | | | | | | | | | | | e1) = all_16_0 & $i(all_16_0)) % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | BETA: splitting (344) gives: % 130.61/18.61 | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | (5377) ~ (op(e0, e3) = e3) % 130.61/18.61 | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 130.61/18.61 | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | (5378) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 130.61/18.61 | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | BETA: splitting (5378) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | (5379) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (4291), (4295), (5371), (5379) are inconsistent by % 130.61/18.61 | | | | | | | | | | | | | | | | | sub-proof #3. % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | (5380) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (5243), (5380), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | End of split % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | (5381) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 130.61/18.61 | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | BETA: splitting (5381) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | (5382) all_57_11 = e3 & op(e1, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (5369), (5382), (function-axioms) are % 130.61/18.61 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | (5383) all_57_15 = e3 & op(e0, e0) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | ALPHA: (5383) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5384) all_57_15 = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.61 | | | | | | | | | | | | | | | | | all_10_1, e3, e0, simplifying with (173), (5363) % 130.61/18.61 | | | | | | | | | | | | | | | | | gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5385) all_53_3 = all_10_1 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, % 130.61/18.61 | | | | | | | | | | | | | | | | | all_16_1, e3, e0, simplifying with (173), (5375) % 130.61/18.61 | | | | | | | | | | | | | | | | | gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5386) all_53_3 = all_16_1 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | PRED_UNIFY: (9), (5377) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5387) ~ (unit = e0) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | PRED_UNIFY: (5375), (5377) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5388) ~ (all_16_1 = e3) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (5385), (5386) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5389) all_16_1 = all_10_1 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | SIMP: (5389) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5390) all_16_1 = all_10_1 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5385) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5391) all_55_12 = all_10_1 % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REDUCE: (154), (5385) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5392) ~ (all_53_7 = all_10_1) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | SIMP: (5392) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5393) ~ (all_53_7 = all_10_1) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REDUCE: (153), (5385) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5394) ~ (all_53_11 = all_10_1) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | SIMP: (5394) implies: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5395) ~ (all_53_11 = all_10_1) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | REDUCE: (5388), (5390) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | (5396) ~ (all_10_1 = e3) % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | BETA: splitting (5253) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | (5397) unit = e2 % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | REDUCE: (5250), (5397) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | (5398) $false % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | CLOSE: (5398) is inconsistent. % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | (5399) unit = e1 | unit = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | BETA: splitting (5399) gives: % 130.61/18.61 | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | Case 1: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | (5400) unit = e1 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | REDUCE: (4292), (5400) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | (5401) ~ (e3 = e1) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | REDUCE: (5250), (5400) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | (5402) ~ (e2 = e1) % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5400) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | (5403) op(e1, e0) = e0 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | REDUCE: (5), (5400) imply: % 130.61/18.61 | | | | | | | | | | | | | | | | | | | (5404) op(e3, e1) = e3 % 130.61/18.61 | | | | | | | | | | | | | | | | | | | % 130.61/18.61 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5400) imply: % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5405) op(e2, e1) = e2 % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | | REDUCE: (3), (5400) imply: % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5406) op(e1, e1) = e1 % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (5400) imply: % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5407) op(e0, e1) = e0 % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (13), (15), (17), (57), (124), (126), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (131), (132), (134), (135), (137), (139), (148), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (172), (174), (178), (179), (183), (206), (208), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (219), (221), (227), (228), (229), (230), (231), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (234), (235), (236), (238), (239), (248), (249), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (257), (258), (262), (264), (265), (278), (279), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (282), (283), (284), (285), (286), (288), (303), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (306), (309), (319), (321), (323), (324), (326), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (328), (329), (331), (332), (382), (389), (411), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (426), (428), (429), (433), (5248), (5249), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5253), (5364), (5369), (5376), (5377), (5384), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5387), (5390), (5391), (5393), (5395), (5396), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5403), (5404), (5405), (5406), (5407), % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.62 | | | | | | | | | | | | | | | | | | | #14. % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | | (5408) ~ (unit = e1) % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5387), (5399), (5408) are inconsistent by % 130.61/18.62 | | | | | | | | | | | | | | | | | | | sub-proof #278. % 130.61/18.62 | | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | (5409) op(e0, e3) = e3 % 130.61/18.62 | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | | REF_CLOSE: (259), (343), (5368), (5409) are inconsistent by % 130.61/18.62 | | | | | | | | | | | | | | | sub-proof #311. % 130.61/18.62 | | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | (5410) all_8_2 = e1 % 130.61/18.62 | | | | | | | | | | | | (5411) op(e0, e1) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 % 130.61/18.62 | | | | | | | | | | | | = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = % 130.61/18.62 | | | | | | | | | | | | all_8_0 & $i(all_8_0))) % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | ALPHA: (5411) implies: % 130.61/18.62 | | | | | | | | | | | | (5412) op(e0, e1) = all_8_1 % 130.61/18.62 | | | | | | | | | | | | (5413) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, % 130.61/18.62 | | | | | | | | | | | | e2) = all_8_0 & $i(all_8_0)) % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | COMBINE_EQS: (396), (5410) imply: % 130.61/18.62 | | | | | | | | | | | | (5414) all_20_2 = e1 % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | REDUCE: (427), (5410) imply: % 130.61/18.62 | | | | | | | | | | | | (5415) ~ (all_53_7 = e1) % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | REDUCE: (434), (5410) imply: % 130.61/18.62 | | | | | | | | | | | | (5416) ~ (all_53_11 = e1) % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | | REF_CLOSE: (2), (7), (8), (10), (70), (139), (142), (149), % 130.61/18.62 | | | | | | | | | | | | (153), (154), (171), (172), (204), (205), (257), % 130.61/18.62 | | | | | | | | | | | | (258), (261), (334), (335), (337), (5241), (5250), % 130.61/18.62 | | | | | | | | | | | | (5412), (5413), (5414), (5415), (5416), % 130.61/18.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.61/18.62 | | | | | | | | | | | | #13. % 130.61/18.62 | | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | | % 130.61/18.62 | | | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | (5417) op(e2, e3) = e3 % 130.61/18.62 | | | | | | | | | | % 130.61/18.62 | | | | | | | | | | REF_CLOSE: (340), (5239), (5417) are inconsistent by % 130.61/18.62 | | | | | | | | | | sub-proof #353. % 130.61/18.62 | | | | | | | | | | % 130.61/18.62 | | | | | | | | | End of split % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | End of split % 130.61/18.62 | | | | | | | | % 130.61/18.62 | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | % 130.61/18.62 | | | | | | | | (5418) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & % 130.61/18.62 | | | | | | | | op(e2, e0) = e3) % 130.61/18.62 | | | | | | | | % 130.61/18.62 | | | | | | | | BETA: splitting (5418) gives: % 130.61/18.62 | | | | | | | | % 130.61/18.62 | | | | | | | | Case 1: % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | | (5419) all_57_5 = e3 & op(e2, e1) = e3 % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | | REF_CLOSE: (179), (5242), (5419), (function-axioms) are % 130.61/18.62 | | | | | | | | | inconsistent by sub-proof #180. % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | Case 2: % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | | (5420) all_57_10 = e3 & op(e2, e0) = e3 % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | | REF_CLOSE: (178), (5243), (5420), (function-axioms) are % 130.61/18.62 | | | | | | | | | inconsistent by sub-proof #83. % 130.61/18.62 | | | | | | | | | % 130.61/18.62 | | | | | | | | End of split % 130.61/18.62 | | | | | | | | % 130.61/18.62 | | | | | | | End of split % 130.61/18.62 | | | | | | | % 130.61/18.62 | | | | | | End of split % 130.61/18.62 | | | | | | % 130.61/18.62 | | | | | Case 2: % 130.61/18.62 | | | | | | % 130.61/18.62 | | | | | | (5421) op(e3, e0) = e0 % 130.61/18.62 | | | | | | % 130.61/18.62 | | | | | | REF_CLOSE: (326), (4279), (5421) are inconsistent by sub-proof #256. % 130.61/18.62 | | | | | | % 130.61/18.62 | | | | | End of split % 130.61/18.62 | | | | | % 130.61/18.62 | | | | Case 2: % 130.61/18.62 | | | | | % 130.61/18.62 | | | | | (5422) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.62 | | | | | % 130.61/18.62 | | | | | REF_CLOSE: (184), (4277), (5422), (function-axioms) are inconsistent % 130.61/18.62 | | | | | by sub-proof #8. % 130.61/18.62 | | | | | % 130.61/18.62 | | | | End of split % 130.61/18.62 | | | | % 130.61/18.62 | | | Case 2: % 130.61/18.62 | | | | % 130.61/18.62 | | | | (5423) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, % 130.61/18.62 | | | | e0) = e0) % 130.61/18.62 | | | | % 130.61/18.62 | | | | REF_CLOSE: (183), (326), (4278), (4279), (5423), (function-axioms) are % 130.61/18.62 | | | | inconsistent by sub-proof #209. % 130.61/18.62 | | | | % 130.61/18.62 | | | End of split % 130.61/18.62 | | | % 130.61/18.62 | | End of split % 130.61/18.62 | | % 130.61/18.62 | End of split % 130.61/18.62 | % 130.61/18.62 End of proof % 130.61/18.62 % 130.61/18.62 Sub-proof #1 shows that the following formulas are inconsistent: % 130.61/18.62 ---------------------------------------------------------------- % 130.61/18.62 (1) all_55_8 = e1 | all_55_8 = e0 % 130.61/18.62 (2) all_55_8 = all_18_1 % 130.61/18.62 (3) ~ (all_18_1 = e1) % 130.61/18.62 (4) ~ (all_18_1 = e0) % 130.61/18.62 % 130.61/18.62 Begin of proof % 130.61/18.62 | % 130.61/18.62 | BETA: splitting (1) gives: % 130.61/18.62 | % 130.61/18.62 | Case 1: % 130.61/18.62 | | % 130.61/18.62 | | (5) all_55_8 = e1 % 130.61/18.62 | | % 130.61/18.62 | | COMBINE_EQS: (2), (5) imply: % 130.61/18.62 | | (6) all_18_1 = e1 % 130.61/18.62 | | % 130.61/18.62 | | SIMP: (6) implies: % 130.61/18.62 | | (7) all_18_1 = e1 % 130.61/18.62 | | % 130.61/18.62 | | REDUCE: (3), (7) imply: % 130.61/18.62 | | (8) $false % 130.61/18.62 | | % 130.61/18.62 | | CLOSE: (8) is inconsistent. % 130.61/18.62 | | % 130.61/18.62 | Case 2: % 130.61/18.62 | | % 130.61/18.62 | | (9) all_55_8 = e0 % 130.61/18.62 | | % 130.61/18.62 | | COMBINE_EQS: (2), (9) imply: % 130.61/18.62 | | (10) all_18_1 = e0 % 130.61/18.62 | | % 130.61/18.62 | | SIMP: (10) implies: % 130.61/18.62 | | (11) all_18_1 = e0 % 130.61/18.62 | | % 130.61/18.62 | | REDUCE: (4), (11) imply: % 130.61/18.62 | | (12) $false % 130.61/18.62 | | % 130.61/18.62 | | CLOSE: (12) is inconsistent. % 130.61/18.62 | | % 130.61/18.62 | End of split % 130.61/18.62 | % 130.61/18.62 End of proof % 130.61/18.62 % 130.61/18.62 Sub-proof #2 shows that the following formulas are inconsistent: % 130.61/18.62 ---------------------------------------------------------------- % 130.61/18.62 (1) ~ (unit = e0) % 130.61/18.62 (2) unit = e2 | unit = e1 | unit = e0 % 130.61/18.62 (3) op(unit, e0) = e0 % 130.61/18.62 (4) op(e2, unit) = e2 % 130.61/18.62 (5) ~ (all_53_6 = all_53_14) % 130.61/18.62 (6) all_55_9 = all_53_6 % 130.61/18.62 (7) ~ (all_53_2 = e0) % 130.61/18.62 (8) all_38_2 = e0 % 130.61/18.62 (9) op(e1, e0) = all_53_14 % 130.61/18.62 (10) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 130.61/18.62 (11) ~ (all_53_13 = all_6_2) % 130.61/18.62 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.62 (13) all_55_11 = all_53_14 % 130.61/18.62 (14) all_26_2 = e2 | ~ (op(e2, e2) = e2) % 130.61/18.62 (15) op(e1, e0) = all_22_1 % 130.61/18.62 (16) ~ (all_53_1 = all_53_2) % 130.61/18.62 (17) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 130.61/18.62 (18) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 130.61/18.62 (19) all_55_8 = all_53_2 % 130.61/18.62 (20) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 130.61/18.62 $i(all_22_0)) % 130.61/18.62 (21) ~ (all_53_2 = all_53_14) % 130.61/18.62 (22) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 130.61/18.62 (23) op(e1, e3) = all_53_2 % 130.61/18.62 (24) op(e1, unit) = e1 % 130.61/18.62 (25) ~ (all_53_2 = all_53_6) % 130.61/18.62 (26) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 130.61/18.62 (27) ~ (all_38_2 = e0) | (op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 130.61/18.62 (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 130.61/18.62 $i(all_38_0)))) % 130.61/18.62 (28) all_26_2 = all_6_2 % 130.61/18.62 (29) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 130.61/18.62 (30) op(unit, e3) = e3 % 130.61/18.62 (31) ~ (all_53_14 = e0) % 130.61/18.62 % 130.61/18.62 Begin of proof % 130.61/18.62 | % 130.61/18.62 | BETA: splitting (27) gives: % 130.61/18.62 | % 130.61/18.62 | Case 1: % 130.61/18.62 | | % 130.61/18.62 | | (32) ~ (all_38_2 = e0) % 130.61/18.62 | | % 130.61/18.62 | | REDUCE: (8), (32) imply: % 130.61/18.62 | | (33) $false % 130.61/18.62 | | % 130.61/18.62 | | CLOSE: (33) is inconsistent. % 130.61/18.62 | | % 130.61/18.62 | Case 2: % 130.61/18.62 | | % 130.61/18.62 | | (34) op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e2) | ( ~ % 130.61/18.62 | | (all_38_0 = e3) & op(e1, e2) = all_38_0 & $i(all_38_0))) % 130.61/18.62 | | % 130.61/18.62 | | ALPHA: (34) implies: % 130.61/18.62 | | (35) op(e1, e0) = all_38_1 % 130.61/18.62 | | % 130.61/18.62 | | BETA: splitting (29) gives: % 130.61/18.62 | | % 130.61/18.62 | | Case 1: % 130.61/18.62 | | | % 130.61/18.62 | | | (36) ~ (op(e1, e0) = e0) % 130.61/18.62 | | | % 130.61/18.62 | | | GROUND_INST: instantiating (12) with all_53_14, all_22_1, e0, e1, % 130.61/18.62 | | | simplifying with (9), (15) gives: % 130.61/18.62 | | | (37) all_53_14 = all_22_1 % 130.61/18.62 | | | % 130.61/18.62 | | | GROUND_INST: instantiating (12) with all_53_14, all_38_1, e0, e1, % 130.61/18.62 | | | simplifying with (9), (35) gives: % 130.61/18.62 | | | (38) all_53_14 = all_38_1 % 130.61/18.62 | | | % 130.61/18.62 | | | PRED_UNIFY: (3), (36) imply: % 130.61/18.62 | | | (39) ~ (unit = e1) % 130.61/18.62 | | | % 130.61/18.62 | | | PRED_UNIFY: (35), (36) imply: % 130.61/18.62 | | | (40) ~ (all_38_1 = e0) % 130.61/18.62 | | | % 130.61/18.62 | | | COMBINE_EQS: (37), (38) imply: % 130.61/18.62 | | | (41) all_38_1 = all_22_1 % 130.61/18.62 | | | % 130.61/18.62 | | | SIMP: (41) implies: % 130.61/18.62 | | | (42) all_38_1 = all_22_1 % 130.61/18.62 | | | % 130.61/18.62 | | | COMBINE_EQS: (13), (37) imply: % 130.61/18.62 | | | (43) all_55_11 = all_22_1 % 130.61/18.62 | | | % 130.61/18.62 | | | REDUCE: (21), (37) imply: % 130.61/18.63 | | | (44) ~ (all_53_2 = all_22_1) % 130.61/18.63 | | | % 130.61/18.63 | | | REDUCE: (5), (37) imply: % 130.61/18.63 | | | (45) ~ (all_53_6 = all_22_1) % 130.61/18.63 | | | % 130.61/18.63 | | | REDUCE: (40), (42) imply: % 130.61/18.63 | | | (46) ~ (all_22_1 = e0) % 130.61/18.63 | | | % 130.61/18.63 | | | BETA: splitting (2) gives: % 130.61/18.63 | | | % 130.61/18.63 | | | Case 1: % 130.61/18.63 | | | | % 130.61/18.63 | | | | (47) unit = e2 % 130.61/18.63 | | | | % 130.61/18.63 | | | | REDUCE: (30), (47) imply: % 130.61/18.63 | | | | (48) op(e2, e3) = e3 % 130.61/18.63 | | | | % 130.61/18.63 | | | | REDUCE: (4), (47) imply: % 130.61/18.63 | | | | (49) op(e2, e2) = e2 % 130.61/18.63 | | | | % 130.61/18.63 | | | | REF_CLOSE: (2), (4), (6), (7), (10), (11), (12), (14), (16), (17), (18), % 130.61/18.63 | | | | (19), (20), (22), (23), (24), (25), (26), (28), (39), (43), % 130.61/18.63 | | | | (44), (45), (46), (48), (49) are inconsistent by sub-proof % 130.61/18.63 | | | | #71. % 130.61/18.63 | | | | % 130.61/18.63 | | | Case 2: % 130.61/18.63 | | | | % 130.61/18.63 | | | | (50) unit = e1 | unit = e0 % 130.61/18.63 | | | | % 130.61/18.63 | | | | REF_CLOSE: (1), (39), (50) are inconsistent by sub-proof #278. % 130.61/18.63 | | | | % 130.61/18.63 | | | End of split % 130.61/18.63 | | | % 130.61/18.63 | | Case 2: % 130.61/18.63 | | | % 130.61/18.63 | | | (51) op(e1, e0) = e0 % 130.61/18.63 | | | % 130.61/18.63 | | | REF_CLOSE: (29), (31), (51) are inconsistent by sub-proof #355. % 130.61/18.63 | | | % 130.61/18.63 | | End of split % 130.61/18.63 | | % 130.61/18.63 | End of split % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #3 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) all_57_9 = e3 & op(e3, e0) = e3 % 130.61/18.63 (2) all_48_1 = e3 | ~ (op(e3, e0) = e3) % 130.61/18.63 (3) all_48_1 = all_4_1 % 130.61/18.63 (4) ~ (all_4_1 = e3) % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | ALPHA: (1) implies: % 130.61/18.63 | (5) op(e3, e0) = e3 % 130.61/18.63 | % 130.61/18.63 | BETA: splitting (2) gives: % 130.61/18.63 | % 130.61/18.63 | Case 1: % 130.61/18.63 | | % 130.61/18.63 | | (6) ~ (op(e3, e0) = e3) % 130.61/18.63 | | % 130.61/18.63 | | PRED_UNIFY: (5), (6) imply: % 130.61/18.63 | | (7) $false % 130.61/18.63 | | % 130.61/18.63 | | CLOSE: (7) is inconsistent. % 130.61/18.63 | | % 130.61/18.63 | Case 2: % 130.61/18.63 | | % 130.61/18.63 | | (8) all_48_1 = e3 % 130.61/18.63 | | % 130.61/18.63 | | COMBINE_EQS: (3), (8) imply: % 130.61/18.63 | | (9) all_4_1 = e3 % 130.61/18.63 | | % 130.61/18.63 | | SIMP: (9) implies: % 130.61/18.63 | | (10) all_4_1 = e3 % 130.61/18.63 | | % 130.61/18.63 | | REDUCE: (4), (10) imply: % 130.61/18.63 | | (11) $false % 130.61/18.63 | | % 130.61/18.63 | | CLOSE: (11) is inconsistent. % 130.61/18.63 | | % 130.61/18.63 | End of split % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #4 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) unit = e2 | unit = e1 | unit = e0 % 130.61/18.63 (2) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 130.61/18.63 (3) op(e2, unit) = e2 % 130.61/18.63 (4) ~ (all_53_13 = e0) % 130.61/18.63 (5) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 130.61/18.63 (6) ~ (all_53_7 = e0) % 130.61/18.63 (7) ~ (all_53_13 = all_6_2) % 130.61/18.63 (8) all_55_5 = all_6_2 % 130.61/18.63 (9) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 130.61/18.63 (10) ~ (all_6_2 = e3) % 130.61/18.63 (11) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 130.61/18.63 (12) ~ (all_6_2 = e1) % 130.61/18.63 (13) op(e0, unit) = e0 % 130.61/18.63 (14) ~ (unit = e1) % 130.61/18.63 (15) all_55_13 = all_53_7 % 130.61/18.63 (16) ~ (all_6_2 = e0) % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | SIMP: (16) implies: % 130.61/18.63 | (17) ~ (all_6_2 = e0) % 130.61/18.63 | % 130.61/18.63 | BETA: splitting (11) gives: % 130.61/18.63 | % 130.61/18.63 | Case 1: % 130.61/18.63 | | % 130.61/18.63 | | (18) all_55_5 = e3 % 130.61/18.63 | | % 130.61/18.63 | | COMBINE_EQS: (8), (18) imply: % 130.61/18.63 | | (19) all_6_2 = e3 % 130.61/18.63 | | % 130.61/18.63 | | REDUCE: (10), (19) imply: % 130.61/18.63 | | (20) $false % 130.61/18.63 | | % 130.61/18.63 | | CLOSE: (20) is inconsistent. % 130.61/18.63 | | % 130.61/18.63 | Case 2: % 130.61/18.63 | | % 130.61/18.63 | | (21) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 130.61/18.63 | | % 130.61/18.63 | | BETA: splitting (21) gives: % 130.61/18.63 | | % 130.61/18.63 | | Case 1: % 130.61/18.63 | | | % 130.61/18.63 | | | (22) all_55_5 = e2 % 130.61/18.63 | | | % 130.61/18.63 | | | COMBINE_EQS: (8), (22) imply: % 130.61/18.63 | | | (23) all_6_2 = e2 % 130.61/18.63 | | | % 130.61/18.63 | | | REDUCE: (7), (23) imply: % 130.61/18.63 | | | (24) ~ (all_53_13 = e2) % 130.61/18.63 | | | % 130.61/18.63 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (13), (14), (15), (24) are % 130.61/18.63 | | | inconsistent by sub-proof #90. % 130.61/18.63 | | | % 130.61/18.63 | | Case 2: % 130.61/18.63 | | | % 130.61/18.63 | | | (25) all_55_5 = e1 | all_55_5 = e0 % 130.61/18.63 | | | % 130.61/18.63 | | | REF_CLOSE: (8), (12), (17), (25) are inconsistent by sub-proof #251. % 130.61/18.63 | | | % 130.61/18.63 | | End of split % 130.61/18.63 | | % 130.61/18.63 | End of split % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #5 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.63 (3) op(e1, e2) = all_53_6 % 130.61/18.63 (4) ~ (all_53_6 = e0) % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | ALPHA: (1) implies: % 130.61/18.63 | (5) op(e1, e2) = e0 % 130.61/18.63 | % 130.61/18.63 | GROUND_INST: instantiating (2) with all_53_6, e0, e2, e1, simplifying with % 130.61/18.63 | (3), (5) gives: % 130.61/18.63 | (6) all_53_6 = e0 % 130.61/18.63 | % 130.61/18.63 | REDUCE: (4), (6) imply: % 130.61/18.63 | (7) $false % 130.61/18.63 | % 130.61/18.63 | CLOSE: (7) is inconsistent. % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #6 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 130.61/18.63 (2) unit = e2 | unit = e1 | unit = e0 % 130.61/18.63 (3) ~ (all_8_2 = e3) % 130.61/18.63 (4) ~ (all_53_7 = all_8_2) % 130.61/18.63 (5) op(e2, unit) = e2 % 130.61/18.63 (6) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.61/18.63 (7) all_36_2 = all_8_2 % 130.61/18.63 (8) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 130.61/18.63 (9) ~ (all_8_2 = e1) % 130.61/18.63 (10) ~ (op(e2, e1) = e1) % 130.61/18.63 (11) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.63 (12) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 130.61/18.63 (13) ~ (all_36_2 = e2) | (op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 130.61/18.63 (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, e3) = all_36_0 & % 130.61/18.63 $i(all_36_0)))) % 130.61/18.63 (14) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 130.61/18.63 (15) op(e0, unit) = e0 % 130.61/18.63 (16) all_55_15 = all_8_2 % 130.61/18.63 (17) ~ (all_53_7 = all_53_11) % 130.61/18.63 (18) ~ (all_53_13 = all_8_2) % 130.61/18.63 (19) op(unit, e1) = e1 % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | ALPHA: (11) implies: % 130.61/18.63 | (20) op(e0, e2) = e0 % 130.61/18.63 | % 130.61/18.63 | BETA: splitting (1) gives: % 130.61/18.63 | % 130.61/18.63 | Case 1: % 130.61/18.63 | | % 130.61/18.63 | | (21) ~ (op(e0, e2) = e0) % 130.61/18.63 | | % 130.61/18.63 | | PRED_UNIFY: (20), (21) imply: % 130.61/18.63 | | (22) $false % 130.61/18.63 | | % 130.61/18.63 | | CLOSE: (22) is inconsistent. % 130.61/18.63 | | % 130.61/18.63 | Case 2: % 130.61/18.63 | | % 130.61/18.63 | | (23) all_53_7 = e0 % 130.61/18.63 | | % 130.61/18.63 | | REDUCE: (17), (23) imply: % 130.61/18.63 | | (24) ~ (all_53_11 = e0) % 130.61/18.63 | | % 130.61/18.63 | | SIMP: (24) implies: % 130.61/18.63 | | (25) ~ (all_53_11 = e0) % 130.61/18.63 | | % 130.61/18.63 | | REDUCE: (4), (23) imply: % 130.61/18.63 | | (26) ~ (all_8_2 = e0) % 130.61/18.63 | | % 130.61/18.63 | | SIMP: (26) implies: % 130.61/18.63 | | (27) ~ (all_8_2 = e0) % 130.61/18.63 | | % 130.61/18.63 | | BETA: splitting (6) gives: % 130.61/18.63 | | % 130.61/18.63 | | Case 1: % 130.61/18.63 | | | % 130.61/18.63 | | | (28) all_55_15 = e3 % 130.61/18.63 | | | % 130.61/18.63 | | | COMBINE_EQS: (16), (28) imply: % 130.61/18.63 | | | (29) all_8_2 = e3 % 130.61/18.63 | | | % 130.61/18.63 | | | REDUCE: (3), (29) imply: % 130.61/18.63 | | | (30) $false % 130.61/18.63 | | | % 130.61/18.63 | | | CLOSE: (30) is inconsistent. % 130.61/18.63 | | | % 130.61/18.63 | | Case 2: % 130.61/18.63 | | | % 130.61/18.63 | | | (31) ~ (all_55_15 = e3) % 130.61/18.63 | | | (32) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 130.61/18.63 | | | % 130.61/18.63 | | | BETA: splitting (32) gives: % 130.61/18.63 | | | % 130.61/18.63 | | | Case 1: % 130.61/18.63 | | | | % 130.61/18.63 | | | | (33) all_55_15 = e2 % 130.61/18.63 | | | | % 130.61/18.63 | | | | COMBINE_EQS: (16), (33) imply: % 130.61/18.63 | | | | (34) all_8_2 = e2 % 130.61/18.63 | | | | % 130.61/18.63 | | | | COMBINE_EQS: (7), (34) imply: % 130.61/18.63 | | | | (35) all_36_2 = e2 % 130.61/18.63 | | | | % 130.61/18.63 | | | | BETA: splitting (13) gives: % 130.61/18.63 | | | | % 130.61/18.63 | | | | Case 1: % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | (36) ~ (all_36_2 = e2) % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | REDUCE: (35), (36) imply: % 130.61/18.63 | | | | | (37) $false % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | CLOSE: (37) is inconsistent. % 130.61/18.63 | | | | | % 130.61/18.63 | | | | Case 2: % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | PRED_UNIFY: (10), (19) imply: % 130.61/18.63 | | | | | (38) ~ (unit = e2) % 130.61/18.63 | | | | | % 130.61/18.63 | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (12), (14), (15), (16), (18), % 130.61/18.63 | | | | | (25), (27), (38) are inconsistent by sub-proof #109. % 130.61/18.63 | | | | | % 130.61/18.63 | | | | End of split % 130.61/18.63 | | | | % 130.61/18.63 | | | Case 2: % 130.61/18.63 | | | | % 130.61/18.63 | | | | (39) all_55_15 = e1 | all_55_15 = e0 % 130.61/18.63 | | | | % 130.61/18.63 | | | | REF_CLOSE: (9), (16), (27), (39) are inconsistent by sub-proof #144. % 130.61/18.63 | | | | % 130.61/18.63 | | | End of split % 130.61/18.63 | | | % 130.61/18.63 | | End of split % 130.61/18.63 | | % 130.61/18.63 | End of split % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #7 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) op(e2, e2) = e1 % 130.61/18.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.63 (3) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 130.61/18.63 (4) ~ (e1 = e0) % 130.61/18.63 (5) ~ (all_53_4 = e0) % 130.61/18.63 (6) op(e3, e2) = all_53_4 % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | BETA: splitting (3) gives: % 130.61/18.63 | % 130.61/18.63 | Case 1: % 130.61/18.63 | | % 130.61/18.63 | | (7) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.63 | | % 130.61/18.63 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #8. % 130.61/18.63 | | % 130.61/18.63 | Case 2: % 130.61/18.63 | | % 130.61/18.63 | | (8) all_57_3 = e0 & op(e2, e2) = e0 % 130.61/18.63 | | % 130.61/18.63 | | ALPHA: (8) implies: % 130.61/18.63 | | (9) op(e2, e2) = e0 % 130.61/18.63 | | % 130.61/18.63 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #199. % 130.61/18.63 | | % 130.61/18.63 | End of split % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #8 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.63 (3) op(e3, e2) = all_53_4 % 130.61/18.63 (4) ~ (all_53_4 = e0) % 130.61/18.63 % 130.61/18.63 Begin of proof % 130.61/18.63 | % 130.61/18.63 | ALPHA: (1) implies: % 130.61/18.63 | (5) op(e3, e2) = e0 % 130.61/18.63 | % 130.61/18.63 | GROUND_INST: instantiating (2) with all_53_4, e0, e2, e3, simplifying with % 130.61/18.63 | (3), (5) gives: % 130.61/18.63 | (6) all_53_4 = e0 % 130.61/18.63 | % 130.61/18.63 | REDUCE: (4), (6) imply: % 130.61/18.63 | (7) $false % 130.61/18.63 | % 130.61/18.63 | CLOSE: (7) is inconsistent. % 130.61/18.63 | % 130.61/18.63 End of proof % 130.61/18.63 % 130.61/18.63 Sub-proof #9 shows that the following formulas are inconsistent: % 130.61/18.63 ---------------------------------------------------------------- % 130.61/18.63 (1) op(e1, e1) = e1 % 130.61/18.63 (2) op(e2, e2) = e1 % 130.61/18.63 (3) all_50_2 = e1 % 130.61/18.63 (4) all_22_2 = e1 % 130.61/18.63 (5) op(e0, e2) = all_53_7 % 130.61/18.63 (6) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 130.61/18.63 (7) ~ (e3 = e0) % 130.61/18.63 (8) ~ (e2 = e0) % 130.61/18.64 (9) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 130.61/18.64 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 130.61/18.64 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.64 (11) ~ (e3 = e1) % 130.61/18.64 (12) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 130.61/18.64 (13) all_57_0 = e0 % 130.61/18.64 (14) ~ (all_6_2 = e3) % 130.61/18.64 (15) ~ (e2 = e1) % 130.61/18.64 (16) op(e2, e2) = all_6_2 % 130.61/18.64 (17) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 130.61/18.64 (18) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 130.61/18.64 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 130.61/18.64 (19) ~ (e1 = e0) % 130.61/18.64 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 130.61/18.64 (21) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 130.61/18.64 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 130.61/18.64 (22) ~ (e3 = e2) % 130.61/18.64 % 130.61/18.64 Begin of proof % 130.61/18.64 | % 130.61/18.64 | BETA: splitting (20) gives: % 130.61/18.64 | % 130.61/18.64 | Case 1: % 130.61/18.64 | | % 130.61/18.64 | | (23) all_57_0 = e1 & op(e3, e3) = e1 % 130.61/18.64 | | % 130.61/18.64 | | REF_CLOSE: (1), (4), (6), (13), (19), (23) are inconsistent by sub-proof % 130.61/18.64 | | #12. % 130.61/18.64 | | % 130.61/18.64 | Case 2: % 130.61/18.64 | | % 130.61/18.64 | | (24) all_57_1 = e1 & op(e3, e2) = e1 % 130.61/18.64 | | % 130.61/18.64 | | ALPHA: (24) implies: % 130.61/18.64 | | (25) all_57_1 = e1 % 130.61/18.64 | | % 130.61/18.64 | | BETA: splitting (21) gives: % 130.61/18.64 | | % 130.61/18.64 | | Case 1: % 130.61/18.64 | | | % 130.61/18.64 | | | (26) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = % 130.61/18.64 | | | e3) % 130.61/18.64 | | | % 130.61/18.64 | | | BETA: splitting (26) gives: % 130.61/18.64 | | | % 130.61/18.64 | | | Case 1: % 130.61/18.64 | | | | % 130.61/18.64 | | | | (27) all_57_1 = e3 & op(e3, e2) = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | REF_CLOSE: (11), (25), (27) are inconsistent by sub-proof #271. % 130.61/18.64 | | | | % 130.61/18.64 | | | Case 2: % 130.61/18.64 | | | | % 130.61/18.64 | | | | (28) all_57_3 = e3 & op(e2, e2) = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | REF_CLOSE: (10), (14), (16), (28) are inconsistent by sub-proof #352. % 130.61/18.64 | | | | % 130.61/18.64 | | | End of split % 130.61/18.64 | | | % 130.61/18.64 | | Case 2: % 130.61/18.64 | | | % 130.61/18.64 | | | (29) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = % 130.61/18.64 | | | e3) % 130.61/18.64 | | | % 130.61/18.64 | | | BETA: splitting (29) gives: % 130.61/18.64 | | | % 130.61/18.64 | | | Case 1: % 130.61/18.64 | | | | % 130.61/18.64 | | | | (30) all_57_7 = e3 & op(e1, e2) = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | ALPHA: (30) implies: % 130.61/18.64 | | | | (31) all_57_7 = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | BETA: splitting (18) gives: % 130.61/18.64 | | | | % 130.61/18.64 | | | | Case 1: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | (32) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, % 130.61/18.64 | | | | | e2) = e2) % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | REF_CLOSE: (3), (12), (15), (25), (32) are inconsistent by sub-proof % 130.61/18.64 | | | | | #11. % 130.61/18.64 | | | | | % 130.61/18.64 | | | | Case 2: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | (33) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, % 130.61/18.64 | | | | | e2) = e2) % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | BETA: splitting (33) gives: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | Case 1: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | (34) all_57_7 = e2 & op(e1, e2) = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | REF_CLOSE: (22), (31), (34) are inconsistent by sub-proof #306. % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | Case 2: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | (35) all_57_13 = e2 & op(e0, e2) = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | ALPHA: (35) implies: % 130.61/18.64 | | | | | | (36) all_57_13 = e2 % 130.61/18.64 | | | | | | (37) op(e0, e2) = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | BETA: splitting (17) gives: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | Case 1: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | (38) ~ (op(e0, e2) = e2) % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | PRED_UNIFY: (37), (38) imply: % 130.61/18.64 | | | | | | | (39) $false % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | CLOSE: (39) is inconsistent. % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | Case 2: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | (40) all_53_7 = e2 % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | BETA: splitting (9) gives: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | Case 1: % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | (41) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & % 130.61/18.64 | | | | | | | | op(e2, e2) = e0) % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | REF_CLOSE: (2), (10), (19), (25), (41) are inconsistent by % 130.61/18.64 | | | | | | | | sub-proof #10. % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | Case 2: % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | (42) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & % 130.61/18.64 | | | | | | | | op(e0, e2) = e0) % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | BETA: splitting (42) gives: % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | Case 1: % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | (43) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | REF_CLOSE: (7), (31), (43) are inconsistent by sub-proof #307. % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | Case 2: % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | (44) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | ALPHA: (44) implies: % 130.61/18.64 | | | | | | | | | (45) all_57_13 = e0 % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | COMBINE_EQS: (36), (45) imply: % 130.61/18.64 | | | | | | | | | (46) e2 = e0 % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | COMBINE_EQS: (40), (46) imply: % 130.61/18.64 | | | | | | | | | (47) all_53_7 = e0 % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | | REF_CLOSE: (8), (17), (37), (47) are inconsistent by sub-proof % 130.61/18.64 | | | | | | | | | #191. % 130.61/18.64 | | | | | | | | | % 130.61/18.64 | | | | | | | | End of split % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | End of split % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | End of split % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | End of split % 130.61/18.64 | | | | | % 130.61/18.64 | | | | End of split % 130.61/18.64 | | | | % 130.61/18.64 | | | Case 2: % 130.61/18.64 | | | | % 130.61/18.64 | | | | (48) all_57_13 = e3 & op(e0, e2) = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | ALPHA: (48) implies: % 130.61/18.64 | | | | (49) all_57_13 = e3 % 130.61/18.64 | | | | % 130.61/18.64 | | | | BETA: splitting (18) gives: % 130.61/18.64 | | | | % 130.61/18.64 | | | | Case 1: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | (50) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, % 130.61/18.64 | | | | | e2) = e2) % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | REF_CLOSE: (3), (12), (15), (25), (50) are inconsistent by sub-proof % 130.61/18.64 | | | | | #11. % 130.61/18.64 | | | | | % 130.61/18.64 | | | | Case 2: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | (51) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, % 130.61/18.64 | | | | | e2) = e2) % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | BETA: splitting (51) gives: % 130.61/18.64 | | | | | % 130.61/18.64 | | | | | Case 1: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | (52) all_57_7 = e2 & op(e1, e2) = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | ALPHA: (52) implies: % 130.61/18.64 | | | | | | (53) all_57_7 = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | BETA: splitting (9) gives: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | Case 1: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | (54) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & % 130.61/18.64 | | | | | | | op(e2, e2) = e0) % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | REF_CLOSE: (2), (10), (19), (25), (54) are inconsistent by % 130.61/18.64 | | | | | | | sub-proof #10. % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | Case 2: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | (55) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & % 130.61/18.64 | | | | | | | op(e0, e2) = e0) % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | BETA: splitting (55) gives: % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | | Case 1: % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | (56) all_57_7 = e0 & op(e1, e2) = e0 % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | REF_CLOSE: (8), (53), (56) are inconsistent by sub-proof #131. % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | Case 2: % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | (57) all_57_13 = e0 & op(e0, e2) = e0 % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | | REF_CLOSE: (7), (49), (57) are inconsistent by sub-proof #112. % 130.61/18.64 | | | | | | | | % 130.61/18.64 | | | | | | | End of split % 130.61/18.64 | | | | | | | % 130.61/18.64 | | | | | | End of split % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | Case 2: % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | (58) all_57_13 = e2 & op(e0, e2) = e2 % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | | REF_CLOSE: (22), (49), (58) are inconsistent by sub-proof #111. % 130.61/18.64 | | | | | | % 130.61/18.64 | | | | | End of split % 130.61/18.64 | | | | | % 130.61/18.64 | | | | End of split % 130.61/18.64 | | | | % 130.61/18.64 | | | End of split % 130.61/18.64 | | | % 130.61/18.64 | | End of split % 130.61/18.64 | | % 130.61/18.64 | End of split % 130.61/18.64 | % 130.61/18.64 End of proof % 130.61/18.64 % 130.61/18.64 Sub-proof #10 shows that the following formulas are inconsistent: % 130.61/18.64 ---------------------------------------------------------------- % 130.61/18.64 (1) op(e2, e2) = e1 % 130.61/18.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.64 (3) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 130.61/18.64 (4) ~ (e1 = e0) % 130.61/18.64 (5) all_57_1 = e1 % 130.61/18.64 % 130.61/18.64 Begin of proof % 130.61/18.64 | % 130.61/18.64 | BETA: splitting (3) gives: % 130.61/18.64 | % 130.61/18.64 | Case 1: % 130.61/18.64 | | % 130.61/18.64 | | (6) all_57_1 = e0 & op(e3, e2) = e0 % 130.61/18.64 | | % 130.61/18.64 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #286. % 130.61/18.64 | | % 130.61/18.64 | Case 2: % 130.61/18.64 | | % 130.61/18.64 | | (7) all_57_3 = e0 & op(e2, e2) = e0 % 130.61/18.64 | | % 130.61/18.64 | | ALPHA: (7) implies: % 130.61/18.64 | | (8) op(e2, e2) = e0 % 130.61/18.64 | | % 130.61/18.64 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #199. % 130.61/18.64 | | % 130.61/18.64 | End of split % 130.61/18.64 | % 130.61/18.64 End of proof % 130.61/18.64 % 130.61/18.64 Sub-proof #11 shows that the following formulas are inconsistent: % 130.61/18.64 ---------------------------------------------------------------- % 130.61/18.64 (1) all_50_2 = e1 % 130.61/18.64 (2) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 130.61/18.64 (3) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 130.61/18.64 (4) ~ (e2 = e1) % 130.61/18.64 (5) all_57_1 = e1 % 130.61/18.64 % 130.61/18.64 Begin of proof % 130.61/18.64 | % 130.61/18.64 | BETA: splitting (2) gives: % 130.61/18.64 | % 130.61/18.64 | Case 1: % 130.61/18.64 | | % 130.61/18.64 | | (6) all_57_1 = e2 & op(e3, e2) = e2 % 130.61/18.64 | | % 130.61/18.64 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #266. % 130.61/18.64 | | % 130.61/18.64 | Case 2: % 130.61/18.64 | | % 130.61/18.64 | | (7) all_57_3 = e2 & op(e2, e2) = e2 % 130.61/18.64 | | % 130.61/18.64 | | ALPHA: (7) implies: % 130.61/18.64 | | (8) op(e2, e2) = e2 % 130.61/18.64 | | % 130.61/18.64 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #196. % 130.61/18.64 | | % 130.61/18.64 | End of split % 130.61/18.64 | % 130.61/18.64 End of proof % 130.61/18.64 % 130.61/18.64 Sub-proof #12 shows that the following formulas are inconsistent: % 130.61/18.64 ---------------------------------------------------------------- % 130.61/18.64 (1) op(e1, e1) = e1 % 130.61/18.64 (2) all_22_2 = e1 % 130.61/18.64 (3) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 130.61/18.64 (4) all_57_0 = e0 % 130.61/18.64 (5) ~ (e1 = e0) % 130.61/18.64 (6) all_57_0 = e1 & op(e3, e3) = e1 % 130.61/18.64 % 130.61/18.64 Begin of proof % 130.61/18.64 | % 130.61/18.64 | ALPHA: (6) implies: % 130.61/18.64 | (7) all_57_0 = e1 % 130.61/18.64 | % 130.61/18.64 | COMBINE_EQS: (4), (7) imply: % 130.61/18.64 | (8) e1 = e0 % 130.61/18.64 | % 130.61/18.64 | SIMP: (8) implies: % 130.61/18.64 | (9) e1 = e0 % 130.61/18.64 | % 130.61/18.64 | COMBINE_EQS: (2), (9) imply: % 130.61/18.64 | (10) all_22_2 = e0 % 130.61/18.64 | % 130.61/18.64 | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #269. % 130.61/18.64 | % 130.61/18.64 End of proof % 130.61/18.64 % 130.61/18.64 Sub-proof #13 shows that the following formulas are inconsistent: % 130.61/18.64 ---------------------------------------------------------------- % 130.61/18.64 (1) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 130.61/18.64 (2) ~ (all_53_3 = all_53_7) % 130.61/18.64 (3) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 130.61/18.64 (4) ~ (all_53_6 = all_53_7) % 130.61/18.64 (5) all_53_4 = e2 | ~ (op(e3, e2) = e2) % 130.61/18.64 (6) ~ (unit = e2) % 130.61/18.64 (7) op(unit, e2) = e2 % 130.61/18.64 (8) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 130.61/18.64 $i(all_8_0)) % 130.61/18.64 (9) op(e0, e2) = all_53_7 % 130.61/18.64 (10) op(e0, e1) = all_53_11 % 130.61/18.64 (11) unit = e3 | unit = e2 | unit = e1 | unit = e0 % 130.61/18.64 (12) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 130.61/18.65 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 130.61/18.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 130.61/18.65 (14) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 130.61/18.65 (15) ~ (all_53_7 = e1) % 130.61/18.65 (16) all_55_14 = all_53_11 % 130.61/18.65 (17) ~ (all_53_4 = all_53_7) % 130.61/18.65 (18) op(e0, e1) = all_8_1 % 130.61/18.65 (19) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 130.61/18.65 (20) op(e0, unit) = e0 % 130.61/18.65 (21) ~ (all_20_2 = e1) | (op(e0, e1) = all_20_1 & $i(all_20_1) & ( ~ % 130.61/18.65 (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 & % 130.61/18.65 $i(all_20_0)))) % 130.61/18.65 (22) ~ (all_53_7 = all_53_11) % 130.61/18.65 (23) ~ (all_53_7 = e3) % 130.61/18.65 (24) all_55_13 = all_53_7 % 130.61/18.65 (25) all_20_2 = e1 % 130.61/18.65 (26) op(unit, e1) = e1 % 130.61/18.65 (27) ~ (all_53_11 = e1) % 130.61/18.65 (28) ~ (all_53_3 = all_53_11) % 130.61/18.65 % 130.61/18.65 Begin of proof % 130.61/18.65 | % 130.61/18.65 | BETA: splitting (21) gives: % 130.61/18.65 | % 130.61/18.65 | Case 1: % 130.61/18.65 | | % 130.61/18.65 | | (29) ~ (all_20_2 = e1) % 130.61/18.65 | | % 130.61/18.65 | | REDUCE: (25), (29) imply: % 130.61/18.65 | | (30) $false % 130.61/18.65 | | % 130.61/18.65 | | CLOSE: (30) is inconsistent. % 130.61/18.65 | | % 130.61/18.65 | Case 2: % 130.61/18.65 | | % 130.61/18.65 | | (31) op(e0, e1) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e3) | ( ~ % 130.61/18.65 | | (all_20_0 = e2) & op(e0, e3) = all_20_0 & $i(all_20_0))) % 130.61/18.65 | | % 130.61/18.65 | | ALPHA: (31) implies: % 130.61/18.65 | | (32) op(e0, e1) = all_20_1 % 130.61/18.65 | | % 130.61/18.65 | | BETA: splitting (19) gives: % 130.61/18.65 | | % 130.61/18.65 | | Case 1: % 130.61/18.65 | | | % 130.61/18.65 | | | (33) ~ (op(e0, e1) = e1) % 130.61/18.65 | | | % 130.61/18.65 | | | GROUND_INST: instantiating (13) with all_53_11, all_8_1, e1, e0, % 130.61/18.65 | | | simplifying with (10), (18) gives: % 130.61/18.65 | | | (34) all_53_11 = all_8_1 % 130.61/18.65 | | | % 130.61/18.65 | | | GROUND_INST: instantiating (13) with all_53_11, all_20_1, e1, e0, % 130.61/18.65 | | | simplifying with (10), (32) gives: % 130.61/18.65 | | | (35) all_53_11 = all_20_1 % 130.61/18.65 | | | % 130.61/18.65 | | | GROUND_INST: instantiating (13) with e0, all_20_1, e1, e0, simplifying % 130.61/18.65 | | | with (32) gives: % 130.61/18.65 | | | (36) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 130.61/18.65 | | | % 130.61/18.65 | | | PRED_UNIFY: (26), (33) imply: % 130.61/18.65 | | | (37) ~ (unit = e0) % 130.61/18.65 | | | % 130.61/18.65 | | | PRED_UNIFY: (32), (33) imply: % 130.61/18.65 | | | (38) ~ (all_20_1 = e1) % 130.61/18.65 | | | % 130.61/18.65 | | | COMBINE_EQS: (34), (35) imply: % 130.61/18.65 | | | (39) all_20_1 = all_8_1 % 130.61/18.65 | | | % 130.61/18.65 | | | SIMP: (39) implies: % 130.61/18.65 | | | (40) all_20_1 = all_8_1 % 130.61/18.65 | | | % 130.61/18.65 | | | COMBINE_EQS: (16), (34) imply: % 130.61/18.65 | | | (41) all_55_14 = all_8_1 % 130.61/18.65 | | | % 130.61/18.65 | | | REDUCE: (28), (34) imply: % 130.61/18.65 | | | (42) ~ (all_53_3 = all_8_1) % 130.61/18.65 | | | % 130.61/18.65 | | | REDUCE: (22), (34) imply: % 130.61/18.65 | | | (43) ~ (all_53_7 = all_8_1) % 130.61/18.65 | | | % 130.61/18.65 | | | REDUCE: (38), (40) imply: % 131.13/18.65 | | | (44) ~ (all_8_1 = e1) % 131.13/18.65 | | | % 131.13/18.65 | | | BETA: splitting (11) gives: % 131.13/18.65 | | | % 131.13/18.65 | | | Case 1: % 131.13/18.65 | | | | % 131.13/18.65 | | | | (45) unit = e3 % 131.13/18.65 | | | | % 131.13/18.65 | | | | REDUCE: (7), (45) imply: % 131.13/18.65 | | | | (46) op(e3, e2) = e2 % 131.13/18.65 | | | | % 131.13/18.65 | | | | REDUCE: (20), (45) imply: % 131.13/18.65 | | | | (47) op(e0, e3) = e0 % 131.13/18.65 | | | | % 131.13/18.65 | | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (13), (14), (15), (17), (24), % 131.13/18.65 | | | | (41), (42), (43), (44), (46), (47) are inconsistent by % 131.13/18.65 | | | | sub-proof #59. % 131.13/18.65 | | | | % 131.13/18.65 | | | Case 2: % 131.13/18.65 | | | | % 131.13/18.65 | | | | (48) unit = e2 | unit = e1 | unit = e0 % 131.13/18.65 | | | | % 131.13/18.65 | | | | BETA: splitting (48) gives: % 131.13/18.65 | | | | % 131.13/18.65 | | | | Case 1: % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | (49) unit = e2 % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | REDUCE: (6), (49) imply: % 131.13/18.65 | | | | | (50) $false % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | CLOSE: (50) is inconsistent. % 131.13/18.65 | | | | | % 131.13/18.65 | | | | Case 2: % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | (51) unit = e1 | unit = e0 % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | BETA: splitting (51) gives: % 131.13/18.65 | | | | | % 131.13/18.65 | | | | | Case 1: % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | (52) unit = e1 % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | REDUCE: (7), (52) imply: % 131.13/18.65 | | | | | | (53) op(e1, e2) = e2 % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | REDUCE: (20), (52) imply: % 131.13/18.65 | | | | | | (54) op(e0, e1) = e0 % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | BETA: splitting (36) gives: % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | Case 1: % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | (55) ~ (op(e0, e1) = e0) % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | PRED_UNIFY: (54), (55) imply: % 131.13/18.65 | | | | | | | (56) $false % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | CLOSE: (56) is inconsistent. % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | Case 2: % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | (57) all_20_1 = e0 % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | COMBINE_EQS: (40), (57) imply: % 131.13/18.65 | | | | | | | (58) all_8_1 = e0 % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | REDUCE: (43), (58) imply: % 131.13/18.65 | | | | | | | (59) ~ (all_53_7 = e0) % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | BETA: splitting (12) gives: % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | | Case 1: % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | (60) ~ (op(e1, e2) = e2) % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | PRED_UNIFY: (53), (60) imply: % 131.13/18.65 | | | | | | | | (61) $false % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | CLOSE: (61) is inconsistent. % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | Case 2: % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | (62) all_53_6 = e2 % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | REDUCE: (4), (62) imply: % 131.13/18.65 | | | | | | | | (63) ~ (all_53_7 = e2) % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | SIMP: (63) implies: % 131.13/18.65 | | | | | | | | (64) ~ (all_53_7 = e2) % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | BETA: splitting (1) gives: % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | | Case 1: % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | (65) all_55_13 = e3 % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | COMBINE_EQS: (24), (65) imply: % 131.13/18.65 | | | | | | | | | (66) all_53_7 = e3 % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | REDUCE: (23), (66) imply: % 131.13/18.65 | | | | | | | | | (67) $false % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | CLOSE: (67) is inconsistent. % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | Case 2: % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | (68) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | | REF_CLOSE: (15), (24), (59), (64), (68) are inconsistent by % 131.13/18.65 | | | | | | | | | sub-proof #60. % 131.13/18.65 | | | | | | | | | % 131.13/18.65 | | | | | | | | End of split % 131.13/18.65 | | | | | | | | % 131.13/18.65 | | | | | | | End of split % 131.13/18.65 | | | | | | | % 131.13/18.65 | | | | | | End of split % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | Case 2: % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | (69) ~ (unit = e1) % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | | REF_CLOSE: (37), (51), (69) are inconsistent by sub-proof #278. % 131.13/18.65 | | | | | | % 131.13/18.65 | | | | | End of split % 131.13/18.65 | | | | | % 131.13/18.65 | | | | End of split % 131.13/18.65 | | | | % 131.13/18.65 | | | End of split % 131.13/18.65 | | | % 131.13/18.65 | | Case 2: % 131.13/18.65 | | | % 131.13/18.65 | | | (70) op(e0, e1) = e1 % 131.13/18.65 | | | % 131.13/18.65 | | | REF_CLOSE: (19), (27), (70) are inconsistent by sub-proof #333. % 131.13/18.65 | | | % 131.13/18.65 | | End of split % 131.13/18.65 | | % 131.13/18.65 | End of split % 131.13/18.65 | % 131.13/18.65 End of proof % 131.13/18.65 % 131.13/18.65 Sub-proof #14 shows that the following formulas are inconsistent: % 131.13/18.65 ---------------------------------------------------------------- % 131.13/18.65 (1) ~ (all_53_12 = all_53_14) % 131.13/18.65 (2) ~ (all_53_8 = all_4_2) % 131.13/18.65 (3) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.13/18.65 (4) ~ (all_53_9 = all_53_11) % 131.13/18.65 (5) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 131.13/18.65 (6) op(e1, e1) = all_12_2 % 131.13/18.65 (7) ~ (unit = e0) % 131.13/18.65 (8) unit = e2 | unit = e1 | unit = e0 % 131.13/18.65 (9) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 131.13/18.65 (10) op(e1, e1) = e1 % 131.13/18.65 (11) ~ (op(e0, e3) = e3) % 131.13/18.65 (12) all_22_2 = all_12_2 % 131.13/18.65 (13) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.13/18.65 (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 131.13/18.65 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.13/18.65 (15) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 131.13/18.65 $i(all_16_0)) % 131.13/18.65 (16) ~ (all_53_8 = all_53_12) % 131.13/18.65 (17) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 131.13/18.65 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 131.13/18.65 (18) ~ (all_53_14 = e3) % 131.13/18.65 (19) all_55_9 = all_53_6 % 131.13/18.65 (20) ~ (all_53_8 = all_12_2) % 131.13/18.65 (21) all_55_1 = all_53_4 % 131.13/18.65 (22) ~ (all_10_1 = e3) % 131.13/18.65 (23) all_55_6 = all_53_9 % 131.13/18.65 (24) ~ (all_53_9 = all_53_13) % 131.13/18.65 (25) op(e0, e2) = all_53_7 % 131.13/18.65 (26) all_53_6 = e1 | ~ (op(e1, e2) = e1) % 131.13/18.65 (27) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 131.13/18.65 (28) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 131.13/18.65 (29) ~ (all_53_13 = all_53_14) % 131.13/18.65 (30) ~ (all_53_8 = all_53_9) % 131.13/18.65 (31) ~ (all_53_14 = all_12_2) % 131.13/18.65 (32) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 131.13/18.65 (33) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 131.13/18.65 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 131.13/18.65 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.13/18.65 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 131.13/18.65 (34) op(e1, e0) = all_53_14 % 131.13/18.65 (35) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.13/18.65 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.13/18.65 e2) % 131.13/18.65 (36) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 131.13/18.65 (37) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 131.13/18.65 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 131.13/18.65 (38) op(e2, e1) = all_53_9 % 131.13/18.65 (39) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 131.13/18.65 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 131.13/18.65 (40) ~ (all_53_4 = all_53_8) % 131.13/18.65 (41) op(e2, e0) = all_53_13 % 131.13/18.65 (42) op(e0, e1) = e0 % 131.13/18.65 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.13/18.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.13/18.65 (44) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 131.13/18.65 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 131.13/18.65 (45) ~ (e3 = e1) % 131.13/18.65 (46) all_55_6 = e2 | ~ (op(e2, e1) = e2) % 131.13/18.65 (47) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & % 131.13/18.65 $i(all_10_0)) % 131.13/18.65 (48) all_55_14 = all_53_11 % 131.13/18.65 (49) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.13/18.66 (50) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 131.13/18.66 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 131.13/18.66 (51) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 131.13/18.66 (52) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 131.13/18.66 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 131.13/18.66 (53) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.13/18.66 (54) op(e2, e1) = e2 % 131.13/18.66 (55) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 131.13/18.66 (56) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 131.13/18.66 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 131.13/18.66 (57) all_55_12 = all_10_1 % 131.13/18.66 (58) ~ (op(e2, e3) = e3) % 131.13/18.66 (59) ~ (e2 = e1) % 131.13/18.66 (60) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 131.13/18.66 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 131.13/18.66 (61) ~ (e1 = e0) % 131.13/18.66 (62) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 131.13/18.66 (63) ~ (all_53_8 = all_53_11) % 131.13/18.66 (64) ~ (all_53_11 = all_10_1) % 131.13/18.66 (65) op(e0, unit) = e0 % 131.13/18.66 (66) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.13/18.66 (67) ~ (all_53_7 = all_53_11) % 131.13/18.66 (68) all_57_3 = e3 % 131.13/18.66 (69) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 131.13/18.66 (70) op(e1, e0) = e0 % 131.13/18.66 (71) ~ (all_53_9 = all_12_2) % 131.13/18.66 (72) all_16_1 = all_10_1 % 131.13/18.66 (73) all_57_15 = e3 % 131.13/18.66 (74) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 131.13/18.66 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 131.13/18.66 (75) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 131.13/18.66 (76) ~ (all_53_7 = all_10_1) % 131.13/18.66 (77) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 131.13/18.66 (78) all_14_2 = all_4_2 % 131.13/18.66 (79) op(e3, e1) = e3 % 131.13/18.66 (80) all_55_13 = all_53_7 % 131.13/18.66 (81) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 131.13/18.66 (82) op(e3, e1) = all_53_8 % 131.13/18.66 (83) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.13/18.66 (84) op(unit, e1) = e1 % 131.13/18.66 (85) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 131.13/18.66 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.13/18.66 (86) all_55_10 = all_12_2 % 131.13/18.66 (87) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 131.13/18.66 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 131.13/18.66 (88) ~ (all_53_6 = all_12_2) % 131.13/18.66 % 131.13/18.66 Begin of proof % 131.13/18.66 | % 131.13/18.66 | BETA: splitting (36) gives: % 131.13/18.66 | % 131.13/18.66 | Case 1: % 131.13/18.66 | | % 131.13/18.66 | | (89) ~ (op(e0, e1) = e0) % 131.13/18.66 | | % 131.13/18.66 | | PRED_UNIFY: (42), (89) imply: % 131.13/18.66 | | (90) $false % 131.13/18.66 | | % 131.13/18.66 | | CLOSE: (90) is inconsistent. % 131.13/18.66 | | % 131.13/18.66 | Case 2: % 131.13/18.66 | | % 131.13/18.66 | | (91) all_55_14 = e0 % 131.13/18.66 | | % 131.13/18.66 | | COMBINE_EQS: (48), (91) imply: % 131.13/18.66 | | (92) all_53_11 = e0 % 131.13/18.66 | | % 131.13/18.66 | | REDUCE: (67), (92) imply: % 131.13/18.66 | | (93) ~ (all_53_7 = e0) % 131.13/18.66 | | % 131.13/18.66 | | REDUCE: (63), (92) imply: % 131.13/18.66 | | (94) ~ (all_53_8 = e0) % 131.13/18.66 | | % 131.13/18.66 | | REDUCE: (4), (92) imply: % 131.13/18.66 | | (95) ~ (all_53_9 = e0) % 131.13/18.66 | | % 131.13/18.66 | | BETA: splitting (14) gives: % 131.13/18.66 | | % 131.13/18.66 | | Case 1: % 131.13/18.66 | | | % 131.13/18.66 | | | (96) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = % 131.13/18.66 | | | e0) % 131.13/18.66 | | | % 131.13/18.66 | | | BETA: splitting (96) gives: % 131.13/18.66 | | | % 131.13/18.66 | | | Case 1: % 131.13/18.66 | | | | % 131.13/18.66 | | | | (97) all_57_4 = e0 & op(e3, e1) = e0 % 131.13/18.66 | | | | % 131.13/18.66 | | | | REF_CLOSE: (43), (82), (94), (97) are inconsistent by sub-proof #210. % 131.13/18.66 | | | | % 131.13/18.66 | | | Case 2: % 131.13/18.66 | | | | % 131.13/18.66 | | | | (98) all_57_5 = e0 & op(e2, e1) = e0 % 131.13/18.66 | | | | % 131.13/18.66 | | | | REF_CLOSE: (38), (43), (95), (98) are inconsistent by sub-proof #241. % 131.13/18.66 | | | | % 131.13/18.66 | | | End of split % 131.13/18.66 | | | % 131.13/18.66 | | Case 2: % 131.13/18.66 | | | % 131.13/18.66 | | | (99) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 131.13/18.66 | | | e0) % 131.13/18.66 | | | % 131.13/18.66 | | | BETA: splitting (99) gives: % 131.13/18.66 | | | % 131.13/18.66 | | | Case 1: % 131.13/18.66 | | | | % 131.13/18.66 | | | | (100) all_57_8 = e0 & op(e1, e1) = e0 % 131.13/18.66 | | | | % 131.13/18.66 | | | | ALPHA: (100) implies: % 131.13/18.66 | | | | (101) all_57_8 = e0 % 131.13/18.66 | | | | (102) op(e1, e1) = e0 % 131.13/18.66 | | | | % 131.13/18.66 | | | | BETA: splitting (81) gives: % 131.13/18.66 | | | | % 131.13/18.66 | | | | Case 1: % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | (103) ~ (op(e3, e1) = e3) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | PRED_UNIFY: (79), (103) imply: % 131.13/18.66 | | | | | (104) $false % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | CLOSE: (104) is inconsistent. % 131.13/18.66 | | | | | % 131.13/18.66 | | | | Case 2: % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | (105) all_53_8 = e3 % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | REDUCE: (30), (105) imply: % 131.13/18.66 | | | | | (106) ~ (all_53_9 = e3) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | SIMP: (106) implies: % 131.13/18.66 | | | | | (107) ~ (all_53_9 = e3) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | REDUCE: (20), (105) imply: % 131.13/18.66 | | | | | (108) ~ (all_12_2 = e3) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | SIMP: (108) implies: % 131.13/18.66 | | | | | (109) ~ (all_12_2 = e3) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | REDUCE: (94), (105) imply: % 131.13/18.66 | | | | | (110) ~ (e3 = e0) % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | BETA: splitting (17) gives: % 131.13/18.66 | | | | | % 131.13/18.66 | | | | | Case 1: % 131.13/18.66 | | | | | | % 131.13/18.66 | | | | | | (111) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, % 131.13/18.66 | | | | | | e2) = e3) % 131.13/18.66 | | | | | | % 131.13/18.66 | | | | | | BETA: splitting (111) gives: % 131.13/18.66 | | | | | | % 131.13/18.66 | | | | | | Case 1: % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | (112) all_57_6 = e3 & op(e1, e3) = e3 % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | ALPHA: (112) implies: % 131.13/18.66 | | | | | | | (113) all_57_6 = e3 % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | BETA: splitting (75) gives: % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | (114) ~ (op(e1, e0) = e0) % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | PRED_UNIFY: (70), (114) imply: % 131.13/18.66 | | | | | | | | (115) $false % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | CLOSE: (115) is inconsistent. % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | (116) all_53_14 = e0 % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | REDUCE: (31), (116) imply: % 131.13/18.66 | | | | | | | | (117) ~ (all_12_2 = e0) % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | SIMP: (117) implies: % 131.13/18.66 | | | | | | | | (118) ~ (all_12_2 = e0) % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | BETA: splitting (46) gives: % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | (119) ~ (op(e2, e1) = e2) % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | PRED_UNIFY: (54), (119) imply: % 131.13/18.66 | | | | | | | | | (120) $false % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | CLOSE: (120) is inconsistent. % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | (121) all_55_6 = e2 % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | COMBINE_EQS: (23), (121) imply: % 131.13/18.66 | | | | | | | | | (122) all_53_9 = e2 % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | REDUCE: (71), (122) imply: % 131.13/18.66 | | | | | | | | | (123) ~ (all_12_2 = e2) % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | SIMP: (123) implies: % 131.13/18.66 | | | | | | | | | (124) ~ (all_12_2 = e2) % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | BETA: splitting (9) gives: % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | (125) all_55_10 = e3 % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | COMBINE_EQS: (86), (125) imply: % 131.13/18.66 | | | | | | | | | | (126) all_12_2 = e3 % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | REF_CLOSE: (10), (45), (62), (126) are inconsistent by % 131.13/18.66 | | | | | | | | | | sub-proof #174. % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | (127) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | BETA: splitting (37) gives: % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | (128) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 131.13/18.66 | | | | | | | | | | | & op(e1, e2) = e1) % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | BETA: splitting (128) gives: % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | (129) all_57_6 = e1 & op(e1, e3) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | ALPHA: (129) implies: % 131.13/18.66 | | | | | | | | | | | | (130) all_57_6 = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | COMBINE_EQS: (113), (130) imply: % 131.13/18.66 | | | | | | | | | | | | (131) e3 = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | REDUCE: (45), (131) imply: % 131.13/18.66 | | | | | | | | | | | | (132) $false % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | CLOSE: (132) is inconsistent. % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | (133) all_57_7 = e1 & op(e1, e2) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | ALPHA: (133) implies: % 131.13/18.66 | | | | | | | | | | | | (134) op(e1, e2) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | BETA: splitting (26) gives: % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | (135) ~ (op(e1, e2) = e1) % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | PRED_UNIFY: (134), (135) imply: % 131.13/18.66 | | | | | | | | | | | | | (136) $false % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | (137) all_53_6 = e1 % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | REDUCE: (88), (137) imply: % 131.13/18.66 | | | | | | | | | | | | | (138) ~ (all_12_2 = e1) % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | SIMP: (138) implies: % 131.13/18.66 | | | | | | | | | | | | | (139) ~ (all_12_2 = e1) % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | BETA: splitting (127) gives: % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | (140) all_55_10 = e2 % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | REF_CLOSE: (86), (124), (140) are inconsistent by sub-proof % 131.13/18.66 | | | | | | | | | | | | | | #281. % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | (141) all_55_10 = e1 | all_55_10 = e0 % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | BETA: splitting (141) gives: % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | (142) all_55_10 = e1 % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | COMBINE_EQS: (86), (142) imply: % 131.13/18.66 | | | | | | | | | | | | | | | (143) all_12_2 = e1 % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | SIMP: (143) implies: % 131.13/18.66 | | | | | | | | | | | | | | | (144) all_12_2 = e1 % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | REDUCE: (139), (144) imply: % 131.13/18.66 | | | | | | | | | | | | | | | (145) $false % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | (146) all_55_10 = e0 % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | | REF_CLOSE: (86), (118), (146) are inconsistent by sub-proof % 131.13/18.66 | | | | | | | | | | | | | | | #219. % 131.13/18.66 | | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | (147) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 131.13/18.66 | | | | | | | | | | | e1 & op(e1, e0) = e1) % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | BETA: splitting (147) gives: % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | (148) all_57_8 = e1 & op(e1, e1) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | ALPHA: (148) implies: % 131.13/18.66 | | | | | | | | | | | | (149) all_57_8 = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | COMBINE_EQS: (101), (149) imply: % 131.13/18.66 | | | | | | | | | | | | (150) e1 = e0 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | SIMP: (150) implies: % 131.13/18.66 | | | | | | | | | | | | (151) e1 = e0 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | REDUCE: (61), (151) imply: % 131.13/18.66 | | | | | | | | | | | | (152) $false % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | (153) all_57_11 = e1 & op(e1, e0) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | ALPHA: (153) implies: % 131.13/18.66 | | | | | | | | | | | | (154) op(e1, e0) = e1 % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | | REF_CLOSE: (3), (61), (116), (154) are inconsistent by % 131.13/18.66 | | | | | | | | | | | | sub-proof #25. % 131.13/18.66 | | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | | % 131.13/18.66 | | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | | % 131.13/18.66 | | | | | | | | | End of split % 131.13/18.66 | | | | | | | | | % 131.13/18.66 | | | | | | | | End of split % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | End of split % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | Case 2: % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | (155) all_57_7 = e3 & op(e1, e2) = e3 % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | ALPHA: (155) implies: % 131.13/18.66 | | | | | | | (156) all_57_7 = e3 % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | BETA: splitting (75) gives: % 131.13/18.66 | | | | | | | % 131.13/18.66 | | | | | | | Case 1: % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | (157) ~ (op(e1, e0) = e0) % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | PRED_UNIFY: (70), (157) imply: % 131.13/18.66 | | | | | | | | (158) $false % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | CLOSE: (158) is inconsistent. % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | Case 2: % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | (159) all_53_14 = e0 % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | REDUCE: (29), (159) imply: % 131.13/18.66 | | | | | | | | (160) ~ (all_53_13 = e0) % 131.13/18.66 | | | | | | | | % 131.13/18.66 | | | | | | | | REDUCE: (31), (159) imply: % 131.13/18.67 | | | | | | | | (161) ~ (all_12_2 = e0) % 131.13/18.67 | | | | | | | | % 131.13/18.67 | | | | | | | | SIMP: (161) implies: % 131.13/18.67 | | | | | | | | (162) ~ (all_12_2 = e0) % 131.13/18.67 | | | | | | | | % 131.13/18.67 | | | | | | | | REDUCE: (18), (159) imply: % 131.13/18.67 | | | | | | | | (163) ~ (e3 = e0) % 131.13/18.67 | | | | | | | | % 131.13/18.67 | | | | | | | | BETA: splitting (50) gives: % 131.13/18.67 | | | | | | | | % 131.13/18.67 | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | | (164) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & % 131.13/18.67 | | | | | | | | | op(e2, e2) = e0) % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | | BETA: splitting (164) gives: % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | (165) all_57_2 = e0 & op(e2, e3) = e0 % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | ALPHA: (165) implies: % 131.13/18.67 | | | | | | | | | | (166) all_57_2 = e0 % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | BETA: splitting (46) gives: % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | (167) ~ (op(e2, e1) = e2) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | PRED_UNIFY: (54), (167) imply: % 131.13/18.67 | | | | | | | | | | | (168) $false % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | CLOSE: (168) is inconsistent. % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | (169) all_55_6 = e2 % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | COMBINE_EQS: (23), (169) imply: % 131.13/18.67 | | | | | | | | | | | (170) all_53_9 = e2 % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | REDUCE: (71), (170) imply: % 131.13/18.67 | | | | | | | | | | | (171) ~ (all_12_2 = e2) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | SIMP: (171) implies: % 131.13/18.67 | | | | | | | | | | | (172) ~ (all_12_2 = e2) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | REDUCE: (107), (170) imply: % 131.13/18.67 | | | | | | | | | | | (173) ~ (e3 = e2) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | SIMP: (173) implies: % 131.13/18.67 | | | | | | | | | | | (174) ~ (e3 = e2) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | REDUCE: (95), (170) imply: % 131.13/18.67 | | | | | | | | | | | (175) ~ (e2 = e0) % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | BETA: splitting (87) gives: % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | (176) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 131.13/18.67 | | | | | | | | | | | | & op(e2, e2) = e1) % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | BETA: splitting (176) gives: % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | (177) all_57_2 = e1 & op(e2, e3) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | ALPHA: (177) implies: % 131.13/18.67 | | | | | | | | | | | | | (178) all_57_2 = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | COMBINE_EQS: (166), (178) imply: % 131.13/18.67 | | | | | | | | | | | | | (179) e1 = e0 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | SIMP: (179) implies: % 131.13/18.67 | | | | | | | | | | | | | (180) e1 = e0 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | REDUCE: (61), (180) imply: % 131.13/18.67 | | | | | | | | | | | | | (181) $false % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | (182) all_57_3 = e1 & op(e2, e2) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | REF_CLOSE: (45), (68), (182) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | | | | | | | #22. % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | (183) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 131.13/18.67 | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | BETA: splitting (183) gives: % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | (184) all_57_5 = e1 & op(e2, e1) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | ALPHA: (184) implies: % 131.13/18.67 | | | | | | | | | | | | | (185) op(e2, e1) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | BETA: splitting (83) gives: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | (186) ~ (op(e2, e1) = e1) % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | PRED_UNIFY: (185), (186) imply: % 131.13/18.67 | | | | | | | | | | | | | | (187) $false % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | (188) all_53_9 = e1 % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | COMBINE_EQS: (170), (188) imply: % 131.13/18.67 | | | | | | | | | | | | | | (189) e2 = e1 % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | SIMP: (189) implies: % 131.13/18.67 | | | | | | | | | | | | | | (190) e2 = e1 % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | REDUCE: (59), (190) imply: % 131.13/18.67 | | | | | | | | | | | | | | (191) $false % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | (192) all_57_10 = e1 & op(e2, e0) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | ALPHA: (192) implies: % 131.13/18.67 | | | | | | | | | | | | | (193) op(e2, e0) = e1 % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | BETA: splitting (39) gives: % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | (194) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 131.13/18.67 | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (12), (15), (19), (22), (24), % 131.13/18.67 | | | | | | | | | | | | | | (25), (27), (33), (35), (41), (43), (47), (49), % 131.13/18.67 | | | | | | | | | | | | | | (51), (53), (57), (62), (64), (65), (66), (68), % 131.13/18.67 | | | | | | | | | | | | | | (72), (73), (76), (83), (84), (85), (88), (109), % 131.13/18.67 | | | | | | | | | | | | | | (110), (162), (172), (174), (175), (193), (194) % 131.13/18.67 | | | | | | | | | | | | | | are inconsistent by sub-proof #17. % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | (195) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 131.13/18.67 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | BETA: splitting (195) gives: % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | Case 1: % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | (196) all_57_7 = e0 & op(e1, e2) = e0 % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | ALPHA: (196) implies: % 131.13/18.67 | | | | | | | | | | | | | | | (197) all_57_7 = e0 % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | REF_CLOSE: (110), (156), (197) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | | | | | | | | | #321. % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | (198) all_57_13 = e0 & op(e0, e2) = e0 % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | ALPHA: (198) implies: % 131.13/18.67 | | | | | | | | | | | | | | | (199) op(e0, e2) = e0 % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | | REF_CLOSE: (32), (80), (93), (199) are inconsistent by % 131.13/18.67 | | | | | | | | | | | | | | | sub-proof #292. % 131.13/18.67 | | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | (200) all_57_3 = e0 & op(e2, e2) = e0 % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | | REF_CLOSE: (68), (110), (200) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | | | | #49. % 131.13/18.67 | | | | | | | | | | % 131.13/18.67 | | | | | | | | | End of split % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | Case 2: % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | | (201) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & % 131.13/18.67 | | | | | | | | | op(e2, e0) = e0) % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | | REF_CLOSE: (13), (38), (43), (95), (160), (201) are % 131.13/18.67 | | | | | | | | | inconsistent by sub-proof #16. % 131.13/18.67 | | | | | | | | | % 131.13/18.67 | | | | | | | | End of split % 131.13/18.67 | | | | | | | | % 131.13/18.67 | | | | | | | End of split % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | End of split % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | Case 2: % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | (202) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & % 131.13/18.67 | | | | | | op(e1, e0) = e3) % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | BETA: splitting (202) gives: % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | Case 1: % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | (203) all_57_8 = e3 & op(e1, e1) = e3 % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | ALPHA: (203) implies: % 131.13/18.67 | | | | | | | (204) op(e1, e1) = e3 % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | REF_CLOSE: (43), (102), (110), (204) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | #320. % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | Case 2: % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | (205) all_57_11 = e3 & op(e1, e0) = e3 % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | REF_CLOSE: (18), (34), (43), (205) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | #84. % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | End of split % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | End of split % 131.13/18.67 | | | | | % 131.13/18.67 | | | | End of split % 131.13/18.67 | | | | % 131.13/18.67 | | | Case 2: % 131.13/18.67 | | | | % 131.13/18.67 | | | | (206) all_57_14 = e0 & op(e0, e1) = e0 % 131.13/18.67 | | | | % 131.13/18.67 | | | | ALPHA: (206) implies: % 131.13/18.67 | | | | (207) all_57_14 = e0 % 131.13/18.67 | | | | % 131.13/18.67 | | | | BETA: splitting (81) gives: % 131.13/18.67 | | | | % 131.13/18.67 | | | | Case 1: % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | (208) ~ (op(e3, e1) = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | PRED_UNIFY: (79), (208) imply: % 131.13/18.67 | | | | | (209) $false % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | CLOSE: (209) is inconsistent. % 131.13/18.67 | | | | | % 131.13/18.67 | | | | Case 2: % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | (210) all_53_8 = e3 % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | REDUCE: (40), (210) imply: % 131.13/18.67 | | | | | (211) ~ (all_53_4 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | REDUCE: (30), (210) imply: % 131.13/18.67 | | | | | (212) ~ (all_53_9 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | SIMP: (212) implies: % 131.13/18.67 | | | | | (213) ~ (all_53_9 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | REDUCE: (16), (210) imply: % 131.13/18.67 | | | | | (214) ~ (all_53_12 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | SIMP: (214) implies: % 131.13/18.67 | | | | | (215) ~ (all_53_12 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | REDUCE: (20), (210) imply: % 131.13/18.67 | | | | | (216) ~ (all_12_2 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | SIMP: (216) implies: % 131.13/18.67 | | | | | (217) ~ (all_12_2 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | REDUCE: (2), (210) imply: % 131.13/18.67 | | | | | (218) ~ (all_4_2 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | SIMP: (218) implies: % 131.13/18.67 | | | | | (219) ~ (all_4_2 = e3) % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | BETA: splitting (52) gives: % 131.13/18.67 | | | | | % 131.13/18.67 | | | | | Case 1: % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | (220) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, % 131.13/18.67 | | | | | | e3) = e3) % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | BETA: splitting (220) gives: % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | | Case 1: % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | (221) all_57_0 = e3 & op(e3, e3) = e3 % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | REF_CLOSE: (77), (78), (219), (221) are inconsistent by sub-proof % 131.13/18.67 | | | | | | | #206. % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | Case 2: % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | (222) all_57_2 = e3 & op(e2, e3) = e3 % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | | REF_CLOSE: (58), (222) are inconsistent by sub-proof #24. % 131.13/18.67 | | | | | | | % 131.13/18.67 | | | | | | End of split % 131.13/18.67 | | | | | | % 131.13/18.67 | | | | | Case 2: % 131.13/18.67 | | | | | | % 131.49/18.67 | | | | | | (223) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & % 131.49/18.67 | | | | | | op(e0, e3) = e3) % 131.49/18.67 | | | | | | % 131.49/18.67 | | | | | | BETA: splitting (223) gives: % 131.49/18.67 | | | | | | % 131.49/18.67 | | | | | | Case 1: % 131.49/18.67 | | | | | | | % 131.49/18.67 | | | | | | | (224) all_57_6 = e3 & op(e1, e3) = e3 % 131.49/18.67 | | | | | | | % 131.49/18.67 | | | | | | | ALPHA: (224) implies: % 131.49/18.67 | | | | | | | (225) all_57_6 = e3 % 131.49/18.67 | | | | | | | % 131.49/18.67 | | | | | | | BETA: splitting (56) gives: % 131.49/18.67 | | | | | | | % 131.49/18.67 | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | (226) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & % 131.49/18.67 | | | | | | | | op(e3, e2) = e3) % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | BETA: splitting (226) gives: % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | (227) all_57_0 = e3 & op(e3, e3) = e3 % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | REF_CLOSE: (77), (78), (219), (227) are inconsistent by % 131.49/18.67 | | | | | | | | | sub-proof #206. % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | (228) all_57_1 = e3 & op(e3, e2) = e3 % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | REF_CLOSE: (21), (28), (211), (228) are inconsistent by % 131.49/18.67 | | | | | | | | | sub-proof #328. % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | End of split % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | (229) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & % 131.49/18.67 | | | | | | | | op(e3, e0) = e3) % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | BETA: splitting (229) gives: % 131.49/18.67 | | | | | | | | % 131.49/18.67 | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | (230) all_57_4 = e3 & op(e3, e1) = e3 % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | ALPHA: (230) implies: % 131.49/18.67 | | | | | | | | | (231) all_57_4 = e3 % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | BETA: splitting (75) gives: % 131.49/18.67 | | | | | | | | | % 131.49/18.67 | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | (232) ~ (op(e1, e0) = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | PRED_UNIFY: (70), (232) imply: % 131.49/18.67 | | | | | | | | | | (233) $false % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | CLOSE: (233) is inconsistent. % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | (234) all_53_14 = e0 % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | REDUCE: (1), (234) imply: % 131.49/18.67 | | | | | | | | | | (235) ~ (all_53_12 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | REDUCE: (29), (234) imply: % 131.49/18.67 | | | | | | | | | | (236) ~ (all_53_13 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | REDUCE: (31), (234) imply: % 131.49/18.67 | | | | | | | | | | (237) ~ (all_12_2 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | SIMP: (237) implies: % 131.49/18.67 | | | | | | | | | | (238) ~ (all_12_2 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | REDUCE: (18), (234) imply: % 131.49/18.67 | | | | | | | | | | (239) ~ (e3 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | SIMP: (239) implies: % 131.49/18.67 | | | | | | | | | | (240) ~ (e3 = e0) % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | BETA: splitting (50) gives: % 131.49/18.67 | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | (241) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 131.49/18.67 | | | | | | | | | | | & op(e2, e2) = e0) % 131.49/18.67 | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | BETA: splitting (241) gives: % 131.49/18.67 | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | (242) all_57_2 = e0 & op(e2, e3) = e0 % 131.49/18.67 | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | ALPHA: (242) implies: % 131.49/18.67 | | | | | | | | | | | | (243) all_57_2 = e0 % 131.49/18.67 | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | BETA: splitting (33) gives: % 131.49/18.67 | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | (244) all_57_15 = e0 & op(e0, e0) = e0 % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | REF_CLOSE: (73), (240), (244) are inconsistent by sub-proof % 131.49/18.67 | | | | | | | | | | | | | #81. % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | (245) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 131.49/18.67 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 131.49/18.67 | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 131.49/18.67 | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 131.49/18.67 | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | ALPHA: (245) implies: % 131.49/18.67 | | | | | | | | | | | | | (246) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 131.49/18.67 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 131.49/18.67 | | | | | | | | | | | | | e0) = e0) % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | BETA: splitting (246) gives: % 131.49/18.67 | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | (247) all_57_9 = e0 & op(e3, e0) = e0 % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | ALPHA: (247) implies: % 131.49/18.67 | | | | | | | | | | | | | | (248) op(e3, e0) = e0 % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | REF_CLOSE: (5), (235), (248) are inconsistent by sub-proof % 131.49/18.67 | | | | | | | | | | | | | | #256. % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | (249) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 131.49/18.67 | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | BETA: splitting (249) gives: % 131.49/18.67 | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | Case 1: % 131.49/18.67 | | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | | (250) all_57_10 = e0 & op(e2, e0) = e0 % 131.49/18.67 | | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | | ALPHA: (250) implies: % 131.49/18.67 | | | | | | | | | | | | | | | (251) op(e2, e0) = e0 % 131.49/18.67 | | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | | REF_CLOSE: (13), (236), (251) are inconsistent by sub-proof % 131.49/18.67 | | | | | | | | | | | | | | | #356. % 131.49/18.67 | | | | | | | | | | | | | | | % 131.49/18.67 | | | | | | | | | | | | | | Case 2: % 131.49/18.67 | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | (252) all_57_11 = e0 & op(e1, e0) = e0 % 131.49/18.68 | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | ALPHA: (252) implies: % 131.49/18.68 | | | | | | | | | | | | | | | (253) all_57_11 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 131.49/18.68 | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | (254) ~ (op(e2, e1) = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | PRED_UNIFY: (54), (254) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (255) $false % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | CLOSE: (255) is inconsistent. % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | (256) all_55_6 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (256) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (257) all_53_9 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | REDUCE: (24), (257) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (258) ~ (all_53_13 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | SIMP: (258) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | (259) ~ (all_53_13 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | REDUCE: (71), (257) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (260) ~ (all_12_2 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | SIMP: (260) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | (261) ~ (all_12_2 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | REDUCE: (213), (257) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (262) ~ (e3 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | SIMP: (262) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | (263) ~ (e3 = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | REDUCE: (95), (257) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | (264) ~ (e2 = e0) % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | (265) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | (266) all_57_2 = e2 & op(e2, e3) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (264), (266) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | #349. % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | (267) all_57_3 = e2 & op(e2, e2) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (263), (267) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | #46. % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | (268) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 131.49/18.68 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | (269) all_57_5 = e2 & op(e2, e1) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | (270) all_57_5 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | (271) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (272) all_57_2 = e1 & op(e2, e3) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (273) all_57_2 = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (61), (68), (236), (240), (264), % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (270), (273) are inconsistent by sub-proof #48. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (274) all_57_3 = e1 & op(e2, e2) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (68), (274) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | #22. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | (275) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 131.49/18.68 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (276) all_57_5 = e1 & op(e2, e1) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (270), (276) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | #15. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (277) all_57_10 = e1 & op(e2, e0) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | (278) op(e2, e0) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (279) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (12), (15), (19), (22), (24), % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (25), (27), (33), (35), (41), (43), (47), (49), % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (51), (53), (57), (62), (64), (65), (66), (68), % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (72), (73), (76), (83), (84), (85), (88), (217), % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (238), (240), (261), (263), (264), (278), (279) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #17. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | (280) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | (281) all_57_7 = e0 & op(e1, e2) = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | (282) all_57_7 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | (283) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (284) all_57_4 = e1 & op(e3, e1) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (231), (284) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | #103. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (285) all_57_5 = e1 & op(e2, e1) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (270), (285) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | #15. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | (286) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (287) all_57_8 = e1 & op(e1, e1) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (288) all_57_8 = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_57_6 = e2 & op(e1, e3) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_57_6 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (225), (263), (291) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | #135. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_57_7 = e2 & op(e1, e2) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_57_7 = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (293) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e2 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (294) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_57_8 = e2 & op(e1, e1) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (288), (297) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | #44. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_57_11 = e2 & op(e1, e0) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (253), (264), (298) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | #302. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (299) all_57_14 = e1 & op(e0, e1) = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (300) all_57_14 = e1 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (300) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (301) e1 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (302) e1 = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (302) imply: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | (303) $false % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | (304) all_57_13 = e0 & op(e0, e2) = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | (305) op(e0, e2) = e0 % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (80), (93), (305) are inconsistent by % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | sub-proof #292. % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | (306) all_57_10 = e2 & op(e2, e0) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | ALPHA: (306) implies: % 131.49/18.68 | | | | | | | | | | | | | | | | | | (307) op(e2, e0) = e2 % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (259), (307) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | | | | | | | #225. % 131.49/18.68 | | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | (308) all_57_3 = e0 & op(e2, e2) = e0 % 131.49/18.68 | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | | REF_CLOSE: (68), (240), (308) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | | | | #49. % 131.49/18.68 | | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | (309) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 131.49/18.68 | | | | | | | | | | | e0 & op(e2, e0) = e0) % 131.49/18.68 | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | | REF_CLOSE: (13), (38), (43), (95), (236), (309) are % 131.49/18.68 | | | | | | | | | | | inconsistent by sub-proof #16. % 131.49/18.68 | | | | | | | | | | | % 131.49/18.68 | | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | | % 131.49/18.68 | | | | | | | | | End of split % 131.49/18.68 | | | | | | | | | % 131.49/18.68 | | | | | | | | Case 2: % 131.49/18.68 | | | | | | | | | % 131.49/18.68 | | | | | | | | | (310) all_57_9 = e3 & op(e3, e0) = e3 % 131.49/18.68 | | | | | | | | | % 131.49/18.68 | | | | | | | | | ALPHA: (310) implies: % 131.49/18.68 | | | | | | | | | (311) op(e3, e0) = e3 % 131.49/18.68 | | | | | | | | | % 131.49/18.68 | | | | | | | | | REF_CLOSE: (69), (215), (311) are inconsistent by sub-proof % 131.49/18.68 | | | | | | | | | #186. % 131.49/18.68 | | | | | | | | | % 131.49/18.68 | | | | | | | | End of split % 131.49/18.68 | | | | | | | | % 131.49/18.68 | | | | | | | End of split % 131.49/18.68 | | | | | | | % 131.49/18.68 | | | | | | Case 2: % 131.49/18.68 | | | | | | | % 131.49/18.68 | | | | | | | (312) all_57_12 = e3 & op(e0, e3) = e3 % 131.49/18.68 | | | | | | | % 131.49/18.68 | | | | | | | REF_CLOSE: (11), (312) are inconsistent by sub-proof #68. % 131.49/18.68 | | | | | | | % 131.49/18.68 | | | | | | End of split % 131.49/18.68 | | | | | | % 131.49/18.68 | | | | | End of split % 131.49/18.68 | | | | | % 131.49/18.68 | | | | End of split % 131.49/18.68 | | | | % 131.49/18.68 | | | End of split % 131.49/18.68 | | | % 131.49/18.68 | | End of split % 131.49/18.68 | | % 131.49/18.68 | End of split % 131.49/18.68 | % 131.49/18.68 End of proof % 131.49/18.68 % 131.49/18.68 Sub-proof #15 shows that the following formulas are inconsistent: % 131.49/18.68 ---------------------------------------------------------------- % 131.49/18.68 (1) all_57_5 = e1 & op(e2, e1) = e1 % 131.49/18.68 (2) all_57_5 = e2 % 131.49/18.68 (3) ~ (e2 = e1) % 131.49/18.68 % 131.49/18.68 Begin of proof % 131.49/18.68 | % 131.49/18.68 | ALPHA: (1) implies: % 131.49/18.68 | (4) all_57_5 = e1 % 131.49/18.68 | % 131.49/18.68 | COMBINE_EQS: (2), (4) imply: % 131.49/18.68 | (5) e2 = e1 % 131.49/18.68 | % 131.49/18.68 | REDUCE: (3), (5) imply: % 131.49/18.68 | (6) $false % 131.49/18.68 | % 131.49/18.68 | CLOSE: (6) is inconsistent. % 131.49/18.68 | % 131.49/18.68 End of proof % 131.49/18.68 % 131.49/18.68 Sub-proof #16 shows that the following formulas are inconsistent: % 131.49/18.68 ---------------------------------------------------------------- % 131.49/18.68 (1) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.49/18.68 (2) ~ (all_53_9 = e0) % 131.49/18.68 (3) ~ (all_53_13 = e0) % 131.49/18.68 (4) op(e2, e1) = all_53_9 % 131.49/18.68 (5) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 131.49/18.68 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.68 % 131.49/18.68 Begin of proof % 131.49/18.68 | % 131.49/18.68 | BETA: splitting (5) gives: % 131.49/18.68 | % 131.49/18.68 | Case 1: % 131.49/18.68 | | % 131.49/18.68 | | (7) all_57_5 = e0 & op(e2, e1) = e0 % 131.49/18.68 | | % 131.49/18.68 | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #241. % 131.49/18.68 | | % 131.49/18.68 | Case 2: % 131.49/18.68 | | % 131.49/18.68 | | (8) all_57_10 = e0 & op(e2, e0) = e0 % 131.49/18.68 | | % 131.49/18.68 | | ALPHA: (8) implies: % 131.49/18.68 | | (9) op(e2, e0) = e0 % 131.49/18.68 | | % 131.49/18.68 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #356. % 131.49/18.68 | | % 131.49/18.68 | End of split % 131.49/18.68 | % 131.49/18.68 End of proof % 131.49/18.68 % 131.49/18.68 Sub-proof #17 shows that the following formulas are inconsistent: % 131.49/18.68 ---------------------------------------------------------------- % 131.49/18.68 (1) op(e1, e1) = all_12_2 % 131.49/18.68 (2) ~ (unit = e0) % 131.49/18.68 (3) unit = e2 | unit = e1 | unit = e0 % 131.49/18.68 (4) op(e1, e1) = e1 % 131.49/18.68 (5) all_22_2 = all_12_2 % 131.49/18.68 (6) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 131.49/18.68 $i(all_16_0)) % 131.49/18.68 (7) all_55_9 = all_53_6 % 131.49/18.68 (8) ~ (all_12_2 = e2) % 131.49/18.68 (9) ~ (all_12_2 = e0) % 131.49/18.68 (10) ~ (all_10_1 = e3) % 131.49/18.68 (11) ~ (all_53_9 = all_53_13) % 131.49/18.68 (12) op(e0, e2) = all_53_7 % 131.49/18.68 (13) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 131.49/18.69 (14) op(e2, e0) = e1 % 131.49/18.69 (15) ~ (e3 = e0) % 131.49/18.69 (16) ~ (e2 = e0) % 131.49/18.69 (17) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 131.49/18.69 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 131.49/18.69 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.49/18.69 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 131.49/18.69 (18) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.49/18.69 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.49/18.69 e2) % 131.49/18.69 (19) ~ (all_12_2 = e3) % 131.49/18.69 (20) op(e2, e0) = all_53_13 % 131.49/18.69 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.69 (22) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 131.49/18.69 (23) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & % 131.49/18.69 $i(all_10_0)) % 131.49/18.69 (24) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.49/18.69 (25) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.69 (26) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.69 (27) all_55_12 = all_10_1 % 131.49/18.69 (28) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 131.49/18.69 (29) ~ (all_53_11 = all_10_1) % 131.49/18.69 (30) op(e0, unit) = e0 % 131.49/18.69 (31) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.49/18.69 (32) all_57_3 = e3 % 131.49/18.69 (33) all_16_1 = all_10_1 % 131.49/18.69 (34) all_57_15 = e3 % 131.49/18.69 (35) ~ (all_53_7 = all_10_1) % 131.49/18.69 (36) ~ (e3 = e2) % 131.49/18.69 (37) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.69 (38) op(unit, e1) = e1 % 131.49/18.69 (39) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 131.49/18.69 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.49/18.69 (40) ~ (all_53_6 = all_12_2) % 131.49/18.69 % 131.49/18.69 Begin of proof % 131.49/18.69 | % 131.49/18.69 | BETA: splitting (22) gives: % 131.49/18.69 | % 131.49/18.69 | Case 1: % 131.49/18.69 | | % 131.49/18.69 | | (41) all_57_1 = e0 & op(e3, e2) = e0 % 131.49/18.69 | | % 131.49/18.69 | | ALPHA: (41) implies: % 131.49/18.69 | | (42) all_57_1 = e0 % 131.49/18.69 | | % 131.49/18.69 | | BETA: splitting (28) gives: % 131.49/18.69 | | % 131.49/18.69 | | Case 1: % 131.49/18.69 | | | % 131.49/18.69 | | | (43) ~ (op(e1, e1) = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | PRED_UNIFY: (4), (43) imply: % 131.49/18.69 | | | (44) $false % 131.49/18.69 | | | % 131.49/18.69 | | | CLOSE: (44) is inconsistent. % 131.49/18.69 | | | % 131.49/18.69 | | Case 2: % 131.49/18.69 | | | % 131.49/18.69 | | | (45) all_12_2 = e1 % 131.49/18.69 | | | % 131.49/18.69 | | | COMBINE_EQS: (5), (45) imply: % 131.49/18.69 | | | (46) all_22_2 = e1 % 131.49/18.69 | | | % 131.49/18.69 | | | REDUCE: (40), (45) imply: % 131.49/18.69 | | | (47) ~ (all_53_6 = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | REDUCE: (19), (45) imply: % 131.49/18.69 | | | (48) ~ (e3 = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | SIMP: (48) implies: % 131.49/18.69 | | | (49) ~ (e3 = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | REDUCE: (8), (45) imply: % 131.49/18.69 | | | (50) ~ (e2 = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | SIMP: (50) implies: % 131.49/18.69 | | | (51) ~ (e2 = e1) % 131.49/18.69 | | | % 131.49/18.69 | | | REDUCE: (9), (45) imply: % 131.49/18.69 | | | (52) ~ (e1 = e0) % 131.49/18.69 | | | % 131.49/18.69 | | | BETA: splitting (39) gives: % 131.49/18.69 | | | % 131.49/18.69 | | | Case 1: % 131.49/18.69 | | | | % 131.49/18.69 | | | | (53) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) % 131.49/18.69 | | | | = e1) % 131.49/18.69 | | | | % 131.49/18.69 | | | | BETA: splitting (53) gives: % 131.49/18.69 | | | | % 131.49/18.69 | | | | Case 1: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (54) all_57_1 = e1 & op(e3, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | REF_CLOSE: (4), (13), (42), (46), (52), (54) are inconsistent by % 131.49/18.69 | | | | | sub-proof #153. % 131.49/18.69 | | | | | % 131.49/18.69 | | | | Case 2: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (55) all_57_3 = e1 & op(e2, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | ALPHA: (55) implies: % 131.49/18.69 | | | | | (56) all_57_3 = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | COMBINE_EQS: (32), (56) imply: % 131.49/18.69 | | | | | (57) e3 = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | SIMP: (57) implies: % 131.49/18.69 | | | | | (58) e3 = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | REDUCE: (49), (58) imply: % 131.49/18.69 | | | | | (59) $false % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | CLOSE: (59) is inconsistent. % 131.49/18.69 | | | | | % 131.49/18.69 | | | | End of split % 131.49/18.69 | | | | % 131.49/18.69 | | | Case 2: % 131.49/18.69 | | | | % 131.49/18.69 | | | | (60) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) % 131.49/18.69 | | | | = e1) % 131.49/18.69 | | | | % 131.49/18.69 | | | | BETA: splitting (60) gives: % 131.49/18.69 | | | | % 131.49/18.69 | | | | Case 1: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (61) all_57_7 = e1 & op(e1, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | ALPHA: (61) implies: % 131.49/18.69 | | | | | (62) op(e1, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | REF_CLOSE: (7), (31), (47), (62) are inconsistent by sub-proof #341. % 131.49/18.69 | | | | | % 131.49/18.69 | | | | Case 2: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (63) all_57_13 = e1 & op(e0, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | ALPHA: (63) implies: % 131.49/18.69 | | | | | (64) all_57_13 = e1 % 131.49/18.69 | | | | | (65) op(e0, e2) = e1 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | REF_CLOSE: (2), (3), (4), (6), (10), (11), (12), (13), (14), (15), % 131.49/18.69 | | | | | (16), (17), (18), (20), (21), (23), (24), (25), (26), (27), % 131.49/18.69 | | | | | (29), (30), (33), (34), (35), (36), (37), (38), (46), (51), % 131.49/18.69 | | | | | (52), (64), (65) are inconsistent by sub-proof #72. % 131.49/18.69 | | | | | % 131.49/18.69 | | | | End of split % 131.49/18.69 | | | | % 131.49/18.69 | | | End of split % 131.49/18.69 | | | % 131.49/18.69 | | End of split % 131.49/18.69 | | % 131.49/18.69 | Case 2: % 131.49/18.69 | | % 131.49/18.69 | | (66) all_57_3 = e0 & op(e2, e2) = e0 % 131.49/18.69 | | % 131.49/18.69 | | REF_CLOSE: (15), (32), (66) are inconsistent by sub-proof #49. % 131.49/18.69 | | % 131.49/18.69 | End of split % 131.49/18.69 | % 131.49/18.69 End of proof % 131.49/18.69 % 131.49/18.69 Sub-proof #18 shows that the following formulas are inconsistent: % 131.49/18.69 ---------------------------------------------------------------- % 131.49/18.69 (1) unit = e2 | unit = e1 | unit = e0 % 131.49/18.69 (2) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 131.49/18.69 (3) ~ (all_53_9 = e3) % 131.49/18.69 (4) ~ (all_53_8 = all_53_12) % 131.49/18.69 (5) ~ (unit = e2) % 131.49/18.69 (6) op(unit, e2) = e2 % 131.49/18.69 (7) op(e0, e1) = all_53_11 % 131.49/18.69 (8) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 131.49/18.69 (9) op(e2, e1) = all_53_9 % 131.49/18.69 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.69 (11) op(e1, e1) = e2 % 131.49/18.69 (12) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 131.49/18.69 (13) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 131.49/18.69 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 131.49/18.69 (14) ~ (all_53_6 = e2) % 131.49/18.69 (15) ~ (e3 = e2) % 131.49/18.69 (16) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 131.49/18.69 (17) op(unit, e3) = e3 % 131.49/18.69 (18) op(e3, unit) = e3 % 131.49/18.69 (19) ~ (all_53_3 = all_53_11) % 131.49/18.69 % 131.49/18.69 Begin of proof % 131.49/18.69 | % 131.49/18.69 | BETA: splitting (8) gives: % 131.49/18.69 | % 131.49/18.69 | Case 1: % 131.49/18.69 | | % 131.49/18.69 | | (20) ~ (op(e1, e2) = e2) % 131.49/18.69 | | % 131.49/18.69 | | PRED_UNIFY: (6), (20) imply: % 131.49/18.69 | | (21) ~ (unit = e1) % 131.49/18.69 | | % 131.49/18.69 | | BETA: splitting (1) gives: % 131.49/18.69 | | % 131.49/18.69 | | Case 1: % 131.49/18.69 | | | % 131.49/18.69 | | | (22) unit = e2 % 131.49/18.69 | | | % 131.49/18.69 | | | REDUCE: (5), (22) imply: % 131.49/18.69 | | | (23) $false % 131.49/18.69 | | | % 131.49/18.69 | | | CLOSE: (23) is inconsistent. % 131.49/18.69 | | | % 131.49/18.69 | | Case 2: % 131.49/18.69 | | | % 131.49/18.69 | | | (24) unit = e1 | unit = e0 % 131.49/18.69 | | | % 131.49/18.69 | | | BETA: splitting (24) gives: % 131.49/18.69 | | | % 131.49/18.69 | | | Case 1: % 131.49/18.69 | | | | % 131.49/18.69 | | | | (25) unit = e1 % 131.49/18.69 | | | | % 131.49/18.69 | | | | REDUCE: (21), (25) imply: % 131.49/18.69 | | | | (26) $false % 131.49/18.69 | | | | % 131.49/18.69 | | | | CLOSE: (26) is inconsistent. % 131.49/18.69 | | | | % 131.49/18.69 | | | Case 2: % 131.49/18.69 | | | | % 131.49/18.69 | | | | (27) unit = e0 % 131.49/18.69 | | | | % 131.49/18.69 | | | | REDUCE: (17), (27) imply: % 131.49/18.69 | | | | (28) op(e0, e3) = e3 % 131.49/18.69 | | | | % 131.49/18.69 | | | | REDUCE: (18), (27) imply: % 131.49/18.69 | | | | (29) op(e3, e0) = e3 % 131.49/18.69 | | | | % 131.49/18.69 | | | | BETA: splitting (2) gives: % 131.49/18.69 | | | | % 131.49/18.69 | | | | Case 1: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (30) ~ (op(e0, e3) = e3) % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | PRED_UNIFY: (28), (30) imply: % 131.49/18.69 | | | | | (31) $false % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | CLOSE: (31) is inconsistent. % 131.49/18.69 | | | | | % 131.49/18.69 | | | | Case 2: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | (32) all_53_3 = e3 % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | REDUCE: (19), (32) imply: % 131.49/18.69 | | | | | (33) ~ (all_53_11 = e3) % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | SIMP: (33) implies: % 131.49/18.69 | | | | | (34) ~ (all_53_11 = e3) % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | BETA: splitting (13) gives: % 131.49/18.69 | | | | | % 131.49/18.69 | | | | | Case 1: % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | (35) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, % 131.49/18.69 | | | | | | e1) = e3) % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | BETA: splitting (35) gives: % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | Case 1: % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | (36) all_57_4 = e3 & op(e3, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | ALPHA: (36) implies: % 131.49/18.69 | | | | | | | (37) op(e3, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | BETA: splitting (12) gives: % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | Case 1: % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | (38) ~ (op(e3, e0) = e3) % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | PRED_UNIFY: (29), (38) imply: % 131.49/18.69 | | | | | | | | (39) $false % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | CLOSE: (39) is inconsistent. % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | Case 2: % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | (40) all_53_12 = e3 % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | REDUCE: (4), (40) imply: % 131.49/18.69 | | | | | | | | (41) ~ (all_53_8 = e3) % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | | REF_CLOSE: (16), (37), (41) are inconsistent by sub-proof #160. % 131.49/18.69 | | | | | | | | % 131.49/18.69 | | | | | | | End of split % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | Case 2: % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | (42) all_57_5 = e3 & op(e2, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | REF_CLOSE: (3), (9), (10), (42) are inconsistent by sub-proof % 131.49/18.69 | | | | | | | #180. % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | End of split % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | Case 2: % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | (43) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, % 131.49/18.69 | | | | | | e1) = e3) % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | BETA: splitting (43) gives: % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | | Case 1: % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | (44) all_57_8 = e3 & op(e1, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | ALPHA: (44) implies: % 131.49/18.69 | | | | | | | (45) op(e1, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | REF_CLOSE: (10), (11), (15), (45) are inconsistent by sub-proof % 131.49/18.69 | | | | | | | #173. % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | Case 2: % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | (46) all_57_14 = e3 & op(e0, e1) = e3 % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | | REF_CLOSE: (7), (10), (34), (46) are inconsistent by sub-proof % 131.49/18.69 | | | | | | | #121. % 131.49/18.69 | | | | | | | % 131.49/18.69 | | | | | | End of split % 131.49/18.69 | | | | | | % 131.49/18.69 | | | | | End of split % 131.49/18.69 | | | | | % 131.49/18.69 | | | | End of split % 131.49/18.69 | | | | % 131.49/18.69 | | | End of split % 131.49/18.69 | | | % 131.49/18.69 | | End of split % 131.49/18.69 | | % 131.49/18.69 | Case 2: % 131.49/18.69 | | % 131.49/18.69 | | (47) op(e1, e2) = e2 % 131.49/18.69 | | % 131.49/18.69 | | REF_CLOSE: (8), (14), (47) are inconsistent by sub-proof #326. % 131.49/18.69 | | % 131.49/18.69 | End of split % 131.49/18.69 | % 131.49/18.69 End of proof % 131.49/18.69 % 131.49/18.69 Sub-proof #19 shows that the following formulas are inconsistent: % 131.49/18.69 ---------------------------------------------------------------- % 131.49/18.69 (1) all_57_15 = e3 & op(e0, e0) = e3 % 131.49/18.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.70 (3) op(e0, e0) = all_8_2 % 131.49/18.70 (4) ~ (all_8_2 = e3) % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | ALPHA: (1) implies: % 131.49/18.70 | (5) op(e0, e0) = e3 % 131.49/18.70 | % 131.49/18.70 | GROUND_INST: instantiating (2) with all_8_2, e3, e0, e0, simplifying with (3), % 131.49/18.70 | (5) gives: % 131.49/18.70 | (6) all_8_2 = e3 % 131.49/18.70 | % 131.49/18.70 | REDUCE: (4), (6) imply: % 131.49/18.70 | (7) $false % 131.49/18.70 | % 131.49/18.70 | CLOSE: (7) is inconsistent. % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #20 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 131.49/18.70 (2) unit = e2 | unit = e1 | unit = e0 % 131.49/18.70 (3) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 131.49/18.70 (4) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) | % 131.49/18.70 (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = % 131.49/18.70 e0) | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 131.49/18.70 e1) = e0)) % 131.49/18.70 (5) ~ (all_8_2 = e3) % 131.49/18.70 (6) ~ (all_53_7 = all_8_2) % 131.49/18.70 (7) all_57_12 = e3 % 131.49/18.70 (8) op(e2, unit) = e2 % 131.49/18.70 (9) ~ (unit = e2) % 131.49/18.70 (10) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 131.49/18.70 (11) ~ (e3 = e0) % 131.49/18.70 (12) op(e0, e3) = e3 % 131.49/18.70 (13) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.70 (14) ~ (all_8_2 = e1) % 131.49/18.70 (15) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.70 (16) all_57_14 = e1 % 131.49/18.70 (17) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 131.49/18.70 (18) ~ (e1 = e0) % 131.49/18.70 (19) all_53_3 = e3 % 131.49/18.70 (20) op(e0, unit) = e0 % 131.49/18.70 (21) all_55_15 = all_8_2 % 131.49/18.70 (22) ~ (all_53_7 = all_53_11) % 131.49/18.70 (23) ~ (all_53_13 = all_8_2) % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | ALPHA: (4) implies: % 131.49/18.70 | (24) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 131.49/18.70 | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.49/18.70 | % 131.49/18.70 | BETA: splitting (24) gives: % 131.49/18.70 | % 131.49/18.70 | Case 1: % 131.49/18.70 | | % 131.49/18.70 | | (25) all_57_12 = e0 & op(e0, e3) = e0 % 131.49/18.70 | | % 131.49/18.70 | | REF_CLOSE: (3), (7), (11), (12), (19), (25) are inconsistent by sub-proof % 131.49/18.70 | | #21. % 131.49/18.70 | | % 131.49/18.70 | Case 2: % 131.49/18.70 | | % 131.49/18.70 | | (26) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 131.49/18.70 | | e0) % 131.49/18.70 | | % 131.49/18.70 | | BETA: splitting (26) gives: % 131.49/18.70 | | % 131.49/18.70 | | Case 1: % 131.49/18.70 | | | % 131.49/18.70 | | | (27) all_57_13 = e0 & op(e0, e2) = e0 % 131.49/18.70 | | | % 131.49/18.70 | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (13), (14), (15), (17), % 131.49/18.70 | | | (20), (21), (22), (23), (27) are inconsistent by sub-proof % 131.49/18.70 | | | #108. % 131.49/18.70 | | | % 131.49/18.70 | | Case 2: % 131.49/18.70 | | | % 131.49/18.70 | | | (28) all_57_14 = e0 & op(e0, e1) = e0 % 131.49/18.70 | | | % 131.49/18.70 | | | REF_CLOSE: (16), (18), (28) are inconsistent by sub-proof #78. % 131.49/18.70 | | | % 131.49/18.70 | | End of split % 131.49/18.70 | | % 131.49/18.70 | End of split % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #21 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 131.49/18.70 (2) all_57_12 = e3 % 131.49/18.70 (3) ~ (e3 = e0) % 131.49/18.70 (4) op(e0, e3) = e3 % 131.49/18.70 (5) all_53_3 = e3 % 131.49/18.70 (6) all_57_12 = e0 & op(e0, e3) = e0 % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | ALPHA: (6) implies: % 131.49/18.70 | (7) all_57_12 = e0 % 131.49/18.70 | % 131.49/18.70 | COMBINE_EQS: (2), (7) imply: % 131.49/18.70 | (8) e3 = e0 % 131.49/18.70 | % 131.49/18.70 | COMBINE_EQS: (5), (8) imply: % 131.49/18.70 | (9) all_53_3 = e0 % 131.49/18.70 | % 131.49/18.70 | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #299. % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #22 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_57_3 = e1 & op(e2, e2) = e1 % 131.49/18.70 (2) all_57_3 = e3 % 131.49/18.70 (3) ~ (e3 = e1) % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | ALPHA: (1) implies: % 131.49/18.70 | (4) all_57_3 = e1 % 131.49/18.70 | % 131.49/18.70 | COMBINE_EQS: (2), (4) imply: % 131.49/18.70 | (5) e3 = e1 % 131.49/18.70 | % 131.49/18.70 | REDUCE: (3), (5) imply: % 131.49/18.70 | (6) $false % 131.49/18.70 | % 131.49/18.70 | CLOSE: (6) is inconsistent. % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #23 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.49/18.70 (2) all_57_12 = e3 % 131.49/18.70 (3) ~ (e3 = e1) % 131.49/18.70 (4) all_57_13 = e3 % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | BETA: splitting (1) gives: % 131.49/18.70 | % 131.49/18.70 | Case 1: % 131.49/18.70 | | % 131.49/18.70 | | (5) all_57_12 = e1 & op(e0, e3) = e1 % 131.49/18.70 | | % 131.49/18.70 | | ALPHA: (5) implies: % 131.49/18.70 | | (6) all_57_12 = e1 % 131.49/18.70 | | % 131.49/18.70 | | COMBINE_EQS: (2), (6) imply: % 131.49/18.70 | | (7) e3 = e1 % 131.49/18.70 | | % 131.49/18.70 | | REDUCE: (3), (7) imply: % 131.49/18.70 | | (8) $false % 131.49/18.70 | | % 131.49/18.70 | | CLOSE: (8) is inconsistent. % 131.49/18.70 | | % 131.49/18.70 | Case 2: % 131.49/18.70 | | % 131.49/18.70 | | (9) all_57_13 = e1 & op(e0, e2) = e1 % 131.49/18.70 | | % 131.49/18.70 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #120. % 131.49/18.70 | | % 131.49/18.70 | End of split % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #24 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_57_2 = e3 & op(e2, e3) = e3 % 131.49/18.70 (2) ~ (op(e2, e3) = e3) % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | ALPHA: (1) implies: % 131.49/18.70 | (3) op(e2, e3) = e3 % 131.49/18.70 | % 131.49/18.70 | PRED_UNIFY: (2), (3) imply: % 131.49/18.70 | (4) $false % 131.49/18.70 | % 131.49/18.70 | CLOSE: (4) is inconsistent. % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #25 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.49/18.70 (2) op(e1, e0) = e1 % 131.49/18.70 (3) all_53_14 = e0 % 131.49/18.70 (4) ~ (e1 = e0) % 131.49/18.70 % 131.49/18.70 Begin of proof % 131.49/18.70 | % 131.49/18.70 | BETA: splitting (1) gives: % 131.49/18.70 | % 131.49/18.70 | Case 1: % 131.49/18.70 | | % 131.49/18.70 | | (5) ~ (op(e1, e0) = e1) % 131.49/18.70 | | % 131.49/18.70 | | PRED_UNIFY: (2), (5) imply: % 131.49/18.70 | | (6) $false % 131.49/18.70 | | % 131.49/18.70 | | CLOSE: (6) is inconsistent. % 131.49/18.70 | | % 131.49/18.70 | Case 2: % 131.49/18.70 | | % 131.49/18.70 | | (7) all_53_14 = e1 % 131.49/18.70 | | % 131.49/18.70 | | COMBINE_EQS: (3), (7) imply: % 131.49/18.70 | | (8) e1 = e0 % 131.49/18.70 | | % 131.49/18.70 | | REDUCE: (4), (8) imply: % 131.49/18.70 | | (9) $false % 131.49/18.70 | | % 131.49/18.70 | | CLOSE: (9) is inconsistent. % 131.49/18.70 | | % 131.49/18.70 | End of split % 131.49/18.70 | % 131.49/18.70 End of proof % 131.49/18.70 % 131.49/18.70 Sub-proof #26 shows that the following formulas are inconsistent: % 131.49/18.70 ---------------------------------------------------------------- % 131.49/18.70 (1) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.49/18.70 (2) ~ (all_53_2 = all_53_3) % 131.49/18.70 (3) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.49/18.70 (4) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 131.49/18.70 (5) unit = e2 | unit = e1 | unit = e0 % 131.49/18.70 (6) ~ (all_53_3 = all_53_7) % 131.49/18.70 (7) op(unit, e0) = e0 % 131.49/18.70 (8) all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 131.49/18.70 (9) ~ (all_8_2 = e3) % 131.49/18.70 (10) all_22_2 = all_12_2 % 131.49/18.70 (11) ~ (all_53_3 = all_8_2) % 131.49/18.70 (12) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.49/18.70 (13) ~ (all_53_7 = all_8_2) % 131.49/18.70 (14) ~ (all_53_14 = all_8_2) % 131.49/18.70 (15) ~ (all_53_11 = all_8_2) % 131.49/18.70 (16) ~ (all_53_6 = all_53_7) % 131.49/18.70 (17) ~ (all_53_6 = all_53_14) % 131.49/18.70 (18) all_55_9 = all_53_6 % 131.49/18.70 (19) op(e0, e3) = all_53_3 % 131.49/18.70 (20) ~ (all_12_2 = e2) % 131.49/18.70 (21) ~ (unit = e2) % 131.49/18.70 (22) op(unit, e2) = e2 % 131.49/18.70 (23) ~ (all_53_11 = all_12_2) % 131.49/18.70 (24) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 131.49/18.70 (25) ~ (all_53_6 = e3) % 131.49/18.70 (26) op(e0, e2) = all_53_7 % 131.49/18.70 (27) all_36_2 = all_8_2 % 131.49/18.70 (28) ~ (all_53_13 = all_53_14) % 131.49/18.70 (29) ~ (all_53_14 = all_12_2) % 131.49/18.70 (30) ~ (all_28_2 = e2) | (op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 131.49/18.70 (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 131.49/18.70 $i(all_28_0)))) % 131.49/18.70 (31) all_55_8 = e3 | ~ (op(e1, e3) = e3) % 131.49/18.70 (32) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 131.49/18.70 (33) ~ (all_12_2 = e3) % 131.49/18.70 (34) ~ (all_8_2 = e1) % 131.49/18.70 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.70 (36) all_55_11 = all_53_14 % 131.49/18.70 (37) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.49/18.70 (38) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.70 (39) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.70 (40) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 131.49/18.70 (41) ~ (all_36_2 = e2) | (op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ % 131.49/18.70 (all_36_1 = e3) | ( ~ (all_36_0 = e1) & op(e0, e3) = all_36_0 & % 131.49/18.70 $i(all_36_0)))) % 131.49/18.70 (42) all_55_8 = all_53_2 % 131.49/18.70 (43) ~ (all_53_2 = all_53_14) % 131.49/18.70 (44) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 131.49/18.70 (45) op(e1, unit) = e1 % 131.49/18.70 (46) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 131.49/18.70 (47) op(e0, unit) = e0 % 131.49/18.70 (48) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 131.49/18.70 (49) all_55_15 = all_8_2 % 131.49/18.70 (50) ~ (all_53_7 = all_53_11) % 131.49/18.71 (51) ~ (all_53_7 = e3) % 131.49/18.71 (52) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 131.49/18.71 (53) ~ (all_53_9 = all_12_2) % 131.49/18.71 (54) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 131.49/18.71 (55) all_28_2 = all_8_2 % 131.49/18.71 (56) all_55_13 = all_53_7 % 131.49/18.71 (57) ~ (all_22_2 = e0) | (op(e1, e0) = all_22_1 & $i(all_22_1) & ( ~ % 131.49/18.71 (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 131.49/18.71 $i(all_22_0)))) % 131.49/18.71 (58) op(unit, e3) = e3 % 131.49/18.71 (59) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.71 (60) op(unit, e1) = e1 % 131.49/18.71 (61) all_55_12 = all_53_3 % 131.49/18.71 (62) all_55_10 = all_12_2 % 131.49/18.71 (63) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 131.49/18.71 (64) ~ (all_53_6 = all_12_2) % 131.49/18.71 (65) ~ (all_53_3 = all_53_11) % 131.49/18.71 % 131.49/18.71 Begin of proof % 131.49/18.71 | % 131.49/18.71 | BETA: splitting (57) gives: % 131.49/18.71 | % 131.49/18.71 | Case 1: % 131.49/18.71 | | % 131.49/18.71 | | (66) ~ (all_22_2 = e0) % 131.49/18.71 | | % 131.49/18.71 | | REDUCE: (10), (66) imply: % 131.49/18.71 | | (67) ~ (all_12_2 = e0) % 131.49/18.71 | | % 131.49/18.71 | | BETA: splitting (8) gives: % 131.49/18.71 | | % 131.49/18.71 | | Case 1: % 131.49/18.71 | | | % 131.49/18.71 | | | (68) all_55_10 = e3 % 131.49/18.71 | | | % 131.49/18.71 | | | REF_CLOSE: (33), (62), (68) are inconsistent by sub-proof #282. % 131.49/18.71 | | | % 131.49/18.71 | | Case 2: % 131.49/18.71 | | | % 131.49/18.71 | | | (69) all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0 % 131.49/18.71 | | | % 131.49/18.71 | | | BETA: splitting (69) gives: % 131.49/18.71 | | | % 131.49/18.71 | | | Case 1: % 131.49/18.71 | | | | % 131.49/18.71 | | | | (70) all_55_10 = e2 % 131.49/18.71 | | | | % 131.49/18.71 | | | | REF_CLOSE: (20), (62), (70) are inconsistent by sub-proof #281. % 131.49/18.71 | | | | % 131.49/18.71 | | | Case 2: % 131.49/18.71 | | | | % 131.49/18.71 | | | | (71) all_55_10 = e1 | all_55_10 = e0 % 131.49/18.71 | | | | % 131.49/18.71 | | | | BETA: splitting (71) gives: % 131.49/18.71 | | | | % 131.49/18.71 | | | | Case 1: % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | (72) all_55_10 = e1 % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | COMBINE_EQS: (62), (72) imply: % 131.49/18.71 | | | | | (73) all_12_2 = e1 % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | SIMP: (73) implies: % 131.49/18.71 | | | | | (74) all_12_2 = e1 % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | REDUCE: (53), (74) imply: % 131.49/18.71 | | | | | (75) ~ (all_53_9 = e1) % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | REDUCE: (23), (74) imply: % 131.49/18.71 | | | | | (76) ~ (all_53_11 = e1) % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | REDUCE: (29), (74) imply: % 131.49/18.71 | | | | | (77) ~ (all_53_14 = e1) % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | BETA: splitting (30) gives: % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | Case 1: % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | (78) ~ (all_28_2 = e2) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | REDUCE: (55), (78) imply: % 131.49/18.71 | | | | | | (79) ~ (all_8_2 = e2) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | REF_CLOSE: (5), (9), (15), (24), (34), (38), (39), (46), (47), (49), % 131.49/18.71 | | | | | | (59), (60), (75), (76), (79) are inconsistent by % 131.49/18.71 | | | | | | sub-proof #28. % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | Case 2: % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | (80) all_28_2 = e2 % 131.49/18.71 | | | | | | (81) op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e1) | % 131.49/18.71 | | | | | | ( ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 131.49/18.71 | | | | | | $i(all_28_0))) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | ALPHA: (81) implies: % 131.49/18.71 | | | | | | (82) op(e0, e2) = all_28_1 % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | COMBINE_EQS: (55), (80) imply: % 131.49/18.71 | | | | | | (83) all_8_2 = e2 % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | SIMP: (83) implies: % 131.49/18.71 | | | | | | (84) all_8_2 = e2 % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | COMBINE_EQS: (27), (84) imply: % 131.49/18.71 | | | | | | (85) all_36_2 = e2 % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | REDUCE: (11), (84) imply: % 131.49/18.71 | | | | | | (86) ~ (all_53_3 = e2) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | REDUCE: (13), (84) imply: % 131.49/18.71 | | | | | | (87) ~ (all_53_7 = e2) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | REDUCE: (14), (84) imply: % 131.49/18.71 | | | | | | (88) ~ (all_53_14 = e2) % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | BETA: splitting (41) gives: % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | | Case 1: % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | (89) ~ (all_36_2 = e2) % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | REDUCE: (85), (89) imply: % 131.49/18.71 | | | | | | | (90) $false % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | CLOSE: (90) is inconsistent. % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | Case 2: % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | (91) op(e0, e2) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e3) % 131.49/18.71 | | | | | | | | ( ~ (all_36_0 = e1) & op(e0, e3) = all_36_0 & % 131.49/18.71 | | | | | | | $i(all_36_0))) % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | ALPHA: (91) implies: % 131.49/18.71 | | | | | | | (92) op(e0, e2) = all_36_1 % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | BETA: splitting (44) gives: % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | (93) ~ (op(e0, e2) = e2) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | GROUND_INST: instantiating (35) with all_53_7, all_28_1, e2, e0, % 131.49/18.71 | | | | | | | | simplifying with (26), (82) gives: % 131.49/18.71 | | | | | | | | (94) all_53_7 = all_28_1 % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | GROUND_INST: instantiating (35) with all_53_7, all_36_1, e2, e0, % 131.49/18.71 | | | | | | | | simplifying with (26), (92) gives: % 131.49/18.71 | | | | | | | | (95) all_53_7 = all_36_1 % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | PRED_UNIFY: (22), (93) imply: % 131.49/18.71 | | | | | | | | (96) ~ (unit = e0) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | PRED_UNIFY: (92), (93) imply: % 131.49/18.71 | | | | | | | | (97) ~ (all_36_1 = e2) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | COMBINE_EQS: (94), (95) imply: % 131.49/18.71 | | | | | | | | (98) all_36_1 = all_28_1 % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | COMBINE_EQS: (56), (94) imply: % 131.49/18.71 | | | | | | | | (99) all_55_13 = all_28_1 % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | REDUCE: (6), (94) imply: % 131.49/18.71 | | | | | | | | (100) ~ (all_53_3 = all_28_1) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | REDUCE: (50), (94) imply: % 131.49/18.71 | | | | | | | | (101) ~ (all_53_11 = all_28_1) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | SIMP: (101) implies: % 131.49/18.71 | | | | | | | | (102) ~ (all_53_11 = all_28_1) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | REDUCE: (51), (94) imply: % 131.49/18.71 | | | | | | | | (103) ~ (all_28_1 = e3) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | REDUCE: (97), (98) imply: % 131.49/18.71 | | | | | | | | (104) ~ (all_28_1 = e2) % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | BETA: splitting (5) gives: % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | (105) unit = e2 % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | REDUCE: (21), (105) imply: % 131.49/18.71 | | | | | | | | | (106) $false % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | CLOSE: (106) is inconsistent. % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | (107) unit = e1 | unit = e0 % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | BETA: splitting (107) gives: % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | (108) unit = e1 % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | REDUCE: (58), (108) imply: % 131.49/18.71 | | | | | | | | | | (109) op(e1, e3) = e3 % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | REDUCE: (47), (108) imply: % 131.49/18.71 | | | | | | | | | | (110) op(e0, e1) = e0 % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | BETA: splitting (31) gives: % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | (111) ~ (op(e1, e3) = e3) % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | PRED_UNIFY: (109), (111) imply: % 131.49/18.71 | | | | | | | | | | | (112) $false % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | CLOSE: (112) is inconsistent. % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | (113) all_55_8 = e3 % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | COMBINE_EQS: (42), (113) imply: % 131.49/18.71 | | | | | | | | | | | (114) all_53_2 = e3 % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | SIMP: (114) implies: % 131.49/18.71 | | | | | | | | | | | (115) all_53_2 = e3 % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | REDUCE: (43), (115) imply: % 131.49/18.71 | | | | | | | | | | | (116) ~ (all_53_14 = e3) % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | SIMP: (116) implies: % 131.49/18.71 | | | | | | | | | | | (117) ~ (all_53_14 = e3) % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | BETA: splitting (39) gives: % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | (118) ~ (op(e0, e1) = e0) % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | PRED_UNIFY: (110), (118) imply: % 131.49/18.71 | | | | | | | | | | | | (119) $false % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | (120) all_53_11 = e0 % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | REDUCE: (65), (120) imply: % 131.49/18.71 | | | | | | | | | | | | (121) ~ (all_53_3 = e0) % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | REDUCE: (102), (120) imply: % 131.49/18.71 | | | | | | | | | | | | (122) ~ (all_28_1 = e0) % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | SIMP: (122) implies: % 131.49/18.71 | | | | | | | | | | | | (123) ~ (all_28_1 = e0) % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | BETA: splitting (32) gives: % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | (124) all_55_11 = e3 % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | COMBINE_EQS: (36), (124) imply: % 131.49/18.71 | | | | | | | | | | | | | (125) all_53_14 = e3 % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | REDUCE: (117), (125) imply: % 131.49/18.71 | | | | | | | | | | | | | (126) $false % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | (127) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | BETA: splitting (127) gives: % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | (128) all_55_11 = e2 % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | COMBINE_EQS: (36), (128) imply: % 131.49/18.71 | | | | | | | | | | | | | | (129) all_53_14 = e2 % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | REDUCE: (88), (129) imply: % 131.49/18.71 | | | | | | | | | | | | | | (130) $false % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | (131) all_55_11 = e1 | all_55_11 = e0 % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | BETA: splitting (131) gives: % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | (132) all_55_11 = e1 % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | REF_CLOSE: (36), (77), (132) are inconsistent by sub-proof % 131.49/18.71 | | | | | | | | | | | | | | | #27. % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | (133) all_55_11 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | COMBINE_EQS: (36), (133) imply: % 131.49/18.71 | | | | | | | | | | | | | | | (134) all_53_14 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | SIMP: (134) implies: % 131.49/18.71 | | | | | | | | | | | | | | | (135) all_53_14 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | REDUCE: (28), (135) imply: % 131.49/18.71 | | | | | | | | | | | | | | | (136) ~ (all_53_13 = e0) % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | (137) all_55_13 = e3 % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (137) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | (138) all_28_1 = e3 % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | SIMP: (138) implies: % 131.49/18.71 | | | | | | | | | | | | | | | | (139) all_28_1 = e3 % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | REDUCE: (103), (139) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | (140) $false % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | (141) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | (142) all_55_13 = e2 % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (142) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | (143) all_28_1 = e2 % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | SIMP: (143) implies: % 131.49/18.71 | | | | | | | | | | | | | | | | | (144) all_28_1 = e2 % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | REDUCE: (104), (144) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | (145) $false % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | (146) all_55_13 = e1 | all_55_13 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | (147) all_55_13 = e1 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (147) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (148) all_28_1 = e1 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | SIMP: (148) implies: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (149) all_28_1 = e1 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | REDUCE: (100), (149) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (150) ~ (all_53_3 = e1) % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (12), (19), (37), (40), % 131.49/18.71 | | | | | | | | | | | | | | | | | | (45), (48), (58), (61), (77), (86), (121), (136), % 131.49/18.71 | | | | | | | | | | | | | | | | | | (150) are inconsistent by sub-proof #140. % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | (151) all_55_13 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (151) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (152) all_28_1 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | SIMP: (152) implies: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (153) all_28_1 = e0 % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | REDUCE: (123), (153) imply: % 131.49/18.71 | | | | | | | | | | | | | | | | | | (154) $false % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 131.49/18.71 | | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | (155) ~ (unit = e1) % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | | REF_CLOSE: (96), (107), (155) are inconsistent by sub-proof % 131.49/18.71 | | | | | | | | | | #278. % 131.49/18.71 | | | | | | | | | | % 131.49/18.71 | | | | | | | | | End of split % 131.49/18.71 | | | | | | | | | % 131.49/18.71 | | | | | | | | End of split % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | Case 2: % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | (156) op(e0, e2) = e2 % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | | REF_CLOSE: (56), (63), (87), (156) are inconsistent by sub-proof % 131.49/18.71 | | | | | | | | #118. % 131.49/18.71 | | | | | | | | % 131.49/18.71 | | | | | | | End of split % 131.49/18.71 | | | | | | | % 131.49/18.71 | | | | | | End of split % 131.49/18.71 | | | | | | % 131.49/18.71 | | | | | End of split % 131.49/18.71 | | | | | % 131.49/18.71 | | | | Case 2: % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | (157) all_55_10 = e0 % 131.49/18.71 | | | | | % 131.49/18.71 | | | | | REF_CLOSE: (62), (67), (157) are inconsistent by sub-proof #219. % 131.49/18.71 | | | | | % 131.49/18.71 | | | | End of split % 131.49/18.71 | | | | % 131.49/18.71 | | | End of split % 131.49/18.71 | | | % 131.49/18.71 | | End of split % 131.49/18.71 | | % 131.49/18.71 | Case 2: % 131.49/18.71 | | % 131.49/18.71 | | (158) all_22_2 = e0 % 131.49/18.71 | | % 131.49/18.71 | | COMBINE_EQS: (10), (158) imply: % 131.49/18.71 | | (159) all_12_2 = e0 % 131.49/18.71 | | % 131.49/18.71 | | SIMP: (159) implies: % 131.49/18.71 | | (160) all_12_2 = e0 % 131.49/18.71 | | % 131.49/18.71 | | REDUCE: (64), (160) imply: % 131.49/18.71 | | (161) ~ (all_53_6 = e0) % 131.49/18.71 | | % 131.49/18.71 | | REDUCE: (29), (160) imply: % 131.49/18.71 | | (162) ~ (all_53_14 = e0) % 131.49/18.71 | | % 131.49/18.71 | | BETA: splitting (54) gives: % 131.49/18.71 | | % 131.49/18.71 | | Case 1: % 131.49/18.71 | | | % 131.49/18.71 | | | (163) ~ (op(e1, e0) = e0) % 131.49/18.71 | | | % 131.49/18.71 | | | PRED_UNIFY: (7), (163) imply: % 131.49/18.71 | | | (164) ~ (unit = e1) % 131.49/18.71 | | | % 131.49/18.71 | | | REF_CLOSE: (3), (5), (16), (17), (18), (21), (22), (25), (44), (45), (52), % 131.49/18.71 | | | (161), (164) are inconsistent by sub-proof #176. % 131.49/18.71 | | | % 131.49/18.71 | | Case 2: % 131.49/18.71 | | | % 131.49/18.71 | | | (165) op(e1, e0) = e0 % 131.49/18.71 | | | % 131.49/18.71 | | | REF_CLOSE: (54), (162), (165) are inconsistent by sub-proof #355. % 131.49/18.71 | | | % 131.49/18.71 | | End of split % 131.49/18.71 | | % 131.49/18.71 | End of split % 131.49/18.71 | % 131.49/18.71 End of proof % 131.49/18.71 % 131.49/18.71 Sub-proof #27 shows that the following formulas are inconsistent: % 131.49/18.71 ---------------------------------------------------------------- % 131.49/18.71 (1) all_55_11 = all_53_14 % 131.49/18.71 (2) all_55_11 = e1 % 131.49/18.71 (3) ~ (all_53_14 = e1) % 131.49/18.71 % 131.49/18.71 Begin of proof % 131.49/18.71 | % 131.49/18.71 | COMBINE_EQS: (1), (2) imply: % 131.49/18.71 | (4) all_53_14 = e1 % 131.49/18.71 | % 131.49/18.71 | SIMP: (4) implies: % 131.49/18.71 | (5) all_53_14 = e1 % 131.49/18.71 | % 131.49/18.71 | REDUCE: (3), (5) imply: % 131.49/18.71 | (6) $false % 131.49/18.71 | % 131.49/18.71 | CLOSE: (6) is inconsistent. % 131.49/18.71 | % 131.49/18.71 End of proof % 131.49/18.71 % 131.49/18.71 Sub-proof #28 shows that the following formulas are inconsistent: % 131.49/18.71 ---------------------------------------------------------------- % 131.49/18.71 (1) unit = e2 | unit = e1 | unit = e0 % 131.49/18.71 (2) ~ (all_8_2 = e3) % 131.49/18.72 (3) ~ (all_53_11 = all_8_2) % 131.49/18.72 (4) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 131.49/18.72 (5) ~ (all_8_2 = e1) % 131.49/18.72 (6) ~ (all_8_2 = e2) % 131.49/18.72 (7) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.72 (8) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.72 (9) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 131.49/18.72 (10) op(e0, unit) = e0 % 131.49/18.72 (11) all_55_15 = all_8_2 % 131.49/18.72 (12) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.72 (13) op(unit, e1) = e1 % 131.49/18.72 (14) ~ (all_53_11 = e1) % 131.49/18.72 (15) ~ (all_53_9 = e1) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | BETA: splitting (4) gives: % 131.49/18.72 | % 131.49/18.72 | Case 1: % 131.49/18.72 | | % 131.49/18.72 | | (16) all_55_15 = e3 % 131.49/18.72 | | % 131.49/18.72 | | COMBINE_EQS: (11), (16) imply: % 131.49/18.72 | | (17) all_8_2 = e3 % 131.49/18.72 | | % 131.49/18.72 | | REDUCE: (2), (17) imply: % 131.49/18.72 | | (18) $false % 131.49/18.72 | | % 131.49/18.72 | | CLOSE: (18) is inconsistent. % 131.49/18.72 | | % 131.49/18.72 | Case 2: % 131.49/18.72 | | % 131.49/18.72 | | (19) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 131.49/18.72 | | % 131.49/18.72 | | BETA: splitting (19) gives: % 131.49/18.72 | | % 131.49/18.72 | | Case 1: % 131.49/18.72 | | | % 131.49/18.72 | | | (20) all_55_15 = e2 % 131.49/18.72 | | | % 131.49/18.72 | | | COMBINE_EQS: (11), (20) imply: % 131.49/18.72 | | | (21) all_8_2 = e2 % 131.49/18.72 | | | % 131.49/18.72 | | | REDUCE: (6), (21) imply: % 131.49/18.72 | | | (22) $false % 131.49/18.72 | | | % 131.49/18.72 | | | CLOSE: (22) is inconsistent. % 131.49/18.72 | | | % 131.49/18.72 | | Case 2: % 131.49/18.72 | | | % 131.49/18.72 | | | (23) all_55_15 = e1 | all_55_15 = e0 % 131.49/18.72 | | | % 131.49/18.72 | | | BETA: splitting (23) gives: % 131.49/18.72 | | | % 131.49/18.72 | | | Case 1: % 131.49/18.72 | | | | % 131.49/18.72 | | | | (24) all_55_15 = e1 % 131.49/18.72 | | | | % 131.49/18.72 | | | | COMBINE_EQS: (11), (24) imply: % 131.49/18.72 | | | | (25) all_8_2 = e1 % 131.49/18.72 | | | | % 131.49/18.72 | | | | REDUCE: (5), (25) imply: % 131.49/18.72 | | | | (26) $false % 131.49/18.72 | | | | % 131.49/18.72 | | | | CLOSE: (26) is inconsistent. % 131.49/18.72 | | | | % 131.49/18.72 | | | Case 2: % 131.49/18.72 | | | | % 131.49/18.72 | | | | (27) all_55_15 = e0 % 131.49/18.72 | | | | % 131.49/18.72 | | | | COMBINE_EQS: (11), (27) imply: % 131.49/18.72 | | | | (28) all_8_2 = e0 % 131.49/18.72 | | | | % 131.49/18.72 | | | | REDUCE: (3), (28) imply: % 131.49/18.72 | | | | (29) ~ (all_53_11 = e0) % 131.49/18.72 | | | | % 131.49/18.72 | | | | BETA: splitting (9) gives: % 131.49/18.72 | | | | % 131.49/18.72 | | | | Case 1: % 131.49/18.72 | | | | | % 131.49/18.72 | | | | | (30) ~ (op(e0, e1) = e1) % 131.49/18.72 | | | | | % 131.49/18.72 | | | | | PRED_UNIFY: (13), (30) imply: % 131.49/18.72 | | | | | (31) ~ (unit = e0) % 131.49/18.72 | | | | | % 131.49/18.72 | | | | | REF_CLOSE: (1), (7), (8), (10), (12), (13), (15), (29), (31) are % 131.49/18.72 | | | | | inconsistent by sub-proof #242. % 131.49/18.72 | | | | | % 131.49/18.72 | | | | Case 2: % 131.49/18.72 | | | | | % 131.49/18.72 | | | | | (32) op(e0, e1) = e1 % 131.49/18.72 | | | | | % 131.49/18.72 | | | | | REF_CLOSE: (9), (14), (32) are inconsistent by sub-proof #333. % 131.49/18.72 | | | | | % 131.49/18.72 | | | | End of split % 131.49/18.72 | | | | % 131.49/18.72 | | | End of split % 131.49/18.72 | | | % 131.49/18.72 | | End of split % 131.49/18.72 | | % 131.49/18.72 | End of split % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #29 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.49/18.72 (2) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) % 131.49/18.72 (3) ~ (all_53_2 = all_12_2) % 131.49/18.72 (4) all_55_9 = all_53_6 % 131.49/18.72 (5) ~ (all_53_2 = e0) % 131.49/18.72 (6) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 131.49/18.72 (7) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 131.49/18.72 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 131.49/18.72 (8) ~ (all_53_2 = e2) % 131.49/18.72 (9) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 131.49/18.72 (10) all_55_8 = all_53_2 % 131.49/18.72 (11) ~ (all_53_2 = all_53_14) % 131.49/18.72 (12) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 131.49/18.72 (13) ~ (all_53_2 = all_53_6) % 131.49/18.72 (14) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.49/18.72 (15) ~ (all_53_6 = e2) % 131.49/18.72 (16) ~ (all_53_2 = e3) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | BETA: splitting (2) gives: % 131.49/18.72 | % 131.49/18.72 | Case 1: % 131.49/18.72 | | % 131.49/18.72 | | (17) all_57_6 = e2 & op(e1, e3) = e2 % 131.49/18.72 | | % 131.49/18.72 | | ALPHA: (17) implies: % 131.49/18.72 | | (18) all_57_6 = e2 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14), % 131.49/18.72 | | (16), (18) are inconsistent by sub-proof #105. % 131.49/18.72 | | % 131.49/18.72 | Case 2: % 131.49/18.72 | | % 131.49/18.72 | | (19) all_57_7 = e2 & op(e1, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | ALPHA: (19) implies: % 131.49/18.72 | | (20) op(e1, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (6), (15), (20) are inconsistent by sub-proof #326. % 131.49/18.72 | | % 131.49/18.72 | End of split % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #30 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 131.49/18.72 (2) ~ (all_53_7 = e2) % 131.49/18.72 (3) ~ (all_53_6 = e2) % 131.49/18.72 (4) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.49/18.72 (5) all_55_13 = all_53_7 % 131.49/18.72 (6) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | BETA: splitting (4) gives: % 131.49/18.72 | % 131.49/18.72 | Case 1: % 131.49/18.72 | | % 131.49/18.72 | | (7) all_57_7 = e2 & op(e1, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | ALPHA: (7) implies: % 131.49/18.72 | | (8) op(e1, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #326. % 131.49/18.72 | | % 131.49/18.72 | Case 2: % 131.49/18.72 | | % 131.49/18.72 | | (9) all_57_13 = e2 & op(e0, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | ALPHA: (9) implies: % 131.49/18.72 | | (10) op(e0, e2) = e2 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #118. % 131.49/18.72 | | % 131.49/18.72 | End of split % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #31 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 131.49/18.72 (2) op(e3, e3) = e3 % 131.49/18.72 (3) all_4_2 = e3 % 131.49/18.72 (4) all_57_3 = e3 % 131.49/18.72 (5) all_57_3 = e2 & op(e2, e2) = e2 % 131.49/18.72 (6) ~ (e3 = e2) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | ALPHA: (5) implies: % 131.49/18.72 | (7) all_57_3 = e2 % 131.49/18.72 | % 131.49/18.72 | COMBINE_EQS: (4), (7) imply: % 131.49/18.72 | (8) e3 = e2 % 131.49/18.72 | % 131.49/18.72 | SIMP: (8) implies: % 131.49/18.72 | (9) e3 = e2 % 131.49/18.72 | % 131.49/18.72 | COMBINE_EQS: (3), (9) imply: % 131.49/18.72 | (10) all_4_2 = e2 % 131.49/18.72 | % 131.49/18.72 | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #315. % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #32 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) ~ (all_53_1 = e3) % 131.49/18.72 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 131.49/18.72 (3) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 131.49/18.72 (4) all_53_3 = e0 % 131.49/18.72 (5) ~ (e3 = e0) % 131.49/18.72 (6) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 131.49/18.72 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 131.49/18.72 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 131.49/18.72 (8) all_57_0 = e0 % 131.49/18.72 (9) ~ (all_53_2 = e3) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | BETA: splitting (7) gives: % 131.49/18.72 | % 131.49/18.72 | Case 1: % 131.49/18.72 | | % 131.49/18.72 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 131.49/18.72 | | e3) % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (1), (5), (6), (8), (10) are inconsistent by sub-proof #33. % 131.49/18.72 | | % 131.49/18.72 | Case 2: % 131.49/18.72 | | % 131.49/18.72 | | (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 131.49/18.72 | | e3) % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (2), (3), (4), (5), (9), (11) are inconsistent by sub-proof #298. % 131.49/18.72 | | % 131.49/18.72 | End of split % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #33 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) ~ (all_53_1 = e3) % 131.49/18.72 (2) ~ (e3 = e0) % 131.49/18.72 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 131.49/18.72 (4) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 131.49/18.72 (5) all_57_0 = e0 % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | BETA: splitting (3) gives: % 131.49/18.72 | % 131.49/18.72 | Case 1: % 131.49/18.72 | | % 131.49/18.72 | | (6) all_57_0 = e3 & op(e3, e3) = e3 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #34. % 131.49/18.72 | | % 131.49/18.72 | Case 2: % 131.49/18.72 | | % 131.49/18.72 | | (7) all_57_2 = e3 & op(e2, e3) = e3 % 131.49/18.72 | | % 131.49/18.72 | | ALPHA: (7) implies: % 131.49/18.72 | | (8) op(e2, e3) = e3 % 131.49/18.72 | | % 131.49/18.72 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #353. % 131.49/18.72 | | % 131.49/18.72 | End of split % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #34 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) all_57_0 = e3 & op(e3, e3) = e3 % 131.49/18.72 (2) all_57_0 = e0 % 131.49/18.72 (3) ~ (e3 = e0) % 131.49/18.72 % 131.49/18.72 Begin of proof % 131.49/18.72 | % 131.49/18.72 | ALPHA: (1) implies: % 131.49/18.72 | (4) all_57_0 = e3 % 131.49/18.72 | % 131.49/18.72 | COMBINE_EQS: (2), (4) imply: % 131.49/18.72 | (5) e3 = e0 % 131.49/18.72 | % 131.49/18.72 | SIMP: (5) implies: % 131.49/18.72 | (6) e3 = e0 % 131.49/18.72 | % 131.49/18.72 | REDUCE: (3), (6) imply: % 131.49/18.72 | (7) $false % 131.49/18.72 | % 131.49/18.72 | CLOSE: (7) is inconsistent. % 131.49/18.72 | % 131.49/18.72 End of proof % 131.49/18.72 % 131.49/18.72 Sub-proof #35 shows that the following formulas are inconsistent: % 131.49/18.72 ---------------------------------------------------------------- % 131.49/18.72 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.49/18.72 (2) ~ (unit = e0) % 131.49/18.72 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 131.49/18.72 (4) unit = e2 | unit = e1 | unit = e0 % 131.49/18.72 (5) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 131.49/18.72 (6) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 131.49/18.72 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 131.49/18.72 (7) all_55_14 = all_8_1 % 131.49/18.72 (8) ~ (all_8_1 = e2) % 131.49/18.72 (9) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.49/18.72 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 131.49/18.72 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.49/18.73 (11) ~ (all_53_6 = all_53_7) % 131.49/18.73 (12) ~ (op(e0, e1) = e1) % 131.49/18.73 (13) all_57_15 = e1 % 131.49/18.73 (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 131.49/18.73 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 131.49/18.73 (15) op(e2, unit) = e2 % 131.49/18.73 (16) ~ (all_53_6 = all_53_14) % 131.49/18.73 (17) ~ (all_53_7 = all_8_1) % 131.49/18.73 (18) all_12_2 = e2 % 131.49/18.73 (19) op(unit, e2) = e2 % 131.49/18.73 (20) all_30_2 = e2 % 131.49/18.73 (21) all_20_1 = all_8_1 % 131.49/18.73 (22) all_53_5 = e2 | ~ (op(e2, e2) = e2) % 131.49/18.73 (23) ~ (all_53_8 = all_53_9) % 131.49/18.73 (24) ~ (e3 = e0) % 131.49/18.73 (25) ~ (e2 = e0) % 131.49/18.73 (26) op(e1, e2) = all_53_6 % 131.49/18.73 (27) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 131.49/18.73 (28) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 131.49/18.73 (29) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.49/18.73 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.49/18.73 e2) % 131.49/18.73 (30) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 131.49/18.73 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 131.49/18.73 (31) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 131.49/18.73 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.49/18.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.49/18.73 (33) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 131.49/18.73 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 131.49/18.73 (34) ~ (e3 = e1) % 131.49/18.73 (35) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 131.49/18.73 (36) ~ (all_53_1 = all_53_2) % 131.49/18.73 (37) ~ (all_53_7 = all_6_2) % 131.49/18.73 (38) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 131.49/18.73 (39) op(e1, e1) = e2 % 131.49/18.73 (40) ~ (all_20_1 = e3) | ( ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 & % 131.49/18.73 $i(all_20_0)) % 131.49/18.73 (41) op(e0, e1) = all_8_1 % 131.49/18.73 (42) ~ (e2 = e1) % 131.49/18.73 (43) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 131.49/18.73 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 131.49/18.73 (44) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 131.49/18.73 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 131.49/18.73 (45) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 131.49/18.73 (46) ~ (e1 = e0) % 131.49/18.73 (47) op(e1, unit) = e1 % 131.49/18.73 (48) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 131.49/18.73 (49) ~ (all_53_9 = e2) % 131.49/18.73 (50) ~ (all_53_2 = all_53_6) % 131.49/18.73 (51) op(e0, unit) = e0 % 131.49/18.73 (52) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 131.49/18.73 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 131.49/18.73 (53) ~ (all_53_6 = e2) % 131.49/18.73 (54) ~ (all_30_2 = e2) | (op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ % 131.49/18.73 (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e1, e0) = all_30_0 & % 131.49/18.73 $i(all_30_0)))) % 131.49/18.73 (55) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 131.49/18.73 (56) ~ (e3 = e2) % 131.49/18.73 (57) all_55_13 = all_53_7 % 131.49/18.73 (58) ~ (all_53_6 = all_6_2) % 131.49/18.73 (59) op(unit, e3) = e3 % 131.49/18.73 (60) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.49/18.73 (61) op(unit, e1) = e1 % 131.49/18.73 (62) ~ (all_53_9 = all_8_1) % 131.49/18.73 (63) op(e1, e2) = all_12_1 % 131.49/18.73 (64) all_53_5 = all_6_2 % 131.49/18.73 % 131.49/18.73 Begin of proof % 131.49/18.73 | % 131.49/18.73 | BETA: splitting (28) gives: % 131.49/18.73 | % 131.49/18.73 | Case 1: % 131.49/18.73 | | % 131.49/18.73 | | (65) ~ (op(e1, e2) = e2) % 131.49/18.73 | | % 131.49/18.73 | | BETA: splitting (54) gives: % 131.49/18.73 | | % 131.49/18.73 | | Case 1: % 131.49/18.73 | | | % 131.49/18.73 | | | (66) ~ (all_30_2 = e2) % 131.49/18.73 | | | % 131.49/18.73 | | | REDUCE: (20), (66) imply: % 131.49/18.73 | | | (67) $false % 131.49/18.73 | | | % 131.49/18.73 | | | CLOSE: (67) is inconsistent. % 131.49/18.73 | | | % 131.49/18.73 | | Case 2: % 131.49/18.73 | | | % 131.49/18.73 | | | (68) op(e1, e2) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 = e0) | ( ~ % 131.49/18.73 | | | (all_30_0 = e3) & op(e1, e0) = all_30_0 & $i(all_30_0))) % 131.49/18.73 | | | % 131.49/18.73 | | | ALPHA: (68) implies: % 131.49/18.73 | | | (69) op(e1, e2) = all_30_1 % 131.49/18.73 | | | % 131.49/18.73 | | | BETA: splitting (43) gives: % 131.49/18.73 | | | % 131.49/18.73 | | | Case 1: % 131.49/18.73 | | | | % 131.49/18.73 | | | | (70) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) % 131.49/18.73 | | | | = e2) % 131.49/18.73 | | | | % 131.49/18.73 | | | | BETA: splitting (70) gives: % 131.49/18.73 | | | | % 131.49/18.73 | | | | Case 1: % 131.49/18.73 | | | | | % 131.49/18.73 | | | | | (71) all_57_4 = e2 & op(e3, e1) = e2 % 131.49/18.73 | | | | | % 131.49/18.73 | | | | | ALPHA: (71) implies: % 131.49/18.73 | | | | | (72) all_57_4 = e2 % 131.49/18.73 | | | | | % 131.49/18.73 | | | | | BETA: splitting (33) gives: % 131.49/18.73 | | | | | % 131.49/18.73 | | | | | Case 1: % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | (73) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, % 131.49/18.73 | | | | | | e1) = e1) % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | BETA: splitting (73) gives: % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | Case 1: % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | (74) all_57_4 = e1 & op(e3, e1) = e1 % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | REF_CLOSE: (42), (72), (74) are inconsistent by sub-proof #288. % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | Case 2: % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | (75) all_57_5 = e1 & op(e2, e1) = e1 % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | ALPHA: (75) implies: % 131.49/18.73 | | | | | | | (76) all_57_5 = e1 % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | BETA: splitting (10) gives: % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | (77) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & % 131.49/18.73 | | | | | | | | op(e2, e1) = e0) % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | BETA: splitting (77) gives: % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | (78) all_57_4 = e0 & op(e3, e1) = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | REF_CLOSE: (25), (72), (78) are inconsistent by sub-proof % 131.49/18.73 | | | | | | | | | #162. % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | (79) all_57_5 = e0 & op(e2, e1) = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | REF_CLOSE: (46), (76), (79) are inconsistent by sub-proof #40. % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | End of split % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | (80) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & % 131.49/18.73 | | | | | | | | op(e0, e1) = e0) % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | BETA: splitting (80) gives: % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | (81) all_57_8 = e0 & op(e1, e1) = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | ALPHA: (81) implies: % 131.49/18.73 | | | | | | | | | (82) op(e1, e1) = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | REF_CLOSE: (25), (32), (39), (82) are inconsistent by % 131.49/18.73 | | | | | | | | | sub-proof #324. % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | (83) all_57_14 = e0 & op(e0, e1) = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | ALPHA: (83) implies: % 131.49/18.73 | | | | | | | | | (84) all_57_14 = e0 % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | BETA: splitting (52) gives: % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | (85) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & % 131.49/18.73 | | | | | | | | | | op(e2, e1) = e3) % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | BETA: splitting (85) gives: % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | (86) all_57_4 = e3 & op(e3, e1) = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | REF_CLOSE: (56), (72), (86) are inconsistent by sub-proof % 131.49/18.73 | | | | | | | | | | | #125. % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | (87) all_57_5 = e3 & op(e2, e1) = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | REF_CLOSE: (34), (76), (87) are inconsistent by sub-proof % 131.49/18.73 | | | | | | | | | | | #39. % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | End of split % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | (88) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 % 131.49/18.73 | | | | | | | | | | & op(e0, e1) = e3) % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | BETA: splitting (88) gives: % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | Case 1: % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | (89) all_57_8 = e3 & op(e1, e1) = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | ALPHA: (89) implies: % 131.49/18.73 | | | | | | | | | | | (90) op(e1, e1) = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | REF_CLOSE: (32), (39), (56), (90) are inconsistent by % 131.49/18.73 | | | | | | | | | | | sub-proof #173. % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | Case 2: % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | (91) all_57_14 = e3 & op(e0, e1) = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | ALPHA: (91) implies: % 131.49/18.73 | | | | | | | | | | | (92) all_57_14 = e3 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | COMBINE_EQS: (84), (92) imply: % 131.49/18.73 | | | | | | | | | | | (93) e3 = e0 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | SIMP: (93) implies: % 131.49/18.73 | | | | | | | | | | | (94) e3 = e0 % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | REDUCE: (24), (94) imply: % 131.49/18.73 | | | | | | | | | | | (95) $false % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | | CLOSE: (95) is inconsistent. % 131.49/18.73 | | | | | | | | | | | % 131.49/18.73 | | | | | | | | | | End of split % 131.49/18.73 | | | | | | | | | | % 131.49/18.73 | | | | | | | | | End of split % 131.49/18.73 | | | | | | | | | % 131.49/18.73 | | | | | | | | End of split % 131.49/18.73 | | | | | | | | % 131.49/18.73 | | | | | | | End of split % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | End of split % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | Case 2: % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | (96) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, % 131.49/18.73 | | | | | | e1) = e1) % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | BETA: splitting (96) gives: % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | | Case 1: % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | (97) all_57_8 = e1 & op(e1, e1) = e1 % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | REF_CLOSE: (18), (42), (48), (97) are inconsistent by sub-proof % 131.49/18.73 | | | | | | | #86. % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | Case 2: % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | (98) all_57_14 = e1 & op(e0, e1) = e1 % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | | REF_CLOSE: (12), (98) are inconsistent by sub-proof #53. % 131.49/18.73 | | | | | | | % 131.49/18.73 | | | | | | End of split % 131.49/18.73 | | | | | | % 131.49/18.73 | | | | | End of split % 131.49/18.73 | | | | | % 131.49/18.73 | | | | Case 2: % 131.49/18.73 | | | | | % 131.49/18.74 | | | | | (99) all_57_5 = e2 & op(e2, e1) = e2 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | ALPHA: (99) implies: % 131.49/18.74 | | | | | (100) op(e2, e1) = e2 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | REF_CLOSE: (35), (49), (100) are inconsistent by sub-proof #347. % 131.49/18.74 | | | | | % 131.49/18.74 | | | | End of split % 131.49/18.74 | | | | % 131.49/18.74 | | | Case 2: % 131.49/18.74 | | | | % 131.49/18.74 | | | | (101) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, % 131.49/18.74 | | | | e1) = e2) % 131.49/18.74 | | | | % 131.49/18.74 | | | | BETA: splitting (101) gives: % 131.49/18.74 | | | | % 131.49/18.74 | | | | Case 1: % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | (102) all_57_8 = e2 & op(e1, e1) = e2 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | ALPHA: (102) implies: % 131.49/18.74 | | | | | (103) all_57_8 = e2 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | GROUND_INST: instantiating (32) with all_53_6, all_12_1, e2, e1, % 131.49/18.74 | | | | | simplifying with (26), (63) gives: % 131.49/18.74 | | | | | (104) all_53_6 = all_12_1 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | GROUND_INST: instantiating (32) with all_53_6, all_30_1, e2, e1, % 131.49/18.74 | | | | | simplifying with (26), (69) gives: % 131.49/18.74 | | | | | (105) all_53_6 = all_30_1 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | GROUND_INST: instantiating (32) with e1, all_30_1, e2, e1, simplifying % 131.49/18.74 | | | | | with (69) gives: % 131.49/18.74 | | | | | (106) all_30_1 = e1 | ~ (op(e1, e2) = e1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | PRED_UNIFY: (19), (65) imply: % 131.49/18.74 | | | | | (107) ~ (unit = e1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | COMBINE_EQS: (104), (105) imply: % 131.49/18.74 | | | | | (108) all_30_1 = all_12_1 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | SIMP: (108) implies: % 131.49/18.74 | | | | | (109) all_30_1 = all_12_1 % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | REDUCE: (50), (104) imply: % 131.49/18.74 | | | | | (110) ~ (all_53_2 = all_12_1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | REDUCE: (11), (104) imply: % 131.49/18.74 | | | | | (111) ~ (all_53_7 = all_12_1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | SIMP: (111) implies: % 131.49/18.74 | | | | | (112) ~ (all_53_7 = all_12_1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | REDUCE: (16), (104) imply: % 131.49/18.74 | | | | | (113) ~ (all_53_14 = all_12_1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | SIMP: (113) implies: % 131.49/18.74 | | | | | (114) ~ (all_53_14 = all_12_1) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | REDUCE: (58), (104) imply: % 131.49/18.74 | | | | | (115) ~ (all_12_1 = all_6_2) % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | BETA: splitting (4) gives: % 131.49/18.74 | | | | | % 131.49/18.74 | | | | | Case 1: % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | (116) unit = e2 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | REDUCE: (59), (116) imply: % 131.49/18.74 | | | | | | (117) op(e2, e3) = e3 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | REDUCE: (61), (116) imply: % 131.49/18.74 | | | | | | (118) op(e2, e1) = e1 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | REDUCE: (15), (116) imply: % 131.49/18.74 | | | | | | (119) op(e2, e2) = e2 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | REDUCE: (47), (116) imply: % 131.49/18.74 | | | | | | (120) op(e1, e2) = e1 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | REDUCE: (51), (116) imply: % 131.49/18.74 | | | | | | (121) op(e0, e2) = e0 % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | BETA: splitting (60) gives: % 131.49/18.74 | | | | | | % 131.49/18.74 | | | | | | Case 1: % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | (122) ~ (op(e2, e1) = e1) % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | PRED_UNIFY: (118), (122) imply: % 131.49/18.74 | | | | | | | (123) $false % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | CLOSE: (123) is inconsistent. % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | Case 2: % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | (124) all_53_9 = e1 % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | REDUCE: (23), (124) imply: % 131.49/18.74 | | | | | | | (125) ~ (all_53_8 = e1) % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | REDUCE: (62), (124) imply: % 131.49/18.74 | | | | | | | (126) ~ (all_8_1 = e1) % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | SIMP: (126) implies: % 131.49/18.74 | | | | | | | (127) ~ (all_8_1 = e1) % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | BETA: splitting (22) gives: % 131.49/18.74 | | | | | | | % 131.49/18.74 | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | (128) ~ (op(e2, e2) = e2) % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | PRED_UNIFY: (119), (128) imply: % 131.49/18.74 | | | | | | | | (129) $false % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | CLOSE: (129) is inconsistent. % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | (130) all_53_5 = e2 % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | COMBINE_EQS: (64), (130) imply: % 131.49/18.74 | | | | | | | | (131) all_6_2 = e2 % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | REDUCE: (37), (131) imply: % 131.49/18.74 | | | | | | | | (132) ~ (all_53_7 = e2) % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | REDUCE: (115), (131) imply: % 131.49/18.74 | | | | | | | | (133) ~ (all_12_1 = e2) % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | BETA: splitting (106) gives: % 131.49/18.74 | | | | | | | | % 131.49/18.74 | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | (134) ~ (op(e1, e2) = e1) % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | PRED_UNIFY: (120), (134) imply: % 131.49/18.74 | | | | | | | | | (135) $false % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | CLOSE: (135) is inconsistent. % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | (136) all_30_1 = e1 % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | COMBINE_EQS: (109), (136) imply: % 131.49/18.74 | | | | | | | | | (137) all_12_1 = e1 % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | SIMP: (137) implies: % 131.49/18.74 | | | | | | | | | (138) all_12_1 = e1 % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | REDUCE: (110), (138) imply: % 131.49/18.74 | | | | | | | | | (139) ~ (all_53_2 = e1) % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | REDUCE: (112), (138) imply: % 131.49/18.74 | | | | | | | | | (140) ~ (all_53_7 = e1) % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | REDUCE: (114), (138) imply: % 131.49/18.74 | | | | | | | | | (141) ~ (all_53_14 = e1) % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | REDUCE: (133), (138) imply: % 131.49/18.74 | | | | | | | | | (142) ~ (e2 = e1) % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | BETA: splitting (38) gives: % 131.49/18.74 | | | | | | | | | % 131.49/18.74 | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | (143) ~ (op(e2, e3) = e3) % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | PRED_UNIFY: (117), (143) imply: % 131.49/18.74 | | | | | | | | | | (144) $false % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | CLOSE: (144) is inconsistent. % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | (145) all_53_1 = e3 % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | REDUCE: (36), (145) imply: % 131.49/18.74 | | | | | | | | | | (146) ~ (all_53_2 = e3) % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | SIMP: (146) implies: % 131.49/18.74 | | | | | | | | | | (147) ~ (all_53_2 = e3) % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | BETA: splitting (27) gives: % 131.49/18.74 | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | (148) ~ (op(e0, e2) = e0) % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | PRED_UNIFY: (121), (148) imply: % 131.49/18.74 | | | | | | | | | | | (149) $false % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | CLOSE: (149) is inconsistent. % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | (150) all_55_13 = e0 % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | COMBINE_EQS: (57), (150) imply: % 131.49/18.74 | | | | | | | | | | | (151) all_53_7 = e0 % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | REDUCE: (17), (151) imply: % 131.49/18.74 | | | | | | | | | | | (152) ~ (all_8_1 = e0) % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | SIMP: (152) implies: % 131.49/18.74 | | | | | | | | | | | (153) ~ (all_8_1 = e0) % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | REDUCE: (132), (151) imply: % 131.49/18.74 | | | | | | | | | | | (154) ~ (e2 = e0) % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | REDUCE: (140), (151) imply: % 131.49/18.74 | | | | | | | | | | | (155) ~ (e1 = e0) % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | BETA: splitting (30) gives: % 131.49/18.74 | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | (156) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 131.49/18.74 | | | | | | | | | | | | & op(e1, e2) = e1) % 131.49/18.74 | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | BETA: splitting (156) gives: % 131.49/18.74 | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | (157) all_57_6 = e1 & op(e1, e3) = e1 % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | ALPHA: (157) implies: % 131.49/18.74 | | | | | | | | | | | | | (158) op(e1, e3) = e1 % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | REF_CLOSE: (55), (139), (158) are inconsistent by sub-proof % 131.49/18.74 | | | | | | | | | | | | | #280. % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | (159) all_57_7 = e1 & op(e1, e2) = e1 % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | ALPHA: (159) implies: % 131.49/18.74 | | | | | | | | | | | | | (160) all_57_7 = e1 % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | BETA: splitting (9) gives: % 131.49/18.74 | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | (161) all_55_14 = e3 % 131.49/18.74 | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | COMBINE_EQS: (7), (161) imply: % 131.49/18.74 | | | | | | | | | | | | | | (162) all_8_1 = e3 % 131.49/18.74 | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | COMBINE_EQS: (21), (162) imply: % 131.49/18.74 | | | | | | | | | | | | | | (163) all_20_1 = e3 % 131.49/18.74 | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | BETA: splitting (33) gives: % 131.49/18.74 | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | (164) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 131.49/18.74 | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 131.49/18.74 | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 131.49/18.74 | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | (165) all_57_4 = e1 & op(e3, e1) = e1 % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | (166) op(e3, e1) = e1 % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (125), (166) are inconsistent by sub-proof % 131.49/18.74 | | | | | | | | | | | | | | | | #238. % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | (167) all_57_5 = e1 & op(e2, e1) = e1 % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | (168) all_57_5 = e1 % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | (169) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | (170) all_57_6 = e3 & op(e1, e3) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | (171) op(e1, e3) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (147), (171) are inconsistent by sub-proof % 131.49/18.74 | | | | | | | | | | | | | | | | | | #323. % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | (172) all_57_7 = e3 & op(e1, e2) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (160), (172) are inconsistent by sub-proof % 131.49/18.74 | | | | | | | | | | | | | | | | | | #190. % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | End of split % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | (173) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 131.49/18.74 | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | (174) all_57_8 = e3 & op(e1, e1) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | (175) op(e1, e1) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (39), (56), (175) are inconsistent by % 131.49/18.74 | | | | | | | | | | | | | | | | | | sub-proof #173. % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | (176) all_57_11 = e3 & op(e1, e0) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | ALPHA: (176) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | (177) all_57_11 = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | (178) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 131.49/18.74 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (179) all_57_12 = e2 & op(e0, e3) = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (180) op(e0, e3) = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (181) ~ (all_20_1 = e3) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (181) imply: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (182) $false % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_20_0 = e2) & op(e0, e3) = all_20_0 & % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | $i(all_20_0) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_20_0 = e2) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (185) op(e0, e3) = all_20_0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with e2, all_20_0, e3, e0, % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | simplifying with (180), (185) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (186) all_20_0 = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (186) imply: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (187) $false % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (188) all_57_13 = e2 & op(e0, e2) = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (189) op(e0, e2) = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (45), (151), (189) are inconsistent by % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | sub-proof #191. % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | (190) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 131.49/18.74 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (191) all_57_14 = e2 & op(e0, e1) = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | (192) all_57_14 = e2 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | (193) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | (194) all_57_4 = e3 & op(e3, e1) = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | (195) all_57_4 = e3 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | (196) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | (197) all_57_6 = e0 & op(e1, e3) = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | (198) all_57_6 = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | (199) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_57_4 = e0 & op(e3, e1) = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_57_4 = e0 % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (32), (34), (39), (52), (56), (168), (192), % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (201) are inconsistent by sub-proof #37. % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_57_5 = e0 & op(e2, e1) = e0 % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (168), (202) are inconsistent by sub-proof % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | #40. % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | (203) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_57_8 = e0 & op(e1, e1) = e0 % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_57_8 = e0 % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (206) op(e1, e1) = e0 % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.49/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_57_6 = e2 & op(e1, e3) = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (198), (208) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_57_7 = e2 & op(e1, e2) = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_57_7 = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (210) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e1 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e2 = e1 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (212) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) $false % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (103), (205) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #317. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_57_11 = e2 & op(e1, e0) = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_57_11 = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (32), (34), (56), (160), (198), (206), % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) are inconsistent by sub-proof #188. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_57_14 = e0 & op(e0, e1) = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e0, e1) = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) ~ (op(e0, e1) = e0) % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (218), (219) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) $false % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_20_1 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (221) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_8_1 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_8_1 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (223) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (225) all_57_7 = e0 & op(e1, e2) = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (226) all_57_7 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (160), (226) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | #175. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | (227) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (228) all_57_8 = e0 & op(e1, e1) = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (229) all_57_8 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (103), (229) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | #317. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_57_11 = e0 & op(e1, e0) = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (231) all_57_11 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (231) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (232) e3 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (233) e3 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (233) imply: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (234) all_57_4 = e0 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (32), (34), (39), (52), (56), (168), (192), % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (234) are inconsistent by sub-proof #37. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | (235) all_57_5 = e3 & op(e2, e1) = e3 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (168), (235) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | #39. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | (236) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (39), (56), (192), (236) are inconsistent by % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | sub-proof #38. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | (237) all_57_15 = e2 & op(e0, e0) = e2 % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (42), (237) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | #42. % 131.81/18.75 | | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | (238) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 131.81/18.75 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 131.81/18.75 | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 131.81/18.75 | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | (239) all_57_8 = e1 & op(e1, e1) = e1 % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (103), (239) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | | | | #36. % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | (240) all_57_14 = e1 & op(e0, e1) = e1 % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (240) are inconsistent by sub-proof #53. % 131.81/18.75 | | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | (241) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.81/18.75 | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (127), (153), (241) are inconsistent by % 131.81/18.75 | | | | | | | | | | | | | | sub-proof #63. % 131.81/18.75 | | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | (242) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 131.81/18.75 | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 131.81/18.75 | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | BETA: splitting (242) gives: % 131.81/18.75 | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | Case 1: % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | (243) all_57_8 = e1 & op(e1, e1) = e1 % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | REF_CLOSE: (42), (103), (243) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | #36. % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | Case 2: % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | (244) all_57_11 = e1 & op(e1, e0) = e1 % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | ALPHA: (244) implies: % 131.81/18.75 | | | | | | | | | | | | | (245) op(e1, e0) = e1 % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | | REF_CLOSE: (1), (141), (245) are inconsistent by sub-proof % 131.81/18.75 | | | | | | | | | | | | | #339. % 131.81/18.75 | | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | | % 131.81/18.75 | | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | | % 131.81/18.75 | | | | | | | | | End of split % 131.81/18.75 | | | | | | | | | % 131.81/18.75 | | | | | | | | End of split % 131.81/18.75 | | | | | | | | % 131.81/18.75 | | | | | | | End of split % 131.81/18.75 | | | | | | | % 131.81/18.75 | | | | | | End of split % 131.81/18.75 | | | | | | % 131.81/18.75 | | | | | Case 2: % 131.81/18.75 | | | | | | % 131.81/18.75 | | | | | | (246) unit = e1 | unit = e0 % 131.81/18.75 | | | | | | % 131.81/18.75 | | | | | | REF_CLOSE: (2), (107), (246) are inconsistent by sub-proof #278. % 131.81/18.75 | | | | | | % 131.81/18.75 | | | | | End of split % 131.81/18.75 | | | | | % 131.81/18.75 | | | | Case 2: % 131.81/18.75 | | | | | % 131.81/18.75 | | | | | (247) all_57_14 = e2 & op(e0, e1) = e2 % 131.81/18.75 | | | | | % 131.81/18.75 | | | | | ALPHA: (247) implies: % 131.81/18.75 | | | | | (248) op(e0, e1) = e2 % 131.81/18.75 | | | | | % 131.81/18.75 | | | | | GROUND_INST: instantiating (32) with all_8_1, e2, e1, e0, simplifying % 131.81/18.75 | | | | | with (41), (248) gives: % 131.81/18.75 | | | | | (249) all_8_1 = e2 % 131.81/18.75 | | | | | % 131.81/18.75 | | | | | REDUCE: (8), (249) imply: % 131.81/18.75 | | | | | (250) $false % 131.81/18.75 | | | | | % 131.81/18.75 | | | | | CLOSE: (250) is inconsistent. % 131.81/18.75 | | | | | % 131.81/18.75 | | | | End of split % 131.81/18.75 | | | | % 131.81/18.75 | | | End of split % 131.81/18.75 | | | % 131.81/18.75 | | End of split % 131.81/18.75 | | % 131.81/18.75 | Case 2: % 131.81/18.75 | | % 131.81/18.75 | | (251) op(e1, e2) = e2 % 131.81/18.75 | | % 131.81/18.75 | | REF_CLOSE: (28), (53), (251) are inconsistent by sub-proof #326. % 131.81/18.75 | | % 131.81/18.75 | End of split % 131.81/18.75 | % 131.81/18.75 End of proof % 131.81/18.75 % 131.81/18.75 Sub-proof #36 shows that the following formulas are inconsistent: % 131.81/18.75 ---------------------------------------------------------------- % 131.81/18.75 (1) all_57_8 = e1 & op(e1, e1) = e1 % 131.81/18.75 (2) all_57_8 = e2 % 131.81/18.75 (3) ~ (e2 = e1) % 131.81/18.75 % 131.81/18.75 Begin of proof % 131.81/18.75 | % 131.81/18.75 | ALPHA: (1) implies: % 131.81/18.75 | (4) all_57_8 = e1 % 131.81/18.75 | % 131.81/18.75 | COMBINE_EQS: (2), (4) imply: % 131.81/18.75 | (5) e2 = e1 % 131.81/18.75 | % 131.81/18.75 | REDUCE: (3), (5) imply: % 131.81/18.75 | (6) $false % 131.81/18.75 | % 131.81/18.75 | CLOSE: (6) is inconsistent. % 131.81/18.75 | % 131.81/18.75 End of proof % 131.81/18.75 % 131.81/18.75 Sub-proof #37 shows that the following formulas are inconsistent: % 131.81/18.75 ---------------------------------------------------------------- % 131.81/18.75 (1) ~ (e3 = e0) % 131.81/18.75 (2) all_57_4 = e0 % 131.81/18.75 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.81/18.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.81/18.75 (4) ~ (e3 = e1) % 131.81/18.75 (5) op(e1, e1) = e2 % 131.81/18.75 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 131.81/18.75 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 131.81/18.75 (7) all_57_5 = e1 % 131.81/18.75 (8) ~ (e3 = e2) % 131.81/18.75 (9) all_57_14 = e2 % 131.81/18.75 % 131.81/18.75 Begin of proof % 131.81/18.75 | % 131.81/18.75 | BETA: splitting (6) gives: % 131.81/18.75 | % 131.81/18.75 | Case 1: % 131.81/18.75 | | % 131.81/18.75 | | (10) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = % 131.81/18.75 | | e3) % 131.81/18.75 | | % 131.81/18.75 | | BETA: splitting (10) gives: % 131.81/18.75 | | % 131.81/18.75 | | Case 1: % 131.81/18.75 | | | % 131.81/18.75 | | | (11) all_57_4 = e3 & op(e3, e1) = e3 % 131.81/18.75 | | | % 131.81/18.75 | | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #247. % 131.81/18.75 | | | % 131.81/18.75 | | Case 2: % 131.81/18.75 | | | % 131.81/18.75 | | | (12) all_57_5 = e3 & op(e2, e1) = e3 % 131.81/18.75 | | | % 131.81/18.75 | | | REF_CLOSE: (4), (7), (12) are inconsistent by sub-proof #39. % 131.81/18.75 | | | % 131.81/18.75 | | End of split % 131.81/18.75 | | % 131.81/18.75 | Case 2: % 131.81/18.75 | | % 131.81/18.75 | | (13) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = % 131.81/18.75 | | e3) % 131.81/18.75 | | % 131.81/18.75 | | REF_CLOSE: (3), (5), (8), (9), (13) are inconsistent by sub-proof #38. % 131.81/18.75 | | % 131.81/18.75 | End of split % 131.81/18.75 | % 131.81/18.75 End of proof % 131.81/18.75 % 131.81/18.75 Sub-proof #38 shows that the following formulas are inconsistent: % 131.81/18.75 ---------------------------------------------------------------- % 131.81/18.75 (1) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 131.81/18.75 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.81/18.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.81/18.75 (3) op(e1, e1) = e2 % 131.81/18.75 (4) ~ (e3 = e2) % 131.81/18.75 (5) all_57_14 = e2 % 131.81/18.75 % 131.81/18.75 Begin of proof % 131.81/18.75 | % 131.81/18.75 | BETA: splitting (1) gives: % 131.81/18.75 | % 131.81/18.75 | Case 1: % 131.81/18.75 | | % 131.81/18.75 | | (6) all_57_8 = e3 & op(e1, e1) = e3 % 131.81/18.75 | | % 131.81/18.75 | | ALPHA: (6) implies: % 131.81/18.75 | | (7) op(e1, e1) = e3 % 131.81/18.75 | | % 131.81/18.75 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #173. % 131.81/18.75 | | % 131.81/18.75 | Case 2: % 131.81/18.75 | | % 131.81/18.75 | | (8) all_57_14 = e3 & op(e0, e1) = e3 % 131.81/18.75 | | % 131.81/18.75 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #56. % 131.81/18.75 | | % 131.81/18.75 | End of split % 131.81/18.75 | % 131.81/18.75 End of proof % 131.81/18.75 % 131.81/18.75 Sub-proof #39 shows that the following formulas are inconsistent: % 131.81/18.75 ---------------------------------------------------------------- % 131.81/18.75 (1) all_57_5 = e3 & op(e2, e1) = e3 % 131.81/18.75 (2) all_57_5 = e1 % 131.81/18.75 (3) ~ (e3 = e1) % 131.81/18.75 % 131.81/18.75 Begin of proof % 131.81/18.75 | % 131.81/18.75 | ALPHA: (1) implies: % 131.81/18.75 | (4) all_57_5 = e3 % 131.81/18.75 | % 131.81/18.75 | COMBINE_EQS: (2), (4) imply: % 131.81/18.75 | (5) e3 = e1 % 131.81/18.75 | % 131.81/18.75 | SIMP: (5) implies: % 131.81/18.75 | (6) e3 = e1 % 131.81/18.75 | % 131.81/18.75 | REDUCE: (3), (6) imply: % 131.81/18.75 | (7) $false % 131.81/18.75 | % 131.81/18.75 | CLOSE: (7) is inconsistent. % 131.81/18.75 | % 131.81/18.75 End of proof % 131.81/18.75 % 131.81/18.75 Sub-proof #40 shows that the following formulas are inconsistent: % 131.81/18.75 ---------------------------------------------------------------- % 131.81/18.75 (1) all_57_5 = e0 & op(e2, e1) = e0 % 131.81/18.75 (2) all_57_5 = e1 % 131.81/18.75 (3) ~ (e1 = e0) % 131.81/18.75 % 131.81/18.75 Begin of proof % 131.81/18.75 | % 131.81/18.75 | ALPHA: (1) implies: % 131.81/18.75 | (4) all_57_5 = e0 % 131.81/18.75 | % 131.81/18.75 | COMBINE_EQS: (2), (4) imply: % 131.81/18.75 | (5) e1 = e0 % 131.81/18.75 | % 131.81/18.75 | REDUCE: (3), (5) imply: % 131.81/18.75 | (6) $false % 131.81/18.75 | % 131.81/18.75 | CLOSE: (6) is inconsistent. % 131.81/18.75 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #41 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) op(e0, e3) = all_53_3 % 131.81/18.76 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.81/18.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.81/18.76 (3) ~ (all_53_2 = e1) % 131.81/18.76 (4) ~ (all_53_3 = e1) % 131.81/18.76 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 131.81/18.76 (6) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | BETA: splitting (5) gives: % 131.81/18.76 | % 131.81/18.76 | Case 1: % 131.81/18.76 | | % 131.81/18.76 | | (7) all_57_6 = e1 & op(e1, e3) = e1 % 131.81/18.76 | | % 131.81/18.76 | | ALPHA: (7) implies: % 131.81/18.76 | | (8) op(e1, e3) = e1 % 131.81/18.76 | | % 131.81/18.76 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #280. % 131.81/18.76 | | % 131.81/18.76 | Case 2: % 131.81/18.76 | | % 131.81/18.76 | | (9) all_57_12 = e1 & op(e0, e3) = e1 % 131.81/18.76 | | % 131.81/18.76 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #272. % 131.81/18.76 | | % 131.81/18.76 | End of split % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #42 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_57_15 = e2 & op(e0, e0) = e2 % 131.81/18.76 (2) all_57_15 = e1 % 131.81/18.76 (3) ~ (e2 = e1) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (1) implies: % 131.81/18.76 | (4) all_57_15 = e2 % 131.81/18.76 | % 131.81/18.76 | COMBINE_EQS: (2), (4) imply: % 131.81/18.76 | (5) e2 = e1 % 131.81/18.76 | % 131.81/18.76 | SIMP: (5) implies: % 131.81/18.76 | (6) e2 = e1 % 131.81/18.76 | % 131.81/18.76 | REDUCE: (3), (6) imply: % 131.81/18.76 | (7) $false % 131.81/18.76 | % 131.81/18.76 | CLOSE: (7) is inconsistent. % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #43 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) ~ (unit = e0) % 131.81/18.76 (2) unit = e2 | unit = e1 | unit = e0 % 131.81/18.76 (3) op(e2, unit) = e2 % 131.81/18.76 (4) all_55_9 = all_53_6 % 131.81/18.76 (5) all_57_3 = e0 % 131.81/18.76 (6) ~ (all_53_9 = all_53_13) % 131.81/18.76 (7) ~ (e2 = e0) % 131.81/18.76 (8) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 131.81/18.76 (9) ~ (all_53_1 = e2) % 131.81/18.76 (10) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 131.81/18.76 (11) op(e1, unit) = e1 % 131.81/18.76 (12) ~ (all_53_6 = e1) % 131.81/18.76 (13) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.81/18.76 (14) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 131.81/18.76 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 131.81/18.76 (15) all_55_4 = all_53_1 % 131.81/18.76 (16) all_57_5 = e0 % 131.81/18.76 (17) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | BETA: splitting (14) gives: % 131.81/18.76 | % 131.81/18.76 | Case 1: % 131.81/18.76 | | % 131.81/18.76 | | (18) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = % 131.81/18.76 | | e2) % 131.81/18.76 | | % 131.81/18.76 | | BETA: splitting (18) gives: % 131.81/18.76 | | % 131.81/18.76 | | Case 1: % 131.81/18.76 | | | % 131.81/18.76 | | | (19) all_57_2 = e2 & op(e2, e3) = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | ALPHA: (19) implies: % 131.81/18.76 | | | (20) op(e2, e3) = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (9), (15), (17), (20) are inconsistent by sub-proof #346. % 131.81/18.76 | | | % 131.81/18.76 | | Case 2: % 131.81/18.76 | | | % 131.81/18.76 | | | (21) all_57_3 = e2 & op(e2, e2) = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | ALPHA: (21) implies: % 131.81/18.76 | | | (22) all_57_3 = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | COMBINE_EQS: (5), (22) imply: % 131.81/18.76 | | | (23) e2 = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | SIMP: (23) implies: % 131.81/18.76 | | | (24) e2 = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | REDUCE: (7), (24) imply: % 131.81/18.76 | | | (25) $false % 131.81/18.76 | | | % 131.81/18.76 | | | CLOSE: (25) is inconsistent. % 131.81/18.76 | | | % 131.81/18.76 | | End of split % 131.81/18.76 | | % 131.81/18.76 | Case 2: % 131.81/18.76 | | % 131.81/18.76 | | (26) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 131.81/18.76 | | e2) % 131.81/18.76 | | % 131.81/18.76 | | BETA: splitting (26) gives: % 131.81/18.76 | | % 131.81/18.76 | | Case 1: % 131.81/18.76 | | | % 131.81/18.76 | | | (27) all_57_5 = e2 & op(e2, e1) = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (7), (16), (27) are inconsistent by sub-proof #45. % 131.81/18.76 | | | % 131.81/18.76 | | Case 2: % 131.81/18.76 | | | % 131.81/18.76 | | | (28) all_57_10 = e2 & op(e2, e0) = e2 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (13), (28) are % 131.81/18.76 | | | inconsistent by sub-proof #47. % 131.81/18.76 | | | % 131.81/18.76 | | End of split % 131.81/18.76 | | % 131.81/18.76 | End of split % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #44 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_57_8 = e2 & op(e1, e1) = e2 % 131.81/18.76 (2) all_57_8 = e1 % 131.81/18.76 (3) ~ (e2 = e1) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (1) implies: % 131.81/18.76 | (4) all_57_8 = e2 % 131.81/18.76 | % 131.81/18.76 | COMBINE_EQS: (2), (4) imply: % 131.81/18.76 | (5) e2 = e1 % 131.81/18.76 | % 131.81/18.76 | REDUCE: (3), (5) imply: % 131.81/18.76 | (6) $false % 131.81/18.76 | % 131.81/18.76 | CLOSE: (6) is inconsistent. % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #45 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_57_5 = e2 & op(e2, e1) = e2 % 131.81/18.76 (2) all_57_5 = e0 % 131.81/18.76 (3) ~ (e2 = e0) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (1) implies: % 131.81/18.76 | (4) all_57_5 = e2 % 131.81/18.76 | % 131.81/18.76 | COMBINE_EQS: (2), (4) imply: % 131.81/18.76 | (5) e2 = e0 % 131.81/18.76 | % 131.81/18.76 | REDUCE: (3), (5) imply: % 131.81/18.76 | (6) $false % 131.81/18.76 | % 131.81/18.76 | CLOSE: (6) is inconsistent. % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #46 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_57_3 = e2 & op(e2, e2) = e2 % 131.81/18.76 (2) all_57_3 = e3 % 131.81/18.76 (3) ~ (e3 = e2) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (1) implies: % 131.81/18.76 | (4) all_57_3 = e2 % 131.81/18.76 | % 131.81/18.76 | COMBINE_EQS: (2), (4) imply: % 131.81/18.76 | (5) e3 = e2 % 131.81/18.76 | % 131.81/18.76 | REDUCE: (3), (5) imply: % 131.81/18.76 | (6) $false % 131.81/18.76 | % 131.81/18.76 | CLOSE: (6) is inconsistent. % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #47 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) ~ (unit = e0) % 131.81/18.76 (2) unit = e2 | unit = e1 | unit = e0 % 131.81/18.76 (3) op(e2, unit) = e2 % 131.81/18.76 (4) all_55_9 = all_53_6 % 131.81/18.76 (5) all_57_10 = e2 & op(e2, e0) = e2 % 131.81/18.76 (6) ~ (all_53_9 = all_53_13) % 131.81/18.76 (7) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 131.81/18.76 (8) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 131.81/18.76 (9) op(e1, unit) = e1 % 131.81/18.76 (10) ~ (all_53_6 = e1) % 131.81/18.76 (11) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (5) implies: % 131.81/18.76 | (12) op(e2, e0) = e2 % 131.81/18.76 | % 131.81/18.76 | BETA: splitting (8) gives: % 131.81/18.76 | % 131.81/18.76 | Case 1: % 131.81/18.76 | | % 131.81/18.76 | | (13) ~ (op(e2, e0) = e2) % 131.81/18.76 | | % 131.81/18.76 | | PRED_UNIFY: (12), (13) imply: % 131.81/18.76 | | (14) $false % 131.81/18.76 | | % 131.81/18.76 | | CLOSE: (14) is inconsistent. % 131.81/18.76 | | % 131.81/18.76 | Case 2: % 131.81/18.76 | | % 131.81/18.76 | | (15) all_53_13 = e2 % 131.81/18.76 | | % 131.81/18.76 | | REDUCE: (6), (15) imply: % 131.81/18.76 | | (16) ~ (all_53_9 = e2) % 131.81/18.76 | | % 131.81/18.76 | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (16) are inconsistent % 131.81/18.76 | | by sub-proof #252. % 131.81/18.76 | | % 131.81/18.76 | End of split % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #48 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.81/18.76 (2) ~ (all_53_13 = e0) % 131.81/18.76 (3) ~ (e3 = e0) % 131.81/18.76 (4) ~ (e2 = e0) % 131.81/18.76 (5) all_57_2 = e1 % 131.81/18.76 (6) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 131.81/18.76 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 131.81/18.76 (7) ~ (e1 = e0) % 131.81/18.76 (8) all_57_3 = e3 % 131.81/18.76 (9) all_57_5 = e2 % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | BETA: splitting (6) gives: % 131.81/18.76 | % 131.81/18.76 | Case 1: % 131.81/18.76 | | % 131.81/18.76 | | (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 131.81/18.76 | | e0) % 131.81/18.76 | | % 131.81/18.76 | | BETA: splitting (10) gives: % 131.81/18.76 | | % 131.81/18.76 | | Case 1: % 131.81/18.76 | | | % 131.81/18.76 | | | (11) all_57_2 = e0 & op(e2, e3) = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #166. % 131.81/18.76 | | | % 131.81/18.76 | | Case 2: % 131.81/18.76 | | | % 131.81/18.76 | | | (12) all_57_3 = e0 & op(e2, e2) = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #49. % 131.81/18.76 | | | % 131.81/18.76 | | End of split % 131.81/18.76 | | % 131.81/18.76 | Case 2: % 131.81/18.76 | | % 131.81/18.76 | | (13) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 131.81/18.76 | | e0) % 131.81/18.76 | | % 131.81/18.76 | | BETA: splitting (13) gives: % 131.81/18.76 | | % 131.81/18.76 | | Case 1: % 131.81/18.76 | | | % 131.81/18.76 | | | (14) all_57_5 = e0 & op(e2, e1) = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | ALPHA: (14) implies: % 131.81/18.76 | | | (15) all_57_5 = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | COMBINE_EQS: (9), (15) imply: % 131.81/18.76 | | | (16) e2 = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | REDUCE: (4), (16) imply: % 131.81/18.76 | | | (17) $false % 131.81/18.76 | | | % 131.81/18.76 | | | CLOSE: (17) is inconsistent. % 131.81/18.76 | | | % 131.81/18.76 | | Case 2: % 131.81/18.76 | | | % 131.81/18.76 | | | (18) all_57_10 = e0 & op(e2, e0) = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | ALPHA: (18) implies: % 131.81/18.76 | | | (19) op(e2, e0) = e0 % 131.81/18.76 | | | % 131.81/18.76 | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #356. % 131.81/18.76 | | | % 131.81/18.76 | | End of split % 131.81/18.76 | | % 131.81/18.76 | End of split % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #49 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_57_3 = e0 & op(e2, e2) = e0 % 131.81/18.76 (2) all_57_3 = e3 % 131.81/18.76 (3) ~ (e3 = e0) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | ALPHA: (1) implies: % 131.81/18.76 | (4) all_57_3 = e0 % 131.81/18.76 | % 131.81/18.76 | COMBINE_EQS: (2), (4) imply: % 131.81/18.76 | (5) e3 = e0 % 131.81/18.76 | % 131.81/18.76 | REDUCE: (3), (5) imply: % 131.81/18.76 | (6) $false % 131.81/18.76 | % 131.81/18.76 | CLOSE: (6) is inconsistent. % 131.81/18.76 | % 131.81/18.76 End of proof % 131.81/18.76 % 131.81/18.76 Sub-proof #50 shows that the following formulas are inconsistent: % 131.81/18.76 ---------------------------------------------------------------- % 131.81/18.76 (1) all_55_2 = all_32_0 % 131.81/18.76 (2) ~ (all_32_0 = e1) % 131.81/18.76 (3) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 131.81/18.76 (4) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 131.81/18.76 (5) ~ (all_53_12 = all_32_0) % 131.81/18.76 (6) all_57_4 = e0 % 131.81/18.76 (7) ~ (all_32_0 = e0) % 131.81/18.76 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 131.81/18.76 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 131.81/18.76 (9) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 131.81/18.76 (10) all_4_2 = e2 % 131.81/18.76 (11) all_57_1 = e1 % 131.81/18.76 (12) ~ (all_32_0 = e2) % 131.81/18.76 % 131.81/18.76 Begin of proof % 131.81/18.76 | % 131.81/18.76 | BETA: splitting (3) gives: % 131.81/18.76 | % 131.81/18.76 | Case 1: % 131.81/18.76 | | % 131.81/18.76 | | (13) all_55_2 = e3 % 131.81/18.76 | | % 131.81/18.76 | | COMBINE_EQS: (1), (13) imply: % 131.81/18.76 | | (14) all_32_0 = e3 % 131.81/18.76 | | % 131.81/18.76 | | REDUCE: (5), (14) imply: % 131.81/18.77 | | (15) ~ (all_53_12 = e3) % 131.81/18.77 | | % 131.81/18.77 | | REDUCE: (12), (14) imply: % 131.81/18.77 | | (16) ~ (e3 = e2) % 131.81/18.77 | | % 131.81/18.77 | | REDUCE: (2), (14) imply: % 131.81/18.77 | | (17) ~ (e3 = e1) % 131.81/18.77 | | % 131.81/18.77 | | REDUCE: (7), (14) imply: % 131.81/18.77 | | (18) ~ (e3 = e0) % 131.81/18.77 | | % 131.81/18.77 | | BETA: splitting (8) gives: % 131.81/18.77 | | % 131.81/18.77 | | Case 1: % 131.81/18.77 | | | % 131.81/18.77 | | | (19) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 131.81/18.77 | | | e3) % 131.81/18.77 | | | % 131.81/18.77 | | | REF_CLOSE: (4), (10), (11), (16), (17), (19) are inconsistent by sub-proof % 131.81/18.77 | | | #126. % 131.81/18.77 | | | % 131.81/18.77 | | Case 2: % 131.81/18.77 | | | % 131.81/18.77 | | | (20) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 131.81/18.77 | | | e3) % 131.81/18.77 | | | % 131.81/18.77 | | | BETA: splitting (20) gives: % 131.81/18.77 | | | % 131.81/18.77 | | | Case 1: % 131.81/18.77 | | | | % 131.81/18.77 | | | | (21) all_57_4 = e3 & op(e3, e1) = e3 % 131.81/18.77 | | | | % 131.81/18.77 | | | | REF_CLOSE: (6), (18), (21) are inconsistent by sub-proof #247. % 131.81/18.77 | | | | % 131.81/18.77 | | | Case 2: % 131.81/18.77 | | | | % 131.81/18.77 | | | | (22) all_57_9 = e3 & op(e3, e0) = e3 % 131.81/18.77 | | | | % 131.81/18.77 | | | | ALPHA: (22) implies: % 131.81/18.77 | | | | (23) op(e3, e0) = e3 % 131.81/18.77 | | | | % 131.81/18.77 | | | | REF_CLOSE: (9), (15), (23) are inconsistent by sub-proof #186. % 131.81/18.77 | | | | % 131.81/18.77 | | | End of split % 131.81/18.77 | | | % 131.81/18.77 | | End of split % 131.81/18.77 | | % 131.81/18.77 | Case 2: % 131.81/18.77 | | % 131.81/18.77 | | (24) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 131.81/18.77 | | % 131.81/18.77 | | BETA: splitting (24) gives: % 131.81/18.77 | | % 131.81/18.77 | | Case 1: % 131.81/18.77 | | | % 131.81/18.77 | | | (25) all_55_2 = e2 % 131.81/18.77 | | | % 131.81/18.77 | | | COMBINE_EQS: (1), (25) imply: % 131.81/18.77 | | | (26) all_32_0 = e2 % 131.81/18.77 | | | % 131.81/18.77 | | | REDUCE: (12), (26) imply: % 131.81/18.77 | | | (27) $false % 131.81/18.77 | | | % 131.81/18.77 | | | CLOSE: (27) is inconsistent. % 131.81/18.77 | | | % 131.81/18.77 | | Case 2: % 131.81/18.77 | | | % 131.81/18.77 | | | (28) all_55_2 = e1 | all_55_2 = e0 % 131.81/18.77 | | | % 131.81/18.77 | | | BETA: splitting (28) gives: % 131.81/18.77 | | | % 131.81/18.77 | | | Case 1: % 131.81/18.77 | | | | % 131.81/18.77 | | | | (29) all_55_2 = e1 % 131.81/18.77 | | | | % 131.81/18.77 | | | | COMBINE_EQS: (1), (29) imply: % 131.81/18.77 | | | | (30) all_32_0 = e1 % 131.81/18.77 | | | | % 131.81/18.77 | | | | REDUCE: (2), (30) imply: % 131.81/18.77 | | | | (31) $false % 131.81/18.77 | | | | % 131.81/18.77 | | | | CLOSE: (31) is inconsistent. % 131.81/18.77 | | | | % 131.81/18.77 | | | Case 2: % 131.81/18.77 | | | | % 131.81/18.77 | | | | (32) all_55_2 = e0 % 131.81/18.77 | | | | % 131.81/18.77 | | | | COMBINE_EQS: (1), (32) imply: % 131.81/18.77 | | | | (33) all_32_0 = e0 % 131.81/18.77 | | | | % 131.81/18.77 | | | | REDUCE: (7), (33) imply: % 131.81/18.77 | | | | (34) $false % 131.81/18.77 | | | | % 131.81/18.77 | | | | CLOSE: (34) is inconsistent. % 131.81/18.77 | | | | % 131.81/18.77 | | | End of split % 131.81/18.77 | | | % 131.81/18.77 | | End of split % 131.81/18.77 | | % 131.81/18.77 | End of split % 131.81/18.77 | % 131.81/18.77 End of proof % 131.81/18.77 % 131.81/18.77 Sub-proof #51 shows that the following formulas are inconsistent: % 131.81/18.77 ---------------------------------------------------------------- % 131.81/18.77 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 131.81/18.77 (2) op(e1, e1) = all_12_2 % 131.81/18.77 (3) ~ (unit = e0) % 131.81/18.77 (4) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 131.81/18.77 (5) unit = e2 | unit = e1 | unit = e0 % 131.81/18.77 (6) ~ (all_53_3 = all_53_7) % 131.81/18.77 (7) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 131.81/18.77 (8) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 131.81/18.77 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 131.81/18.77 (9) all_55_14 = all_8_1 % 131.81/18.77 (10) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.81/18.77 (11) ~ (all_53_2 = all_12_2) % 131.81/18.77 (12) ~ (all_12_2 = all_8_1) % 131.81/18.77 (13) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 131.81/18.77 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.81/18.77 (14) ~ (op(e0, e1) = e1) % 131.81/18.77 (15) all_57_15 = e1 % 131.81/18.77 (16) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 131.81/18.77 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 131.81/18.77 (17) op(e2, unit) = e2 % 131.81/18.77 (18) ~ (all_53_7 = all_8_1) % 131.81/18.77 (19) ~ (all_12_2 = e2) % 131.81/18.77 (20) all_20_1 = all_8_1 % 131.81/18.77 (21) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 131.81/18.77 $i(all_8_0)) % 131.81/18.77 (22) ~ (all_53_8 = all_53_9) % 131.81/18.77 (23) ~ (e3 = e0) % 131.81/18.77 (24) ~ (all_53_14 = all_12_2) % 131.81/18.77 (25) ~ (e2 = e0) % 131.81/18.77 (26) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 131.81/18.77 (27) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 131.81/18.77 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 131.81/18.77 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.81/18.77 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 131.81/18.77 (28) op(e1, e0) = all_53_14 % 131.81/18.77 (29) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.81/18.77 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.81/18.77 e2) % 131.81/18.77 (30) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 131.81/18.77 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 131.81/18.77 (31) all_12_2 = e3 % 131.81/18.77 (32) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 131.81/18.77 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.81/18.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.81/18.77 (34) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 131.81/18.77 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 131.81/18.77 (35) ~ (e3 = e1) % 131.81/18.77 (36) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 131.81/18.77 (37) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 131.81/18.77 (38) ~ (all_53_7 = e1) % 131.81/18.77 (39) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 131.91/18.77 (40) all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0 % 131.91/18.77 (41) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 131.91/18.77 (42) ~ (all_53_1 = all_53_9) % 131.91/18.77 (43) ~ (all_53_1 = all_6_2) % 131.91/18.77 (44) ~ (e2 = e1) % 131.91/18.77 (45) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 131.91/18.77 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 131.91/18.77 (46) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 131.91/18.77 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 131.91/18.77 (47) ~ (e1 = e0) % 131.91/18.77 (48) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 131.91/18.77 (49) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.77 (50) op(e0, unit) = e0 % 131.91/18.77 (51) ~ (all_53_14 = e1) % 131.91/18.77 (52) ~ (all_53_9 = all_6_2) % 131.91/18.77 (53) ~ (all_53_9 = all_12_2) % 131.91/18.77 (54) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 131.91/18.77 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 131.91/18.77 e3) % 131.91/18.77 (55) all_42_2 = all_6_2 % 131.91/18.77 (56) all_55_4 = all_53_1 % 131.91/18.77 (57) ~ (all_53_1 = all_53_3) % 131.91/18.77 (58) all_55_13 = all_53_7 % 131.91/18.77 (59) op(unit, e3) = e3 % 131.91/18.77 (60) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.77 (61) op(unit, e1) = e1 % 131.91/18.77 (62) all_55_12 = all_53_3 % 131.91/18.77 (63) ~ (all_53_9 = all_8_1) % 131.91/18.77 % 131.91/18.77 Begin of proof % 131.91/18.77 | % 131.91/18.77 | REDUCE: (11), (31) imply: % 131.91/18.77 | (64) ~ (all_53_2 = e3) % 131.91/18.77 | % 131.91/18.77 | REDUCE: (31), (53) imply: % 131.91/18.77 | (65) ~ (all_53_9 = e3) % 131.91/18.77 | % 131.91/18.77 | REDUCE: (24), (31) imply: % 131.91/18.77 | (66) ~ (all_53_14 = e3) % 131.91/18.77 | % 131.91/18.77 | REDUCE: (12), (31) imply: % 131.91/18.77 | (67) ~ (all_8_1 = e3) % 131.91/18.77 | % 131.91/18.77 | SIMP: (67) implies: % 131.91/18.77 | (68) ~ (all_8_1 = e3) % 131.91/18.77 | % 131.91/18.77 | REDUCE: (19), (31) imply: % 131.91/18.77 | (69) ~ (e3 = e2) % 131.91/18.77 | % 131.91/18.77 | REDUCE: (2), (31) imply: % 131.91/18.77 | (70) op(e1, e1) = e3 % 131.91/18.77 | % 131.91/18.77 | BETA: splitting (4) gives: % 131.91/18.77 | % 131.91/18.77 | Case 1: % 131.91/18.77 | | % 131.91/18.77 | | (71) ~ (op(e1, e3) = e3) % 131.91/18.77 | | % 131.91/18.77 | | BETA: splitting (16) gives: % 131.91/18.77 | | % 131.91/18.77 | | Case 1: % 131.91/18.77 | | | % 131.91/18.77 | | | (72) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 131.91/18.77 | | | e3) % 131.91/18.77 | | | % 131.91/18.77 | | | BETA: splitting (72) gives: % 131.91/18.77 | | | % 131.91/18.77 | | | Case 1: % 131.91/18.77 | | | | % 131.91/18.77 | | | | (73) all_57_6 = e3 & op(e1, e3) = e3 % 131.91/18.77 | | | | % 131.91/18.77 | | | | ALPHA: (73) implies: % 131.91/18.77 | | | | (74) op(e1, e3) = e3 % 131.91/18.77 | | | | % 131.91/18.77 | | | | PRED_UNIFY: (71), (74) imply: % 131.91/18.77 | | | | (75) $false % 131.91/18.77 | | | | % 131.91/18.77 | | | | CLOSE: (75) is inconsistent. % 131.91/18.77 | | | | % 131.91/18.77 | | | Case 2: % 131.91/18.77 | | | | % 131.91/18.77 | | | | (76) all_57_7 = e3 & op(e1, e2) = e3 % 131.91/18.77 | | | | % 131.91/18.77 | | | | ALPHA: (76) implies: % 131.91/18.77 | | | | (77) all_57_7 = e3 % 131.91/18.77 | | | | % 131.91/18.77 | | | | BETA: splitting (30) gives: % 131.91/18.77 | | | | % 131.91/18.77 | | | | Case 1: % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | (78) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, % 131.91/18.77 | | | | | e2) = e1) % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | BETA: splitting (78) gives: % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | Case 1: % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | (79) all_57_6 = e1 & op(e1, e3) = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | ALPHA: (79) implies: % 131.91/18.77 | | | | | | (80) all_57_6 = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | REF_CLOSE: (8), (23), (25), (33), (44), (46), (47), (69), (70), % 131.91/18.77 | | | | | | (77), (80) are inconsistent by sub-proof #304. % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | Case 2: % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | (81) all_57_7 = e1 & op(e1, e2) = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | REF_CLOSE: (35), (77), (81) are inconsistent by sub-proof #96. % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | End of split % 131.91/18.77 | | | | | % 131.91/18.77 | | | | Case 2: % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | (82) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, % 131.91/18.77 | | | | | e0) = e1) % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | BETA: splitting (82) gives: % 131.91/18.77 | | | | | % 131.91/18.77 | | | | | Case 1: % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | (83) all_57_8 = e1 & op(e1, e1) = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | ALPHA: (83) implies: % 131.91/18.77 | | | | | | (84) op(e1, e1) = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | REF_CLOSE: (31), (35), (48), (84) are inconsistent by sub-proof % 131.91/18.77 | | | | | | #174. % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | Case 2: % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | (85) all_57_11 = e1 & op(e1, e0) = e1 % 131.91/18.77 | | | | | | % 131.91/18.77 | | | | | | ALPHA: (85) implies: % 131.91/18.78 | | | | | | (86) op(e1, e0) = e1 % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | REF_CLOSE: (1), (51), (86) are inconsistent by sub-proof #339. % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | End of split % 131.91/18.78 | | | | | % 131.91/18.78 | | | | End of split % 131.91/18.78 | | | | % 131.91/18.78 | | | End of split % 131.91/18.78 | | | % 131.91/18.78 | | Case 2: % 131.91/18.78 | | | % 131.91/18.78 | | | (87) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 131.91/18.78 | | | e3) % 131.91/18.78 | | | % 131.91/18.78 | | | BETA: splitting (87) gives: % 131.91/18.78 | | | % 131.91/18.78 | | | Case 1: % 131.91/18.78 | | | | % 131.91/18.78 | | | | (88) all_57_8 = e3 & op(e1, e1) = e3 % 131.91/18.78 | | | | % 131.91/18.78 | | | | ALPHA: (88) implies: % 131.91/18.78 | | | | (89) all_57_8 = e3 % 131.91/18.78 | | | | % 131.91/18.78 | | | | PRED_UNIFY: (59), (71) imply: % 131.91/18.78 | | | | (90) ~ (unit = e1) % 131.91/18.78 | | | | % 131.91/18.78 | | | | BETA: splitting (5) gives: % 131.91/18.78 | | | | % 131.91/18.78 | | | | Case 1: % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | (91) unit = e2 % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | REDUCE: (59), (91) imply: % 131.91/18.78 | | | | | (92) op(e2, e3) = e3 % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | REDUCE: (61), (91) imply: % 131.91/18.78 | | | | | (93) op(e2, e1) = e1 % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | REDUCE: (17), (91) imply: % 131.91/18.78 | | | | | (94) op(e2, e2) = e2 % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | REDUCE: (50), (91) imply: % 131.91/18.78 | | | | | (95) op(e0, e2) = e0 % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | BETA: splitting (49) gives: % 131.91/18.78 | | | | | % 131.91/18.78 | | | | | Case 1: % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | (96) ~ (op(e2, e2) = e2) % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | PRED_UNIFY: (94), (96) imply: % 131.91/18.78 | | | | | | (97) $false % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | CLOSE: (97) is inconsistent. % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | Case 2: % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | (98) all_42_2 = e2 % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | COMBINE_EQS: (55), (98) imply: % 131.91/18.78 | | | | | | (99) all_6_2 = e2 % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | SIMP: (99) implies: % 131.91/18.78 | | | | | | (100) all_6_2 = e2 % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | REDUCE: (43), (100) imply: % 131.91/18.78 | | | | | | (101) ~ (all_53_1 = e2) % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | REDUCE: (52), (100) imply: % 131.91/18.78 | | | | | | (102) ~ (all_53_9 = e2) % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | BETA: splitting (60) gives: % 131.91/18.78 | | | | | | % 131.91/18.78 | | | | | | Case 1: % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | (103) ~ (op(e2, e1) = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | PRED_UNIFY: (93), (103) imply: % 131.91/18.78 | | | | | | | (104) $false % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | CLOSE: (104) is inconsistent. % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | Case 2: % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | (105) all_53_9 = e1 % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | REDUCE: (42), (105) imply: % 131.91/18.78 | | | | | | | (106) ~ (all_53_1 = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | REDUCE: (22), (105) imply: % 131.91/18.78 | | | | | | | (107) ~ (all_53_8 = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | REDUCE: (63), (105) imply: % 131.91/18.78 | | | | | | | (108) ~ (all_8_1 = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | SIMP: (108) implies: % 131.91/18.78 | | | | | | | (109) ~ (all_8_1 = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | REDUCE: (65), (105) imply: % 131.91/18.78 | | | | | | | (110) ~ (e3 = e1) % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | BETA: splitting (26) gives: % 131.91/18.78 | | | | | | | % 131.91/18.78 | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | (111) ~ (op(e0, e2) = e0) % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | PRED_UNIFY: (95), (111) imply: % 131.91/18.78 | | | | | | | | (112) $false % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | CLOSE: (112) is inconsistent. % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | (113) all_55_13 = e0 % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | COMBINE_EQS: (58), (113) imply: % 131.91/18.78 | | | | | | | | (114) all_53_7 = e0 % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | REDUCE: (6), (114) imply: % 131.91/18.78 | | | | | | | | (115) ~ (all_53_3 = e0) % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | REDUCE: (18), (114) imply: % 131.91/18.78 | | | | | | | | (116) ~ (all_8_1 = e0) % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | SIMP: (116) implies: % 131.91/18.78 | | | | | | | | (117) ~ (all_8_1 = e0) % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | REDUCE: (38), (114) imply: % 131.91/18.78 | | | | | | | | (118) ~ (e1 = e0) % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | BETA: splitting (10) gives: % 131.91/18.78 | | | | | | | | % 131.91/18.78 | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | (119) all_55_14 = e3 % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | COMBINE_EQS: (9), (119) imply: % 131.91/18.78 | | | | | | | | | (120) all_8_1 = e3 % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | REDUCE: (68), (120) imply: % 131.91/18.78 | | | | | | | | | (121) $false % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | CLOSE: (121) is inconsistent. % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | (122) ~ (all_55_14 = e3) % 131.91/18.78 | | | | | | | | | (123) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | BETA: splitting (123) gives: % 131.91/18.78 | | | | | | | | | % 131.91/18.78 | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | (124) all_55_14 = e2 % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | COMBINE_EQS: (9), (124) imply: % 131.91/18.78 | | | | | | | | | | (125) all_8_1 = e2 % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | COMBINE_EQS: (20), (125) imply: % 131.91/18.78 | | | | | | | | | | (126) all_20_1 = e2 % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | REDUCE: (68), (125) imply: % 131.91/18.78 | | | | | | | | | | (127) ~ (e3 = e2) % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | BETA: splitting (32) gives: % 131.91/18.78 | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | (128) ~ (op(e3, e1) = e1) % 131.91/18.78 | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | BETA: splitting (13) gives: % 131.91/18.78 | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | (129) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 131.91/18.78 | | | | | | | | | | | | & op(e2, e1) = e0) % 131.91/18.78 | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | BETA: splitting (129) gives: % 131.91/18.78 | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | (130) all_57_4 = e0 & op(e3, e1) = e0 % 131.91/18.78 | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | ALPHA: (130) implies: % 131.91/18.78 | | | | | | | | | | | | | (131) all_57_4 = e0 % 131.91/18.78 | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | BETA: splitting (27) gives: % 131.91/18.78 | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | (132) all_57_15 = e0 & op(e0, e0) = e0 % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | ALPHA: (132) implies: % 131.91/18.78 | | | | | | | | | | | | | | (133) all_57_15 = e0 % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | COMBINE_EQS: (15), (133) imply: % 131.91/18.78 | | | | | | | | | | | | | | (134) e1 = e0 % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | REDUCE: (47), (134) imply: % 131.91/18.78 | | | | | | | | | | | | | | (135) $false % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | (136) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 131.91/18.78 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 131.91/18.78 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 131.91/18.78 | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 131.91/18.78 | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | ALPHA: (136) implies: % 131.91/18.78 | | | | | | | | | | | | | | (137) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 131.91/18.78 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 131.91/18.78 | | | | | | | | | | | | | | e1) = e0) % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | BETA: splitting (21) gives: % 131.91/18.78 | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | (138) ~ (all_8_1 = e2) % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | REF_CLOSE: (9), (109), (117), (123), (138) are inconsistent % 131.91/18.78 | | | | | | | | | | | | | | | by sub-proof #63. % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | (139) ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 131.91/18.78 | | | | | | | | | | | | | | | $i(all_8_0) % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | ALPHA: (139) implies: % 131.91/18.78 | | | | | | | | | | | | | | | (140) ~ (all_8_0 = e3) % 131.91/18.78 | | | | | | | | | | | | | | | (141) op(e0, e2) = all_8_0 % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | BETA: splitting (29) gives: % 131.91/18.78 | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | (142) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 131.91/18.78 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | (143) all_57_12 = e2 & op(e0, e3) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | (144) all_57_12 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | BETA: splitting (45) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | (145) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (146) all_57_4 = e2 & op(e3, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (147) all_57_4 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (147) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (148) e2 = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REDUCE: (25), (148) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (149) $false % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (150) all_57_5 = e2 & op(e2, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (151) op(e2, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (102), (151) are inconsistent by sub-proof % 131.91/18.78 | | | | | | | | | | | | | | | | | | | #347. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | (152) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (153) all_57_8 = e2 & op(e1, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (154) all_57_8 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (154) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (155) e3 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | SIMP: (155) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (156) e3 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REDUCE: (69), (156) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (157) $false % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (158) all_57_14 = e2 & op(e0, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (159) all_57_14 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (160) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | (161) all_57_12 = e3 & op(e0, e3) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (144), (161) are inconsistent by sub-proof % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | #204. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | (162) all_57_13 = e3 & op(e0, e2) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | (163) op(e0, e2) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (140), (141), (163) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | sub-proof #62. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (164) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (35), (69), (159), (164) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | sub-proof #55. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | (165) all_57_13 = e2 & op(e0, e2) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | (166) all_57_13 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | (167) all_57_12 = e0 & op(e0, e3) = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (115), (167) are inconsistent by sub-proof % 131.91/18.78 | | | | | | | | | | | | | | | | | | #237. % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | (168) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (169) all_57_13 = e0 & op(e0, e2) = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (170) all_57_13 = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (170) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (171) e2 = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | SIMP: (171) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (172) e2 = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REDUCE: (25), (172) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (173) $false % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (174) all_57_14 = e0 & op(e0, e1) = e0 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (126), (174) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | sub-proof #54. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | (175) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 131.91/18.78 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | (176) all_57_14 = e2 & op(e0, e1) = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | ALPHA: (176) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | (177) all_57_14 = e2 % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | (178) all_55_4 = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (178) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | (179) all_53_1 = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | REDUCE: (57), (179) imply: % 131.91/18.78 | | | | | | | | | | | | | | | | | | (180) ~ (all_53_3 = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | SIMP: (180) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | (181) ~ (all_53_3 = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (182) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | Case 1: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (183) all_57_12 = e3 & op(e0, e3) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (184) op(e0, e3) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (62), (181), (184) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | sub-proof #311. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (185) all_57_13 = e3 & op(e0, e2) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | (186) op(e0, e2) = e3 % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (140), (141), (186) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | sub-proof #62. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | (187) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 131.91/18.78 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (35), (69), (177), (187) are inconsistent by % 131.91/18.78 | | | | | | | | | | | | | | | | | | | sub-proof #55. % 131.91/18.78 | | | | | | | | | | | | | | | | | | | % 131.91/18.78 | | | | | | | | | | | | | | | | | | End of split % 131.91/18.78 | | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | | (188) ~ (all_55_4 = e3) % 131.91/18.79 | | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | | REDUCE: (56), (188) imply: % 131.91/18.79 | | | | | | | | | | | | | | | | | | (189) ~ (all_53_1 = e3) % 131.91/18.79 | | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (92), (189) are inconsistent by sub-proof % 131.91/18.79 | | | | | | | | | | | | | | | | | | #353. % 131.91/18.79 | | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | (190) all_57_15 = e2 & op(e0, e0) = e2 % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | ALPHA: (190) implies: % 131.91/18.79 | | | | | | | | | | | | | | | | | (191) all_57_15 = e2 % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (191) imply: % 131.91/18.79 | | | | | | | | | | | | | | | | | (192) e2 = e1 % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | REDUCE: (44), (192) imply: % 131.91/18.79 | | | | | | | | | | | | | | | | | (193) $false % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 131.91/18.79 | | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | (194) all_57_5 = e0 & op(e2, e1) = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | ALPHA: (194) implies: % 131.91/18.79 | | | | | | | | | | | | | (195) all_57_5 = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | REF_CLOSE: (14), (34), (35), (47), (89), (128), (195) are % 131.91/18.79 | | | | | | | | | | | | | inconsistent by sub-proof #52. % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | (196) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 131.91/18.79 | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 131.91/18.79 | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | BETA: splitting (196) gives: % 131.91/18.79 | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | Case 1: % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | (197) all_57_8 = e0 & op(e1, e1) = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | ALPHA: (197) implies: % 131.91/18.79 | | | | | | | | | | | | | (198) all_57_8 = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | COMBINE_EQS: (89), (198) imply: % 131.91/18.79 | | | | | | | | | | | | | (199) e3 = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | REDUCE: (23), (199) imply: % 131.91/18.79 | | | | | | | | | | | | | (200) $false % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | (201) all_57_14 = e0 & op(e0, e1) = e0 % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | | REF_CLOSE: (7), (25), (126), (201) are inconsistent by % 131.91/18.79 | | | | | | | | | | | | | sub-proof #54. % 131.91/18.79 | | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | (202) all_53_8 = e1 % 131.91/18.79 | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | REDUCE: (107), (202) imply: % 131.91/18.79 | | | | | | | | | | | (203) $false % 131.91/18.79 | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | | CLOSE: (203) is inconsistent. % 131.91/18.79 | | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | | % 131.91/18.79 | | | | | | | | | Case 2: % 131.91/18.79 | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | (204) all_55_14 = e1 | all_55_14 = e0 % 131.91/18.79 | | | | | | | | | | % 131.91/18.79 | | | | | | | | | | REF_CLOSE: (9), (109), (117), (204) are inconsistent by % 131.91/18.79 | | | | | | | | | | sub-proof #64. % 131.91/18.79 | | | | | | | | | | % 131.91/18.79 | | | | | | | | | End of split % 131.91/18.79 | | | | | | | | | % 131.91/18.79 | | | | | | | | End of split % 131.91/18.79 | | | | | | | | % 131.91/18.79 | | | | | | | End of split % 131.91/18.79 | | | | | | | % 131.91/18.79 | | | | | | End of split % 131.91/18.79 | | | | | | % 131.91/18.79 | | | | | End of split % 131.91/18.79 | | | | | % 131.91/18.79 | | | | Case 2: % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | (205) unit = e1 | unit = e0 % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | REF_CLOSE: (3), (90), (205) are inconsistent by sub-proof #278. % 131.91/18.79 | | | | | % 131.91/18.79 | | | | End of split % 131.91/18.79 | | | | % 131.91/18.79 | | | Case 2: % 131.91/18.79 | | | | % 131.91/18.79 | | | | (206) all_57_11 = e3 & op(e1, e0) = e3 % 131.91/18.79 | | | | % 131.91/18.79 | | | | REF_CLOSE: (28), (33), (66), (206) are inconsistent by sub-proof #84. % 131.91/18.79 | | | | % 131.91/18.79 | | | End of split % 131.91/18.79 | | | % 131.91/18.79 | | End of split % 131.91/18.79 | | % 131.91/18.79 | Case 2: % 131.91/18.79 | | % 131.91/18.79 | | (207) all_53_2 = e3 % 131.91/18.79 | | % 131.91/18.79 | | REDUCE: (64), (207) imply: % 131.91/18.79 | | (208) $false % 131.91/18.79 | | % 131.91/18.79 | | CLOSE: (208) is inconsistent. % 131.91/18.79 | | % 131.91/18.79 | End of split % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #52 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) ~ (op(e0, e1) = e1) % 131.91/18.79 (2) ~ (op(e3, e1) = e1) % 131.91/18.79 (3) all_57_8 = e3 % 131.91/18.79 (4) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 131.91/18.79 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 131.91/18.79 (5) ~ (e3 = e1) % 131.91/18.79 (6) ~ (e1 = e0) % 131.91/18.79 (7) all_57_5 = e0 % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | BETA: splitting (4) gives: % 131.91/18.79 | % 131.91/18.79 | Case 1: % 131.91/18.79 | | % 131.91/18.79 | | (8) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 131.91/18.79 | | % 131.91/18.79 | | BETA: splitting (8) gives: % 131.91/18.79 | | % 131.91/18.79 | | Case 1: % 131.91/18.79 | | | % 131.91/18.79 | | | (9) all_57_4 = e1 & op(e3, e1) = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | REF_CLOSE: (2), (9) are inconsistent by sub-proof #239. % 131.91/18.79 | | | % 131.91/18.79 | | Case 2: % 131.91/18.79 | | | % 131.91/18.79 | | | (10) all_57_5 = e1 & op(e2, e1) = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | ALPHA: (10) implies: % 131.91/18.79 | | | (11) all_57_5 = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #70. % 131.91/18.79 | | | % 131.91/18.79 | | End of split % 131.91/18.79 | | % 131.91/18.79 | Case 2: % 131.91/18.79 | | % 131.91/18.79 | | (12) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 131.91/18.79 | | e1) % 131.91/18.79 | | % 131.91/18.79 | | BETA: splitting (12) gives: % 131.91/18.79 | | % 131.91/18.79 | | Case 1: % 131.91/18.79 | | | % 131.91/18.79 | | | (13) all_57_8 = e1 & op(e1, e1) = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | ALPHA: (13) implies: % 131.91/18.79 | | | (14) all_57_8 = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | COMBINE_EQS: (3), (14) imply: % 131.91/18.79 | | | (15) e3 = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | REDUCE: (5), (15) imply: % 131.91/18.79 | | | (16) $false % 131.91/18.79 | | | % 131.91/18.79 | | | CLOSE: (16) is inconsistent. % 131.91/18.79 | | | % 131.91/18.79 | | Case 2: % 131.91/18.79 | | | % 131.91/18.79 | | | (17) all_57_14 = e1 & op(e0, e1) = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | REF_CLOSE: (1), (17) are inconsistent by sub-proof #53. % 131.91/18.79 | | | % 131.91/18.79 | | End of split % 131.91/18.79 | | % 131.91/18.79 | End of split % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #53 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) all_57_14 = e1 & op(e0, e1) = e1 % 131.91/18.79 (2) ~ (op(e0, e1) = e1) % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | ALPHA: (1) implies: % 131.91/18.79 | (3) op(e0, e1) = e1 % 131.91/18.79 | % 131.91/18.79 | PRED_UNIFY: (2), (3) imply: % 131.91/18.79 | (4) $false % 131.91/18.79 | % 131.91/18.79 | CLOSE: (4) is inconsistent. % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #54 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) all_57_14 = e0 & op(e0, e1) = e0 % 131.91/18.79 (2) all_20_1 = e0 | ~ (op(e0, e1) = e0) % 131.91/18.79 (3) all_20_1 = e2 % 131.91/18.79 (4) ~ (e2 = e0) % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | ALPHA: (1) implies: % 131.91/18.79 | (5) op(e0, e1) = e0 % 131.91/18.79 | % 131.91/18.79 | BETA: splitting (2) gives: % 131.91/18.79 | % 131.91/18.79 | Case 1: % 131.91/18.79 | | % 131.91/18.79 | | (6) ~ (op(e0, e1) = e0) % 131.91/18.79 | | % 131.91/18.79 | | PRED_UNIFY: (5), (6) imply: % 131.91/18.79 | | (7) $false % 131.91/18.79 | | % 131.91/18.79 | | CLOSE: (7) is inconsistent. % 131.91/18.79 | | % 131.91/18.79 | Case 2: % 131.91/18.79 | | % 131.91/18.79 | | (8) all_20_1 = e0 % 131.91/18.79 | | % 131.91/18.79 | | COMBINE_EQS: (3), (8) imply: % 131.91/18.79 | | (9) e2 = e0 % 131.91/18.79 | | % 131.91/18.79 | | REDUCE: (4), (9) imply: % 131.91/18.79 | | (10) $false % 131.91/18.79 | | % 131.91/18.79 | | CLOSE: (10) is inconsistent. % 131.91/18.79 | | % 131.91/18.79 | End of split % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #55 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) all_57_15 = e1 % 131.91/18.79 (2) ~ (e3 = e1) % 131.91/18.79 (3) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 131.91/18.79 (4) ~ (e3 = e2) % 131.91/18.79 (5) all_57_14 = e2 % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | BETA: splitting (3) gives: % 131.91/18.79 | % 131.91/18.79 | Case 1: % 131.91/18.79 | | % 131.91/18.79 | | (6) all_57_14 = e3 & op(e0, e1) = e3 % 131.91/18.79 | | % 131.91/18.79 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #56. % 131.91/18.79 | | % 131.91/18.79 | Case 2: % 131.91/18.79 | | % 131.91/18.79 | | (7) all_57_15 = e3 & op(e0, e0) = e3 % 131.91/18.79 | | % 131.91/18.79 | | ALPHA: (7) implies: % 131.91/18.79 | | (8) all_57_15 = e3 % 131.91/18.79 | | % 131.91/18.79 | | COMBINE_EQS: (1), (8) imply: % 131.91/18.79 | | (9) e3 = e1 % 131.91/18.79 | | % 131.91/18.79 | | REDUCE: (2), (9) imply: % 131.91/18.79 | | (10) $false % 131.91/18.79 | | % 131.91/18.79 | | CLOSE: (10) is inconsistent. % 131.91/18.79 | | % 131.91/18.79 | End of split % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #56 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) all_57_14 = e3 & op(e0, e1) = e3 % 131.91/18.79 (2) all_57_14 = e2 % 131.91/18.79 (3) ~ (e3 = e2) % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | ALPHA: (1) implies: % 131.91/18.79 | (4) all_57_14 = e3 % 131.91/18.79 | % 131.91/18.79 | COMBINE_EQS: (2), (4) imply: % 131.91/18.79 | (5) e3 = e2 % 131.91/18.79 | % 131.91/18.79 | REDUCE: (3), (5) imply: % 131.91/18.79 | (6) $false % 131.91/18.79 | % 131.91/18.79 | CLOSE: (6) is inconsistent. % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #57 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) ~ (unit = e0) % 131.91/18.79 (2) unit = e2 | unit = e1 | unit = e0 % 131.91/18.79 (3) op(unit, e0) = e0 % 131.91/18.79 (4) all_22_2 = all_12_2 % 131.91/18.79 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.91/18.79 (6) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 131.91/18.79 (7) ~ (all_53_8 = all_53_12) % 131.91/18.79 (8) ~ (all_53_8 = all_12_2) % 131.91/18.79 (9) ~ (all_53_12 = e1) % 131.91/18.79 (10) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 131.91/18.79 (11) all_22_2 = e0 % 131.91/18.79 (12) ~ (all_53_8 = all_53_9) % 131.91/18.79 (13) ~ (all_53_14 = all_12_2) % 131.91/18.79 (14) ~ (all_53_12 = all_53_13) % 131.91/18.79 (15) ~ (all_53_4 = all_53_8) % 131.91/18.79 (16) all_55_3 = all_53_12 % 131.91/18.79 (17) all_55_2 = all_53_8 % 131.91/18.79 (18) all_53_4 = e3 | ~ (op(e3, e2) = e3) % 131.91/18.79 (19) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 131.91/18.79 (20) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.79 (21) op(unit, e1) = e1 % 131.91/18.79 (22) op(e3, unit) = e3 % 131.91/18.79 (23) ~ (all_53_4 = all_53_12) % 131.91/18.79 % 131.91/18.79 Begin of proof % 131.91/18.79 | % 131.91/18.79 | COMBINE_EQS: (4), (11) imply: % 131.91/18.79 | (24) all_12_2 = e0 % 131.91/18.79 | % 131.91/18.79 | SIMP: (24) implies: % 131.91/18.79 | (25) all_12_2 = e0 % 131.91/18.79 | % 131.91/18.79 | REDUCE: (8), (25) imply: % 131.91/18.79 | (26) ~ (all_53_8 = e0) % 131.91/18.79 | % 131.91/18.79 | REDUCE: (13), (25) imply: % 131.91/18.79 | (27) ~ (all_53_14 = e0) % 131.91/18.79 | % 131.91/18.79 | BETA: splitting (19) gives: % 131.91/18.79 | % 131.91/18.79 | Case 1: % 131.91/18.79 | | % 131.91/18.79 | | (28) ~ (op(e1, e0) = e0) % 131.91/18.79 | | % 131.91/18.79 | | PRED_UNIFY: (3), (28) imply: % 131.91/18.79 | | (29) ~ (unit = e1) % 131.91/18.79 | | % 131.91/18.79 | | BETA: splitting (2) gives: % 131.91/18.79 | | % 131.91/18.79 | | Case 1: % 131.91/18.79 | | | % 131.91/18.79 | | | (30) unit = e2 % 131.91/18.79 | | | % 131.91/18.79 | | | REDUCE: (21), (30) imply: % 131.91/18.79 | | | (31) op(e2, e1) = e1 % 131.91/18.79 | | | % 131.91/18.79 | | | REDUCE: (3), (30) imply: % 131.91/18.79 | | | (32) op(e2, e0) = e0 % 131.91/18.79 | | | % 131.91/18.79 | | | REDUCE: (22), (30) imply: % 131.91/18.79 | | | (33) op(e3, e2) = e3 % 131.91/18.79 | | | % 131.91/18.79 | | | BETA: splitting (5) gives: % 131.91/18.79 | | | % 131.91/18.79 | | | Case 1: % 131.91/18.79 | | | | % 131.91/18.79 | | | | (34) ~ (op(e2, e0) = e0) % 131.91/18.79 | | | | % 131.91/18.79 | | | | PRED_UNIFY: (32), (34) imply: % 131.91/18.79 | | | | (35) $false % 131.91/18.79 | | | | % 131.91/18.79 | | | | CLOSE: (35) is inconsistent. % 131.91/18.79 | | | | % 131.91/18.79 | | | Case 2: % 131.91/18.79 | | | | % 131.91/18.79 | | | | (36) all_53_13 = e0 % 131.91/18.79 | | | | % 131.91/18.79 | | | | REDUCE: (14), (36) imply: % 131.91/18.79 | | | | (37) ~ (all_53_12 = e0) % 131.91/18.79 | | | | % 131.91/18.79 | | | | BETA: splitting (20) gives: % 131.91/18.79 | | | | % 131.91/18.79 | | | | Case 1: % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | (38) ~ (op(e2, e1) = e1) % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | PRED_UNIFY: (31), (38) imply: % 131.91/18.79 | | | | | (39) $false % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | CLOSE: (39) is inconsistent. % 131.91/18.79 | | | | | % 131.91/18.79 | | | | Case 2: % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | (40) all_53_9 = e1 % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | REDUCE: (12), (40) imply: % 131.91/18.79 | | | | | (41) ~ (all_53_8 = e1) % 131.91/18.79 | | | | | % 131.91/18.79 | | | | | REF_CLOSE: (6), (7), (9), (10), (15), (16), (17), (18), (23), (26), % 131.91/18.79 | | | | | (33), (37), (41) are inconsistent by sub-proof #211. % 131.91/18.79 | | | | | % 131.91/18.79 | | | | End of split % 131.91/18.79 | | | | % 131.91/18.79 | | | End of split % 131.91/18.79 | | | % 131.91/18.79 | | Case 2: % 131.91/18.79 | | | % 131.91/18.79 | | | (42) unit = e1 | unit = e0 % 131.91/18.79 | | | % 131.91/18.79 | | | REF_CLOSE: (1), (29), (42) are inconsistent by sub-proof #278. % 131.91/18.79 | | | % 131.91/18.79 | | End of split % 131.91/18.79 | | % 131.91/18.79 | Case 2: % 131.91/18.79 | | % 131.91/18.79 | | (43) all_53_14 = e0 % 131.91/18.79 | | % 131.91/18.79 | | REDUCE: (27), (43) imply: % 131.91/18.79 | | (44) $false % 131.91/18.79 | | % 131.91/18.79 | | CLOSE: (44) is inconsistent. % 131.91/18.79 | | % 131.91/18.79 | End of split % 131.91/18.79 | % 131.91/18.79 End of proof % 131.91/18.79 % 131.91/18.79 Sub-proof #58 shows that the following formulas are inconsistent: % 131.91/18.79 ---------------------------------------------------------------- % 131.91/18.79 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 131.91/18.79 (2) ~ (all_53_12 = e1) % 131.91/18.80 (3) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 131.91/18.80 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.80 (5) op(e3, e0) = all_53_12 % 131.91/18.80 (6) ~ (all_53_8 = e1) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (1) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (7) all_57_4 = e1 & op(e3, e1) = e1 % 131.91/18.80 | | % 131.91/18.80 | | ALPHA: (7) implies: % 131.91/18.80 | | (8) op(e3, e1) = e1 % 131.91/18.80 | | % 131.91/18.80 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #238. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (9) all_57_9 = e1 & op(e3, e0) = e1 % 131.91/18.80 | | % 131.91/18.80 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #273. % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #59 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.91/18.80 (2) ~ (all_53_3 = all_53_7) % 131.91/18.80 (3) all_55_14 = all_8_1 % 131.91/18.80 (4) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.91/18.80 (5) ~ (all_53_7 = all_8_1) % 131.91/18.80 (6) all_53_4 = e2 | ~ (op(e3, e2) = e2) % 131.91/18.80 (7) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & % 131.91/18.80 $i(all_8_0)) % 131.91/18.80 (8) op(e0, e2) = all_53_7 % 131.91/18.80 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.80 (10) op(e0, e3) = e0 % 131.91/18.80 (11) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 131.91/18.80 (12) ~ (all_53_7 = e1) % 131.91/18.80 (13) ~ (all_53_4 = all_53_7) % 131.91/18.80 (14) ~ (all_8_1 = e1) % 131.91/18.80 (15) op(e3, e2) = e2 % 131.91/18.80 (16) all_55_13 = all_53_7 % 131.91/18.80 (17) ~ (all_53_3 = all_8_1) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (11) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (18) ~ (op(e0, e3) = e0) % 131.91/18.80 | | % 131.91/18.80 | | PRED_UNIFY: (10), (18) imply: % 131.91/18.80 | | (19) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (19) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (20) all_53_3 = e0 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (2), (20) imply: % 131.91/18.80 | | (21) ~ (all_53_7 = e0) % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (21) implies: % 131.91/18.80 | | (22) ~ (all_53_7 = e0) % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (17), (20) imply: % 131.91/18.80 | | (23) ~ (all_8_1 = e0) % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (23) implies: % 131.91/18.80 | | (24) ~ (all_8_1 = e0) % 131.91/18.80 | | % 131.91/18.80 | | BETA: splitting (6) gives: % 131.91/18.80 | | % 131.91/18.80 | | Case 1: % 131.91/18.80 | | | % 131.91/18.80 | | | (25) ~ (op(e3, e2) = e2) % 131.91/18.80 | | | % 131.91/18.80 | | | PRED_UNIFY: (15), (25) imply: % 131.91/18.80 | | | (26) $false % 131.91/18.80 | | | % 131.91/18.80 | | | CLOSE: (26) is inconsistent. % 131.91/18.80 | | | % 131.91/18.80 | | Case 2: % 131.91/18.80 | | | % 131.91/18.80 | | | (27) all_53_4 = e2 % 131.91/18.80 | | | % 131.91/18.80 | | | REDUCE: (13), (27) imply: % 131.91/18.80 | | | (28) ~ (all_53_7 = e2) % 131.91/18.80 | | | % 131.91/18.80 | | | SIMP: (28) implies: % 131.91/18.80 | | | (29) ~ (all_53_7 = e2) % 131.91/18.80 | | | % 131.91/18.80 | | | BETA: splitting (1) gives: % 131.91/18.80 | | | % 131.91/18.80 | | | Case 1: % 131.91/18.80 | | | | % 131.91/18.80 | | | | (30) all_55_13 = e3 % 131.91/18.80 | | | | % 131.91/18.80 | | | | COMBINE_EQS: (16), (30) imply: % 131.91/18.80 | | | | (31) all_53_7 = e3 % 131.91/18.80 | | | | % 131.91/18.80 | | | | REDUCE: (5), (31) imply: % 131.91/18.80 | | | | (32) ~ (all_8_1 = e3) % 131.91/18.80 | | | | % 131.91/18.80 | | | | SIMP: (32) implies: % 131.91/18.80 | | | | (33) ~ (all_8_1 = e3) % 131.91/18.80 | | | | % 131.91/18.80 | | | | REDUCE: (8), (31) imply: % 131.91/18.80 | | | | (34) op(e0, e2) = e3 % 131.91/18.80 | | | | % 131.91/18.80 | | | | BETA: splitting (4) gives: % 131.91/18.80 | | | | % 131.91/18.80 | | | | Case 1: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (35) all_55_14 = e3 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | COMBINE_EQS: (3), (35) imply: % 131.91/18.80 | | | | | (36) all_8_1 = e3 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | REDUCE: (33), (36) imply: % 131.91/18.80 | | | | | (37) $false % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | CLOSE: (37) is inconsistent. % 131.91/18.80 | | | | | % 131.91/18.80 | | | | Case 2: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (38) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | BETA: splitting (7) gives: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | Case 1: % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | | (39) ~ (all_8_1 = e2) % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | | REF_CLOSE: (3), (14), (24), (38), (39) are inconsistent by sub-proof % 131.91/18.80 | | | | | | #63. % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | Case 2: % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | | (40) ~ (all_8_0 = e3) & op(e0, e2) = all_8_0 & $i(all_8_0) % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | | ALPHA: (40) implies: % 131.91/18.80 | | | | | | (41) ~ (all_8_0 = e3) % 131.91/18.80 | | | | | | (42) op(e0, e2) = all_8_0 % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | | REF_CLOSE: (9), (34), (41), (42) are inconsistent by sub-proof #62. % 131.91/18.80 | | | | | | % 131.91/18.80 | | | | | End of split % 131.91/18.80 | | | | | % 131.91/18.80 | | | | End of split % 131.91/18.80 | | | | % 131.91/18.80 | | | Case 2: % 131.91/18.80 | | | | % 131.91/18.80 | | | | (43) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.91/18.80 | | | | % 131.91/18.80 | | | | REF_CLOSE: (12), (16), (22), (29), (43) are inconsistent by sub-proof % 131.91/18.80 | | | | #60. % 131.91/18.80 | | | | % 131.91/18.80 | | | End of split % 131.91/18.80 | | | % 131.91/18.80 | | End of split % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #60 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0 % 131.91/18.80 (2) ~ (all_53_7 = e0) % 131.91/18.80 (3) ~ (all_53_7 = e1) % 131.91/18.80 (4) ~ (all_53_7 = e2) % 131.91/18.80 (5) all_55_13 = all_53_7 % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (1) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (6) all_55_13 = e2 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (5), (6) imply: % 131.91/18.80 | | (7) all_53_7 = e2 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (4), (7) imply: % 131.91/18.80 | | (8) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (8) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (9) all_55_13 = e1 | all_55_13 = e0 % 131.91/18.80 | | % 131.91/18.80 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #61. % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #61 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) all_55_13 = e1 | all_55_13 = e0 % 131.91/18.80 (2) all_55_13 = all_53_7 % 131.91/18.80 (3) ~ (all_53_7 = e1) % 131.91/18.80 (4) ~ (all_53_7 = e0) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (1) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (5) all_55_13 = e1 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (2), (5) imply: % 131.91/18.80 | | (6) all_53_7 = e1 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (3), (6) imply: % 131.91/18.80 | | (7) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (7) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (8) all_55_13 = e0 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (2), (8) imply: % 131.91/18.80 | | (9) all_53_7 = e0 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (4), (9) imply: % 131.91/18.80 | | (10) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (10) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #62 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.80 (2) op(e0, e2) = all_8_0 % 131.91/18.80 (3) op(e0, e2) = e3 % 131.91/18.80 (4) ~ (all_8_0 = e3) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | GROUND_INST: instantiating (1) with e3, all_8_0, e2, e0, simplifying with (2), % 131.91/18.80 | (3) gives: % 131.91/18.80 | (5) all_8_0 = e3 % 131.91/18.80 | % 131.91/18.80 | REDUCE: (4), (5) imply: % 131.91/18.80 | (6) $false % 131.91/18.80 | % 131.91/18.80 | CLOSE: (6) is inconsistent. % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #63 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) all_55_14 = all_8_1 % 131.91/18.80 (2) ~ (all_8_1 = e2) % 131.91/18.80 (3) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 131.91/18.80 (4) ~ (all_8_1 = e1) % 131.91/18.80 (5) ~ (all_8_1 = e0) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (3) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (6) all_55_14 = e2 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (1), (6) imply: % 131.91/18.80 | | (7) all_8_1 = e2 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (2), (7) imply: % 131.91/18.80 | | (8) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (8) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (9) all_55_14 = e1 | all_55_14 = e0 % 131.91/18.80 | | % 131.91/18.80 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #64. % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #64 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) all_55_14 = e1 | all_55_14 = e0 % 131.91/18.80 (2) all_55_14 = all_8_1 % 131.91/18.80 (3) ~ (all_8_1 = e1) % 131.91/18.80 (4) ~ (all_8_1 = e0) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (1) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (5) all_55_14 = e1 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (2), (5) imply: % 131.91/18.80 | | (6) all_8_1 = e1 % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (6) implies: % 131.91/18.80 | | (7) all_8_1 = e1 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (3), (7) imply: % 131.91/18.80 | | (8) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (8) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (9) all_55_14 = e0 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (2), (9) imply: % 131.91/18.80 | | (10) all_8_1 = e0 % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (10) implies: % 131.91/18.80 | | (11) all_8_1 = e0 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (4), (11) imply: % 131.91/18.80 | | (12) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (12) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #65 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) ~ (all_53_9 = all_53_11) % 131.91/18.80 (2) op(e2, unit) = e2 % 131.91/18.80 (3) all_30_1 = all_12_1 % 131.91/18.80 (4) unit = e2 % 131.91/18.80 (5) ~ (all_53_11 = e2) % 131.91/18.80 (6) op(e0, e2) = all_53_7 % 131.91/18.80 (7) op(e0, e1) = all_53_11 % 131.91/18.80 (8) op(e0, e0) = all_8_2 % 131.91/18.80 (9) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | % 131.91/18.80 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 131.91/18.80 (10) ~ (all_8_2 = e1) % 131.91/18.80 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.80 (12) all_26_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.80 (13) all_50_2 = all_6_2 % 131.91/18.80 (14) ~ (all_12_1 = all_6_2) % 131.91/18.80 (15) ~ (all_53_7 = all_6_2) % 131.91/18.80 (16) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.80 (17) ~ (all_6_2 = e3) % 131.91/18.80 (18) all_30_1 = e1 | ~ (op(e1, e2) = e1) % 131.91/18.80 (19) ~ (all_53_7 = all_12_1) % 131.91/18.80 (20) op(e2, e2) = all_6_2 % 131.91/18.80 (21) op(e1, unit) = e1 % 131.91/18.80 (22) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 131.91/18.80 (23) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.91/18.80 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 131.91/18.80 e1) % 131.91/18.80 (24) all_57_15 = e3 % 131.91/18.80 (25) all_26_2 = all_6_2 % 131.91/18.80 (26) all_55_13 = all_53_7 % 131.91/18.80 (27) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.80 (28) op(unit, e1) = e1 % 131.91/18.80 (29) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 131.91/18.80 % 131.91/18.80 Begin of proof % 131.91/18.80 | % 131.91/18.80 | REDUCE: (4), (28) imply: % 131.91/18.80 | (30) op(e2, e1) = e1 % 131.91/18.80 | % 131.91/18.80 | REDUCE: (2), (4) imply: % 131.91/18.80 | (31) op(e2, e2) = e2 % 131.91/18.80 | % 131.91/18.80 | REDUCE: (4), (21) imply: % 131.91/18.80 | (32) op(e1, e2) = e1 % 131.91/18.80 | % 131.91/18.80 | BETA: splitting (12) gives: % 131.91/18.80 | % 131.91/18.80 | Case 1: % 131.91/18.80 | | % 131.91/18.80 | | (33) ~ (op(e2, e2) = e2) % 131.91/18.80 | | % 131.91/18.80 | | PRED_UNIFY: (31), (33) imply: % 131.91/18.80 | | (34) $false % 131.91/18.80 | | % 131.91/18.80 | | CLOSE: (34) is inconsistent. % 131.91/18.80 | | % 131.91/18.80 | Case 2: % 131.91/18.80 | | % 131.91/18.80 | | (35) all_26_2 = e2 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (25), (35) imply: % 131.91/18.80 | | (36) all_6_2 = e2 % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (36) implies: % 131.91/18.80 | | (37) all_6_2 = e2 % 131.91/18.80 | | % 131.91/18.80 | | COMBINE_EQS: (13), (37) imply: % 131.91/18.80 | | (38) all_50_2 = e2 % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (15), (37) imply: % 131.91/18.80 | | (39) ~ (all_53_7 = e2) % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (14), (37) imply: % 131.91/18.80 | | (40) ~ (all_12_1 = e2) % 131.91/18.80 | | % 131.91/18.80 | | REDUCE: (17), (37) imply: % 131.91/18.80 | | (41) ~ (e3 = e2) % 131.91/18.80 | | % 131.91/18.80 | | SIMP: (41) implies: % 131.91/18.80 | | (42) ~ (e3 = e2) % 131.91/18.80 | | % 131.91/18.80 | | BETA: splitting (18) gives: % 131.91/18.80 | | % 131.91/18.80 | | Case 1: % 131.91/18.80 | | | % 131.91/18.80 | | | (43) ~ (op(e1, e2) = e1) % 131.91/18.80 | | | % 131.91/18.80 | | | PRED_UNIFY: (32), (43) imply: % 131.91/18.80 | | | (44) $false % 131.91/18.80 | | | % 131.91/18.80 | | | CLOSE: (44) is inconsistent. % 131.91/18.80 | | | % 131.91/18.80 | | Case 2: % 131.91/18.80 | | | % 131.91/18.80 | | | (45) all_30_1 = e1 % 131.91/18.80 | | | % 131.91/18.80 | | | COMBINE_EQS: (3), (45) imply: % 131.91/18.80 | | | (46) all_12_1 = e1 % 131.91/18.80 | | | % 131.91/18.80 | | | SIMP: (46) implies: % 131.91/18.80 | | | (47) all_12_1 = e1 % 131.91/18.80 | | | % 131.91/18.80 | | | REDUCE: (19), (47) imply: % 131.91/18.80 | | | (48) ~ (all_53_7 = e1) % 131.91/18.80 | | | % 131.91/18.80 | | | REDUCE: (40), (47) imply: % 131.91/18.80 | | | (49) ~ (e2 = e1) % 131.91/18.80 | | | % 131.91/18.80 | | | SIMP: (49) implies: % 131.91/18.80 | | | (50) ~ (e2 = e1) % 131.91/18.80 | | | % 131.91/18.80 | | | BETA: splitting (9) gives: % 131.91/18.80 | | | % 131.91/18.80 | | | Case 1: % 131.91/18.80 | | | | % 131.91/18.80 | | | | (51) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 131.91/18.80 | | | | e2) = e2) % 131.91/18.80 | | | | % 131.91/18.80 | | | | BETA: splitting (51) gives: % 131.91/18.80 | | | | % 131.91/18.80 | | | | Case 1: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (52) all_57_12 = e2 & op(e0, e3) = e2 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | REF_CLOSE: (1), (6), (8), (10), (11), (16), (22), (23), (27), (30), % 131.91/18.80 | | | | | (31), (38), (48), (50), (52) are inconsistent by sub-proof % 131.91/18.80 | | | | | #67. % 131.91/18.80 | | | | | % 131.91/18.80 | | | | Case 2: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (53) all_57_13 = e2 & op(e0, e2) = e2 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | ALPHA: (53) implies: % 131.91/18.80 | | | | | (54) op(e0, e2) = e2 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | REF_CLOSE: (26), (29), (39), (54) are inconsistent by sub-proof #118. % 131.91/18.80 | | | | | % 131.91/18.80 | | | | End of split % 131.91/18.80 | | | | % 131.91/18.80 | | | Case 2: % 131.91/18.80 | | | | % 131.91/18.80 | | | | (55) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 131.91/18.80 | | | | e0) = e2) % 131.91/18.80 | | | | % 131.91/18.80 | | | | BETA: splitting (55) gives: % 131.91/18.80 | | | | % 131.91/18.80 | | | | Case 1: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (56) all_57_14 = e2 & op(e0, e1) = e2 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | REF_CLOSE: (5), (7), (11), (56) are inconsistent by sub-proof #119. % 131.91/18.80 | | | | | % 131.91/18.80 | | | | Case 2: % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | (57) all_57_15 = e2 & op(e0, e0) = e2 % 131.91/18.80 | | | | | % 131.91/18.80 | | | | | REF_CLOSE: (24), (42), (57) are inconsistent by sub-proof #80. % 131.91/18.80 | | | | | % 131.91/18.80 | | | | End of split % 131.91/18.80 | | | | % 131.91/18.80 | | | End of split % 131.91/18.80 | | | % 131.91/18.80 | | End of split % 131.91/18.80 | | % 131.91/18.80 | End of split % 131.91/18.80 | % 131.91/18.80 End of proof % 131.91/18.80 % 131.91/18.80 Sub-proof #66 shows that the following formulas are inconsistent: % 131.91/18.80 ---------------------------------------------------------------- % 131.91/18.80 (1) ~ (all_53_9 = all_53_11) % 131.91/18.80 (2) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 131.91/18.80 $i(all_16_0)) % 131.91/18.80 (3) ~ (all_53_6 = all_53_7) % 131.91/18.80 (4) all_53_5 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.80 (5) ~ (all_10_1 = e3) % 131.91/18.80 (6) op(e0, e2) = all_53_7 % 131.91/18.80 (7) all_53_6 = e1 | ~ (op(e1, e2) = e1) % 131.91/18.80 (8) op(e0, e0) = all_8_2 % 131.91/18.80 (9) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 131.91/18.80 (10) op(e2, e2) = e2 % 131.91/18.80 (11) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.91/18.80 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.91/18.80 e2) % 131.91/18.80 (12) ~ (all_8_2 = e1) % 131.91/18.80 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.80 (14) op(e0, e2) = e0 % 131.91/18.80 (15) all_50_2 = all_6_2 % 131.91/18.80 (16) ~ (all_53_7 = all_6_2) % 131.91/18.80 (17) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.91/18.80 (18) op(e1, e2) = e1 % 131.91/18.80 (19) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.80 (20) ~ (all_6_2 = e3) % 131.91/18.80 (21) all_55_12 = all_10_1 % 131.91/18.80 (22) op(e2, e2) = all_6_2 % 131.91/18.80 (23) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 131.91/18.80 (24) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 131.91/18.81 (25) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.91/18.81 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 131.91/18.81 e1) % 131.91/18.81 (26) all_16_1 = all_10_1 % 131.91/18.81 (27) all_57_15 = e3 % 131.91/18.81 (28) ~ (all_10_1 = e2) % 131.91/18.81 (29) ~ (all_53_7 = all_10_1) % 131.91/18.81 (30) all_55_13 = all_53_7 % 131.91/18.81 (31) ~ (all_53_6 = all_6_2) % 131.91/18.81 (32) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.81 (33) op(e2, e1) = e1 % 131.91/18.81 (34) all_53_5 = all_6_2 % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | BETA: splitting (7) gives: % 131.91/18.81 | % 131.91/18.81 | Case 1: % 131.91/18.81 | | % 131.91/18.81 | | (35) ~ (op(e1, e2) = e1) % 131.91/18.81 | | % 131.91/18.81 | | PRED_UNIFY: (18), (35) imply: % 131.91/18.81 | | (36) $false % 131.91/18.81 | | % 131.91/18.81 | | CLOSE: (36) is inconsistent. % 131.91/18.81 | | % 131.91/18.81 | Case 2: % 131.91/18.81 | | % 131.91/18.81 | | (37) all_53_6 = e1 % 131.91/18.81 | | % 131.91/18.81 | | REDUCE: (3), (37) imply: % 131.91/18.81 | | (38) ~ (all_53_7 = e1) % 131.91/18.81 | | % 131.91/18.81 | | SIMP: (38) implies: % 131.91/18.81 | | (39) ~ (all_53_7 = e1) % 131.91/18.81 | | % 131.91/18.81 | | REDUCE: (31), (37) imply: % 131.91/18.81 | | (40) ~ (all_6_2 = e1) % 131.91/18.81 | | % 131.91/18.81 | | SIMP: (40) implies: % 131.91/18.81 | | (41) ~ (all_6_2 = e1) % 131.91/18.81 | | % 131.91/18.81 | | BETA: splitting (4) gives: % 131.91/18.81 | | % 131.91/18.81 | | Case 1: % 131.91/18.81 | | | % 131.91/18.81 | | | (42) ~ (op(e2, e2) = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | PRED_UNIFY: (10), (42) imply: % 131.91/18.81 | | | (43) $false % 131.91/18.81 | | | % 131.91/18.81 | | | CLOSE: (43) is inconsistent. % 131.91/18.81 | | | % 131.91/18.81 | | Case 2: % 131.91/18.81 | | | % 131.91/18.81 | | | (44) all_53_5 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | COMBINE_EQS: (34), (44) imply: % 131.91/18.81 | | | (45) all_6_2 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | COMBINE_EQS: (15), (45) imply: % 131.91/18.81 | | | (46) all_50_2 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | REDUCE: (16), (45) imply: % 131.91/18.81 | | | (47) ~ (all_53_7 = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | REDUCE: (20), (45) imply: % 131.91/18.81 | | | (48) ~ (e3 = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | SIMP: (48) implies: % 131.91/18.81 | | | (49) ~ (e3 = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | REDUCE: (41), (45) imply: % 131.91/18.81 | | | (50) ~ (e2 = e1) % 131.91/18.81 | | | % 131.91/18.81 | | | BETA: splitting (9) gives: % 131.91/18.81 | | | % 131.91/18.81 | | | Case 1: % 131.91/18.81 | | | | % 131.91/18.81 | | | | (51) ~ (op(e0, e2) = e0) % 131.91/18.81 | | | | % 131.91/18.81 | | | | PRED_UNIFY: (14), (51) imply: % 131.91/18.81 | | | | (52) $false % 131.91/18.81 | | | | % 131.91/18.81 | | | | CLOSE: (52) is inconsistent. % 131.91/18.81 | | | | % 131.91/18.81 | | | Case 2: % 131.91/18.81 | | | | % 131.91/18.81 | | | | (53) all_55_13 = e0 % 131.91/18.81 | | | | % 131.91/18.81 | | | | COMBINE_EQS: (30), (53) imply: % 131.91/18.81 | | | | (54) all_53_7 = e0 % 131.91/18.81 | | | | % 131.91/18.81 | | | | REDUCE: (29), (54) imply: % 131.91/18.81 | | | | (55) ~ (all_10_1 = e0) % 131.91/18.81 | | | | % 131.91/18.81 | | | | SIMP: (55) implies: % 131.91/18.81 | | | | (56) ~ (all_10_1 = e0) % 131.91/18.81 | | | | % 131.91/18.81 | | | | REDUCE: (47), (54) imply: % 131.91/18.81 | | | | (57) ~ (e2 = e0) % 131.91/18.81 | | | | % 131.91/18.81 | | | | SIMP: (57) implies: % 131.91/18.81 | | | | (58) ~ (e2 = e0) % 131.91/18.81 | | | | % 131.91/18.81 | | | | BETA: splitting (11) gives: % 131.91/18.81 | | | | % 131.91/18.81 | | | | Case 1: % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | (59) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 131.91/18.81 | | | | | e2) = e2) % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | BETA: splitting (59) gives: % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | Case 1: % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | (60) all_57_12 = e2 & op(e0, e3) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | REF_CLOSE: (1), (6), (8), (10), (12), (13), (19), (24), (25), (32), % 131.91/18.81 | | | | | | (33), (39), (46), (50), (60) are inconsistent by % 131.91/18.81 | | | | | | sub-proof #67. % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | Case 2: % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | (61) all_57_13 = e2 & op(e0, e2) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | ALPHA: (61) implies: % 131.91/18.81 | | | | | | (62) op(e0, e2) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | REF_CLOSE: (23), (54), (58), (62) are inconsistent by sub-proof % 131.91/18.81 | | | | | | #191. % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | End of split % 131.91/18.81 | | | | | % 131.91/18.81 | | | | Case 2: % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | (63) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 131.91/18.81 | | | | | e0) = e2) % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | BETA: splitting (63) gives: % 131.91/18.81 | | | | | % 131.91/18.81 | | | | | Case 1: % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | (64) all_57_14 = e2 & op(e0, e1) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | ALPHA: (64) implies: % 131.91/18.81 | | | | | | (65) op(e0, e1) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | BETA: splitting (17) gives: % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | Case 1: % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | (66) all_55_12 = e3 % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | COMBINE_EQS: (21), (66) imply: % 131.91/18.81 | | | | | | | (67) all_10_1 = e3 % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | SIMP: (67) implies: % 131.91/18.81 | | | | | | | (68) all_10_1 = e3 % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | REDUCE: (5), (68) imply: % 131.91/18.81 | | | | | | | (69) $false % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | CLOSE: (69) is inconsistent. % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | Case 2: % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | (70) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | BETA: splitting (70) gives: % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | | Case 1: % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | (71) all_55_12 = e2 % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | COMBINE_EQS: (21), (71) imply: % 131.91/18.81 | | | | | | | | (72) all_10_1 = e2 % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | SIMP: (72) implies: % 131.91/18.81 | | | | | | | | (73) all_10_1 = e2 % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | REDUCE: (28), (73) imply: % 131.91/18.81 | | | | | | | | (74) $false % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | CLOSE: (74) is inconsistent. % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | Case 2: % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | (75) all_55_12 = e1 | all_55_12 = e0 % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | BETA: splitting (75) gives: % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | | Case 1: % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | (76) all_55_12 = e1 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | COMBINE_EQS: (21), (76) imply: % 131.91/18.81 | | | | | | | | | (77) all_10_1 = e1 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | SIMP: (77) implies: % 131.91/18.81 | | | | | | | | | (78) all_10_1 = e1 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | REF_CLOSE: (2), (13), (26), (65), (78) are inconsistent by % 131.91/18.81 | | | | | | | | | sub-proof #73. % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | Case 2: % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | (79) all_55_12 = e0 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | COMBINE_EQS: (21), (79) imply: % 131.91/18.81 | | | | | | | | | (80) all_10_1 = e0 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | SIMP: (80) implies: % 131.91/18.81 | | | | | | | | | (81) all_10_1 = e0 % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | REDUCE: (56), (81) imply: % 131.91/18.81 | | | | | | | | | (82) $false % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | | CLOSE: (82) is inconsistent. % 131.91/18.81 | | | | | | | | | % 131.91/18.81 | | | | | | | | End of split % 131.91/18.81 | | | | | | | | % 131.91/18.81 | | | | | | | End of split % 131.91/18.81 | | | | | | | % 131.91/18.81 | | | | | | End of split % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | Case 2: % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | (83) all_57_15 = e2 & op(e0, e0) = e2 % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | | REF_CLOSE: (27), (49), (83) are inconsistent by sub-proof #80. % 131.91/18.81 | | | | | | % 131.91/18.81 | | | | | End of split % 131.91/18.81 | | | | | % 131.91/18.81 | | | | End of split % 131.91/18.81 | | | | % 131.91/18.81 | | | End of split % 131.91/18.81 | | | % 131.91/18.81 | | End of split % 131.91/18.81 | | % 131.91/18.81 | End of split % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #67 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) ~ (all_53_9 = all_53_11) % 131.91/18.81 (2) all_57_12 = e2 & op(e0, e3) = e2 % 131.91/18.81 (3) op(e0, e2) = all_53_7 % 131.91/18.81 (4) op(e0, e0) = all_8_2 % 131.91/18.81 (5) op(e2, e2) = e2 % 131.91/18.81 (6) ~ (all_8_2 = e1) % 131.91/18.81 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.81 (8) ~ (all_53_7 = e1) % 131.91/18.81 (9) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.81 (10) all_50_2 = e2 % 131.91/18.81 (11) ~ (e2 = e1) % 131.91/18.81 (12) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 131.91/18.81 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 131.91/18.81 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 131.91/18.81 e1) % 131.91/18.81 (14) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.81 (15) op(e2, e1) = e1 % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | ALPHA: (2) implies: % 131.91/18.81 | (16) all_57_12 = e2 % 131.91/18.81 | % 131.91/18.81 | BETA: splitting (13) gives: % 131.91/18.81 | % 131.91/18.81 | Case 1: % 131.91/18.81 | | % 131.91/18.81 | | (17) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 131.91/18.81 | | e1) % 131.91/18.81 | | % 131.91/18.81 | | BETA: splitting (17) gives: % 131.91/18.81 | | % 131.91/18.81 | | Case 1: % 131.91/18.81 | | | % 131.91/18.81 | | | (18) all_57_12 = e1 & op(e0, e3) = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | ALPHA: (18) implies: % 131.91/18.81 | | | (19) all_57_12 = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | COMBINE_EQS: (16), (19) imply: % 131.91/18.81 | | | (20) e2 = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | SIMP: (20) implies: % 131.91/18.81 | | | (21) e2 = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | COMBINE_EQS: (10), (21) imply: % 131.91/18.81 | | | (22) all_50_2 = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | REF_CLOSE: (5), (9), (11), (22) are inconsistent by sub-proof #196. % 131.91/18.81 | | | % 131.91/18.81 | | Case 2: % 131.91/18.81 | | | % 131.91/18.81 | | | (23) all_57_13 = e1 & op(e0, e2) = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | REF_CLOSE: (3), (7), (8), (23) are inconsistent by sub-proof #106. % 131.91/18.81 | | | % 131.91/18.81 | | End of split % 131.91/18.81 | | % 131.91/18.81 | Case 2: % 131.91/18.81 | | % 131.91/18.81 | | (24) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 131.91/18.81 | | e1) % 131.91/18.81 | | % 131.91/18.81 | | BETA: splitting (24) gives: % 131.91/18.81 | | % 131.91/18.81 | | Case 1: % 131.91/18.81 | | | % 131.91/18.81 | | | (25) all_57_14 = e1 & op(e0, e1) = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | ALPHA: (25) implies: % 131.91/18.81 | | | (26) op(e0, e1) = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | BETA: splitting (12) gives: % 131.91/18.81 | | | % 131.91/18.81 | | | Case 1: % 131.91/18.81 | | | | % 131.91/18.81 | | | | (27) ~ (op(e0, e1) = e1) % 131.91/18.81 | | | | % 131.91/18.81 | | | | PRED_UNIFY: (26), (27) imply: % 131.91/18.81 | | | | (28) $false % 131.91/18.81 | | | | % 131.91/18.81 | | | | CLOSE: (28) is inconsistent. % 131.91/18.81 | | | | % 131.91/18.81 | | | Case 2: % 131.91/18.81 | | | | % 131.91/18.81 | | | | (29) all_53_11 = e1 % 131.91/18.81 | | | | % 131.91/18.81 | | | | REDUCE: (1), (29) imply: % 131.91/18.81 | | | | (30) ~ (all_53_9 = e1) % 131.91/18.81 | | | | % 131.91/18.81 | | | | REF_CLOSE: (14), (15), (30) are inconsistent by sub-proof #334. % 131.91/18.81 | | | | % 131.91/18.81 | | | End of split % 131.91/18.81 | | | % 131.91/18.81 | | Case 2: % 131.91/18.81 | | | % 131.91/18.81 | | | (31) all_57_15 = e1 & op(e0, e0) = e1 % 131.91/18.81 | | | % 131.91/18.81 | | | REF_CLOSE: (4), (6), (7), (31) are inconsistent by sub-proof #294. % 131.91/18.81 | | | % 131.91/18.81 | | End of split % 131.91/18.81 | | % 131.91/18.81 | End of split % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #68 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) all_57_12 = e3 & op(e0, e3) = e3 % 131.91/18.81 (2) ~ (op(e0, e3) = e3) % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | ALPHA: (1) implies: % 131.91/18.81 | (3) op(e0, e3) = e3 % 131.91/18.81 | % 131.91/18.81 | PRED_UNIFY: (2), (3) imply: % 131.91/18.81 | (4) $false % 131.91/18.81 | % 131.91/18.81 | CLOSE: (4) is inconsistent. % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #69 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.91/18.81 (2) ~ (all_53_11 = e0) % 131.91/18.81 (3) ~ (e3 = e0) % 131.91/18.81 (4) op(e1, e1) = e3 % 131.91/18.81 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.81 (6) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | BETA: splitting (1) gives: % 131.91/18.81 | % 131.91/18.81 | Case 1: % 131.91/18.81 | | % 131.91/18.81 | | (7) all_57_8 = e0 & op(e1, e1) = e0 % 131.91/18.81 | | % 131.91/18.81 | | ALPHA: (7) implies: % 131.91/18.81 | | (8) op(e1, e1) = e0 % 131.91/18.81 | | % 131.91/18.81 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #320. % 131.91/18.81 | | % 131.91/18.81 | Case 2: % 131.91/18.81 | | % 131.91/18.81 | | (9) all_57_14 = e0 & op(e0, e1) = e0 % 131.91/18.81 | | % 131.91/18.81 | | ALPHA: (9) implies: % 131.91/18.81 | | (10) op(e0, e1) = e0 % 131.91/18.81 | | % 131.91/18.81 | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #296. % 131.91/18.81 | | % 131.91/18.81 | End of split % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #70 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) all_57_5 = e1 % 131.91/18.81 (2) all_57_5 = e0 % 131.91/18.81 (3) ~ (e1 = e0) % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | COMBINE_EQS: (1), (2) imply: % 131.91/18.81 | (4) e1 = e0 % 131.91/18.81 | % 131.91/18.81 | SIMP: (4) implies: % 131.91/18.81 | (5) e1 = e0 % 131.91/18.81 | % 131.91/18.81 | REDUCE: (3), (5) imply: % 131.91/18.81 | (6) $false % 131.91/18.81 | % 131.91/18.81 | CLOSE: (6) is inconsistent. % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #71 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) unit = e2 | unit = e1 | unit = e0 % 131.91/18.81 (2) op(e2, unit) = e2 % 131.91/18.81 (3) all_55_9 = all_53_6 % 131.91/18.81 (4) all_55_11 = all_22_1 % 131.91/18.81 (5) ~ (all_53_2 = all_22_1) % 131.91/18.81 (6) ~ (all_53_2 = e0) % 131.91/18.81 (7) op(e2, e2) = e2 % 131.91/18.81 (8) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 131.91/18.81 (9) ~ (all_53_13 = all_6_2) % 131.91/18.81 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.81 (11) all_26_2 = e2 | ~ (op(e2, e2) = e2) % 131.91/18.81 (12) ~ (all_53_1 = all_53_2) % 131.91/18.81 (13) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 131.91/18.81 (14) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 131.91/18.81 (15) all_55_8 = all_53_2 % 131.91/18.81 (16) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 131.91/18.81 $i(all_22_0)) % 131.91/18.81 (17) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 131.91/18.81 (18) op(e1, e3) = all_53_2 % 131.91/18.81 (19) op(e1, unit) = e1 % 131.91/18.81 (20) ~ (all_53_2 = all_53_6) % 131.91/18.81 (21) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.91/18.81 (22) op(e2, e3) = e3 % 131.91/18.81 (23) all_26_2 = all_6_2 % 131.91/18.81 (24) ~ (unit = e1) % 131.91/18.81 (25) ~ (all_53_6 = all_22_1) % 131.91/18.81 (26) ~ (all_22_1 = e0) % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | BETA: splitting (13) gives: % 131.91/18.81 | % 131.91/18.81 | Case 1: % 131.91/18.81 | | % 131.91/18.81 | | (27) ~ (op(e2, e3) = e3) % 131.91/18.81 | | % 131.91/18.81 | | PRED_UNIFY: (22), (27) imply: % 131.91/18.81 | | (28) $false % 131.91/18.81 | | % 131.91/18.81 | | CLOSE: (28) is inconsistent. % 131.91/18.81 | | % 131.91/18.81 | Case 2: % 131.91/18.81 | | % 131.91/18.81 | | (29) all_53_1 = e3 % 131.91/18.81 | | % 131.91/18.81 | | REDUCE: (12), (29) imply: % 131.91/18.81 | | (30) ~ (all_53_2 = e3) % 131.91/18.81 | | % 131.91/18.81 | | SIMP: (30) implies: % 131.91/18.81 | | (31) ~ (all_53_2 = e3) % 131.91/18.81 | | % 131.91/18.81 | | BETA: splitting (11) gives: % 131.91/18.81 | | % 131.91/18.81 | | Case 1: % 131.91/18.81 | | | % 131.91/18.81 | | | (32) ~ (op(e2, e2) = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | PRED_UNIFY: (7), (32) imply: % 131.91/18.81 | | | (33) $false % 131.91/18.81 | | | % 131.91/18.81 | | | CLOSE: (33) is inconsistent. % 131.91/18.81 | | | % 131.91/18.81 | | Case 2: % 131.91/18.81 | | | % 131.91/18.81 | | | (34) all_26_2 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | COMBINE_EQS: (23), (34) imply: % 131.91/18.81 | | | (35) all_6_2 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | SIMP: (35) implies: % 131.91/18.81 | | | (36) all_6_2 = e2 % 131.91/18.81 | | | % 131.91/18.81 | | | REDUCE: (9), (36) imply: % 131.91/18.81 | | | (37) ~ (all_53_13 = e2) % 131.91/18.81 | | | % 131.91/18.81 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (14), (15), (16), % 131.91/18.81 | | | (17), (18), (19), (20), (21), (24), (25), (26), (31), (37) are % 131.91/18.81 | | | inconsistent by sub-proof #214. % 131.91/18.81 | | | % 131.91/18.81 | | End of split % 131.91/18.81 | | % 131.91/18.81 | End of split % 131.91/18.81 | % 131.91/18.81 End of proof % 131.91/18.81 % 131.91/18.81 Sub-proof #72 shows that the following formulas are inconsistent: % 131.91/18.81 ---------------------------------------------------------------- % 131.91/18.81 (1) ~ (unit = e0) % 131.91/18.81 (2) unit = e2 | unit = e1 | unit = e0 % 131.91/18.81 (3) op(e1, e1) = e1 % 131.91/18.81 (4) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 131.91/18.81 $i(all_16_0)) % 131.91/18.81 (5) all_57_13 = e1 % 131.91/18.81 (6) ~ (all_10_1 = e3) % 131.91/18.81 (7) ~ (all_53_9 = all_53_13) % 131.91/18.81 (8) all_22_2 = e1 % 131.91/18.81 (9) op(e0, e2) = all_53_7 % 131.91/18.81 (10) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 131.91/18.81 (11) op(e2, e0) = e1 % 131.91/18.81 (12) ~ (e3 = e0) % 131.91/18.81 (13) ~ (e2 = e0) % 131.91/18.81 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 131.91/18.81 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 131.91/18.81 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.91/18.81 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 131.91/18.81 (15) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 131.91/18.81 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 131.91/18.81 e2) % 131.91/18.81 (16) op(e2, e0) = all_53_13 % 131.91/18.81 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.81 (18) ~ (all_10_1 = e2) | ( ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & % 131.91/18.81 $i(all_10_0)) % 131.91/18.81 (19) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.91/18.81 (20) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.81 (21) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 131.91/18.81 (22) all_55_12 = all_10_1 % 131.91/18.81 (23) ~ (e2 = e1) % 131.91/18.81 (24) ~ (e1 = e0) % 131.91/18.81 (25) ~ (all_53_11 = all_10_1) % 131.91/18.81 (26) op(e0, e2) = e1 % 131.91/18.81 (27) op(e0, unit) = e0 % 131.91/18.81 (28) all_16_1 = all_10_1 % 131.91/18.81 (29) all_57_15 = e3 % 131.91/18.81 (30) ~ (all_53_7 = all_10_1) % 131.91/18.81 (31) ~ (e3 = e2) % 131.91/18.81 (32) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 131.91/18.81 (33) op(unit, e1) = e1 % 131.91/18.81 % 131.91/18.81 Begin of proof % 131.91/18.81 | % 131.91/18.81 | GROUND_INST: instantiating (17) with all_53_7, e1, e2, e0, simplifying with % 131.91/18.81 | (9), (26) gives: % 131.91/18.81 | (34) all_53_7 = e1 % 131.91/18.81 | % 131.91/18.82 | GROUND_INST: instantiating (17) with all_53_13, e1, e0, e2, simplifying with % 131.91/18.82 | (11), (16) gives: % 131.91/18.82 | (35) all_53_13 = e1 % 131.91/18.82 | % 131.91/18.82 | REDUCE: (30), (34) imply: % 131.91/18.82 | (36) ~ (all_10_1 = e1) % 131.91/18.82 | % 131.91/18.82 | SIMP: (36) implies: % 131.91/18.82 | (37) ~ (all_10_1 = e1) % 131.91/18.82 | % 131.91/18.82 | REDUCE: (7), (35) imply: % 131.91/18.82 | (38) ~ (all_53_9 = e1) % 131.91/18.82 | % 131.91/18.82 | BETA: splitting (18) gives: % 131.91/18.82 | % 131.91/18.82 | Case 1: % 131.91/18.82 | | % 131.91/18.82 | | (39) ~ (all_10_1 = e2) % 131.91/18.82 | | % 131.91/18.82 | | BETA: splitting (19) gives: % 131.91/18.82 | | % 131.91/18.82 | | Case 1: % 131.91/18.82 | | | % 131.91/18.82 | | | (40) all_55_12 = e3 % 131.91/18.82 | | | % 131.91/18.82 | | | COMBINE_EQS: (22), (40) imply: % 131.91/18.82 | | | (41) all_10_1 = e3 % 131.91/18.82 | | | % 131.91/18.82 | | | REDUCE: (6), (41) imply: % 131.91/18.82 | | | (42) $false % 131.91/18.82 | | | % 131.91/18.82 | | | CLOSE: (42) is inconsistent. % 131.91/18.82 | | | % 131.91/18.82 | | Case 2: % 131.91/18.82 | | | % 131.91/18.82 | | | (43) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 131.91/18.82 | | | % 131.91/18.82 | | | BETA: splitting (15) gives: % 131.91/18.82 | | | % 131.91/18.82 | | | Case 1: % 131.91/18.82 | | | | % 131.91/18.82 | | | | (44) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 131.91/18.82 | | | | e2) = e2) % 131.91/18.82 | | | | % 131.91/18.82 | | | | BETA: splitting (44) gives: % 131.91/18.82 | | | | % 131.91/18.82 | | | | Case 1: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | (45) all_57_12 = e2 & op(e0, e3) = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | ALPHA: (45) implies: % 131.91/18.82 | | | | | (46) all_57_12 = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | BETA: splitting (14) gives: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | Case 1: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | (47) all_57_15 = e0 & op(e0, e0) = e0 % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | REF_CLOSE: (12), (29), (47) are inconsistent by sub-proof #81. % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | Case 2: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | (48) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & % 131.91/18.82 | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 131.91/18.82 | | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.91/18.82 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | ALPHA: (48) implies: % 131.91/18.82 | | | | | | (49) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 131.91/18.82 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | BETA: splitting (49) gives: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | Case 1: % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | (50) all_57_12 = e0 & op(e0, e3) = e0 % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | REF_CLOSE: (13), (46), (50) are inconsistent by sub-proof #79. % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | Case 2: % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | (51) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & % 131.91/18.82 | | | | | | | op(e0, e1) = e0) % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | BETA: splitting (51) gives: % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | Case 1: % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | (52) all_57_13 = e0 & op(e0, e2) = e0 % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | REF_CLOSE: (3), (5), (8), (10), (24), (52) are inconsistent by % 131.91/18.82 | | | | | | | | sub-proof #228. % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | Case 2: % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | (53) all_57_14 = e0 & op(e0, e1) = e0 % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | ALPHA: (53) implies: % 131.91/18.82 | | | | | | | | (54) op(e0, e1) = e0 % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | BETA: splitting (21) gives: % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | | Case 1: % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | (55) ~ (op(e0, e1) = e0) % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | PRED_UNIFY: (54), (55) imply: % 131.91/18.82 | | | | | | | | | (56) $false % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | CLOSE: (56) is inconsistent. % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | Case 2: % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | (57) all_53_11 = e0 % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | REDUCE: (25), (57) imply: % 131.91/18.82 | | | | | | | | | (58) ~ (all_10_1 = e0) % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | SIMP: (58) implies: % 131.91/18.82 | | | | | | | | | (59) ~ (all_10_1 = e0) % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | BETA: splitting (43) gives: % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | | Case 1: % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | (60) all_55_12 = e2 % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | COMBINE_EQS: (22), (60) imply: % 131.91/18.82 | | | | | | | | | | (61) all_10_1 = e2 % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | REDUCE: (39), (61) imply: % 131.91/18.82 | | | | | | | | | | (62) $false % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | CLOSE: (62) is inconsistent. % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | Case 2: % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | (63) all_55_12 = e1 | all_55_12 = e0 % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | | REF_CLOSE: (22), (37), (59), (63) are inconsistent by % 131.91/18.82 | | | | | | | | | | sub-proof #74. % 131.91/18.82 | | | | | | | | | | % 131.91/18.82 | | | | | | | | | End of split % 131.91/18.82 | | | | | | | | | % 131.91/18.82 | | | | | | | | End of split % 131.91/18.82 | | | | | | | | % 131.91/18.82 | | | | | | | End of split % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | End of split % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | End of split % 131.91/18.82 | | | | | % 131.91/18.82 | | | | Case 2: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | (64) all_57_13 = e2 & op(e0, e2) = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | ALPHA: (64) implies: % 131.91/18.82 | | | | | (65) all_57_13 = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | COMBINE_EQS: (5), (65) imply: % 131.91/18.82 | | | | | (66) e2 = e1 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | SIMP: (66) implies: % 131.91/18.82 | | | | | (67) e2 = e1 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | REDUCE: (23), (67) imply: % 131.91/18.82 | | | | | (68) $false % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | CLOSE: (68) is inconsistent. % 131.91/18.82 | | | | | % 131.91/18.82 | | | | End of split % 131.91/18.82 | | | | % 131.91/18.82 | | | Case 2: % 131.91/18.82 | | | | % 131.91/18.82 | | | | (69) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 131.91/18.82 | | | | e0) = e2) % 131.91/18.82 | | | | % 131.91/18.82 | | | | BETA: splitting (69) gives: % 131.91/18.82 | | | | % 131.91/18.82 | | | | Case 1: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | (70) all_57_14 = e2 & op(e0, e1) = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | ALPHA: (70) implies: % 131.91/18.82 | | | | | (71) op(e0, e1) = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | BETA: splitting (43) gives: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | Case 1: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | (72) all_55_12 = e2 % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | COMBINE_EQS: (22), (72) imply: % 131.91/18.82 | | | | | | (73) all_10_1 = e2 % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | REDUCE: (39), (73) imply: % 131.91/18.82 | | | | | | (74) $false % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | CLOSE: (74) is inconsistent. % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | Case 2: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | (75) all_55_12 = e1 | all_55_12 = e0 % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | BETA: splitting (75) gives: % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | | Case 1: % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | (76) all_55_12 = e1 % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | COMBINE_EQS: (22), (76) imply: % 131.91/18.82 | | | | | | | (77) all_10_1 = e1 % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | REF_CLOSE: (4), (17), (28), (71), (77) are inconsistent by % 131.91/18.82 | | | | | | | sub-proof #73. % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | Case 2: % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | (78) all_55_12 = e0 % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | COMBINE_EQS: (22), (78) imply: % 131.91/18.82 | | | | | | | (79) all_10_1 = e0 % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | REDUCE: (25), (79) imply: % 131.91/18.82 | | | | | | | (80) ~ (all_53_11 = e0) % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | | REF_CLOSE: (1), (2), (20), (21), (27), (32), (33), (38), (80) are % 131.91/18.82 | | | | | | | inconsistent by sub-proof #242. % 131.91/18.82 | | | | | | | % 131.91/18.82 | | | | | | End of split % 131.91/18.82 | | | | | | % 131.91/18.82 | | | | | End of split % 131.91/18.82 | | | | | % 131.91/18.82 | | | | Case 2: % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | (81) all_57_15 = e2 & op(e0, e0) = e2 % 131.91/18.82 | | | | | % 131.91/18.82 | | | | | REF_CLOSE: (29), (31), (81) are inconsistent by sub-proof #80. % 131.91/18.82 | | | | | % 131.91/18.82 | | | | End of split % 131.91/18.82 | | | | % 131.91/18.82 | | | End of split % 131.91/18.82 | | | % 131.91/18.82 | | End of split % 131.91/18.82 | | % 131.91/18.82 | Case 2: % 131.91/18.82 | | % 131.91/18.82 | | (82) ~ (all_10_0 = e1) & op(e0, e2) = all_10_0 & $i(all_10_0) % 131.91/18.82 | | % 131.91/18.82 | | ALPHA: (82) implies: % 131.91/18.82 | | (83) ~ (all_10_0 = e1) % 131.91/18.82 | | (84) op(e0, e2) = all_10_0 % 131.91/18.82 | | % 131.91/18.82 | | GROUND_INST: instantiating (17) with e1, all_10_0, e2, e0, simplifying with % 131.91/18.82 | | (26), (84) gives: % 131.91/18.82 | | (85) all_10_0 = e1 % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (83), (85) imply: % 131.91/18.82 | | (86) $false % 131.91/18.82 | | % 131.91/18.82 | | CLOSE: (86) is inconsistent. % 131.91/18.82 | | % 131.91/18.82 | End of split % 131.91/18.82 | % 131.91/18.82 End of proof % 131.91/18.82 % 131.91/18.82 Sub-proof #73 shows that the following formulas are inconsistent: % 131.91/18.82 ---------------------------------------------------------------- % 131.91/18.82 (1) ~ (all_16_1 = e1) | ( ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & % 131.91/18.82 $i(all_16_0)) % 131.91/18.82 (2) all_10_1 = e1 % 131.91/18.82 (3) op(e0, e1) = e2 % 131.91/18.82 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.82 (5) all_16_1 = all_10_1 % 131.91/18.82 % 131.91/18.82 Begin of proof % 131.91/18.82 | % 131.91/18.82 | COMBINE_EQS: (2), (5) imply: % 131.91/18.82 | (6) all_16_1 = e1 % 131.91/18.82 | % 131.91/18.82 | BETA: splitting (1) gives: % 131.91/18.82 | % 131.91/18.82 | Case 1: % 131.91/18.82 | | % 131.91/18.82 | | (7) ~ (all_16_1 = e1) % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (6), (7) imply: % 131.91/18.82 | | (8) $false % 131.91/18.82 | | % 131.91/18.82 | | CLOSE: (8) is inconsistent. % 131.91/18.82 | | % 131.91/18.82 | Case 2: % 131.91/18.82 | | % 131.91/18.82 | | (9) ~ (all_16_0 = e2) & op(e0, e1) = all_16_0 & $i(all_16_0) % 131.91/18.82 | | % 131.91/18.82 | | ALPHA: (9) implies: % 131.91/18.82 | | (10) ~ (all_16_0 = e2) % 131.91/18.82 | | (11) op(e0, e1) = all_16_0 % 131.91/18.82 | | % 131.91/18.82 | | GROUND_INST: instantiating (4) with e2, all_16_0, e1, e0, simplifying with % 131.91/18.82 | | (3), (11) gives: % 131.91/18.82 | | (12) all_16_0 = e2 % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (10), (12) imply: % 131.91/18.82 | | (13) $false % 131.91/18.82 | | % 131.91/18.82 | | CLOSE: (13) is inconsistent. % 131.91/18.82 | | % 131.91/18.82 | End of split % 131.91/18.82 | % 131.91/18.82 End of proof % 131.91/18.82 % 131.91/18.82 Sub-proof #74 shows that the following formulas are inconsistent: % 131.91/18.82 ---------------------------------------------------------------- % 131.91/18.82 (1) all_55_12 = e1 | all_55_12 = e0 % 131.91/18.82 (2) all_55_12 = all_10_1 % 131.91/18.82 (3) ~ (all_10_1 = e1) % 131.91/18.82 (4) ~ (all_10_1 = e0) % 131.91/18.82 % 131.91/18.82 Begin of proof % 131.91/18.82 | % 131.91/18.82 | BETA: splitting (1) gives: % 131.91/18.82 | % 131.91/18.82 | Case 1: % 131.91/18.82 | | % 131.91/18.82 | | (5) all_55_12 = e1 % 131.91/18.82 | | % 131.91/18.82 | | COMBINE_EQS: (2), (5) imply: % 131.91/18.82 | | (6) all_10_1 = e1 % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (3), (6) imply: % 131.91/18.82 | | (7) $false % 131.91/18.82 | | % 131.91/18.82 | | CLOSE: (7) is inconsistent. % 131.91/18.82 | | % 131.91/18.82 | Case 2: % 131.91/18.82 | | % 131.91/18.82 | | (8) all_55_12 = e0 % 131.91/18.82 | | % 131.91/18.82 | | COMBINE_EQS: (2), (8) imply: % 131.91/18.82 | | (9) all_10_1 = e0 % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (4), (9) imply: % 131.91/18.82 | | (10) $false % 131.91/18.82 | | % 131.91/18.82 | | CLOSE: (10) is inconsistent. % 131.91/18.82 | | % 131.91/18.82 | End of split % 131.91/18.82 | % 131.91/18.82 End of proof % 131.91/18.82 % 131.91/18.82 Sub-proof #75 shows that the following formulas are inconsistent: % 131.91/18.82 ---------------------------------------------------------------- % 131.91/18.82 (1) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 131.91/18.82 (2) ~ (all_53_4 = all_53_6) % 131.91/18.82 (3) ~ (unit = e0) % 131.91/18.82 (4) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 131.91/18.82 (5) op(e3, e2) = e1 % 131.91/18.82 (6) unit = e2 | unit = e1 | unit = e0 % 131.91/18.82 (7) op(unit, e0) = e0 % 131.91/18.82 (8) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 131.91/18.82 (9) op(e2, unit) = e2 % 131.91/18.82 (10) all_55_9 = all_53_6 % 131.91/18.82 (11) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 131.91/18.82 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 131.91/18.82 $i(all_42_0)))) % 131.91/18.82 (12) ~ (all_53_13 = all_6_2) % 131.91/18.82 (13) all_55_5 = all_6_2 % 131.91/18.82 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.91/18.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 131.91/18.82 (15) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 131.91/18.82 (16) ~ (all_53_4 = all_4_2) % 131.91/18.82 (17) ~ (all_6_2 = e3) % 131.91/18.82 (18) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 131.91/18.82 (19) op(e1, unit) = e1 % 131.91/18.82 (20) ~ (all_53_2 = all_4_2) % 131.91/18.82 (21) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 131.91/18.82 (22) ~ (all_53_9 = all_6_2) % 131.91/18.82 (23) all_42_2 = all_6_2 % 131.91/18.82 (24) ~ (all_4_2 = e2) % 131.91/18.82 (25) op(unit, e3) = e3 % 131.91/18.82 (26) ~ (all_53_4 = all_6_2) % 131.91/18.82 (27) op(e3, e2) = all_53_4 % 131.91/18.82 (28) ~ (all_4_2 = e0) % 131.91/18.82 (29) all_55_0 = all_4_2 % 131.91/18.82 % 131.91/18.82 Begin of proof % 131.91/18.82 | % 131.91/18.82 | GROUND_INST: instantiating (14) with all_53_4, e1, e2, e3, simplifying with % 131.91/18.82 | (5), (27) gives: % 131.91/18.82 | (30) all_53_4 = e1 % 131.91/18.82 | % 131.91/18.82 | REDUCE: (2), (30) imply: % 131.91/18.82 | (31) ~ (all_53_6 = e1) % 131.91/18.82 | % 131.91/18.82 | SIMP: (31) implies: % 131.91/18.82 | (32) ~ (all_53_6 = e1) % 131.91/18.82 | % 131.91/18.82 | REDUCE: (26), (30) imply: % 131.91/18.82 | (33) ~ (all_6_2 = e1) % 131.91/18.82 | % 131.91/18.82 | SIMP: (33) implies: % 131.91/18.82 | (34) ~ (all_6_2 = e1) % 131.91/18.82 | % 131.91/18.82 | REDUCE: (16), (30) imply: % 131.91/18.82 | (35) ~ (all_4_2 = e1) % 131.91/18.82 | % 131.91/18.82 | SIMP: (35) implies: % 131.91/18.82 | (36) ~ (all_4_2 = e1) % 131.91/18.82 | % 131.91/18.82 | BETA: splitting (1) gives: % 131.91/18.82 | % 131.91/18.82 | Case 1: % 131.91/18.82 | | % 131.91/18.82 | | (37) all_55_0 = e3 % 131.91/18.82 | | % 131.91/18.82 | | COMBINE_EQS: (29), (37) imply: % 131.91/18.82 | | (38) all_4_2 = e3 % 131.91/18.82 | | % 131.91/18.82 | | REDUCE: (20), (38) imply: % 132.12/18.82 | | (39) ~ (all_53_2 = e3) % 132.12/18.82 | | % 132.12/18.82 | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (15), (17), % 132.12/18.82 | | (18), (19), (21), (22), (23), (25), (32), (34), (39) are % 132.12/18.82 | | inconsistent by sub-proof #232. % 132.12/18.82 | | % 132.12/18.82 | Case 2: % 132.12/18.82 | | % 132.12/18.82 | | (40) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.12/18.82 | | % 132.12/18.82 | | REF_CLOSE: (24), (28), (29), (36), (40) are inconsistent by sub-proof #274. % 132.12/18.82 | | % 132.12/18.82 | End of split % 132.12/18.82 | % 132.12/18.82 End of proof % 132.12/18.82 % 132.12/18.82 Sub-proof #76 shows that the following formulas are inconsistent: % 132.12/18.82 ---------------------------------------------------------------- % 132.12/18.82 (1) ~ (all_53_14 = e3) % 132.12/18.82 (2) ~ (e3 = e0) % 132.12/18.82 (3) op(e0, e0) = all_8_2 % 132.12/18.82 (4) ~ (e2 = e0) % 132.12/18.82 (5) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 132.12/18.82 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 132.12/18.82 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 132.12/18.82 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 132.12/18.82 (6) op(e1, e0) = all_53_14 % 132.12/18.82 (7) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | % 132.12/18.82 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 132.12/18.82 (8) ~ (all_8_2 = e1) % 132.12/18.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.82 (10) ~ (e3 = e1) % 132.12/18.82 (11) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 132.12/18.82 (12) ~ (e2 = e1) % 132.12/18.82 (13) ~ (e1 = e0) % 132.12/18.82 (14) all_57_13 = e3 % 132.12/18.82 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 132.12/18.82 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 132.12/18.82 e1) % 132.12/18.82 (16) ~ (e3 = e2) % 132.12/18.82 % 132.12/18.82 Begin of proof % 132.12/18.82 | % 132.12/18.82 | BETA: splitting (11) gives: % 132.12/18.82 | % 132.12/18.82 | Case 1: % 132.12/18.82 | | % 132.12/18.82 | | (17) all_57_11 = e3 & op(e1, e0) = e3 % 132.12/18.82 | | % 132.12/18.82 | | REF_CLOSE: (1), (6), (9), (17) are inconsistent by sub-proof #84. % 132.12/18.82 | | % 132.12/18.82 | Case 2: % 132.12/18.82 | | % 132.12/18.82 | | (18) all_57_15 = e3 & op(e0, e0) = e3 % 132.12/18.82 | | % 132.12/18.82 | | ALPHA: (18) implies: % 132.12/18.82 | | (19) all_57_15 = e3 % 132.12/18.82 | | % 132.12/18.82 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 132.12/18.82 | | (16), (19) are inconsistent by sub-proof #77. % 132.12/18.82 | | % 132.12/18.82 | End of split % 132.12/18.82 | % 132.12/18.82 End of proof % 132.12/18.82 % 132.12/18.82 Sub-proof #77 shows that the following formulas are inconsistent: % 132.12/18.82 ---------------------------------------------------------------- % 132.12/18.82 (1) ~ (e3 = e0) % 132.12/18.82 (2) op(e0, e0) = all_8_2 % 132.12/18.82 (3) ~ (e2 = e0) % 132.12/18.82 (4) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 132.12/18.82 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 132.12/18.82 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 132.12/18.82 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 132.12/18.82 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | % 132.12/18.82 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 132.12/18.82 (6) ~ (all_8_2 = e1) % 132.12/18.82 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.82 (8) ~ (e3 = e1) % 132.12/18.82 (9) ~ (e2 = e1) % 132.12/18.82 (10) ~ (e1 = e0) % 132.12/18.82 (11) all_57_13 = e3 % 132.12/18.82 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 132.12/18.82 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 132.12/18.82 e1) % 132.12/18.82 (13) all_57_15 = e3 % 132.12/18.82 (14) ~ (e3 = e2) % 132.12/18.82 % 132.12/18.82 Begin of proof % 132.12/18.82 | % 132.12/18.82 | BETA: splitting (12) gives: % 132.12/18.82 | % 132.12/18.82 | Case 1: % 132.12/18.82 | | % 132.12/18.82 | | (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 132.12/18.82 | | e1) % 132.12/18.82 | | % 132.12/18.82 | | BETA: splitting (15) gives: % 132.12/18.82 | | % 132.12/18.82 | | Case 1: % 132.12/18.82 | | | % 132.12/18.82 | | | (16) all_57_12 = e1 & op(e0, e3) = e1 % 132.12/18.82 | | | % 132.12/18.82 | | | ALPHA: (16) implies: % 132.12/18.82 | | | (17) all_57_12 = e1 % 132.12/18.82 | | | % 132.12/18.82 | | | BETA: splitting (4) gives: % 132.12/18.82 | | | % 132.12/18.82 | | | Case 1: % 132.12/18.82 | | | | % 132.12/18.82 | | | | (18) all_57_15 = e0 & op(e0, e0) = e0 % 132.12/18.82 | | | | % 132.12/18.82 | | | | REF_CLOSE: (1), (13), (18) are inconsistent by sub-proof #81. % 132.12/18.82 | | | | % 132.12/18.82 | | | Case 2: % 132.12/18.82 | | | | % 132.12/18.82 | | | | (19) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, % 132.12/18.82 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 132.12/18.82 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 132.12/18.82 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.12/18.82 | | | | % 132.12/18.82 | | | | ALPHA: (19) implies: % 132.12/18.82 | | | | (20) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 132.12/18.82 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.12/18.82 | | | | % 132.12/18.82 | | | | BETA: splitting (5) gives: % 132.12/18.82 | | | | % 132.12/18.82 | | | | Case 1: % 132.12/18.82 | | | | | % 132.12/18.82 | | | | | (21) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 132.12/18.82 | | | | | e2) = e2) % 132.12/18.82 | | | | | % 132.12/18.82 | | | | | BETA: splitting (21) gives: % 132.12/18.82 | | | | | % 132.12/18.82 | | | | | Case 1: % 132.12/18.82 | | | | | | % 132.12/18.82 | | | | | | (22) all_57_12 = e2 & op(e0, e3) = e2 % 132.12/18.82 | | | | | | % 132.12/18.82 | | | | | | ALPHA: (22) implies: % 132.12/18.82 | | | | | | (23) all_57_12 = e2 % 132.12/18.82 | | | | | | % 132.12/18.82 | | | | | | COMBINE_EQS: (17), (23) imply: % 132.12/18.83 | | | | | | (24) e2 = e1 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | SIMP: (24) implies: % 132.12/18.83 | | | | | | (25) e2 = e1 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REDUCE: (9), (25) imply: % 132.12/18.83 | | | | | | (26) $false % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | CLOSE: (26) is inconsistent. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | Case 2: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (27) all_57_13 = e2 & op(e0, e2) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REF_CLOSE: (11), (14), (27) are inconsistent by sub-proof #111. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | End of split % 132.12/18.83 | | | | | % 132.12/18.83 | | | | Case 2: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | (28) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 132.12/18.83 | | | | | e0) = e2) % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | BETA: splitting (28) gives: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | Case 1: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (29) all_57_14 = e2 & op(e0, e1) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | ALPHA: (29) implies: % 132.12/18.83 | | | | | | (30) all_57_14 = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | BETA: splitting (20) gives: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | Case 1: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | (31) all_57_12 = e0 & op(e0, e3) = e0 % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | ALPHA: (31) implies: % 132.12/18.83 | | | | | | | (32) all_57_12 = e0 % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | COMBINE_EQS: (17), (32) imply: % 132.12/18.83 | | | | | | | (33) e1 = e0 % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | REDUCE: (10), (33) imply: % 132.12/18.83 | | | | | | | (34) $false % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | CLOSE: (34) is inconsistent. % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | Case 2: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | (35) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & % 132.12/18.83 | | | | | | | op(e0, e1) = e0) % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | BETA: splitting (35) gives: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | Case 1: % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | (36) all_57_13 = e0 & op(e0, e2) = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | REF_CLOSE: (1), (11), (36) are inconsistent by sub-proof #112. % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | Case 2: % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | (37) all_57_14 = e0 & op(e0, e1) = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | ALPHA: (37) implies: % 132.12/18.83 | | | | | | | | (38) all_57_14 = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | COMBINE_EQS: (30), (38) imply: % 132.12/18.83 | | | | | | | | (39) e2 = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | REDUCE: (3), (39) imply: % 132.12/18.83 | | | | | | | | (40) $false % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | CLOSE: (40) is inconsistent. % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | End of split % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | End of split % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | Case 2: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (41) all_57_15 = e2 & op(e0, e0) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REF_CLOSE: (13), (14), (41) are inconsistent by sub-proof #80. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | End of split % 132.12/18.83 | | | | | % 132.12/18.83 | | | | End of split % 132.12/18.83 | | | | % 132.12/18.83 | | | End of split % 132.12/18.83 | | | % 132.12/18.83 | | Case 2: % 132.12/18.83 | | | % 132.12/18.83 | | | (42) all_57_13 = e1 & op(e0, e2) = e1 % 132.12/18.83 | | | % 132.12/18.83 | | | REF_CLOSE: (8), (11), (42) are inconsistent by sub-proof #120. % 132.12/18.83 | | | % 132.12/18.83 | | End of split % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (43) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 132.12/18.83 | | e1) % 132.12/18.83 | | % 132.12/18.83 | | BETA: splitting (43) gives: % 132.12/18.83 | | % 132.12/18.83 | | Case 1: % 132.12/18.83 | | | % 132.12/18.83 | | | (44) all_57_14 = e1 & op(e0, e1) = e1 % 132.12/18.83 | | | % 132.12/18.83 | | | ALPHA: (44) implies: % 132.12/18.83 | | | (45) all_57_14 = e1 % 132.12/18.83 | | | % 132.12/18.83 | | | BETA: splitting (4) gives: % 132.12/18.83 | | | % 132.12/18.83 | | | Case 1: % 132.12/18.83 | | | | % 132.12/18.83 | | | | (46) all_57_15 = e0 & op(e0, e0) = e0 % 132.12/18.83 | | | | % 132.12/18.83 | | | | REF_CLOSE: (1), (13), (46) are inconsistent by sub-proof #81. % 132.12/18.83 | | | | % 132.12/18.83 | | | Case 2: % 132.12/18.83 | | | | % 132.12/18.83 | | | | (47) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, % 132.12/18.83 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 132.12/18.83 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 132.12/18.83 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.12/18.83 | | | | % 132.12/18.83 | | | | ALPHA: (47) implies: % 132.12/18.83 | | | | (48) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 132.12/18.83 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.12/18.83 | | | | % 132.12/18.83 | | | | BETA: splitting (5) gives: % 132.12/18.83 | | | | % 132.12/18.83 | | | | Case 1: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | (49) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 132.12/18.83 | | | | | e2) = e2) % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | BETA: splitting (49) gives: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | Case 1: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (50) all_57_12 = e2 & op(e0, e3) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | ALPHA: (50) implies: % 132.12/18.83 | | | | | | (51) all_57_12 = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | BETA: splitting (48) gives: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | Case 1: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | (52) all_57_12 = e0 & op(e0, e3) = e0 % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | REF_CLOSE: (3), (51), (52) are inconsistent by sub-proof #79. % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | Case 2: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | (53) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & % 132.12/18.83 | | | | | | | op(e0, e1) = e0) % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | BETA: splitting (53) gives: % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | | Case 1: % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | (54) all_57_13 = e0 & op(e0, e2) = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | REF_CLOSE: (1), (11), (54) are inconsistent by sub-proof #112. % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | Case 2: % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | (55) all_57_14 = e0 & op(e0, e1) = e0 % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | | REF_CLOSE: (10), (45), (55) are inconsistent by sub-proof #78. % 132.12/18.83 | | | | | | | | % 132.12/18.83 | | | | | | | End of split % 132.12/18.83 | | | | | | | % 132.12/18.83 | | | | | | End of split % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | Case 2: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (56) all_57_13 = e2 & op(e0, e2) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REF_CLOSE: (11), (14), (56) are inconsistent by sub-proof #111. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | End of split % 132.12/18.83 | | | | | % 132.12/18.83 | | | | Case 2: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | (57) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 132.12/18.83 | | | | | e0) = e2) % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | BETA: splitting (57) gives: % 132.12/18.83 | | | | | % 132.12/18.83 | | | | | Case 1: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (58) all_57_14 = e2 & op(e0, e1) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REF_CLOSE: (9), (45), (58) are inconsistent by sub-proof #197. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | Case 2: % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | (59) all_57_15 = e2 & op(e0, e0) = e2 % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | | REF_CLOSE: (13), (14), (59) are inconsistent by sub-proof #80. % 132.12/18.83 | | | | | | % 132.12/18.83 | | | | | End of split % 132.12/18.83 | | | | | % 132.12/18.83 | | | | End of split % 132.12/18.83 | | | | % 132.12/18.83 | | | End of split % 132.12/18.83 | | | % 132.12/18.83 | | Case 2: % 132.12/18.83 | | | % 132.12/18.83 | | | (60) all_57_15 = e1 & op(e0, e0) = e1 % 132.12/18.83 | | | % 132.12/18.83 | | | REF_CLOSE: (2), (6), (7), (60) are inconsistent by sub-proof #294. % 132.12/18.83 | | | % 132.12/18.83 | | End of split % 132.12/18.83 | | % 132.12/18.83 | End of split % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #78 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_14 = e0 & op(e0, e1) = e0 % 132.12/18.83 (2) all_57_14 = e1 % 132.12/18.83 (3) ~ (e1 = e0) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (4) all_57_14 = e0 % 132.12/18.83 | % 132.12/18.83 | COMBINE_EQS: (2), (4) imply: % 132.12/18.83 | (5) e1 = e0 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (3), (5) imply: % 132.12/18.83 | (6) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (6) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #79 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_12 = e0 & op(e0, e3) = e0 % 132.12/18.83 (2) all_57_12 = e2 % 132.12/18.83 (3) ~ (e2 = e0) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (4) all_57_12 = e0 % 132.12/18.83 | % 132.12/18.83 | COMBINE_EQS: (2), (4) imply: % 132.12/18.83 | (5) e2 = e0 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (3), (5) imply: % 132.12/18.83 | (6) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (6) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #80 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_15 = e2 & op(e0, e0) = e2 % 132.12/18.83 (2) all_57_15 = e3 % 132.12/18.83 (3) ~ (e3 = e2) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (4) all_57_15 = e2 % 132.12/18.83 | % 132.12/18.83 | COMBINE_EQS: (2), (4) imply: % 132.12/18.83 | (5) e3 = e2 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (3), (5) imply: % 132.12/18.83 | (6) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (6) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #81 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_15 = e0 & op(e0, e0) = e0 % 132.12/18.83 (2) all_57_15 = e3 % 132.12/18.83 (3) ~ (e3 = e0) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (4) all_57_15 = e0 % 132.12/18.83 | % 132.12/18.83 | COMBINE_EQS: (2), (4) imply: % 132.12/18.83 | (5) e3 = e0 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (3), (5) imply: % 132.12/18.83 | (6) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (6) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #82 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) ~ (all_53_13 = e3) % 132.12/18.83 (2) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.12/18.83 (3) op(e2, e0) = all_53_13 % 132.12/18.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.83 (5) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.12/18.83 (6) ~ (all_53_12 = e3) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | BETA: splitting (2) gives: % 132.12/18.83 | % 132.12/18.83 | Case 1: % 132.12/18.83 | | % 132.12/18.83 | | (7) all_57_9 = e3 & op(e3, e0) = e3 % 132.12/18.83 | | % 132.12/18.83 | | ALPHA: (7) implies: % 132.12/18.83 | | (8) op(e3, e0) = e3 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #186. % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (9) all_57_10 = e3 & op(e2, e0) = e3 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #83. % 132.12/18.83 | | % 132.12/18.83 | End of split % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #83 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_10 = e3 & op(e2, e0) = e3 % 132.12/18.83 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.83 (3) op(e2, e0) = all_53_13 % 132.12/18.83 (4) ~ (all_53_13 = e3) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (5) op(e2, e0) = e3 % 132.12/18.83 | % 132.12/18.83 | GROUND_INST: instantiating (2) with all_53_13, e3, e0, e2, simplifying with % 132.12/18.83 | (3), (5) gives: % 132.12/18.83 | (6) all_53_13 = e3 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (4), (6) imply: % 132.12/18.83 | (7) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (7) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #84 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_11 = e3 & op(e1, e0) = e3 % 132.12/18.83 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.83 (3) op(e1, e0) = all_53_14 % 132.12/18.83 (4) ~ (all_53_14 = e3) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (5) op(e1, e0) = e3 % 132.12/18.83 | % 132.12/18.83 | GROUND_INST: instantiating (2) with all_53_14, e3, e0, e1, simplifying with % 132.12/18.83 | (3), (5) gives: % 132.12/18.83 | (6) all_53_14 = e3 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (4), (6) imply: % 132.12/18.83 | (7) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (7) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #85 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_2 = e3 & op(e2, e3) = e3 % 132.12/18.83 (2) all_57_2 = e1 % 132.12/18.83 (3) ~ (e3 = e1) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (4) all_57_2 = e3 % 132.12/18.83 | % 132.12/18.83 | COMBINE_EQS: (2), (4) imply: % 132.12/18.83 | (5) e3 = e1 % 132.12/18.83 | % 132.12/18.83 | SIMP: (5) implies: % 132.12/18.83 | (6) e3 = e1 % 132.12/18.83 | % 132.12/18.83 | REDUCE: (3), (6) imply: % 132.12/18.83 | (7) $false % 132.12/18.83 | % 132.12/18.83 | CLOSE: (7) is inconsistent. % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #86 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) all_57_8 = e1 & op(e1, e1) = e1 % 132.12/18.83 (2) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.12/18.83 (3) all_12_2 = e2 % 132.12/18.83 (4) ~ (e2 = e1) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (1) implies: % 132.12/18.83 | (5) op(e1, e1) = e1 % 132.12/18.83 | % 132.12/18.83 | BETA: splitting (2) gives: % 132.12/18.83 | % 132.12/18.83 | Case 1: % 132.12/18.83 | | % 132.12/18.83 | | (6) ~ (op(e1, e1) = e1) % 132.12/18.83 | | % 132.12/18.83 | | PRED_UNIFY: (5), (6) imply: % 132.12/18.83 | | (7) $false % 132.12/18.83 | | % 132.12/18.83 | | CLOSE: (7) is inconsistent. % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (8) all_12_2 = e1 % 132.12/18.83 | | % 132.12/18.83 | | COMBINE_EQS: (3), (8) imply: % 132.12/18.83 | | (9) e2 = e1 % 132.12/18.83 | | % 132.12/18.83 | | SIMP: (9) implies: % 132.12/18.83 | | (10) e2 = e1 % 132.12/18.83 | | % 132.12/18.83 | | REDUCE: (4), (10) imply: % 132.12/18.83 | | (11) $false % 132.12/18.83 | | % 132.12/18.83 | | CLOSE: (11) is inconsistent. % 132.12/18.83 | | % 132.12/18.83 | End of split % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #87 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.12/18.83 (2) ~ (all_53_11 = e0) % 132.12/18.83 (3) ~ (e2 = e0) % 132.12/18.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.83 (5) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.12/18.83 (6) op(e1, e1) = e2 % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | BETA: splitting (1) gives: % 132.12/18.83 | % 132.12/18.83 | Case 1: % 132.12/18.83 | | % 132.12/18.83 | | (7) all_57_8 = e0 & op(e1, e1) = e0 % 132.12/18.83 | | % 132.12/18.83 | | ALPHA: (7) implies: % 132.12/18.83 | | (8) op(e1, e1) = e0 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #324. % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (9) all_57_14 = e0 & op(e0, e1) = e0 % 132.12/18.83 | | % 132.12/18.83 | | ALPHA: (9) implies: % 132.12/18.83 | | (10) op(e0, e1) = e0 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #296. % 132.12/18.83 | | % 132.12/18.83 | End of split % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #88 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) op(e0, e3) = all_53_3 % 132.12/18.83 (2) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 132.12/18.83 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.83 (4) ~ (all_53_2 = e2) % 132.12/18.83 (5) op(e1, e3) = all_53_2 % 132.12/18.83 (6) ~ (all_53_3 = e2) % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | BETA: splitting (2) gives: % 132.12/18.83 | % 132.12/18.83 | Case 1: % 132.12/18.83 | | % 132.12/18.83 | | (7) all_57_6 = e2 & op(e1, e3) = e2 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #93. % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (8) all_57_12 = e2 & op(e0, e3) = e2 % 132.12/18.83 | | % 132.12/18.83 | | ALPHA: (8) implies: % 132.12/18.83 | | (9) op(e0, e3) = e2 % 132.12/18.83 | | % 132.12/18.83 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #99. % 132.12/18.83 | | % 132.12/18.83 | End of split % 132.12/18.83 | % 132.12/18.83 End of proof % 132.12/18.83 % 132.12/18.83 Sub-proof #89 shows that the following formulas are inconsistent: % 132.12/18.83 ---------------------------------------------------------------- % 132.12/18.83 (1) unit = e2 | unit = e1 | unit = e0 % 132.12/18.83 (2) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.12/18.83 (3) all_57_2 = e2 & op(e2, e3) = e2 % 132.12/18.83 (4) op(e2, unit) = e2 % 132.12/18.83 (5) ~ (all_53_1 = all_53_13) % 132.12/18.83 (6) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.12/18.83 (7) ~ (all_53_13 = all_6_2) % 132.12/18.83 (8) all_55_5 = all_6_2 % 132.12/18.83 (9) ~ (all_53_7 = all_6_2) % 132.12/18.83 (10) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.12/18.83 (11) ~ (all_6_2 = e3) % 132.12/18.83 (12) ~ (all_53_1 = all_6_2) % 132.12/18.83 (13) all_53_1 = e2 | ~ (op(e2, e3) = e2) % 132.12/18.83 (14) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.12/18.83 (15) ~ (all_6_2 = e1) % 132.12/18.83 (16) op(e0, unit) = e0 % 132.12/18.83 (17) ~ (unit = e1) % 132.12/18.83 (18) all_55_13 = all_53_7 % 132.12/18.83 % 132.12/18.83 Begin of proof % 132.12/18.83 | % 132.12/18.83 | ALPHA: (3) implies: % 132.12/18.83 | (19) op(e2, e3) = e2 % 132.12/18.83 | % 132.12/18.83 | BETA: splitting (13) gives: % 132.12/18.83 | % 132.12/18.83 | Case 1: % 132.12/18.83 | | % 132.12/18.83 | | (20) ~ (op(e2, e3) = e2) % 132.12/18.83 | | % 132.12/18.83 | | PRED_UNIFY: (19), (20) imply: % 132.12/18.83 | | (21) $false % 132.12/18.83 | | % 132.12/18.83 | | CLOSE: (21) is inconsistent. % 132.12/18.83 | | % 132.12/18.83 | Case 2: % 132.12/18.83 | | % 132.12/18.83 | | (22) all_53_1 = e2 % 132.12/18.83 | | % 132.12/18.83 | | REDUCE: (5), (22) imply: % 132.12/18.83 | | (23) ~ (all_53_13 = e2) % 132.12/18.83 | | % 132.12/18.83 | | SIMP: (23) implies: % 132.12/18.83 | | (24) ~ (all_53_13 = e2) % 132.12/18.83 | | % 132.12/18.83 | | REDUCE: (12), (22) imply: % 132.12/18.83 | | (25) ~ (all_6_2 = e2) % 132.12/18.83 | | % 132.12/18.83 | | SIMP: (25) implies: % 132.12/18.83 | | (26) ~ (all_6_2 = e2) % 132.12/18.83 | | % 132.12/18.83 | | BETA: splitting (14) gives: % 132.12/18.83 | | % 132.12/18.83 | | Case 1: % 132.12/18.83 | | | % 132.12/18.83 | | | (27) all_55_5 = e3 % 132.12/18.83 | | | % 132.12/18.83 | | | COMBINE_EQS: (8), (27) imply: % 132.12/18.83 | | | (28) all_6_2 = e3 % 132.12/18.83 | | | % 132.12/18.83 | | | REDUCE: (11), (28) imply: % 132.12/18.83 | | | (29) $false % 132.12/18.83 | | | % 132.12/18.83 | | | CLOSE: (29) is inconsistent. % 132.12/18.83 | | | % 132.12/18.83 | | Case 2: % 132.12/18.83 | | | % 132.12/18.83 | | | (30) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.12/18.83 | | | % 132.12/18.83 | | | BETA: splitting (30) gives: % 132.12/18.83 | | | % 132.12/18.83 | | | Case 1: % 132.12/18.83 | | | | % 132.12/18.83 | | | | (31) all_55_5 = e2 % 132.12/18.83 | | | | % 132.12/18.83 | | | | COMBINE_EQS: (8), (31) imply: % 132.12/18.83 | | | | (32) all_6_2 = e2 % 132.12/18.83 | | | | % 132.12/18.83 | | | | REDUCE: (26), (32) imply: % 132.12/18.84 | | | | (33) $false % 132.12/18.84 | | | | % 132.12/18.84 | | | | CLOSE: (33) is inconsistent. % 132.12/18.84 | | | | % 132.12/18.84 | | | Case 2: % 132.12/18.84 | | | | % 132.12/18.84 | | | | (34) all_55_5 = e1 | all_55_5 = e0 % 132.12/18.84 | | | | % 132.12/18.84 | | | | BETA: splitting (34) gives: % 132.12/18.84 | | | | % 132.12/18.84 | | | | Case 1: % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | (35) all_55_5 = e1 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | COMBINE_EQS: (8), (35) imply: % 132.12/18.84 | | | | | (36) all_6_2 = e1 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | REDUCE: (15), (36) imply: % 132.12/18.84 | | | | | (37) $false % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | CLOSE: (37) is inconsistent. % 132.12/18.84 | | | | | % 132.12/18.84 | | | | Case 2: % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | (38) all_55_5 = e0 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | COMBINE_EQS: (8), (38) imply: % 132.12/18.84 | | | | | (39) all_6_2 = e0 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | REDUCE: (9), (39) imply: % 132.12/18.84 | | | | | (40) ~ (all_53_7 = e0) % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | REDUCE: (7), (39) imply: % 132.12/18.84 | | | | | (41) ~ (all_53_13 = e0) % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (16), (17), (18), (24), (40), % 132.12/18.84 | | | | | (41) are inconsistent by sub-proof #90. % 132.12/18.84 | | | | | % 132.12/18.84 | | | | End of split % 132.12/18.84 | | | | % 132.12/18.84 | | | End of split % 132.12/18.84 | | | % 132.12/18.84 | | End of split % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #90 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) unit = e2 | unit = e1 | unit = e0 % 132.12/18.84 (2) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.12/18.84 (3) op(e2, unit) = e2 % 132.12/18.84 (4) ~ (all_53_13 = e0) % 132.12/18.84 (5) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.12/18.84 (6) ~ (all_53_13 = e2) % 132.12/18.84 (7) ~ (all_53_7 = e0) % 132.12/18.84 (8) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.12/18.84 (9) op(e0, unit) = e0 % 132.12/18.84 (10) ~ (unit = e1) % 132.12/18.84 (11) all_55_13 = all_53_7 % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (5) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (12) ~ (op(e0, e2) = e0) % 132.12/18.84 | | % 132.12/18.84 | | BETA: splitting (2) gives: % 132.12/18.84 | | % 132.12/18.84 | | Case 1: % 132.12/18.84 | | | % 132.12/18.84 | | | % 132.12/18.84 | | | PRED_UNIFY: (9), (12) imply: % 132.12/18.84 | | | (13) ~ (unit = e2) % 132.12/18.84 | | | % 132.12/18.84 | | | REF_CLOSE: (1), (3), (6), (8), (10), (13) are inconsistent by sub-proof % 132.12/18.84 | | | #217. % 132.12/18.84 | | | % 132.12/18.84 | | Case 2: % 132.12/18.84 | | | % 132.12/18.84 | | | (14) op(e2, e0) = e0 % 132.12/18.84 | | | % 132.12/18.84 | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #356. % 132.12/18.84 | | | % 132.12/18.84 | | End of split % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (15) op(e0, e2) = e0 % 132.12/18.84 | | % 132.12/18.84 | | REF_CLOSE: (5), (7), (11), (15) are inconsistent by sub-proof #292. % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #91 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_0 = e2 & op(e3, e3) = e2 % 132.12/18.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (3) op(e3, e3) = all_4_2 % 132.12/18.84 (4) ~ (all_4_2 = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | ALPHA: (1) implies: % 132.12/18.84 | (5) op(e3, e3) = e2 % 132.12/18.84 | % 132.12/18.84 | GROUND_INST: instantiating (2) with all_4_2, e2, e3, e3, simplifying with (3), % 132.12/18.84 | (5) gives: % 132.12/18.84 | (6) all_4_2 = e2 % 132.12/18.84 | % 132.12/18.84 | REDUCE: (4), (6) imply: % 132.12/18.84 | (7) $false % 132.12/18.84 | % 132.12/18.84 | CLOSE: (7) is inconsistent. % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #92 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.12/18.84 (2) ~ (all_53_2 = all_53_3) % 132.12/18.84 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.12/18.84 (4) op(e2, unit) = e2 % 132.12/18.84 (5) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 132.12/18.84 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 132.12/18.84 (6) ~ (all_53_1 = all_53_13) % 132.12/18.84 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (8) ~ (all_53_2 = e2) % 132.12/18.84 (9) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.12/18.84 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.12/18.84 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.12/18.84 (11) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.12/18.84 (12) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.12/18.84 (13) op(e1, e3) = all_53_2 % 132.12/18.84 (14) ~ (all_53_3 = all_4_2) % 132.12/18.84 (15) op(e3, e3) = all_4_2 % 132.12/18.84 (16) ~ (all_4_2 = e2) % 132.12/18.84 (17) ~ (unit = e1) % 132.12/18.84 (18) all_55_4 = all_53_1 % 132.12/18.84 (19) ~ (all_53_1 = all_53_3) % 132.12/18.84 (20) ~ (e3 = e2) % 132.12/18.84 (21) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.12/18.84 (22) all_14_2 = all_4_2 % 132.12/18.84 (23) op(unit, e3) = e3 % 132.12/18.84 (24) all_55_12 = all_53_3 % 132.12/18.84 (25) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 132.12/18.84 (26) ~ (all_4_2 = e0) % 132.12/18.84 (27) all_55_0 = all_4_2 % 132.12/18.84 (28) unit = e1 | unit = e0 % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (28) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (29) unit = e1 % 132.12/18.84 | | % 132.12/18.84 | | REDUCE: (17), (29) imply: % 132.12/18.84 | | (30) $false % 132.12/18.84 | | % 132.12/18.84 | | CLOSE: (30) is inconsistent. % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (31) unit = e0 % 132.12/18.84 | | % 132.12/18.84 | | REDUCE: (23), (31) imply: % 132.12/18.84 | | (32) op(e0, e3) = e3 % 132.12/18.84 | | % 132.12/18.84 | | REDUCE: (4), (31) imply: % 132.12/18.84 | | (33) op(e2, e0) = e2 % 132.12/18.84 | | % 132.12/18.84 | | BETA: splitting (11) gives: % 132.12/18.84 | | % 132.12/18.84 | | Case 1: % 132.12/18.84 | | | % 132.12/18.84 | | | (34) ~ (op(e0, e3) = e3) % 132.12/18.84 | | | % 132.12/18.84 | | | PRED_UNIFY: (32), (34) imply: % 132.12/18.84 | | | (35) $false % 132.12/18.84 | | | % 132.12/18.84 | | | CLOSE: (35) is inconsistent. % 132.12/18.84 | | | % 132.12/18.84 | | Case 2: % 132.12/18.84 | | | % 132.12/18.84 | | | (36) all_55_12 = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | COMBINE_EQS: (24), (36) imply: % 132.12/18.84 | | | (37) all_53_3 = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | SIMP: (37) implies: % 132.12/18.84 | | | (38) all_53_3 = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | REDUCE: (19), (38) imply: % 132.12/18.84 | | | (39) ~ (all_53_1 = e3) % 132.12/18.84 | | | % 132.12/18.84 | | | REDUCE: (2), (38) imply: % 132.12/18.84 | | | (40) ~ (all_53_2 = e3) % 132.12/18.84 | | | % 132.12/18.84 | | | REDUCE: (14), (38) imply: % 132.12/18.84 | | | (41) ~ (all_4_2 = e3) % 132.12/18.84 | | | % 132.12/18.84 | | | SIMP: (41) implies: % 132.12/18.84 | | | (42) ~ (all_4_2 = e3) % 132.12/18.84 | | | % 132.12/18.84 | | | BETA: splitting (12) gives: % 132.12/18.84 | | | % 132.12/18.84 | | | Case 1: % 132.12/18.84 | | | | % 132.12/18.84 | | | | (43) ~ (op(e2, e0) = e2) % 132.12/18.84 | | | | % 132.12/18.84 | | | | PRED_UNIFY: (33), (43) imply: % 132.12/18.84 | | | | (44) $false % 132.12/18.84 | | | | % 132.12/18.84 | | | | CLOSE: (44) is inconsistent. % 132.12/18.84 | | | | % 132.12/18.84 | | | Case 2: % 132.12/18.84 | | | | % 132.12/18.84 | | | | (45) all_53_13 = e2 % 132.12/18.84 | | | | % 132.12/18.84 | | | | REDUCE: (6), (45) imply: % 132.12/18.84 | | | | (46) ~ (all_53_1 = e2) % 132.12/18.84 | | | | % 132.12/18.84 | | | | BETA: splitting (1) gives: % 132.12/18.84 | | | | % 132.12/18.84 | | | | Case 1: % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | (47) all_55_0 = e3 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | COMBINE_EQS: (27), (47) imply: % 132.12/18.84 | | | | | (48) all_4_2 = e3 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | REDUCE: (42), (48) imply: % 132.12/18.84 | | | | | (49) $false % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | CLOSE: (49) is inconsistent. % 132.12/18.84 | | | | | % 132.12/18.84 | | | | Case 2: % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | (50) ~ (all_55_0 = e3) % 132.12/18.84 | | | | | (51) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | BETA: splitting (51) gives: % 132.12/18.84 | | | | | % 132.12/18.84 | | | | | Case 1: % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | (52) all_55_0 = e2 % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | COMBINE_EQS: (27), (52) imply: % 132.12/18.84 | | | | | | (53) all_4_2 = e2 % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | REDUCE: (16), (53) imply: % 132.12/18.84 | | | | | | (54) $false % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | CLOSE: (54) is inconsistent. % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | Case 2: % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | (55) ~ (all_55_0 = e2) % 132.12/18.84 | | | | | | (56) all_55_0 = e1 | all_55_0 = e0 % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | BETA: splitting (56) gives: % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | | Case 1: % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | (57) all_55_0 = e1 % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | COMBINE_EQS: (27), (57) imply: % 132.12/18.84 | | | | | | | (58) all_4_2 = e1 % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | REDUCE: (16), (58) imply: % 132.12/18.84 | | | | | | | (59) ~ (e2 = e1) % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | SIMP: (59) implies: % 132.12/18.84 | | | | | | | (60) ~ (e2 = e1) % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | REDUCE: (15), (58) imply: % 132.12/18.84 | | | | | | | (61) op(e3, e3) = e1 % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | BETA: splitting (5) gives: % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | Case 1: % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | (62) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & % 132.12/18.84 | | | | | | | | op(e2, e3) = e2) % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | BETA: splitting (62) gives: % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | Case 1: % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | (63) all_57_0 = e2 & op(e3, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | ALPHA: (63) implies: % 132.12/18.84 | | | | | | | | | (64) op(e3, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | REF_CLOSE: (7), (60), (61), (64) are inconsistent by sub-proof % 132.12/18.84 | | | | | | | | | #267. % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | Case 2: % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | (65) all_57_2 = e2 & op(e2, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | ALPHA: (65) implies: % 132.12/18.84 | | | | | | | | | (66) op(e2, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | REF_CLOSE: (18), (25), (46), (66) are inconsistent by % 132.12/18.84 | | | | | | | | | sub-proof #346. % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | End of split % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | Case 2: % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | (67) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & % 132.12/18.84 | | | | | | | | op(e0, e3) = e2) % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | BETA: splitting (67) gives: % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | | Case 1: % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | (68) all_57_6 = e2 & op(e1, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | REF_CLOSE: (7), (8), (13), (68) are inconsistent by sub-proof % 132.12/18.84 | | | | | | | | | #93. % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | Case 2: % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | (69) all_57_12 = e2 & op(e0, e3) = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | ALPHA: (69) implies: % 132.12/18.84 | | | | | | | | | (70) all_57_12 = e2 % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | | REF_CLOSE: (3), (9), (10), (20), (21), (22), (39), (40), (42), % 132.12/18.84 | | | | | | | | | (70) are inconsistent by sub-proof #203. % 132.12/18.84 | | | | | | | | | % 132.12/18.84 | | | | | | | | End of split % 132.12/18.84 | | | | | | | | % 132.12/18.84 | | | | | | | End of split % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | Case 2: % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | (71) all_55_0 = e0 % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | COMBINE_EQS: (27), (71) imply: % 132.12/18.84 | | | | | | | (72) all_4_2 = e0 % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | REDUCE: (26), (72) imply: % 132.12/18.84 | | | | | | | (73) $false % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | | CLOSE: (73) is inconsistent. % 132.12/18.84 | | | | | | | % 132.12/18.84 | | | | | | End of split % 132.12/18.84 | | | | | | % 132.12/18.84 | | | | | End of split % 132.12/18.84 | | | | | % 132.12/18.84 | | | | End of split % 132.12/18.84 | | | | % 132.12/18.84 | | | End of split % 132.12/18.84 | | | % 132.12/18.84 | | End of split % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #93 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_6 = e2 & op(e1, e3) = e2 % 132.12/18.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (3) op(e1, e3) = all_53_2 % 132.12/18.84 (4) ~ (all_53_2 = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | ALPHA: (1) implies: % 132.12/18.84 | (5) op(e1, e3) = e2 % 132.12/18.84 | % 132.12/18.84 | GROUND_INST: instantiating (2) with all_53_2, e2, e3, e1, simplifying with % 132.12/18.84 | (3), (5) gives: % 132.12/18.84 | (6) all_53_2 = e2 % 132.12/18.84 | % 132.12/18.84 | REDUCE: (4), (6) imply: % 132.12/18.84 | (7) $false % 132.12/18.84 | % 132.12/18.84 | CLOSE: (7) is inconsistent. % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #94 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_53_4 = e2 | ~ (op(e3, e2) = e2) % 132.12/18.84 (2) op(e3, e2) = e2 % 132.12/18.84 (3) ~ (all_53_4 = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (1) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (4) ~ (op(e3, e2) = e2) % 132.12/18.84 | | % 132.12/18.84 | | PRED_UNIFY: (2), (4) imply: % 132.12/18.84 | | (5) $false % 132.12/18.84 | | % 132.12/18.84 | | CLOSE: (5) is inconsistent. % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (6) all_53_4 = e2 % 132.12/18.84 | | % 132.12/18.84 | | REDUCE: (3), (6) imply: % 132.12/18.84 | | (7) $false % 132.12/18.84 | | % 132.12/18.84 | | CLOSE: (7) is inconsistent. % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #95 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.12/18.84 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.12/18.84 (2) ~ (e3 = e0) % 132.12/18.84 (3) ~ (e2 = e0) % 132.12/18.84 (4) op(e1, e1) = e3 % 132.12/18.84 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (6) ~ (e3 = e1) % 132.12/18.84 (7) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) % 132.12/18.84 (8) ~ (e2 = e1) % 132.12/18.84 (9) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.12/18.84 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.12/18.84 (10) ~ (e1 = e0) % 132.12/18.84 (11) ~ (e3 = e2) % 132.12/18.84 (12) all_57_7 = e3 % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (7) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (13) all_57_6 = e1 & op(e1, e3) = e1 % 132.12/18.84 | | % 132.12/18.84 | | ALPHA: (13) implies: % 132.12/18.84 | | (14) all_57_6 = e1 % 132.12/18.84 | | % 132.12/18.84 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (14) are % 132.12/18.84 | | inconsistent by sub-proof #304. % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (15) all_57_7 = e1 & op(e1, e2) = e1 % 132.12/18.84 | | % 132.12/18.84 | | REF_CLOSE: (6), (12), (15) are inconsistent by sub-proof #96. % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #96 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_7 = e1 & op(e1, e2) = e1 % 132.12/18.84 (2) all_57_7 = e3 % 132.12/18.84 (3) ~ (e3 = e1) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | ALPHA: (1) implies: % 132.12/18.84 | (4) all_57_7 = e1 % 132.12/18.84 | % 132.12/18.84 | COMBINE_EQS: (2), (4) imply: % 132.12/18.84 | (5) e3 = e1 % 132.12/18.84 | % 132.12/18.84 | REDUCE: (3), (5) imply: % 132.12/18.84 | (6) $false % 132.12/18.84 | % 132.12/18.84 | CLOSE: (6) is inconsistent. % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #97 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_11 = e0 & op(e1, e0) = e0 % 132.12/18.84 (2) ~ (op(e1, e0) = e0) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | ALPHA: (1) implies: % 132.12/18.84 | (3) op(e1, e0) = e0 % 132.12/18.84 | % 132.12/18.84 | PRED_UNIFY: (2), (3) imply: % 132.12/18.84 | (4) $false % 132.12/18.84 | % 132.12/18.84 | CLOSE: (4) is inconsistent. % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #98 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_15 = e1 % 132.12/18.84 (2) ~ (e3 = e0) % 132.12/18.84 (3) all_57_10 = e1 % 132.12/18.84 (4) ~ (e3 = e1) % 132.12/18.84 (5) all_57_11 = e2 % 132.12/18.84 (6) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.12/18.84 (7) all_53_12 = e0 % 132.12/18.84 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 132.12/18.84 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 132.12/18.84 (9) ~ (e3 = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (8) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 132.12/18.84 | | e3) % 132.12/18.84 | | % 132.12/18.84 | | BETA: splitting (10) gives: % 132.12/18.84 | | % 132.12/18.84 | | Case 1: % 132.12/18.84 | | | % 132.12/18.84 | | | (11) all_57_9 = e3 & op(e3, e0) = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | ALPHA: (11) implies: % 132.12/18.84 | | | (12) op(e3, e0) = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | REF_CLOSE: (2), (6), (7), (12) are inconsistent by sub-proof #163. % 132.12/18.84 | | | % 132.12/18.84 | | Case 2: % 132.12/18.84 | | | % 132.12/18.84 | | | (13) all_57_10 = e3 & op(e2, e0) = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #284. % 132.12/18.84 | | | % 132.12/18.84 | | End of split % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (14) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 132.12/18.84 | | e3) % 132.12/18.84 | | % 132.12/18.84 | | BETA: splitting (14) gives: % 132.12/18.84 | | % 132.12/18.84 | | Case 1: % 132.12/18.84 | | | % 132.12/18.84 | | | (15) all_57_11 = e3 & op(e1, e0) = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #260. % 132.12/18.84 | | | % 132.12/18.84 | | Case 2: % 132.12/18.84 | | | % 132.12/18.84 | | | (16) all_57_15 = e3 & op(e0, e0) = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | ALPHA: (16) implies: % 132.12/18.84 | | | (17) all_57_15 = e3 % 132.12/18.84 | | | % 132.12/18.84 | | | COMBINE_EQS: (1), (17) imply: % 132.12/18.84 | | | (18) e3 = e1 % 132.12/18.84 | | | % 132.12/18.84 | | | SIMP: (18) implies: % 132.12/18.84 | | | (19) e3 = e1 % 132.12/18.84 | | | % 132.12/18.84 | | | REDUCE: (4), (19) imply: % 132.12/18.84 | | | (20) $false % 132.12/18.84 | | | % 132.12/18.84 | | | CLOSE: (20) is inconsistent. % 132.12/18.84 | | | % 132.12/18.84 | | End of split % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #99 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (2) op(e0, e3) = all_53_3 % 132.12/18.84 (3) op(e0, e3) = e2 % 132.12/18.84 (4) ~ (all_53_3 = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | GROUND_INST: instantiating (1) with all_53_3, e2, e3, e0, simplifying with % 132.12/18.84 | (2), (3) gives: % 132.12/18.84 | (5) all_53_3 = e2 % 132.12/18.84 | % 132.12/18.84 | REDUCE: (4), (5) imply: % 132.12/18.84 | (6) $false % 132.12/18.84 | % 132.12/18.84 | CLOSE: (6) is inconsistent. % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #100 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) ~ (all_53_11 = e2) % 132.12/18.84 (2) op(e0, e1) = all_53_11 % 132.12/18.84 (3) ~ (e2 = e0) % 132.12/18.84 (4) op(e1, e1) = e0 % 132.12/18.84 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (6) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.84 | BETA: splitting (6) gives: % 132.12/18.84 | % 132.12/18.84 | Case 1: % 132.12/18.84 | | % 132.12/18.84 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 132.12/18.84 | | % 132.12/18.84 | | ALPHA: (7) implies: % 132.12/18.84 | | (8) op(e1, e1) = e2 % 132.12/18.84 | | % 132.12/18.84 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #324. % 132.12/18.84 | | % 132.12/18.84 | Case 2: % 132.12/18.84 | | % 132.12/18.84 | | (9) all_57_14 = e2 & op(e0, e1) = e2 % 132.12/18.84 | | % 132.12/18.84 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #119. % 132.12/18.84 | | % 132.12/18.84 | End of split % 132.12/18.84 | % 132.12/18.84 End of proof % 132.12/18.84 % 132.12/18.84 Sub-proof #101 shows that the following formulas are inconsistent: % 132.12/18.84 ---------------------------------------------------------------- % 132.12/18.84 (1) all_57_6 = e0 & op(e1, e3) = e0 % 132.12/18.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.12/18.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.12/18.84 (3) op(e1, e3) = all_53_2 % 132.12/18.84 (4) ~ (all_53_2 = e0) % 132.12/18.84 % 132.12/18.84 Begin of proof % 132.12/18.84 | % 132.12/18.85 | ALPHA: (1) implies: % 132.12/18.85 | (5) op(e1, e3) = e0 % 132.12/18.85 | % 132.12/18.85 | GROUND_INST: instantiating (2) with all_53_2, e0, e3, e1, simplifying with % 132.12/18.85 | (3), (5) gives: % 132.12/18.85 | (6) all_53_2 = e0 % 132.12/18.85 | % 132.12/18.85 | REDUCE: (4), (6) imply: % 132.12/18.85 | (7) $false % 132.12/18.85 | % 132.12/18.85 | CLOSE: (7) is inconsistent. % 132.12/18.85 | % 132.12/18.85 End of proof % 132.12/18.85 % 132.12/18.85 Sub-proof #102 shows that the following formulas are inconsistent: % 132.12/18.85 ---------------------------------------------------------------- % 132.12/18.85 (1) ~ (all_53_13 = e2) % 132.12/18.85 (2) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.12/18.85 (3) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 132.12/18.85 (4) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.12/18.85 (5) ~ (all_53_9 = e2) % 132.12/18.85 % 132.12/18.85 Begin of proof % 132.12/18.85 | % 132.12/18.85 | BETA: splitting (3) gives: % 132.12/18.85 | % 132.12/18.85 | Case 1: % 132.12/18.85 | | % 132.12/18.85 | | (6) all_57_5 = e2 & op(e2, e1) = e2 % 132.12/18.85 | | % 132.12/18.85 | | ALPHA: (6) implies: % 132.12/18.85 | | (7) op(e2, e1) = e2 % 132.12/18.85 | | % 132.12/18.85 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #347. % 132.12/18.85 | | % 132.12/18.85 | Case 2: % 132.12/18.85 | | % 132.12/18.85 | | (8) all_57_10 = e2 & op(e2, e0) = e2 % 132.12/18.85 | | % 132.12/18.85 | | ALPHA: (8) implies: % 132.12/18.85 | | (9) op(e2, e0) = e2 % 132.12/18.85 | | % 132.12/18.85 | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #225. % 132.12/18.85 | | % 132.12/18.85 | End of split % 132.12/18.85 | % 132.12/18.85 End of proof % 132.12/18.85 % 132.12/18.85 Sub-proof #103 shows that the following formulas are inconsistent: % 132.12/18.85 ---------------------------------------------------------------- % 132.12/18.85 (1) all_57_4 = e1 & op(e3, e1) = e1 % 132.12/18.85 (2) all_57_4 = e3 % 132.12/18.85 (3) ~ (e3 = e1) % 132.12/18.85 % 132.12/18.85 Begin of proof % 132.12/18.85 | % 132.12/18.85 | ALPHA: (1) implies: % 132.12/18.85 | (4) all_57_4 = e1 % 132.12/18.85 | % 132.12/18.85 | COMBINE_EQS: (2), (4) imply: % 132.12/18.85 | (5) e3 = e1 % 132.12/18.85 | % 132.12/18.85 | REDUCE: (3), (5) imply: % 132.12/18.85 | (6) $false % 132.12/18.85 | % 132.12/18.85 | CLOSE: (6) is inconsistent. % 132.12/18.85 | % 132.12/18.85 End of proof % 132.12/18.85 % 132.12/18.85 Sub-proof #104 shows that the following formulas are inconsistent: % 132.12/18.85 ---------------------------------------------------------------- % 132.12/18.85 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.12/18.85 (2) ~ (all_53_2 = all_12_2) % 132.12/18.85 (3) all_55_9 = all_53_6 % 132.12/18.85 (4) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.12/18.85 (5) ~ (all_53_2 = e0) % 132.12/18.85 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.12/18.85 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.12/18.85 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 132.12/18.85 (8) ~ (all_53_2 = e2) % 132.12/18.85 (9) ~ (all_53_1 = all_53_2) % 132.12/18.85 (10) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.12/18.85 (11) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.12/18.85 (12) all_55_8 = all_53_2 % 132.12/18.85 (13) ~ (all_53_2 = all_53_14) % 132.12/18.85 (14) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.12/18.85 (15) ~ (all_53_2 = all_53_6) % 132.12/18.85 (16) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.12/18.85 (17) all_4_2 = e2 % 132.12/18.85 (18) ~ (e3 = e2) % 132.12/18.85 (19) all_57_6 = e2 % 132.12/18.85 % 132.12/18.85 Begin of proof % 132.12/18.85 | % 132.12/18.85 | BETA: splitting (7) gives: % 132.12/18.85 | % 132.12/18.85 | Case 1: % 132.12/18.85 | | % 132.12/18.85 | | (20) all_57_0 = e3 & op(e3, e3) = e3 % 132.12/18.85 | | % 132.12/18.85 | | ALPHA: (20) implies: % 132.12/18.85 | | (21) op(e3, e3) = e3 % 132.12/18.85 | | % 132.12/18.85 | | REF_CLOSE: (4), (17), (18), (21) are inconsistent by sub-proof #315. % 132.12/18.85 | | % 132.12/18.85 | Case 2: % 132.12/18.85 | | % 132.12/18.85 | | (22) all_57_2 = e3 & op(e2, e3) = e3 % 132.12/18.85 | | % 132.12/18.85 | | ALPHA: (22) implies: % 132.12/18.85 | | (23) op(e2, e3) = e3 % 132.12/18.85 | | % 132.12/18.85 | | BETA: splitting (10) gives: % 132.12/18.85 | | % 132.12/18.85 | | Case 1: % 132.12/18.85 | | | % 132.12/18.85 | | | (24) ~ (op(e2, e3) = e3) % 132.12/18.85 | | | % 132.12/18.85 | | | PRED_UNIFY: (23), (24) imply: % 132.12/18.85 | | | (25) $false % 132.12/18.85 | | | % 132.12/18.85 | | | CLOSE: (25) is inconsistent. % 132.12/18.85 | | | % 132.12/18.85 | | Case 2: % 132.12/18.85 | | | % 132.12/18.85 | | | (26) all_53_1 = e3 % 132.12/18.85 | | | % 132.12/18.85 | | | REDUCE: (9), (26) imply: % 132.12/18.85 | | | (27) ~ (all_53_2 = e3) % 132.12/18.85 | | | % 132.12/18.85 | | | SIMP: (27) implies: % 132.12/18.85 | | | (28) ~ (all_53_2 = e3) % 132.12/18.85 | | | % 132.12/18.85 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (11), (12), (13), (14), (15), % 132.12/18.85 | | | (16), (19), (28) are inconsistent by sub-proof #105. % 132.12/18.85 | | | % 132.12/18.85 | | End of split % 132.12/18.85 | | % 132.12/18.85 | End of split % 132.12/18.85 | % 132.12/18.85 End of proof % 132.12/18.85 % 132.12/18.85 Sub-proof #105 shows that the following formulas are inconsistent: % 132.12/18.85 ---------------------------------------------------------------- % 132.12/18.85 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.12/18.85 (2) ~ (all_53_2 = all_12_2) % 132.12/18.85 (3) all_55_9 = all_53_6 % 132.12/18.85 (4) ~ (all_53_2 = e0) % 132.12/18.85 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.12/18.85 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.12/18.85 (6) ~ (all_53_2 = e2) % 132.12/18.85 (7) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.12/18.85 (8) all_55_8 = all_53_2 % 132.12/18.85 (9) ~ (all_53_2 = all_53_14) % 132.12/18.85 (10) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.12/18.85 (11) ~ (all_53_2 = all_53_6) % 132.12/18.85 (12) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.12/18.85 (13) ~ (all_53_2 = e3) % 132.12/18.85 (14) all_57_6 = e2 % 132.12/18.85 % 132.12/18.85 Begin of proof % 132.12/18.85 | % 132.12/18.85 | BETA: splitting (7) gives: % 132.12/18.85 | % 132.12/18.85 | Case 1: % 132.12/18.85 | | % 132.12/18.85 | | (15) all_55_8 = e3 % 132.12/18.85 | | % 132.12/18.85 | | COMBINE_EQS: (8), (15) imply: % 132.12/18.85 | | (16) all_53_2 = e3 % 132.12/18.85 | | % 132.12/18.85 | | REDUCE: (13), (16) imply: % 132.12/18.85 | | (17) $false % 132.12/18.85 | | % 132.24/18.85 | | CLOSE: (17) is inconsistent. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (18) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.24/18.85 | | % 132.24/18.85 | | BETA: splitting (18) gives: % 132.24/18.85 | | % 132.24/18.85 | | Case 1: % 132.24/18.85 | | | % 132.24/18.85 | | | (19) all_55_8 = e2 % 132.24/18.85 | | | % 132.24/18.85 | | | COMBINE_EQS: (8), (19) imply: % 132.24/18.85 | | | (20) all_53_2 = e2 % 132.24/18.85 | | | % 132.24/18.85 | | | REDUCE: (6), (20) imply: % 132.24/18.85 | | | (21) $false % 132.24/18.85 | | | % 132.24/18.85 | | | CLOSE: (21) is inconsistent. % 132.24/18.85 | | | % 132.24/18.85 | | Case 2: % 132.24/18.85 | | | % 132.24/18.85 | | | (22) ~ (all_55_8 = e2) % 132.24/18.85 | | | (23) all_55_8 = e1 | all_55_8 = e0 % 132.24/18.85 | | | % 132.24/18.85 | | | BETA: splitting (23) gives: % 132.24/18.85 | | | % 132.24/18.85 | | | Case 1: % 132.24/18.85 | | | | % 132.24/18.85 | | | | (24) all_55_8 = e1 % 132.24/18.85 | | | | % 132.24/18.85 | | | | COMBINE_EQS: (8), (24) imply: % 132.24/18.85 | | | | (25) all_53_2 = e1 % 132.24/18.85 | | | | % 132.24/18.85 | | | | REDUCE: (11), (25) imply: % 132.24/18.85 | | | | (26) ~ (all_53_6 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | SIMP: (26) implies: % 132.24/18.85 | | | | (27) ~ (all_53_6 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | REDUCE: (9), (25) imply: % 132.24/18.85 | | | | (28) ~ (all_53_14 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | SIMP: (28) implies: % 132.24/18.85 | | | | (29) ~ (all_53_14 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | REDUCE: (2), (25) imply: % 132.24/18.85 | | | | (30) ~ (all_12_2 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | SIMP: (30) implies: % 132.24/18.85 | | | | (31) ~ (all_12_2 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | REDUCE: (6), (25) imply: % 132.24/18.85 | | | | (32) ~ (e2 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | SIMP: (32) implies: % 132.24/18.85 | | | | (33) ~ (e2 = e1) % 132.24/18.85 | | | | % 132.24/18.85 | | | | REF_CLOSE: (1), (3), (5), (10), (12), (14), (27), (29), (31), (33) are % 132.24/18.85 | | | | inconsistent by sub-proof #327. % 132.24/18.85 | | | | % 132.24/18.85 | | | Case 2: % 132.24/18.85 | | | | % 132.24/18.85 | | | | (34) all_55_8 = e0 % 132.24/18.85 | | | | % 132.24/18.85 | | | | COMBINE_EQS: (8), (34) imply: % 132.24/18.85 | | | | (35) all_53_2 = e0 % 132.24/18.85 | | | | % 132.24/18.85 | | | | REDUCE: (4), (35) imply: % 132.24/18.85 | | | | (36) $false % 132.24/18.85 | | | | % 132.24/18.85 | | | | CLOSE: (36) is inconsistent. % 132.24/18.85 | | | | % 132.24/18.85 | | | End of split % 132.24/18.85 | | | % 132.24/18.85 | | End of split % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #106 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_57_13 = e1 & op(e0, e2) = e1 % 132.24/18.85 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.85 (3) op(e0, e2) = all_53_7 % 132.24/18.85 (4) ~ (all_53_7 = e1) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | ALPHA: (1) implies: % 132.24/18.85 | (5) op(e0, e2) = e1 % 132.24/18.85 | % 132.24/18.85 | GROUND_INST: instantiating (2) with all_53_7, e1, e2, e0, simplifying with % 132.24/18.85 | (3), (5) gives: % 132.24/18.85 | (6) all_53_7 = e1 % 132.24/18.85 | % 132.24/18.85 | REDUCE: (4), (6) imply: % 132.24/18.85 | (7) $false % 132.24/18.85 | % 132.24/18.85 | CLOSE: (7) is inconsistent. % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #107 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.85 (2) op(e3, e0) = all_14_0 % 132.24/18.85 (3) op(e3, e0) = e1 % 132.24/18.85 (4) ~ (all_14_0 = e1) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | GROUND_INST: instantiating (1) with e1, all_14_0, e0, e3, simplifying with % 132.24/18.85 | (2), (3) gives: % 132.24/18.85 | (5) all_14_0 = e1 % 132.24/18.85 | % 132.24/18.85 | REDUCE: (4), (5) imply: % 132.24/18.85 | (6) $false % 132.24/18.85 | % 132.24/18.85 | CLOSE: (6) is inconsistent. % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #108 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.85 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.85 (3) ~ (all_8_2 = e3) % 132.24/18.85 (4) ~ (all_53_7 = all_8_2) % 132.24/18.85 (5) op(e2, unit) = e2 % 132.24/18.85 (6) ~ (unit = e2) % 132.24/18.85 (7) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.24/18.85 (8) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (9) ~ (all_8_2 = e1) % 132.24/18.85 (10) all_57_13 = e0 & op(e0, e2) = e0 % 132.24/18.85 (11) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (12) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.24/18.85 (13) op(e0, unit) = e0 % 132.24/18.85 (14) all_55_15 = all_8_2 % 132.24/18.85 (15) ~ (all_53_7 = all_53_11) % 132.24/18.85 (16) ~ (all_53_13 = all_8_2) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | ALPHA: (10) implies: % 132.24/18.85 | (17) op(e0, e2) = e0 % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (1) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (18) ~ (op(e0, e2) = e0) % 132.24/18.85 | | % 132.24/18.85 | | PRED_UNIFY: (17), (18) imply: % 132.24/18.85 | | (19) $false % 132.24/18.85 | | % 132.24/18.85 | | CLOSE: (19) is inconsistent. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (20) all_53_7 = e0 % 132.24/18.85 | | % 132.24/18.85 | | REDUCE: (15), (20) imply: % 132.24/18.85 | | (21) ~ (all_53_11 = e0) % 132.24/18.85 | | % 132.24/18.85 | | SIMP: (21) implies: % 132.24/18.85 | | (22) ~ (all_53_11 = e0) % 132.24/18.85 | | % 132.24/18.85 | | REDUCE: (4), (20) imply: % 132.24/18.85 | | (23) ~ (all_8_2 = e0) % 132.24/18.85 | | % 132.24/18.85 | | SIMP: (23) implies: % 132.24/18.85 | | (24) ~ (all_8_2 = e0) % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14), (16), % 132.24/18.85 | | (22), (24) are inconsistent by sub-proof #109. % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #109 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) unit = e2 | unit = e1 | unit = e0 % 132.24/18.85 (2) ~ (all_53_11 = e0) % 132.24/18.85 (3) ~ (all_8_2 = e3) % 132.24/18.85 (4) op(e2, unit) = e2 % 132.24/18.85 (5) ~ (unit = e2) % 132.24/18.85 (6) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.24/18.85 (7) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (8) ~ (all_8_2 = e1) % 132.24/18.85 (9) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (10) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.24/18.85 (11) op(e0, unit) = e0 % 132.24/18.85 (12) all_55_15 = all_8_2 % 132.24/18.85 (13) ~ (all_8_2 = e0) % 132.24/18.85 (14) ~ (all_53_13 = all_8_2) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (6) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (15) all_55_15 = e3 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (3), (12), (15) are inconsistent by sub-proof #145. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (16) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.24/18.85 | | % 132.24/18.85 | | BETA: splitting (16) gives: % 132.24/18.85 | | % 132.24/18.85 | | Case 1: % 132.24/18.85 | | | % 132.24/18.85 | | | (17) all_55_15 = e2 % 132.24/18.85 | | | % 132.24/18.85 | | | COMBINE_EQS: (12), (17) imply: % 132.24/18.85 | | | (18) all_8_2 = e2 % 132.24/18.85 | | | % 132.24/18.85 | | | SIMP: (18) implies: % 132.24/18.85 | | | (19) all_8_2 = e2 % 132.24/18.85 | | | % 132.24/18.85 | | | REDUCE: (14), (19) imply: % 132.24/18.85 | | | (20) ~ (all_53_13 = e2) % 132.24/18.85 | | | % 132.24/18.85 | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (20) are inconsistent % 132.24/18.85 | | | by sub-proof #110. % 132.24/18.85 | | | % 132.24/18.85 | | Case 2: % 132.24/18.85 | | | % 132.24/18.85 | | | (21) all_55_15 = e1 | all_55_15 = e0 % 132.24/18.85 | | | % 132.24/18.85 | | | REF_CLOSE: (8), (12), (13), (21) are inconsistent by sub-proof #144. % 132.24/18.85 | | | % 132.24/18.85 | | End of split % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #110 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) unit = e2 | unit = e1 | unit = e0 % 132.24/18.85 (2) ~ (all_53_11 = e0) % 132.24/18.85 (3) op(e2, unit) = e2 % 132.24/18.85 (4) ~ (unit = e2) % 132.24/18.85 (5) ~ (all_53_13 = e2) % 132.24/18.85 (6) all_55_14 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (7) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.24/18.85 (8) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.24/18.85 (9) op(e0, unit) = e0 % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (6) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (10) ~ (op(e0, e1) = e0) % 132.24/18.85 | | % 132.24/18.85 | | PRED_UNIFY: (9), (10) imply: % 132.24/18.85 | | (11) ~ (unit = e1) % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (1), (3), (4), (5), (8), (11) are inconsistent by sub-proof #217. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (12) op(e0, e1) = e0 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #296. % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #111 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_57_13 = e2 & op(e0, e2) = e2 % 132.24/18.85 (2) all_57_13 = e3 % 132.24/18.85 (3) ~ (e3 = e2) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | ALPHA: (1) implies: % 132.24/18.85 | (4) all_57_13 = e2 % 132.24/18.85 | % 132.24/18.85 | COMBINE_EQS: (2), (4) imply: % 132.24/18.85 | (5) e3 = e2 % 132.24/18.85 | % 132.24/18.85 | REDUCE: (3), (5) imply: % 132.24/18.85 | (6) $false % 132.24/18.85 | % 132.24/18.85 | CLOSE: (6) is inconsistent. % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #112 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_57_13 = e0 & op(e0, e2) = e0 % 132.24/18.85 (2) all_57_13 = e3 % 132.24/18.85 (3) ~ (e3 = e0) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | ALPHA: (1) implies: % 132.24/18.85 | (4) all_57_13 = e0 % 132.24/18.85 | % 132.24/18.85 | COMBINE_EQS: (2), (4) imply: % 132.24/18.85 | (5) e3 = e0 % 132.24/18.85 | % 132.24/18.85 | REDUCE: (3), (5) imply: % 132.24/18.85 | (6) $false % 132.24/18.85 | % 132.24/18.85 | CLOSE: (6) is inconsistent. % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #113 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_50_2 = e1 % 132.24/18.85 (2) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 132.24/18.85 (3) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 132.24/18.85 (4) ~ (e2 = e1) % 132.24/18.85 (5) ~ (op(e3, e2) = e2) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (2) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (6) all_57_1 = e2 & op(e3, e2) = e2 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (5), (6) are inconsistent by sub-proof #137. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (7) all_57_3 = e2 & op(e2, e2) = e2 % 132.24/18.85 | | % 132.24/18.85 | | ALPHA: (7) implies: % 132.24/18.85 | | (8) op(e2, e2) = e2 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #196. % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #114 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) all_57_12 = e3 & op(e0, e3) = e3 % 132.24/18.85 (2) all_57_12 = e1 % 132.24/18.85 (3) ~ (e3 = e1) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | ALPHA: (1) implies: % 132.24/18.85 | (4) all_57_12 = e3 % 132.24/18.85 | % 132.24/18.85 | COMBINE_EQS: (2), (4) imply: % 132.24/18.85 | (5) e3 = e1 % 132.24/18.85 | % 132.24/18.85 | SIMP: (5) implies: % 132.24/18.85 | (6) e3 = e1 % 132.24/18.85 | % 132.24/18.85 | REDUCE: (3), (6) imply: % 132.24/18.85 | (7) $false % 132.24/18.85 | % 132.24/18.85 | CLOSE: (7) is inconsistent. % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #115 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) ~ (all_53_8 = e3) % 132.24/18.85 (2) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.85 (3) ~ (e3 = e0) % 132.24/18.85 (4) all_57_1 = e0 % 132.24/18.85 (5) ~ (e3 = e1) % 132.24/18.85 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.24/18.85 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.24/18.85 (7) all_57_9 = e1 % 132.24/18.85 (8) all_4_2 = e2 % 132.24/18.85 (9) ~ (e3 = e2) % 132.24/18.85 (10) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (6) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 132.24/18.85 | | e3) % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (2), (3), (4), (8), (9), (11) are inconsistent by sub-proof #152. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (12) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 132.24/18.85 | | e3) % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (1), (5), (7), (10), (12) are inconsistent by sub-proof #116. % 132.24/18.85 | | % 132.24/18.85 | End of split % 132.24/18.85 | % 132.24/18.85 End of proof % 132.24/18.85 % 132.24/18.85 Sub-proof #116 shows that the following formulas are inconsistent: % 132.24/18.85 ---------------------------------------------------------------- % 132.24/18.85 (1) ~ (all_53_8 = e3) % 132.24/18.85 (2) ~ (e3 = e1) % 132.24/18.85 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.24/18.85 (4) all_57_9 = e1 % 132.24/18.85 (5) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 132.24/18.85 % 132.24/18.85 Begin of proof % 132.24/18.85 | % 132.24/18.85 | BETA: splitting (3) gives: % 132.24/18.85 | % 132.24/18.85 | Case 1: % 132.24/18.85 | | % 132.24/18.85 | | (6) all_57_4 = e3 & op(e3, e1) = e3 % 132.24/18.85 | | % 132.24/18.85 | | ALPHA: (6) implies: % 132.24/18.85 | | (7) op(e3, e1) = e3 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #160. % 132.24/18.85 | | % 132.24/18.85 | Case 2: % 132.24/18.85 | | % 132.24/18.85 | | (8) all_57_9 = e3 & op(e3, e0) = e3 % 132.24/18.85 | | % 132.24/18.85 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #151. % 132.24/18.85 | | % 132.24/18.86 | End of split % 132.24/18.86 | % 132.24/18.86 End of proof % 132.24/18.86 % 132.24/18.86 Sub-proof #117 shows that the following formulas are inconsistent: % 132.24/18.86 ---------------------------------------------------------------- % 132.24/18.86 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.86 (2) op(e3, e3) = e2 % 132.24/18.86 (3) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 132.24/18.86 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 132.24/18.86 (4) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.86 (5) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.86 (6) unit = e2 | unit = e1 | unit = e0 % 132.24/18.86 (7) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.86 (8) op(e1, e1) = e1 % 132.24/18.86 (9) all_14_1 = e3 | ~ (op(e3, e2) = e3) % 132.24/18.86 (10) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.24/18.86 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.24/18.86 (11) all_55_9 = all_53_6 % 132.24/18.86 (12) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.86 (13) op(unit, e2) = e2 % 132.24/18.86 (14) ~ (all_53_11 = e2) % 132.24/18.86 (15) ~ (all_53_8 = e2) % 132.24/18.86 (16) all_22_2 = e1 % 132.24/18.86 (17) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.86 (18) ~ (e3 = e0) % 132.24/18.86 (19) op(e0, e1) = all_53_11 % 132.24/18.86 (20) op(e0, e0) = all_8_2 % 132.24/18.86 (21) ~ (e2 = e0) % 132.24/18.86 (22) ~ (all_53_14 = e2) % 132.24/18.86 (23) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 132.24/18.86 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.24/18.86 (24) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.86 (25) op(e1, e0) = all_53_14 % 132.24/18.86 (26) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 132.24/18.86 (27) all_55_5 = all_6_2 % 132.24/18.86 (28) ~ (all_8_2 = e1) % 132.24/18.86 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.86 (30) ~ (e3 = e1) % 132.24/18.86 (31) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.24/18.86 (32) ~ (all_53_1 = all_53_2) % 132.24/18.86 (33) ~ (all_53_7 = all_6_2) % 132.24/18.86 (34) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.24/18.86 (35) ~ (all_53_8 = all_14_1) % 132.24/18.86 (36) ~ (all_6_2 = e3) % 132.24/18.86 (37) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.24/18.86 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.24/18.86 (38) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.24/18.86 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.24/18.86 (39) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.86 (40) ~ (e2 = e1) % 132.24/18.86 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 132.24/18.86 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 132.24/18.86 (42) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.86 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.86 (43) op(e2, e2) = all_6_2 % 132.24/18.86 (44) op(e3, e3) = all_4_2 % 132.24/18.86 (45) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.86 (46) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 132.24/18.86 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 132.24/18.86 (47) ~ (all_6_2 = e1) % 132.24/18.86 (48) ~ (e1 = e0) % 132.24/18.86 (49) op(e1, unit) = e1 % 132.24/18.86 (50) ~ (all_53_8 = all_53_11) % 132.24/18.86 (51) op(e3, e0) = all_53_12 % 132.24/18.86 (52) all_57_8 = e1 % 132.24/18.86 (53) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 132.24/18.86 (54) ~ (all_53_6 = e1) % 132.24/18.86 (55) op(e0, unit) = e0 % 132.24/18.86 (56) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.24/18.86 (57) ~ (all_53_7 = e2) % 132.24/18.86 (58) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.86 (59) ~ (all_53_14 = e1) % 132.24/18.86 (60) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 132.24/18.86 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 132.24/18.86 (61) ~ (all_53_9 = all_6_2) % 132.24/18.86 (62) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 132.24/18.86 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 132.24/18.86 (63) all_42_2 = all_6_2 % 132.24/18.86 (64) all_4_2 = e2 % 132.24/18.86 (65) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.24/18.86 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 132.24/18.86 (66) ~ (e3 = e2) % 132.24/18.86 (67) ~ (all_53_8 = e1) % 132.24/18.86 (68) all_55_13 = all_53_7 % 132.24/18.86 (69) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 132.24/18.86 (70) ~ (all_53_6 = all_6_2) % 132.24/18.86 (71) op(e3, e1) = all_53_8 % 132.24/18.86 (72) ~ (op(e3, e2) = e2) % 132.24/18.86 (73) op(unit, e3) = e3 % 132.24/18.86 (74) op(e3, unit) = e3 % 132.24/18.86 (75) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 132.24/18.86 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 132.24/18.86 (76) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.86 (77) ~ (all_4_2 = e0) % 132.24/18.86 % 132.24/18.86 Begin of proof % 132.24/18.86 | % 132.24/18.86 | BETA: splitting (45) gives: % 132.24/18.86 | % 132.24/18.86 | Case 1: % 132.24/18.86 | | % 132.24/18.86 | | (78) ~ (op(e0, e2) = e2) % 132.24/18.86 | | % 132.24/18.86 | | BETA: splitting (42) gives: % 132.24/18.86 | | % 132.24/18.86 | | Case 1: % 132.24/18.86 | | | % 132.24/18.86 | | | (79) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 132.24/18.86 | | | e2) % 132.24/18.86 | | | % 132.24/18.86 | | | BETA: splitting (79) gives: % 132.24/18.86 | | | % 132.24/18.86 | | | Case 1: % 132.24/18.86 | | | | % 132.24/18.86 | | | | (80) all_57_6 = e2 & op(e1, e3) = e2 % 132.24/18.86 | | | | % 132.24/18.86 | | | | ALPHA: (80) implies: % 132.24/18.86 | | | | (81) all_57_6 = e2 % 132.24/18.86 | | | | % 132.24/18.86 | | | | BETA: splitting (41) gives: % 132.24/18.86 | | | | % 132.24/18.86 | | | | Case 1: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | (82) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, % 132.24/18.86 | | | | | e1) = e2) % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | BETA: splitting (82) gives: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | Case 1: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | (83) all_57_4 = e2 & op(e3, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | ALPHA: (83) implies: % 132.24/18.86 | | | | | | (84) op(e3, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | GROUND_INST: instantiating (29) with all_53_8, e2, e1, e3, % 132.24/18.86 | | | | | | simplifying with (71), (84) gives: % 132.24/18.86 | | | | | | (85) all_53_8 = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | REDUCE: (15), (85) imply: % 132.24/18.86 | | | | | | (86) $false % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | CLOSE: (86) is inconsistent. % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | Case 2: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | (87) all_57_5 = e2 & op(e2, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | ALPHA: (87) implies: % 132.24/18.86 | | | | | | (88) op(e2, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | BETA: splitting (31) gives: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | Case 1: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | (89) ~ (op(e2, e1) = e2) % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | PRED_UNIFY: (88), (89) imply: % 132.24/18.86 | | | | | | | (90) $false % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | CLOSE: (90) is inconsistent. % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | Case 2: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | (91) all_53_9 = e2 % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | REDUCE: (61), (91) imply: % 132.24/18.86 | | | | | | | (92) ~ (all_6_2 = e2) % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | SIMP: (92) implies: % 132.24/18.86 | | | | | | | (93) ~ (all_6_2 = e2) % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | BETA: splitting (46) gives: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | (94) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & % 132.24/18.86 | | | | | | | | op(e2, e2) = e2) % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | REF_CLOSE: (53), (63), (72), (93), (94) are inconsistent by % 132.24/18.86 | | | | | | | | sub-proof #136. % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | (95) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & % 132.24/18.86 | | | | | | | | op(e0, e2) = e2) % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | BETA: splitting (95) gives: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | (96) all_57_7 = e2 & op(e1, e2) = e2 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | ALPHA: (96) implies: % 132.24/18.86 | | | | | | | | | (97) all_57_7 = e2 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | REF_CLOSE: (7), (8), (10), (16), (17), (18), (21), (30), (48), % 132.24/18.86 | | | | | | | | | (52), (66), (81), (97) are inconsistent by % 132.24/18.86 | | | | | | | | | sub-proof #130. % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | (98) all_57_13 = e2 & op(e0, e2) = e2 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | REF_CLOSE: (78), (98) are inconsistent by sub-proof #129. % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | End of split % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | End of split % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | End of split % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | End of split % 132.24/18.86 | | | | | % 132.24/18.86 | | | | Case 2: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | (99) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, % 132.24/18.86 | | | | | e1) = e2) % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | BETA: splitting (99) gives: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | Case 1: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | (100) all_57_8 = e2 & op(e1, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | REF_CLOSE: (40), (52), (100) are inconsistent by sub-proof #262. % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | Case 2: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | (101) all_57_14 = e2 & op(e0, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | ALPHA: (101) implies: % 132.24/18.86 | | | | | | (102) op(e0, e1) = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | GROUND_INST: instantiating (29) with all_53_11, e2, e1, e0, % 132.24/18.86 | | | | | | simplifying with (19), (102) gives: % 132.24/18.86 | | | | | | (103) all_53_11 = e2 % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | REDUCE: (14), (103) imply: % 132.24/18.86 | | | | | | (104) $false % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | CLOSE: (104) is inconsistent. % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | End of split % 132.24/18.86 | | | | | % 132.24/18.86 | | | | End of split % 132.24/18.86 | | | | % 132.24/18.86 | | | Case 2: % 132.24/18.86 | | | | % 132.24/18.86 | | | | (105) all_57_7 = e2 & op(e1, e2) = e2 % 132.24/18.86 | | | | % 132.24/18.86 | | | | ALPHA: (105) implies: % 132.24/18.86 | | | | (106) all_57_7 = e2 % 132.24/18.86 | | | | (107) op(e1, e2) = e2 % 132.24/18.86 | | | | % 132.24/18.86 | | | | BETA: splitting (26) gives: % 132.24/18.86 | | | | % 132.24/18.86 | | | | Case 1: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | (108) ~ (op(e1, e2) = e2) % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | PRED_UNIFY: (107), (108) imply: % 132.24/18.86 | | | | | (109) $false % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | CLOSE: (109) is inconsistent. % 132.24/18.86 | | | | | % 132.24/18.86 | | | | Case 2: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | (110) all_53_6 = e2 % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | REDUCE: (70), (110) imply: % 132.24/18.86 | | | | | (111) ~ (all_6_2 = e2) % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | SIMP: (111) implies: % 132.24/18.86 | | | | | (112) ~ (all_6_2 = e2) % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | BETA: splitting (41) gives: % 132.24/18.86 | | | | | % 132.24/18.86 | | | | | Case 1: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | (113) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, % 132.24/18.86 | | | | | | e1) = e2) % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | BETA: splitting (113) gives: % 132.24/18.86 | | | | | | % 132.24/18.86 | | | | | | Case 1: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | (114) all_57_4 = e2 & op(e3, e1) = e2 % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | REF_CLOSE: (15), (29), (71), (114) are inconsistent by sub-proof % 132.24/18.86 | | | | | | | #128. % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | Case 2: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | (115) all_57_5 = e2 & op(e2, e1) = e2 % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | ALPHA: (115) implies: % 132.24/18.86 | | | | | | | (116) all_57_5 = e2 % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | BETA: splitting (39) gives: % 132.24/18.86 | | | | | | | % 132.24/18.86 | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | (117) all_55_5 = e3 % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | COMBINE_EQS: (27), (117) imply: % 132.24/18.86 | | | | | | | | (118) all_6_2 = e3 % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | REDUCE: (36), (118) imply: % 132.24/18.86 | | | | | | | | (119) $false % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | CLOSE: (119) is inconsistent. % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | (120) ~ (all_55_5 = e3) % 132.24/18.86 | | | | | | | | (121) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | BETA: splitting (121) gives: % 132.24/18.86 | | | | | | | | % 132.24/18.86 | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | (122) all_55_5 = e2 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | COMBINE_EQS: (27), (122) imply: % 132.24/18.86 | | | | | | | | | (123) all_6_2 = e2 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | REDUCE: (112), (123) imply: % 132.24/18.86 | | | | | | | | | (124) $false % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | CLOSE: (124) is inconsistent. % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | (125) ~ (all_55_5 = e2) % 132.24/18.86 | | | | | | | | | (126) all_55_5 = e1 | all_55_5 = e0 % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | BETA: splitting (126) gives: % 132.24/18.86 | | | | | | | | | % 132.24/18.86 | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | (127) all_55_5 = e1 % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | COMBINE_EQS: (27), (127) imply: % 132.24/18.86 | | | | | | | | | | (128) all_6_2 = e1 % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | REDUCE: (47), (128) imply: % 132.24/18.86 | | | | | | | | | | (129) $false % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | CLOSE: (129) is inconsistent. % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | (130) all_55_5 = e0 % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | COMBINE_EQS: (27), (130) imply: % 132.24/18.86 | | | | | | | | | | (131) all_6_2 = e0 % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | REDUCE: (33), (131) imply: % 132.24/18.86 | | | | | | | | | | (132) ~ (all_53_7 = e0) % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | REDUCE: (36), (131) imply: % 132.24/18.86 | | | | | | | | | | (133) ~ (e3 = e0) % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | REDUCE: (112), (131) imply: % 132.24/18.86 | | | | | | | | | | (134) ~ (e2 = e0) % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | REDUCE: (43), (131) imply: % 132.24/18.86 | | | | | | | | | | (135) op(e2, e2) = e0 % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | BETA: splitting (1) gives: % 132.24/18.86 | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | (136) ~ (op(e0, e2) = e0) % 132.24/18.86 | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | PRED_UNIFY: (55), (136) imply: % 132.24/18.86 | | | | | | | | | | | (137) ~ (unit = e2) % 132.24/18.86 | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | PRED_UNIFY: (13), (78) imply: % 132.24/18.86 | | | | | | | | | | | (138) ~ (unit = e0) % 132.24/18.86 | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | BETA: splitting (6) gives: % 132.24/18.86 | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | (139) unit = e2 % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | REDUCE: (137), (139) imply: % 132.24/18.86 | | | | | | | | | | | | (140) $false % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | (141) unit = e1 | unit = e0 % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | BETA: splitting (141) gives: % 132.24/18.86 | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | (142) unit = e1 % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | REDUCE: (137), (142) imply: % 132.24/18.86 | | | | | | | | | | | | | (143) ~ (e2 = e1) % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | REDUCE: (73), (142) imply: % 132.24/18.86 | | | | | | | | | | | | | (144) op(e1, e3) = e3 % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | REDUCE: (74), (142) imply: % 132.24/18.86 | | | | | | | | | | | | | (145) op(e3, e1) = e3 % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | BETA: splitting (5) gives: % 132.24/18.86 | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | (146) ~ (op(e1, e3) = e3) % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | PRED_UNIFY: (144), (146) imply: % 132.24/18.86 | | | | | | | | | | | | | | (147) $false % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | (148) all_53_2 = e3 % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | REDUCE: (32), (148) imply: % 132.24/18.86 | | | | | | | | | | | | | | (149) ~ (all_53_1 = e3) % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | BETA: splitting (69) gives: % 132.24/18.86 | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | (150) ~ (op(e3, e1) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | PRED_UNIFY: (145), (150) imply: % 132.24/18.86 | | | | | | | | | | | | | | | (151) $false % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | (152) all_53_8 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | REDUCE: (50), (152) imply: % 132.24/18.86 | | | | | | | | | | | | | | | (153) ~ (all_53_11 = e3) % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | SIMP: (153) implies: % 132.24/18.86 | | | | | | | | | | | | | | | (154) ~ (all_53_11 = e3) % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | REDUCE: (35), (152) imply: % 132.24/18.86 | | | | | | | | | | | | | | | (155) ~ (all_14_1 = e3) % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | SIMP: (155) implies: % 132.24/18.86 | | | | | | | | | | | | | | | (156) ~ (all_14_1 = e3) % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 132.24/18.86 | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | (157) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | (158) all_57_1 = e3 & op(e3, e2) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (158) are inconsistent by sub-proof % 132.24/18.86 | | | | | | | | | | | | | | | | | #127. % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | (159) all_57_3 = e3 & op(e2, e2) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (36), (43), (159) are inconsistent by % 132.24/18.86 | | | | | | | | | | | | | | | | | sub-proof #352. % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | End of split % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | (160) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 132.24/18.86 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | (161) all_57_7 = e3 & op(e1, e2) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (106), (161) are inconsistent by sub-proof % 132.24/18.86 | | | | | | | | | | | | | | | | | #134. % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | (162) all_57_13 = e3 & op(e0, e2) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 132.24/18.86 | | | | | | | | | | | | | | | | | (163) all_57_13 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | (164) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 132.24/18.86 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 132.24/18.86 | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | (165) all_57_1 = e1 & op(e3, e2) = e1 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | (166) all_57_1 = e1 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | (167) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | (168) all_57_4 = e3 & op(e3, e1) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | (169) all_57_4 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | (170) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (34), (36), (43), (149), (170) are % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #351. % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | (171) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (172) all_57_5 = e3 & op(e2, e1) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (173) all_57_5 = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (173) imply: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (174) e3 = e2 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (174) imply: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (175) all_57_4 = e2 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (18), (21), (23), (29), (30), (38), % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (48), (51), (58), (64), (66), (166), (175) are % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #124. % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (176) all_57_10 = e3 & op(e2, e0) = e3 % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies: % 132.24/18.86 | | | | | | | | | | | | | | | | | | | | | | | (177) all_57_10 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (178) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_57_9 = e1 & op(e3, e0) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_57_9 = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (181) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_57_0 = e2 & op(e3, e3) = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_57_0 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_57_0 = e3 & op(e3, e3) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_57_0 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (186) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) e3 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (187) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) e3 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (188) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) $false % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_57_1 = e3 & op(e3, e2) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (166), (190) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #271. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (16), (17), (21), (29), (48), (166), % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) are inconsistent by sub-proof #123. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_57_4 = e0 & op(e3, e1) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_57_4 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (195) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (196) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) $false % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_57_9 = e0 & op(e3, e0) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (17), (48), (180), (198) are % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_57_9 = e3 & op(e3, e0) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (180), (199) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_57_1 = e2 & op(e3, e2) = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (166), (200) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | #266. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_57_4 = e2 & op(e3, e1) = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_57_4 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_57_0 = e0 & op(e3, e3) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (44), (77), (205) are inconsistent by % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #270. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_57_1 = e0 & op(e3, e2) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (17), (48), (166), (206) are % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #268. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_57_4 = e0 & op(e3, e1) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (203), (208) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #162. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_57_9 = e0 & op(e3, e0) = e0 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (17), (48), (180), (209) are % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_57_9 = e2 & op(e3, e0) = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_57_9 = e2 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (211) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e2 = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (212) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) $false % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_57_10 = e1 & op(e2, e0) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (177), (214) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | #179. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (215) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (28), (29), (59), (215) are % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #283. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (216) all_57_5 = e3 & op(e2, e1) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (217) all_57_5 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (116), (217) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | #194. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | (218) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (219) all_57_8 = e3 & op(e1, e1) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (220) all_57_8 = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (220) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (221) e3 = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (221) imply: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (222) $false % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | (223) all_57_14 = e3 & op(e0, e1) = e3 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (29), (154), (223) are inconsistent by % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | sub-proof #121. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | (224) all_57_3 = e1 & op(e2, e2) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | (225) op(e2, e2) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (48), (135), (225) are inconsistent by % 132.24/18.87 | | | | | | | | | | | | | | | | | | | sub-proof #199. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | (226) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 132.24/18.87 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.24/18.87 | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 132.24/18.87 | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | Case 1: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | (227) all_57_7 = e1 & op(e1, e2) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | (228) op(e1, e2) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (54), (56), (228) are inconsistent by % 132.24/18.87 | | | | | | | | | | | | | | | | | | | sub-proof #341. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | (229) all_57_13 = e1 & op(e0, e2) = e1 % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (163), (229) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | | | | | | | #120. % 132.24/18.87 | | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | (230) ~ (unit = e1) % 132.24/18.87 | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | | REF_CLOSE: (138), (141), (230) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | | | | | | | #278. % 132.24/18.87 | | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | Case 2: % 132.24/18.87 | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | (231) op(e0, e2) = e0 % 132.24/18.87 | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | | REF_CLOSE: (24), (68), (132), (231) are inconsistent by % 132.24/18.87 | | | | | | | | | | | sub-proof #292. % 132.24/18.87 | | | | | | | | | | | % 132.24/18.87 | | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | | % 132.24/18.87 | | | | | | | | | End of split % 132.24/18.87 | | | | | | | | | % 132.24/18.87 | | | | | | | | End of split % 132.24/18.87 | | | | | | | | % 132.24/18.87 | | | | | | | End of split % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | End of split % 132.24/18.87 | | | | | | % 132.24/18.87 | | | | | Case 2: % 132.24/18.87 | | | | | | % 132.24/18.87 | | | | | | (232) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & % 132.24/18.87 | | | | | | op(e0, e1) = e2) % 132.24/18.87 | | | | | | % 132.24/18.87 | | | | | | BETA: splitting (232) gives: % 132.24/18.87 | | | | | | % 132.24/18.87 | | | | | | Case 1: % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | | (233) all_57_8 = e2 & op(e1, e1) = e2 % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | | REF_CLOSE: (40), (52), (233) are inconsistent by sub-proof #262. % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | Case 2: % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | | (234) all_57_14 = e2 & op(e0, e1) = e2 % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | | REF_CLOSE: (14), (19), (29), (234) are inconsistent by sub-proof % 132.24/18.87 | | | | | | | #119. % 132.24/18.87 | | | | | | | % 132.24/18.87 | | | | | | End of split % 132.24/18.87 | | | | | | % 132.24/18.87 | | | | | End of split % 132.24/18.87 | | | | | % 132.24/18.87 | | | | End of split % 132.24/18.87 | | | | % 132.24/18.87 | | | End of split % 132.24/18.87 | | | % 132.24/18.87 | | Case 2: % 132.24/18.87 | | | % 132.24/18.87 | | | (235) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) % 132.24/18.87 | | | = e2) % 132.24/18.87 | | | % 132.24/18.87 | | | BETA: splitting (235) gives: % 132.24/18.87 | | | % 132.24/18.87 | | | Case 1: % 132.24/18.87 | | | | % 132.24/18.87 | | | | (236) all_57_8 = e2 & op(e1, e1) = e2 % 132.24/18.87 | | | | % 132.24/18.87 | | | | REF_CLOSE: (40), (52), (236) are inconsistent by sub-proof #262. % 132.24/18.87 | | | | % 132.24/18.87 | | | Case 2: % 132.24/18.87 | | | | % 132.24/18.87 | | | | (237) all_57_11 = e2 & op(e1, e0) = e2 % 132.24/18.87 | | | | % 132.24/18.87 | | | | REF_CLOSE: (22), (25), (29), (237) are inconsistent by sub-proof #224. % 132.24/18.87 | | | | % 132.24/18.87 | | | End of split % 132.24/18.87 | | | % 132.24/18.87 | | End of split % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (238) op(e0, e2) = e2 % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (57), (68), (76), (238) are inconsistent by sub-proof #118. % 132.24/18.87 | | % 132.24/18.87 | End of split % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #118 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_55_13 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.87 (2) op(e0, e2) = e2 % 132.24/18.87 (3) all_55_13 = all_53_7 % 132.24/18.87 (4) ~ (all_53_7 = e2) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | BETA: splitting (1) gives: % 132.24/18.87 | % 132.24/18.87 | Case 1: % 132.24/18.87 | | % 132.24/18.87 | | (5) ~ (op(e0, e2) = e2) % 132.24/18.87 | | % 132.24/18.87 | | PRED_UNIFY: (2), (5) imply: % 132.24/18.87 | | (6) $false % 132.24/18.87 | | % 132.24/18.87 | | CLOSE: (6) is inconsistent. % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (7) all_55_13 = e2 % 132.24/18.87 | | % 132.24/18.87 | | COMBINE_EQS: (3), (7) imply: % 132.24/18.87 | | (8) all_53_7 = e2 % 132.24/18.87 | | % 132.24/18.87 | | REDUCE: (4), (8) imply: % 132.24/18.87 | | (9) $false % 132.24/18.87 | | % 132.24/18.87 | | CLOSE: (9) is inconsistent. % 132.24/18.87 | | % 132.24/18.87 | End of split % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #119 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_57_14 = e2 & op(e0, e1) = e2 % 132.24/18.87 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.87 (3) op(e0, e1) = all_53_11 % 132.24/18.87 (4) ~ (all_53_11 = e2) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (1) implies: % 132.24/18.87 | (5) op(e0, e1) = e2 % 132.24/18.87 | % 132.24/18.87 | GROUND_INST: instantiating (2) with all_53_11, e2, e1, e0, simplifying with % 132.24/18.87 | (3), (5) gives: % 132.24/18.87 | (6) all_53_11 = e2 % 132.24/18.87 | % 132.24/18.87 | REDUCE: (4), (6) imply: % 132.24/18.87 | (7) $false % 132.24/18.87 | % 132.24/18.87 | CLOSE: (7) is inconsistent. % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #120 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_57_13 = e1 & op(e0, e2) = e1 % 132.24/18.87 (2) all_57_13 = e3 % 132.24/18.87 (3) ~ (e3 = e1) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (1) implies: % 132.24/18.87 | (4) all_57_13 = e1 % 132.24/18.87 | % 132.24/18.87 | COMBINE_EQS: (2), (4) imply: % 132.24/18.87 | (5) e3 = e1 % 132.24/18.87 | % 132.24/18.87 | REDUCE: (3), (5) imply: % 132.24/18.87 | (6) $false % 132.24/18.87 | % 132.24/18.87 | CLOSE: (6) is inconsistent. % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #121 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_57_14 = e3 & op(e0, e1) = e3 % 132.24/18.87 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.87 (3) op(e0, e1) = all_53_11 % 132.24/18.87 (4) ~ (all_53_11 = e3) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (1) implies: % 132.24/18.87 | (5) op(e0, e1) = e3 % 132.24/18.87 | % 132.24/18.87 | GROUND_INST: instantiating (2) with all_53_11, e3, e1, e0, simplifying with % 132.24/18.87 | (3), (5) gives: % 132.24/18.87 | (6) all_53_11 = e3 % 132.24/18.87 | % 132.24/18.87 | REDUCE: (4), (6) imply: % 132.24/18.87 | (7) $false % 132.24/18.87 | % 132.24/18.87 | CLOSE: (7) is inconsistent. % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #122 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) op(e1, e1) = e1 % 132.24/18.87 (2) all_22_2 = e1 % 132.24/18.87 (3) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.87 (4) all_57_9 = e0 & op(e3, e0) = e0 % 132.24/18.87 (5) ~ (e1 = e0) % 132.24/18.87 (6) all_57_9 = e1 % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (4) implies: % 132.24/18.87 | (7) all_57_9 = e0 % 132.24/18.87 | % 132.24/18.87 | COMBINE_EQS: (6), (7) imply: % 132.24/18.87 | (8) e1 = e0 % 132.24/18.87 | % 132.24/18.87 | COMBINE_EQS: (2), (8) imply: % 132.24/18.87 | (9) all_22_2 = e0 % 132.24/18.87 | % 132.24/18.87 | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #269. % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #123 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) op(e3, e3) = e2 % 132.24/18.87 (2) op(e1, e1) = e1 % 132.24/18.87 (3) all_22_2 = e1 % 132.24/18.87 (4) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.87 (5) ~ (e2 = e0) % 132.24/18.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.87 (7) ~ (e1 = e0) % 132.24/18.87 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 132.24/18.87 (9) all_57_1 = e1 % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | BETA: splitting (8) gives: % 132.24/18.87 | % 132.24/18.87 | Case 1: % 132.24/18.87 | | % 132.24/18.87 | | (10) all_57_0 = e0 & op(e3, e3) = e0 % 132.24/18.87 | | % 132.24/18.87 | | ALPHA: (10) implies: % 132.24/18.87 | | (11) op(e3, e3) = e0 % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #350. % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (12) all_57_1 = e0 & op(e3, e2) = e0 % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (2), (3), (4), (7), (9), (12) are inconsistent by sub-proof #268. % 132.24/18.87 | | % 132.24/18.87 | End of split % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #124 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) op(e3, e3) = e2 % 132.24/18.87 (2) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.87 (3) ~ (e3 = e0) % 132.24/18.87 (4) ~ (e2 = e0) % 132.24/18.87 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 132.24/18.87 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.24/18.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.87 (7) ~ (e3 = e1) % 132.24/18.87 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.24/18.87 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.24/18.87 (9) ~ (e1 = e0) % 132.24/18.87 (10) op(e3, e0) = all_53_12 % 132.24/18.87 (11) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.87 (12) all_4_2 = e2 % 132.24/18.87 (13) all_57_4 = e2 % 132.24/18.87 (14) ~ (e3 = e2) % 132.24/18.87 (15) all_57_1 = e1 % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | BETA: splitting (8) gives: % 132.24/18.87 | % 132.24/18.87 | Case 1: % 132.24/18.87 | | % 132.24/18.87 | | (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 132.24/18.87 | | e3) % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (2), (7), (12), (14), (15), (16) are inconsistent by sub-proof % 132.24/18.87 | | #126. % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (17) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 132.24/18.87 | | e3) % 132.24/18.87 | | % 132.24/18.87 | | BETA: splitting (17) gives: % 132.24/18.87 | | % 132.24/18.87 | | Case 1: % 132.24/18.87 | | | % 132.24/18.87 | | | (18) all_57_4 = e3 & op(e3, e1) = e3 % 132.24/18.87 | | | % 132.24/18.87 | | | REF_CLOSE: (13), (14), (18) are inconsistent by sub-proof #125. % 132.24/18.87 | | | % 132.24/18.87 | | Case 2: % 132.24/18.87 | | | % 132.24/18.87 | | | (19) all_57_9 = e3 & op(e3, e0) = e3 % 132.24/18.87 | | | % 132.24/18.87 | | | ALPHA: (19) implies: % 132.24/18.87 | | | (20) all_57_9 = e3 % 132.24/18.87 | | | (21) op(e3, e0) = e3 % 132.24/18.87 | | | % 132.24/18.87 | | | BETA: splitting (11) gives: % 132.24/18.87 | | | % 132.24/18.87 | | | Case 1: % 132.24/18.87 | | | | % 132.24/18.87 | | | | (22) ~ (op(e3, e0) = e3) % 132.24/18.87 | | | | % 132.24/18.87 | | | | PRED_UNIFY: (21), (22) imply: % 132.24/18.87 | | | | (23) $false % 132.24/18.87 | | | | % 132.24/18.87 | | | | CLOSE: (23) is inconsistent. % 132.24/18.87 | | | | % 132.24/18.87 | | | Case 2: % 132.24/18.87 | | | | % 132.24/18.87 | | | | (24) all_53_12 = e3 % 132.24/18.87 | | | | % 132.24/18.87 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (11), (13), (15), (20), (21), % 132.24/18.87 | | | | (24) are inconsistent by sub-proof #161. % 132.24/18.87 | | | | % 132.24/18.87 | | | End of split % 132.24/18.87 | | | % 132.24/18.87 | | End of split % 132.24/18.87 | | % 132.24/18.87 | End of split % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #125 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_57_4 = e3 & op(e3, e1) = e3 % 132.24/18.87 (2) all_57_4 = e2 % 132.24/18.87 (3) ~ (e3 = e2) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (1) implies: % 132.24/18.87 | (4) all_57_4 = e3 % 132.24/18.87 | % 132.24/18.87 | COMBINE_EQS: (2), (4) imply: % 132.24/18.87 | (5) e3 = e2 % 132.24/18.87 | % 132.24/18.87 | SIMP: (5) implies: % 132.24/18.87 | (6) e3 = e2 % 132.24/18.87 | % 132.24/18.87 | REDUCE: (3), (6) imply: % 132.24/18.87 | (7) $false % 132.24/18.87 | % 132.24/18.87 | CLOSE: (7) is inconsistent. % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #126 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 132.24/18.87 (2) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.87 (3) ~ (e3 = e1) % 132.24/18.87 (4) all_4_2 = e2 % 132.24/18.87 (5) ~ (e3 = e2) % 132.24/18.87 (6) all_57_1 = e1 % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | BETA: splitting (1) gives: % 132.24/18.87 | % 132.24/18.87 | Case 1: % 132.24/18.87 | | % 132.24/18.87 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 132.24/18.87 | | % 132.24/18.87 | | ALPHA: (7) implies: % 132.24/18.87 | | (8) op(e3, e3) = e3 % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #315. % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (9) all_57_1 = e3 & op(e3, e2) = e3 % 132.24/18.87 | | % 132.24/18.87 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #271. % 132.24/18.87 | | % 132.24/18.87 | End of split % 132.24/18.87 | % 132.24/18.87 End of proof % 132.24/18.87 % 132.24/18.87 Sub-proof #127 shows that the following formulas are inconsistent: % 132.24/18.87 ---------------------------------------------------------------- % 132.24/18.87 (1) all_57_1 = e3 & op(e3, e2) = e3 % 132.24/18.87 (2) all_14_1 = e3 | ~ (op(e3, e2) = e3) % 132.24/18.87 (3) ~ (all_14_1 = e3) % 132.24/18.87 % 132.24/18.87 Begin of proof % 132.24/18.87 | % 132.24/18.87 | ALPHA: (1) implies: % 132.24/18.87 | (4) op(e3, e2) = e3 % 132.24/18.87 | % 132.24/18.87 | BETA: splitting (2) gives: % 132.24/18.87 | % 132.24/18.87 | Case 1: % 132.24/18.87 | | % 132.24/18.87 | | (5) ~ (op(e3, e2) = e3) % 132.24/18.87 | | % 132.24/18.87 | | PRED_UNIFY: (4), (5) imply: % 132.24/18.87 | | (6) $false % 132.24/18.87 | | % 132.24/18.87 | | CLOSE: (6) is inconsistent. % 132.24/18.87 | | % 132.24/18.87 | Case 2: % 132.24/18.87 | | % 132.24/18.87 | | (7) all_14_1 = e3 % 132.24/18.87 | | % 132.24/18.87 | | REDUCE: (3), (7) imply: % 132.24/18.87 | | (8) $false % 132.24/18.87 | | % 132.24/18.88 | | CLOSE: (8) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #128 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_4 = e2 & op(e3, e1) = e2 % 132.24/18.88 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.88 (3) op(e3, e1) = all_53_8 % 132.24/18.88 (4) ~ (all_53_8 = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (5) op(e3, e1) = e2 % 132.24/18.88 | % 132.24/18.88 | GROUND_INST: instantiating (2) with all_53_8, e2, e1, e3, simplifying with % 132.24/18.88 | (3), (5) gives: % 132.24/18.88 | (6) all_53_8 = e2 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (4), (6) imply: % 132.24/18.88 | (7) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (7) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #129 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_13 = e2 & op(e0, e2) = e2 % 132.24/18.88 (2) ~ (op(e0, e2) = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (3) op(e0, e2) = e2 % 132.24/18.88 | % 132.24/18.88 | PRED_UNIFY: (2), (3) imply: % 132.24/18.88 | (4) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (4) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #130 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_7 = e2 % 132.24/18.88 (2) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.88 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.88 (3) op(e1, e1) = e1 % 132.24/18.88 (4) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.24/18.88 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.24/18.88 (5) all_22_2 = e1 % 132.24/18.88 (6) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.88 (7) ~ (e3 = e0) % 132.24/18.88 (8) ~ (e2 = e0) % 132.24/18.88 (9) ~ (e3 = e1) % 132.24/18.88 (10) ~ (e1 = e0) % 132.24/18.88 (11) all_57_8 = e1 % 132.24/18.88 (12) ~ (e3 = e2) % 132.24/18.88 (13) all_57_6 = e2 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (4) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 132.24/18.88 | | e3) % 132.24/18.88 | | % 132.24/18.88 | | BETA: splitting (14) gives: % 132.24/18.88 | | % 132.24/18.88 | | Case 1: % 132.24/18.88 | | | % 132.24/18.88 | | | (15) all_57_6 = e3 & op(e1, e3) = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | ALPHA: (15) implies: % 132.24/18.88 | | | (16) all_57_6 = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | REF_CLOSE: (12), (13), (16) are inconsistent by sub-proof #135. % 132.24/18.88 | | | % 132.24/18.88 | | Case 2: % 132.24/18.88 | | | % 132.24/18.88 | | | (17) all_57_7 = e3 & op(e1, e2) = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | REF_CLOSE: (1), (12), (17) are inconsistent by sub-proof #134. % 132.24/18.88 | | | % 132.24/18.88 | | End of split % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (18) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 132.24/18.88 | | e3) % 132.24/18.88 | | % 132.24/18.88 | | BETA: splitting (18) gives: % 132.24/18.88 | | % 132.24/18.88 | | Case 1: % 132.24/18.88 | | | % 132.24/18.88 | | | (19) all_57_8 = e3 & op(e1, e1) = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | REF_CLOSE: (9), (11), (19) are inconsistent by sub-proof #133. % 132.24/18.88 | | | % 132.24/18.88 | | Case 2: % 132.24/18.88 | | | % 132.24/18.88 | | | (20) all_57_11 = e3 & op(e1, e0) = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | ALPHA: (20) implies: % 132.24/18.88 | | | (21) all_57_11 = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | BETA: splitting (2) gives: % 132.24/18.88 | | | % 132.24/18.88 | | | Case 1: % 132.24/18.88 | | | | % 132.24/18.88 | | | | (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) % 132.24/18.88 | | | | = e0) % 132.24/18.88 | | | | % 132.24/18.88 | | | | BETA: splitting (22) gives: % 132.24/18.88 | | | | % 132.24/18.88 | | | | Case 1: % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | (23) all_57_6 = e0 & op(e1, e3) = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | REF_CLOSE: (8), (13), (23) are inconsistent by sub-proof #132. % 132.24/18.88 | | | | | % 132.24/18.88 | | | | Case 2: % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | (24) all_57_7 = e0 & op(e1, e2) = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | REF_CLOSE: (1), (8), (24) are inconsistent by sub-proof #131. % 132.24/18.88 | | | | | % 132.24/18.88 | | | | End of split % 132.24/18.88 | | | | % 132.24/18.88 | | | Case 2: % 132.24/18.88 | | | | % 132.24/18.88 | | | | (25) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) % 132.24/18.88 | | | | = e0) % 132.24/18.88 | | | | % 132.24/18.88 | | | | BETA: splitting (25) gives: % 132.24/18.88 | | | | % 132.24/18.88 | | | | Case 1: % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | (26) all_57_8 = e0 & op(e1, e1) = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | REF_CLOSE: (3), (5), (6), (10), (11), (26) are inconsistent by % 132.24/18.88 | | | | | sub-proof #257. % 132.24/18.88 | | | | | % 132.24/18.88 | | | | Case 2: % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | (27) all_57_11 = e0 & op(e1, e0) = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | ALPHA: (27) implies: % 132.24/18.88 | | | | | (28) all_57_11 = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | COMBINE_EQS: (21), (28) imply: % 132.24/18.88 | | | | | (29) e3 = e0 % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | REDUCE: (7), (29) imply: % 132.24/18.88 | | | | | (30) $false % 132.24/18.88 | | | | | % 132.24/18.88 | | | | | CLOSE: (30) is inconsistent. % 132.24/18.88 | | | | | % 132.24/18.88 | | | | End of split % 132.24/18.88 | | | | % 132.24/18.88 | | | End of split % 132.24/18.88 | | | % 132.24/18.88 | | End of split % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #131 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_7 = e0 & op(e1, e2) = e0 % 132.24/18.88 (2) all_57_7 = e2 % 132.24/18.88 (3) ~ (e2 = e0) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (4) all_57_7 = e0 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (2), (4) imply: % 132.24/18.88 | (5) e2 = e0 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (5) imply: % 132.24/18.88 | (6) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (6) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #132 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_6 = e0 & op(e1, e3) = e0 % 132.24/18.88 (2) all_57_6 = e2 % 132.24/18.88 (3) ~ (e2 = e0) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (4) all_57_6 = e0 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (2), (4) imply: % 132.24/18.88 | (5) e2 = e0 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (5) imply: % 132.24/18.88 | (6) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (6) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #133 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_8 = e3 & op(e1, e1) = e3 % 132.24/18.88 (2) all_57_8 = e1 % 132.24/18.88 (3) ~ (e3 = e1) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (4) all_57_8 = e3 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (2), (4) imply: % 132.24/18.88 | (5) e3 = e1 % 132.24/18.88 | % 132.24/18.88 | SIMP: (5) implies: % 132.24/18.88 | (6) e3 = e1 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (6) imply: % 132.24/18.88 | (7) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (7) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #134 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_7 = e3 & op(e1, e2) = e3 % 132.24/18.88 (2) all_57_7 = e2 % 132.24/18.88 (3) ~ (e3 = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (4) all_57_7 = e3 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (2), (4) imply: % 132.24/18.88 | (5) e3 = e2 % 132.24/18.88 | % 132.24/18.88 | SIMP: (5) implies: % 132.24/18.88 | (6) e3 = e2 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (6) imply: % 132.24/18.88 | (7) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (7) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #135 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_6 = e3 % 132.24/18.88 (2) all_57_6 = e2 % 132.24/18.88 (3) ~ (e3 = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (1), (2) imply: % 132.24/18.88 | (4) e3 = e2 % 132.24/18.88 | % 132.24/18.88 | SIMP: (4) implies: % 132.24/18.88 | (5) e3 = e2 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (5) imply: % 132.24/18.88 | (6) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (6) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #136 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 132.24/18.88 (2) ~ (all_6_2 = e2) % 132.24/18.88 (3) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 132.24/18.88 (4) all_42_2 = all_6_2 % 132.24/18.88 (5) ~ (op(e3, e2) = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (1) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (6) all_57_1 = e2 & op(e3, e2) = e2 % 132.24/18.88 | | % 132.24/18.88 | | REF_CLOSE: (5), (6) are inconsistent by sub-proof #137. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (7) all_57_3 = e2 & op(e2, e2) = e2 % 132.24/18.88 | | % 132.24/18.88 | | ALPHA: (7) implies: % 132.24/18.88 | | (8) op(e2, e2) = e2 % 132.24/18.88 | | % 132.24/18.88 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #348. % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #137 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_1 = e2 & op(e3, e2) = e2 % 132.24/18.88 (2) ~ (op(e3, e2) = e2) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (3) op(e3, e2) = e2 % 132.24/18.88 | % 132.24/18.88 | PRED_UNIFY: (2), (3) imply: % 132.24/18.88 | (4) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (4) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #138 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) ~ (all_32_0 = e0) & op(e3, e1) = all_32_0 & $i(all_32_0) % 132.24/18.88 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.88 (3) op(e3, e1) = e0 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (1) implies: % 132.24/18.88 | (4) ~ (all_32_0 = e0) % 132.24/18.88 | (5) op(e3, e1) = all_32_0 % 132.24/18.88 | % 132.24/18.88 | GROUND_INST: instantiating (2) with e0, all_32_0, e1, e3, simplifying with % 132.24/18.88 | (3), (5) gives: % 132.24/18.88 | (6) all_32_0 = e0 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (4), (6) imply: % 132.24/18.88 | (7) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (7) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #139 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) ~ (all_14_1 = e2) % 132.24/18.88 (2) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 132.24/18.88 (3) all_55_1 = all_14_1 % 132.24/18.88 (4) ~ (all_14_1 = e0) % 132.24/18.88 (5) ~ (all_14_1 = e1) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (2) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (6) all_55_1 = e2 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (3), (6) imply: % 132.24/18.88 | | (7) all_14_1 = e2 % 132.24/18.88 | | % 132.24/18.88 | | SIMP: (7) implies: % 132.24/18.88 | | (8) all_14_1 = e2 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (1), (8) imply: % 132.24/18.88 | | (9) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (9) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (10) all_55_1 = e1 | all_55_1 = e0 % 132.24/18.88 | | % 132.24/18.88 | | BETA: splitting (10) gives: % 132.24/18.88 | | % 132.24/18.88 | | Case 1: % 132.24/18.88 | | | % 132.24/18.88 | | | (11) all_55_1 = e1 % 132.24/18.88 | | | % 132.24/18.88 | | | COMBINE_EQS: (3), (11) imply: % 132.24/18.88 | | | (12) all_14_1 = e1 % 132.24/18.88 | | | % 132.24/18.88 | | | REDUCE: (5), (12) imply: % 132.24/18.88 | | | (13) $false % 132.24/18.88 | | | % 132.24/18.88 | | | CLOSE: (13) is inconsistent. % 132.24/18.88 | | | % 132.24/18.88 | | Case 2: % 132.24/18.88 | | | % 132.24/18.88 | | | (14) all_55_1 = e0 % 132.24/18.88 | | | % 132.24/18.88 | | | COMBINE_EQS: (3), (14) imply: % 132.24/18.88 | | | (15) all_14_1 = e0 % 132.24/18.88 | | | % 132.24/18.88 | | | REDUCE: (4), (15) imply: % 132.24/18.88 | | | (16) $false % 132.24/18.88 | | | % 132.24/18.88 | | | CLOSE: (16) is inconsistent. % 132.24/18.88 | | | % 132.24/18.88 | | End of split % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #140 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) ~ (all_53_2 = all_53_3) % 132.24/18.88 (2) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.88 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.88 (4) unit = e2 | unit = e1 | unit = e0 % 132.24/18.88 (5) op(unit, e0) = e0 % 132.24/18.88 (6) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.88 (7) op(e0, e3) = all_53_3 % 132.24/18.88 (8) ~ (all_53_3 = e0) % 132.24/18.88 (9) ~ (all_53_13 = e0) % 132.24/18.88 (10) all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 132.24/18.88 (11) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.24/18.88 (12) op(e1, unit) = e1 % 132.24/18.88 (13) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.88 (14) ~ (all_53_14 = e1) % 132.24/18.88 (15) ~ (all_53_3 = e1) % 132.24/18.88 (16) op(unit, e3) = e3 % 132.24/18.88 (17) ~ (all_53_3 = e2) % 132.24/18.88 (18) all_55_12 = all_53_3 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (10) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (19) all_55_12 = e3 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (18), (19) imply: % 132.24/18.88 | | (20) all_53_3 = e3 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (7), (20) imply: % 132.24/18.88 | | (21) op(e0, e3) = e3 % 132.24/18.88 | | % 132.24/18.88 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12), (13), (14), (16), % 132.24/18.88 | | (18), (21) are inconsistent by sub-proof #142. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (22) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 132.24/18.88 | | % 132.24/18.88 | | REF_CLOSE: (8), (15), (17), (18), (22) are inconsistent by sub-proof #141. % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #141 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) ~ (all_53_3 = e0) % 132.24/18.88 (2) ~ (all_53_3 = e1) % 132.24/18.88 (3) all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0 % 132.24/18.88 (4) ~ (all_53_3 = e2) % 132.24/18.88 (5) all_55_12 = all_53_3 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (3) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (6) all_55_12 = e2 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (5), (6) imply: % 132.24/18.88 | | (7) all_53_3 = e2 % 132.24/18.88 | | % 132.24/18.88 | | SIMP: (7) implies: % 132.24/18.88 | | (8) all_53_3 = e2 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (4), (8) imply: % 132.24/18.88 | | (9) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (9) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (10) all_55_12 = e1 | all_55_12 = e0 % 132.24/18.88 | | % 132.24/18.88 | | BETA: splitting (10) gives: % 132.24/18.88 | | % 132.24/18.88 | | Case 1: % 132.24/18.88 | | | % 132.24/18.88 | | | (11) all_55_12 = e1 % 132.24/18.88 | | | % 132.24/18.88 | | | COMBINE_EQS: (5), (11) imply: % 132.24/18.88 | | | (12) all_53_3 = e1 % 132.24/18.88 | | | % 132.24/18.88 | | | REDUCE: (2), (12) imply: % 132.24/18.88 | | | (13) $false % 132.24/18.88 | | | % 132.24/18.88 | | | CLOSE: (13) is inconsistent. % 132.24/18.88 | | | % 132.24/18.88 | | Case 2: % 132.24/18.88 | | | % 132.24/18.88 | | | (14) all_55_12 = e0 % 132.24/18.88 | | | % 132.24/18.88 | | | COMBINE_EQS: (5), (14) imply: % 132.24/18.88 | | | (15) all_53_3 = e0 % 132.24/18.88 | | | % 132.24/18.88 | | | REDUCE: (1), (15) imply: % 132.24/18.88 | | | (16) $false % 132.24/18.88 | | | % 132.24/18.88 | | | CLOSE: (16) is inconsistent. % 132.24/18.88 | | | % 132.24/18.88 | | End of split % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #142 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) ~ (all_53_2 = all_53_3) % 132.24/18.88 (2) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.88 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.88 (4) unit = e2 | unit = e1 | unit = e0 % 132.24/18.88 (5) op(unit, e0) = e0 % 132.24/18.88 (6) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.88 (7) ~ (all_53_13 = e0) % 132.24/18.88 (8) op(e0, e3) = e3 % 132.24/18.88 (9) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.24/18.88 (10) op(e1, unit) = e1 % 132.24/18.88 (11) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.88 (12) ~ (all_53_14 = e1) % 132.24/18.88 (13) op(unit, e3) = e3 % 132.24/18.88 (14) all_55_12 = all_53_3 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (9) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (15) ~ (op(e0, e3) = e3) % 132.24/18.88 | | % 132.24/18.88 | | PRED_UNIFY: (8), (15) imply: % 132.24/18.88 | | (16) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (16) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (17) all_55_12 = e3 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (14), (17) imply: % 132.24/18.88 | | (18) all_53_3 = e3 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (1), (18) imply: % 132.24/18.88 | | (19) ~ (all_53_2 = e3) % 132.24/18.88 | | % 132.24/18.88 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (19) are % 132.24/18.88 | | inconsistent by sub-proof #275. % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #143 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.88 (2) ~ (all_8_2 = e3) % 132.24/18.88 (3) ~ (all_53_7 = all_8_2) % 132.24/18.88 (4) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.24/18.88 (5) ~ (all_8_2 = e1) % 132.24/18.88 (6) ~ (all_8_2 = e2) % 132.24/18.88 (7) op(e0, e2) = e0 % 132.24/18.88 (8) all_55_15 = all_8_2 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (1) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (9) ~ (op(e0, e2) = e0) % 132.24/18.88 | | % 132.24/18.88 | | PRED_UNIFY: (7), (9) imply: % 132.24/18.88 | | (10) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (10) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (11) all_53_7 = e0 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (3), (11) imply: % 132.24/18.88 | | (12) ~ (all_8_2 = e0) % 132.24/18.88 | | % 132.24/18.88 | | SIMP: (12) implies: % 132.24/18.88 | | (13) ~ (all_8_2 = e0) % 132.24/18.88 | | % 132.24/18.88 | | BETA: splitting (4) gives: % 132.24/18.88 | | % 132.24/18.88 | | Case 1: % 132.24/18.88 | | | % 132.24/18.88 | | | (14) all_55_15 = e3 % 132.24/18.88 | | | % 132.24/18.88 | | | REF_CLOSE: (2), (8), (14) are inconsistent by sub-proof #145. % 132.24/18.88 | | | % 132.24/18.88 | | Case 2: % 132.24/18.88 | | | % 132.24/18.88 | | | (15) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.24/18.88 | | | % 132.24/18.88 | | | BETA: splitting (15) gives: % 132.24/18.88 | | | % 132.24/18.88 | | | Case 1: % 132.24/18.88 | | | | % 132.24/18.88 | | | | (16) all_55_15 = e2 % 132.24/18.88 | | | | % 132.24/18.88 | | | | COMBINE_EQS: (8), (16) imply: % 132.24/18.88 | | | | (17) all_8_2 = e2 % 132.24/18.88 | | | | % 132.24/18.88 | | | | SIMP: (17) implies: % 132.24/18.88 | | | | (18) all_8_2 = e2 % 132.24/18.88 | | | | % 132.24/18.88 | | | | REDUCE: (6), (18) imply: % 132.24/18.88 | | | | (19) $false % 132.24/18.88 | | | | % 132.24/18.88 | | | | CLOSE: (19) is inconsistent. % 132.24/18.88 | | | | % 132.24/18.88 | | | Case 2: % 132.24/18.88 | | | | % 132.24/18.88 | | | | (20) all_55_15 = e1 | all_55_15 = e0 % 132.24/18.88 | | | | % 132.24/18.88 | | | | REF_CLOSE: (5), (8), (13), (20) are inconsistent by sub-proof #144. % 132.24/18.88 | | | | % 132.24/18.88 | | | End of split % 132.24/18.88 | | | % 132.24/18.88 | | End of split % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #144 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_55_15 = e1 | all_55_15 = e0 % 132.24/18.88 (2) all_55_15 = all_8_2 % 132.24/18.88 (3) ~ (all_8_2 = e1) % 132.24/18.88 (4) ~ (all_8_2 = e0) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | BETA: splitting (1) gives: % 132.24/18.88 | % 132.24/18.88 | Case 1: % 132.24/18.88 | | % 132.24/18.88 | | (5) all_55_15 = e1 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (2), (5) imply: % 132.24/18.88 | | (6) all_8_2 = e1 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (3), (6) imply: % 132.24/18.88 | | (7) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (7) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | Case 2: % 132.24/18.88 | | % 132.24/18.88 | | (8) all_55_15 = e0 % 132.24/18.88 | | % 132.24/18.88 | | COMBINE_EQS: (2), (8) imply: % 132.24/18.88 | | (9) all_8_2 = e0 % 132.24/18.88 | | % 132.24/18.88 | | REDUCE: (4), (9) imply: % 132.24/18.88 | | (10) $false % 132.24/18.88 | | % 132.24/18.88 | | CLOSE: (10) is inconsistent. % 132.24/18.88 | | % 132.24/18.88 | End of split % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #145 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_55_15 = all_8_2 % 132.24/18.88 (2) all_55_15 = e3 % 132.24/18.88 (3) ~ (all_8_2 = e3) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (1), (2) imply: % 132.24/18.88 | (4) all_8_2 = e3 % 132.24/18.88 | % 132.24/18.88 | SIMP: (4) implies: % 132.24/18.88 | (5) all_8_2 = e3 % 132.24/18.88 | % 132.24/18.88 | REDUCE: (3), (5) imply: % 132.24/18.88 | (6) $false % 132.24/18.88 | % 132.24/18.88 | CLOSE: (6) is inconsistent. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #146 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) op(e1, e1) = e1 % 132.24/18.88 (2) all_22_2 = e1 % 132.24/18.88 (3) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.88 (4) ~ (e1 = e0) % 132.24/18.88 (5) all_57_12 = e0 & op(e0, e3) = e0 % 132.24/18.88 (6) all_57_12 = e1 % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | ALPHA: (5) implies: % 132.24/18.88 | (7) all_57_12 = e0 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (6), (7) imply: % 132.24/18.88 | (8) e1 = e0 % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (2), (8) imply: % 132.24/18.88 | (9) all_22_2 = e0 % 132.24/18.88 | % 132.24/18.88 | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #269. % 132.24/18.88 | % 132.24/18.88 End of proof % 132.24/18.88 % 132.24/18.88 Sub-proof #147 shows that the following formulas are inconsistent: % 132.24/18.88 ---------------------------------------------------------------- % 132.24/18.88 (1) all_57_10 = e2 % 132.24/18.88 (2) all_57_10 = e1 % 132.24/18.88 (3) ~ (e2 = e1) % 132.24/18.88 % 132.24/18.88 Begin of proof % 132.24/18.88 | % 132.24/18.88 | COMBINE_EQS: (1), (2) imply: % 132.24/18.89 | (4) e2 = e1 % 132.24/18.89 | % 132.24/18.89 | SIMP: (4) implies: % 132.24/18.89 | (5) e2 = e1 % 132.24/18.89 | % 132.24/18.89 | REDUCE: (3), (5) imply: % 132.24/18.89 | (6) $false % 132.24/18.89 | % 132.24/18.89 | CLOSE: (6) is inconsistent. % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #148 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 132.24/18.89 (2) op(e2, e2) = e2 % 132.24/18.89 (3) all_50_2 = e0 % 132.24/18.89 (4) ~ (e2 = e0) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (1) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (5) ~ (op(e2, e2) = e2) % 132.24/18.89 | | % 132.24/18.89 | | PRED_UNIFY: (2), (5) imply: % 132.24/18.89 | | (6) $false % 132.24/18.89 | | % 132.24/18.89 | | CLOSE: (6) is inconsistent. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (7) all_50_2 = e2 % 132.24/18.89 | | % 132.24/18.89 | | COMBINE_EQS: (3), (7) imply: % 132.24/18.89 | | (8) e2 = e0 % 132.24/18.89 | | % 132.24/18.89 | | REDUCE: (4), (8) imply: % 132.24/18.89 | | (9) $false % 132.24/18.89 | | % 132.24/18.89 | | CLOSE: (9) is inconsistent. % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #149 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) op(e1, e1) = e1 % 132.24/18.89 (2) all_57_2 = e0 % 132.24/18.89 (3) all_22_2 = e1 % 132.24/18.89 (4) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.89 (5) ~ (e1 = e0) % 132.24/18.89 (6) all_57_2 = e1 & op(e2, e3) = e1 % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | ALPHA: (6) implies: % 132.24/18.89 | (7) all_57_2 = e1 % 132.24/18.89 | % 132.24/18.89 | COMBINE_EQS: (2), (7) imply: % 132.24/18.89 | (8) e1 = e0 % 132.24/18.89 | % 132.24/18.89 | SIMP: (8) implies: % 132.24/18.89 | (9) e1 = e0 % 132.24/18.89 | % 132.24/18.89 | COMBINE_EQS: (3), (9) imply: % 132.24/18.89 | (10) all_22_2 = e0 % 132.24/18.89 | % 132.24/18.89 | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #269. % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #150 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.89 (2) ~ (e3 = e0) % 132.24/18.89 (3) all_57_4 = e0 % 132.24/18.89 (4) all_57_1 = e0 % 132.24/18.89 (5) ~ (e3 = e1) % 132.24/18.89 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.24/18.89 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.24/18.89 (7) all_57_9 = e1 % 132.24/18.89 (8) all_4_2 = e2 % 132.24/18.89 (9) ~ (e3 = e2) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (6) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 132.24/18.89 | | e3) % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (1), (2), (4), (8), (9), (10) are inconsistent by sub-proof #152. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (11) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 132.24/18.89 | | e3) % 132.24/18.89 | | % 132.24/18.89 | | BETA: splitting (11) gives: % 132.24/18.89 | | % 132.24/18.89 | | Case 1: % 132.24/18.89 | | | % 132.24/18.89 | | | (12) all_57_4 = e3 & op(e3, e1) = e3 % 132.24/18.89 | | | % 132.24/18.89 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #247. % 132.24/18.89 | | | % 132.24/18.89 | | Case 2: % 132.24/18.89 | | | % 132.24/18.89 | | | (13) all_57_9 = e3 & op(e3, e0) = e3 % 132.24/18.89 | | | % 132.24/18.89 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #151. % 132.24/18.89 | | | % 132.24/18.89 | | End of split % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #151 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_57_9 = e3 & op(e3, e0) = e3 % 132.24/18.89 (2) all_57_9 = e1 % 132.24/18.89 (3) ~ (e3 = e1) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | ALPHA: (1) implies: % 132.24/18.89 | (4) all_57_9 = e3 % 132.24/18.89 | % 132.24/18.89 | COMBINE_EQS: (2), (4) imply: % 132.24/18.89 | (5) e3 = e1 % 132.24/18.89 | % 132.24/18.89 | SIMP: (5) implies: % 132.24/18.89 | (6) e3 = e1 % 132.24/18.89 | % 132.24/18.89 | REDUCE: (3), (6) imply: % 132.24/18.89 | (7) $false % 132.24/18.89 | % 132.24/18.89 | CLOSE: (7) is inconsistent. % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #152 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 132.24/18.89 (2) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.89 (3) ~ (e3 = e0) % 132.24/18.89 (4) all_57_1 = e0 % 132.24/18.89 (5) all_4_2 = e2 % 132.24/18.89 (6) ~ (e3 = e2) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (1) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 132.24/18.89 | | % 132.24/18.89 | | ALPHA: (7) implies: % 132.24/18.89 | | (8) op(e3, e3) = e3 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #315. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (9) all_57_1 = e3 & op(e3, e2) = e3 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #248. % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #153 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) op(e1, e1) = e1 % 132.24/18.89 (2) all_57_1 = e1 & op(e3, e2) = e1 % 132.24/18.89 (3) all_22_2 = e1 % 132.24/18.89 (4) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.89 (5) all_57_1 = e0 % 132.24/18.89 (6) ~ (e1 = e0) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | ALPHA: (2) implies: % 132.24/18.89 | (7) all_57_1 = e1 % 132.24/18.89 | % 132.24/18.89 | COMBINE_EQS: (5), (7) imply: % 132.24/18.89 | (8) e1 = e0 % 132.24/18.89 | % 132.24/18.89 | SIMP: (8) implies: % 132.24/18.89 | (9) e1 = e0 % 132.24/18.89 | % 132.24/18.89 | COMBINE_EQS: (3), (9) imply: % 132.24/18.89 | (10) all_22_2 = e0 % 132.24/18.89 | % 132.24/18.89 | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #269. % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #154 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.24/18.89 (2) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 132.24/18.89 (3) ~ (all_53_8 = e1) % 132.24/18.89 (4) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.24/18.89 (5) ~ (all_53_9 = e1) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (2) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (6) all_57_4 = e1 & op(e3, e1) = e1 % 132.24/18.89 | | % 132.24/18.89 | | ALPHA: (6) implies: % 132.24/18.89 | | (7) op(e3, e1) = e1 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #238. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (8) all_57_5 = e1 & op(e2, e1) = e1 % 132.24/18.89 | | % 132.24/18.89 | | ALPHA: (8) implies: % 132.24/18.89 | | (9) op(e2, e1) = e1 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #334. % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #155 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) ~ (all_53_4 = all_53_6) % 132.24/18.89 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.89 (3) ~ (all_53_6 = all_53_7) % 132.24/18.89 (4) all_55_9 = all_53_6 % 132.24/18.89 (5) op(unit, e2) = e2 % 132.24/18.89 (6) all_55_1 = all_53_4 % 132.24/18.89 (7) ~ (all_53_6 = e3) % 132.24/18.89 (8) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 132.24/18.89 (9) ~ (all_53_4 = e1) % 132.24/18.89 (10) ~ (all_53_4 = all_53_7) % 132.24/18.89 (11) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.89 (12) ~ (all_53_6 = e1) % 132.24/18.89 (13) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.89 (14) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.89 (15) ~ (unit = e1) % 132.24/18.89 (16) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.24/18.89 (17) op(unit, e1) = e1 % 132.24/18.89 (18) op(e3, unit) = e3 % 132.24/18.89 (19) ~ (all_53_9 = e1) % 132.24/18.89 (20) ~ (all_53_4 = all_53_12) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (16) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (21) ~ (op(e2, e1) = e1) % 132.24/18.89 | | % 132.24/18.89 | | PRED_UNIFY: (17), (21) imply: % 132.24/18.89 | | (22) ~ (unit = e2) % 132.24/18.89 | | % 132.24/18.89 | | BETA: splitting (2) gives: % 132.24/18.89 | | % 132.24/18.89 | | Case 1: % 132.24/18.89 | | | % 132.24/18.89 | | | (23) unit = e2 % 132.24/18.89 | | | % 132.24/18.89 | | | REDUCE: (22), (23) imply: % 132.24/18.89 | | | (24) $false % 132.24/18.89 | | | % 132.24/18.89 | | | CLOSE: (24) is inconsistent. % 132.24/18.89 | | | % 132.24/18.89 | | Case 2: % 132.24/18.89 | | | % 132.24/18.89 | | | (25) unit = e1 | unit = e0 % 132.24/18.89 | | | % 132.24/18.89 | | | BETA: splitting (25) gives: % 132.24/18.89 | | | % 132.24/18.89 | | | Case 1: % 132.24/18.89 | | | | % 132.24/18.89 | | | | (26) unit = e1 % 132.24/18.89 | | | | % 132.24/18.89 | | | | REDUCE: (15), (26) imply: % 132.24/18.89 | | | | (27) $false % 132.24/18.89 | | | | % 132.24/18.89 | | | | CLOSE: (27) is inconsistent. % 132.24/18.89 | | | | % 132.24/18.89 | | | Case 2: % 132.24/18.89 | | | | % 132.24/18.89 | | | | (28) unit = e0 % 132.24/18.89 | | | | % 132.24/18.89 | | | | REDUCE: (5), (28) imply: % 132.24/18.89 | | | | (29) op(e0, e2) = e2 % 132.24/18.89 | | | | % 132.24/18.89 | | | | REDUCE: (18), (28) imply: % 132.24/18.89 | | | | (30) op(e3, e0) = e3 % 132.24/18.89 | | | | % 132.24/18.89 | | | | BETA: splitting (11) gives: % 132.24/18.89 | | | | % 132.24/18.89 | | | | Case 1: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | (31) ~ (op(e0, e2) = e2) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | PRED_UNIFY: (29), (31) imply: % 132.24/18.89 | | | | | (32) $false % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | CLOSE: (32) is inconsistent. % 132.24/18.89 | | | | | % 132.24/18.89 | | | | Case 2: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | (33) all_53_7 = e2 % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | REDUCE: (10), (33) imply: % 132.24/18.89 | | | | | (34) ~ (all_53_4 = e2) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | REDUCE: (3), (33) imply: % 132.24/18.89 | | | | | (35) ~ (all_53_6 = e2) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | BETA: splitting (13) gives: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | Case 1: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | (36) ~ (op(e3, e0) = e3) % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | PRED_UNIFY: (30), (36) imply: % 132.24/18.89 | | | | | | (37) $false % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | CLOSE: (37) is inconsistent. % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | Case 2: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | (38) all_53_12 = e3 % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | REDUCE: (20), (38) imply: % 132.24/18.89 | | | | | | (39) ~ (all_53_4 = e3) % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | BETA: splitting (14) gives: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | Case 1: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | (40) all_55_9 = e3 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | COMBINE_EQS: (4), (40) imply: % 132.24/18.89 | | | | | | | (41) all_53_6 = e3 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | REDUCE: (7), (41) imply: % 132.24/18.89 | | | | | | | (42) $false % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | CLOSE: (42) is inconsistent. % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | Case 2: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | (43) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | BETA: splitting (43) gives: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | Case 1: % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | (44) all_55_9 = e2 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | COMBINE_EQS: (4), (44) imply: % 132.24/18.89 | | | | | | | | (45) all_53_6 = e2 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | SIMP: (45) implies: % 132.24/18.89 | | | | | | | | (46) all_53_6 = e2 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | REDUCE: (35), (46) imply: % 132.24/18.89 | | | | | | | | (47) $false % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | CLOSE: (47) is inconsistent. % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | Case 2: % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | (48) all_55_9 = e1 | all_55_9 = e0 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | BETA: splitting (48) gives: % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | Case 1: % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | (49) all_55_9 = e1 % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | REF_CLOSE: (4), (12), (49) are inconsistent by sub-proof #342. % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | Case 2: % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | (50) all_55_9 = e0 % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | COMBINE_EQS: (4), (50) imply: % 132.24/18.89 | | | | | | | | | (51) all_53_6 = e0 % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | SIMP: (51) implies: % 132.24/18.89 | | | | | | | | | (52) all_53_6 = e0 % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | REDUCE: (1), (52) imply: % 132.24/18.89 | | | | | | | | | (53) ~ (all_53_4 = e0) % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | | REF_CLOSE: (6), (8), (9), (34), (39), (53) are inconsistent by % 132.24/18.89 | | | | | | | | | sub-proof #156. % 132.24/18.89 | | | | | | | | | % 132.24/18.89 | | | | | | | | End of split % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | End of split % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | End of split % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | End of split % 132.24/18.89 | | | | | % 132.24/18.89 | | | | End of split % 132.24/18.89 | | | | % 132.24/18.89 | | | End of split % 132.24/18.89 | | | % 132.24/18.89 | | End of split % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (54) op(e2, e1) = e1 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (16), (19), (54) are inconsistent by sub-proof #334. % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #156 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_55_1 = all_53_4 % 132.24/18.89 (2) all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 132.24/18.89 (3) ~ (all_53_4 = e1) % 132.24/18.89 (4) ~ (all_53_4 = e3) % 132.24/18.89 (5) ~ (all_53_4 = e2) % 132.24/18.89 (6) ~ (all_53_4 = e0) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (2) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (7) all_55_1 = e3 % 132.24/18.89 | | % 132.24/18.89 | | COMBINE_EQS: (1), (7) imply: % 132.24/18.89 | | (8) all_53_4 = e3 % 132.24/18.89 | | % 132.24/18.89 | | SIMP: (8) implies: % 132.24/18.89 | | (9) all_53_4 = e3 % 132.24/18.89 | | % 132.24/18.89 | | REDUCE: (4), (9) imply: % 132.24/18.89 | | (10) $false % 132.24/18.89 | | % 132.24/18.89 | | CLOSE: (10) is inconsistent. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (11) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 132.24/18.89 | | % 132.24/18.89 | | REF_CLOSE: (1), (3), (5), (6), (11) are inconsistent by sub-proof #157. % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #157 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) all_55_1 = all_53_4 % 132.24/18.89 (2) all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0 % 132.24/18.89 (3) ~ (all_53_4 = e1) % 132.24/18.89 (4) ~ (all_53_4 = e2) % 132.24/18.89 (5) ~ (all_53_4 = e0) % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (2) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (6) all_55_1 = e2 % 132.24/18.89 | | % 132.24/18.89 | | COMBINE_EQS: (1), (6) imply: % 132.24/18.89 | | (7) all_53_4 = e2 % 132.24/18.89 | | % 132.24/18.89 | | REDUCE: (4), (7) imply: % 132.24/18.89 | | (8) $false % 132.24/18.89 | | % 132.24/18.89 | | CLOSE: (8) is inconsistent. % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (9) all_55_1 = e1 | all_55_1 = e0 % 132.24/18.89 | | % 132.24/18.89 | | BETA: splitting (9) gives: % 132.24/18.89 | | % 132.24/18.89 | | Case 1: % 132.24/18.89 | | | % 132.24/18.89 | | | (10) all_55_1 = e1 % 132.24/18.89 | | | % 132.24/18.89 | | | COMBINE_EQS: (1), (10) imply: % 132.24/18.89 | | | (11) all_53_4 = e1 % 132.24/18.89 | | | % 132.24/18.89 | | | REDUCE: (3), (11) imply: % 132.24/18.89 | | | (12) $false % 132.24/18.89 | | | % 132.24/18.89 | | | CLOSE: (12) is inconsistent. % 132.24/18.89 | | | % 132.24/18.89 | | Case 2: % 132.24/18.89 | | | % 132.24/18.89 | | | (13) all_55_1 = e0 % 132.24/18.89 | | | % 132.24/18.89 | | | COMBINE_EQS: (1), (13) imply: % 132.24/18.89 | | | (14) all_53_4 = e0 % 132.24/18.89 | | | % 132.24/18.89 | | | REDUCE: (5), (14) imply: % 132.24/18.89 | | | (15) $false % 132.24/18.89 | | | % 132.24/18.89 | | | CLOSE: (15) is inconsistent. % 132.24/18.89 | | | % 132.24/18.89 | | End of split % 132.24/18.89 | | % 132.24/18.89 | End of split % 132.24/18.89 | % 132.24/18.89 End of proof % 132.24/18.89 % 132.24/18.89 Sub-proof #158 shows that the following formulas are inconsistent: % 132.24/18.89 ---------------------------------------------------------------- % 132.24/18.89 (1) ~ (all_53_9 = all_53_11) % 132.24/18.89 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.89 (3) unit = e2 | unit = e1 | unit = e0 % 132.24/18.89 (4) op(unit, e0) = e0 % 132.24/18.89 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.89 (6) ~ (all_53_7 = all_8_2) % 132.24/18.89 (7) ~ (all_53_14 = all_8_2) % 132.24/18.89 (8) op(e2, unit) = e2 % 132.24/18.89 (9) ~ (all_53_14 = e3) % 132.24/18.89 (10) ~ (all_53_6 = all_53_14) % 132.24/18.89 (11) all_55_9 = all_53_6 % 132.24/18.89 (12) op(unit, e2) = e2 % 132.24/18.89 (13) all_55_6 = all_53_9 % 132.24/18.89 (14) ~ (all_53_13 = all_53_14) % 132.24/18.89 (15) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.24/18.89 (16) ~ (all_53_13 = all_6_2) % 132.24/18.89 (17) all_55_5 = all_6_2 % 132.24/18.89 (18) all_55_11 = all_53_14 % 132.24/18.89 (19) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.24/18.89 (20) all_8_2 = e2 % 132.24/18.89 (21) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 132.24/18.89 (22) ~ (all_6_2 = e3) % 132.24/18.89 (23) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.89 (24) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.89 (25) ~ (all_6_2 = e1) % 132.24/18.89 (26) op(e1, unit) = e1 % 132.24/18.89 (27) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.24/18.89 (28) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.24/18.89 (29) ~ (all_53_9 = all_6_2) % 132.24/18.89 (30) ~ (all_53_2 = e3) % 132.24/18.89 (31) ~ (unit = e1) % 132.24/18.89 (32) op(unit, e3) = e3 % 132.24/18.89 (33) op(unit, e1) = e1 % 132.24/18.89 % 132.24/18.89 Begin of proof % 132.24/18.89 | % 132.24/18.89 | REDUCE: (6), (20) imply: % 132.24/18.89 | (34) ~ (all_53_7 = e2) % 132.24/18.89 | % 132.24/18.89 | REDUCE: (7), (20) imply: % 132.24/18.89 | (35) ~ (all_53_14 = e2) % 132.24/18.89 | % 132.24/18.89 | BETA: splitting (24) gives: % 132.24/18.89 | % 132.24/18.89 | Case 1: % 132.24/18.89 | | % 132.24/18.89 | | (36) ~ (op(e0, e2) = e2) % 132.24/18.89 | | % 132.24/18.89 | | PRED_UNIFY: (12), (36) imply: % 132.24/18.89 | | (37) ~ (unit = e0) % 132.24/18.89 | | % 132.24/18.89 | | BETA: splitting (3) gives: % 132.24/18.89 | | % 132.24/18.89 | | Case 1: % 132.24/18.89 | | | % 132.24/18.89 | | | (38) unit = e2 % 132.24/18.89 | | | % 132.24/18.89 | | | REDUCE: (33), (38) imply: % 132.24/18.89 | | | (39) op(e2, e1) = e1 % 132.24/18.89 | | | % 132.24/18.89 | | | BETA: splitting (5) gives: % 132.24/18.89 | | | % 132.24/18.89 | | | Case 1: % 132.24/18.89 | | | | % 132.24/18.89 | | | | (40) ~ (op(e2, e0) = e0) % 132.24/18.89 | | | | % 132.24/18.89 | | | | PRED_UNIFY: (4), (40) imply: % 132.24/18.89 | | | | (41) ~ (unit = e2) % 132.24/18.89 | | | | % 132.24/18.89 | | | | REF_CLOSE: (2), (3), (30), (32), (37), (41) are inconsistent by % 132.24/18.89 | | | | sub-proof #276. % 132.24/18.89 | | | | % 132.24/18.89 | | | Case 2: % 132.24/18.89 | | | | % 132.24/18.89 | | | | (42) all_53_13 = e0 % 132.24/18.89 | | | | % 132.24/18.89 | | | | REDUCE: (14), (42) imply: % 132.24/18.89 | | | | (43) ~ (all_53_14 = e0) % 132.24/18.89 | | | | % 132.24/18.89 | | | | SIMP: (43) implies: % 132.24/18.89 | | | | (44) ~ (all_53_14 = e0) % 132.24/18.89 | | | | % 132.24/18.89 | | | | REDUCE: (16), (42) imply: % 132.24/18.89 | | | | (45) ~ (all_6_2 = e0) % 132.24/18.89 | | | | % 132.24/18.89 | | | | SIMP: (45) implies: % 132.24/18.89 | | | | (46) ~ (all_6_2 = e0) % 132.24/18.89 | | | | % 132.24/18.89 | | | | BETA: splitting (21) gives: % 132.24/18.89 | | | | % 132.24/18.89 | | | | Case 1: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | (47) ~ (op(e2, e1) = e1) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | PRED_UNIFY: (39), (47) imply: % 132.24/18.89 | | | | | (48) $false % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | CLOSE: (48) is inconsistent. % 132.24/18.89 | | | | | % 132.24/18.89 | | | | Case 2: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | (49) all_55_6 = e1 % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | COMBINE_EQS: (13), (49) imply: % 132.24/18.89 | | | | | (50) all_53_9 = e1 % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | REDUCE: (1), (50) imply: % 132.24/18.89 | | | | | (51) ~ (all_53_11 = e1) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | SIMP: (51) implies: % 132.24/18.89 | | | | | (52) ~ (all_53_11 = e1) % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | BETA: splitting (15) gives: % 132.24/18.89 | | | | | % 132.24/18.89 | | | | | Case 1: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | (53) all_55_11 = e3 % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | COMBINE_EQS: (18), (53) imply: % 132.24/18.89 | | | | | | (54) all_53_14 = e3 % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | REDUCE: (9), (54) imply: % 132.24/18.89 | | | | | | (55) $false % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | CLOSE: (55) is inconsistent. % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | Case 2: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | (56) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | BETA: splitting (56) gives: % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | | Case 1: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | (57) all_55_11 = e2 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | COMBINE_EQS: (18), (57) imply: % 132.24/18.89 | | | | | | | (58) all_53_14 = e2 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | REDUCE: (35), (58) imply: % 132.24/18.89 | | | | | | | (59) $false % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | CLOSE: (59) is inconsistent. % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | Case 2: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | (60) all_55_11 = e1 | all_55_11 = e0 % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | BETA: splitting (60) gives: % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | | Case 1: % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | (61) all_55_11 = e1 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | COMBINE_EQS: (18), (61) imply: % 132.24/18.89 | | | | | | | | (62) all_53_14 = e1 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | SIMP: (62) implies: % 132.24/18.89 | | | | | | | | (63) all_53_14 = e1 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | REDUCE: (10), (63) imply: % 132.24/18.89 | | | | | | | | (64) ~ (all_53_6 = e1) % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | REF_CLOSE: (3), (8), (11), (17), (19), (22), (23), (25), (26), % 132.24/18.89 | | | | | | | | (27), (28), (29), (33), (46), (52), (64) are % 132.24/18.89 | | | | | | | | inconsistent by sub-proof #249. % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | Case 2: % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | (65) all_55_11 = e0 % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | | REF_CLOSE: (18), (44), (65) are inconsistent by sub-proof #159. % 132.24/18.89 | | | | | | | | % 132.24/18.89 | | | | | | | End of split % 132.24/18.89 | | | | | | | % 132.24/18.89 | | | | | | End of split % 132.24/18.89 | | | | | | % 132.24/18.89 | | | | | End of split % 132.24/18.89 | | | | | % 132.24/18.89 | | | | End of split % 132.24/18.89 | | | | % 132.24/18.89 | | | End of split % 132.24/18.89 | | | % 132.24/18.89 | | Case 2: % 132.24/18.89 | | | % 132.24/18.89 | | | (66) unit = e1 | unit = e0 % 132.24/18.89 | | | % 132.24/18.89 | | | REF_CLOSE: (31), (37), (66) are inconsistent by sub-proof #278. % 132.24/18.89 | | | % 132.24/18.89 | | End of split % 132.24/18.89 | | % 132.24/18.89 | Case 2: % 132.24/18.89 | | % 132.24/18.89 | | (67) all_53_7 = e2 % 132.24/18.89 | | % 132.24/18.89 | | REDUCE: (34), (67) imply: % 132.24/18.89 | | (68) $false % 132.24/18.89 | | % 132.24/18.89 | | CLOSE: (68) is inconsistent. % 132.24/18.89 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #159 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_55_11 = all_53_14 % 132.24/18.90 (2) all_55_11 = e0 % 132.24/18.90 (3) ~ (all_53_14 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | COMBINE_EQS: (1), (2) imply: % 132.24/18.90 | (4) all_53_14 = e0 % 132.24/18.90 | % 132.24/18.90 | SIMP: (4) implies: % 132.24/18.90 | (5) all_53_14 = e0 % 132.24/18.90 | % 132.24/18.90 | REDUCE: (3), (5) imply: % 132.24/18.90 | (6) $false % 132.24/18.90 | % 132.24/18.90 | CLOSE: (6) is inconsistent. % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #160 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 132.24/18.90 (2) op(e3, e1) = e3 % 132.24/18.90 (3) ~ (all_53_8 = e3) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | BETA: splitting (1) gives: % 132.24/18.90 | % 132.24/18.90 | Case 1: % 132.24/18.90 | | % 132.24/18.90 | | (4) ~ (op(e3, e1) = e3) % 132.24/18.90 | | % 132.24/18.90 | | PRED_UNIFY: (2), (4) imply: % 132.24/18.90 | | (5) $false % 132.24/18.90 | | % 132.24/18.90 | | CLOSE: (5) is inconsistent. % 132.24/18.90 | | % 132.24/18.90 | Case 2: % 132.24/18.90 | | % 132.24/18.90 | | (6) all_53_8 = e3 % 132.24/18.90 | | % 132.24/18.90 | | REDUCE: (3), (6) imply: % 132.24/18.90 | | (7) $false % 132.24/18.90 | | % 132.24/18.90 | | CLOSE: (7) is inconsistent. % 132.24/18.90 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #161 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) op(e3, e3) = e2 % 132.24/18.90 (2) all_57_9 = e3 % 132.24/18.90 (3) ~ (e3 = e0) % 132.24/18.90 (4) ~ (e2 = e0) % 132.24/18.90 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 132.24/18.90 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.24/18.90 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.90 (7) ~ (e1 = e0) % 132.24/18.90 (8) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.90 (9) all_53_12 = e3 % 132.24/18.90 (10) op(e3, e0) = e3 % 132.24/18.90 (11) all_57_4 = e2 % 132.24/18.90 (12) all_57_1 = e1 % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | BETA: splitting (5) gives: % 132.24/18.90 | % 132.24/18.90 | Case 1: % 132.24/18.90 | | % 132.24/18.90 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 132.24/18.90 | | e0) % 132.24/18.90 | | % 132.24/18.90 | | BETA: splitting (13) gives: % 132.24/18.90 | | % 132.24/18.90 | | Case 1: % 132.24/18.90 | | | % 132.24/18.90 | | | (14) all_57_0 = e0 & op(e3, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | ALPHA: (14) implies: % 132.24/18.90 | | | (15) op(e3, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (1), (4), (6), (15) are inconsistent by sub-proof #350. % 132.24/18.90 | | | % 132.24/18.90 | | Case 2: % 132.24/18.90 | | | % 132.24/18.90 | | | (16) all_57_1 = e0 & op(e3, e2) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (7), (12), (16) are inconsistent by sub-proof #286. % 132.24/18.90 | | | % 132.24/18.90 | | End of split % 132.24/18.90 | | % 132.24/18.90 | Case 2: % 132.24/18.90 | | % 132.24/18.90 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 132.24/18.90 | | e0) % 132.24/18.90 | | % 132.24/18.90 | | BETA: splitting (17) gives: % 132.24/18.90 | | % 132.24/18.90 | | Case 1: % 132.24/18.90 | | | % 132.24/18.90 | | | (18) all_57_4 = e0 & op(e3, e1) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (4), (11), (18) are inconsistent by sub-proof #162. % 132.24/18.90 | | | % 132.24/18.90 | | Case 2: % 132.24/18.90 | | | % 132.24/18.90 | | | (19) all_57_9 = e0 & op(e3, e0) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | ALPHA: (19) implies: % 132.24/18.90 | | | (20) all_57_9 = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | COMBINE_EQS: (2), (20) imply: % 132.24/18.90 | | | (21) e3 = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | COMBINE_EQS: (9), (21) imply: % 132.24/18.90 | | | (22) all_53_12 = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (3), (8), (10), (22) are inconsistent by sub-proof #163. % 132.24/18.90 | | | % 132.24/18.90 | | End of split % 132.24/18.90 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #162 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_57_4 = e0 & op(e3, e1) = e0 % 132.24/18.90 (2) all_57_4 = e2 % 132.24/18.90 (3) ~ (e2 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | ALPHA: (1) implies: % 132.24/18.90 | (4) all_57_4 = e0 % 132.24/18.90 | % 132.24/18.90 | COMBINE_EQS: (2), (4) imply: % 132.24/18.90 | (5) e2 = e0 % 132.24/18.90 | % 132.24/18.90 | REDUCE: (3), (5) imply: % 132.24/18.90 | (6) $false % 132.24/18.90 | % 132.24/18.90 | CLOSE: (6) is inconsistent. % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #163 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.90 (2) op(e3, e0) = e3 % 132.24/18.90 (3) all_53_12 = e0 % 132.24/18.90 (4) ~ (e3 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | BETA: splitting (1) gives: % 132.24/18.90 | % 132.24/18.90 | Case 1: % 132.24/18.90 | | % 132.24/18.90 | | (5) ~ (op(e3, e0) = e3) % 132.24/18.90 | | % 132.24/18.90 | | PRED_UNIFY: (2), (5) imply: % 132.24/18.90 | | (6) $false % 132.24/18.90 | | % 132.24/18.90 | | CLOSE: (6) is inconsistent. % 132.24/18.90 | | % 132.24/18.90 | Case 2: % 132.24/18.90 | | % 132.24/18.90 | | (7) all_53_12 = e3 % 132.24/18.90 | | % 132.24/18.90 | | COMBINE_EQS: (3), (7) imply: % 132.24/18.90 | | (8) e3 = e0 % 132.24/18.90 | | % 132.24/18.90 | | REDUCE: (4), (8) imply: % 132.24/18.90 | | (9) $false % 132.24/18.90 | | % 132.24/18.90 | | CLOSE: (9) is inconsistent. % 132.24/18.90 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #164 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.90 (2) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 132.24/18.90 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 132.24/18.90 (3) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.90 (4) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.90 (5) unit = e2 | unit = e1 | unit = e0 % 132.24/18.90 (6) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.24/18.90 (7) op(unit, e0) = e0 % 132.24/18.90 (8) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.90 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.90 (9) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.90 (10) ~ (all_53_9 = e3) % 132.24/18.90 (11) ~ (all_53_6 = all_53_7) % 132.24/18.90 (12) ~ (all_53_6 = all_53_14) % 132.24/18.90 (13) all_55_9 = all_53_6 % 132.24/18.90 (14) op(unit, e2) = e2 % 132.24/18.90 (15) ~ (all_53_12 = e1) % 132.24/18.90 (16) ~ (all_53_3 = e0) % 132.24/18.90 (17) ~ (op(e1, e3) = e3) % 132.24/18.90 (18) ~ (all_53_6 = e3) % 132.24/18.90 (19) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.24/18.90 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.24/18.90 $i(all_42_0)))) % 132.24/18.90 (20) op(e0, e0) = all_8_2 % 132.24/18.90 (21) ~ (e2 = e0) % 132.24/18.90 (22) op(e1, e1) = e3 % 132.24/18.90 (23) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.90 (24) ~ (all_53_7 = e0) % 132.24/18.90 (25) ~ (all_53_13 = all_6_2) % 132.24/18.90 (26) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.24/18.90 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.24/18.90 (27) op(e2, e1) = all_53_9 % 132.24/18.90 (28) all_12_2 = e3 % 132.24/18.90 (29) all_55_5 = all_6_2 % 132.24/18.90 (30) ~ (all_8_2 = e1) % 132.24/18.90 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.90 (32) ~ (e3 = e1) % 132.24/18.90 (33) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.24/18.90 (34) ~ (all_53_7 = all_6_2) % 132.24/18.90 (35) all_53_0 = e3 | ~ (op(e3, e3) = e3) % 132.24/18.90 (36) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.24/18.90 (37) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.24/18.90 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.24/18.90 (38) ~ (all_6_2 = e3) % 132.24/18.90 (39) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.24/18.90 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.24/18.90 (40) ~ (all_53_6 = all_18_1) % 132.24/18.90 (41) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.90 (42) ~ (e2 = e1) % 132.24/18.90 (43) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.90 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.90 (44) op(e2, e2) = all_6_2 % 132.24/18.90 (45) op(e3, e3) = all_4_2 % 132.24/18.90 (46) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.90 (47) ~ (all_6_2 = e1) % 132.24/18.90 (48) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 132.24/18.90 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 132.24/18.90 (49) op(e1, unit) = e1 % 132.24/18.90 (50) all_53_0 = e1 % 132.24/18.90 (51) op(e3, e3) = e3 % 132.24/18.90 (52) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.90 (53) op(e3, e0) = all_53_12 % 132.24/18.90 (54) op(e0, unit) = e0 % 132.24/18.90 (55) ~ (all_53_3 = e1) % 132.24/18.90 (56) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.90 (57) op(e1, e3) = all_18_1 % 132.24/18.90 (58) ~ (all_53_2 = e3) % 132.24/18.90 (59) all_42_2 = all_6_2 % 132.24/18.90 (60) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.24/18.90 (61) ~ (unit = e1) % 132.24/18.90 (62) ~ (all_53_1 = all_53_3) % 132.24/18.90 (63) ~ (e3 = e2) % 132.24/18.90 (64) all_55_13 = all_53_7 % 132.24/18.90 (65) ~ (all_53_6 = all_6_2) % 132.24/18.90 (66) op(unit, e3) = e3 % 132.24/18.90 (67) ~ (all_53_14 = e0) % 132.24/18.90 (68) all_57_0 = e3 % 132.24/18.90 (69) ~ (all_4_2 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | BETA: splitting (35) gives: % 132.24/18.90 | % 132.24/18.90 | Case 1: % 132.24/18.90 | | % 132.24/18.90 | | (70) ~ (op(e3, e3) = e3) % 132.24/18.90 | | % 132.24/18.90 | | PRED_UNIFY: (51), (70) imply: % 132.24/18.90 | | (71) $false % 132.24/18.90 | | % 132.24/18.90 | | CLOSE: (71) is inconsistent. % 132.24/18.90 | | % 132.24/18.90 | Case 2: % 132.24/18.90 | | % 132.24/18.90 | | (72) all_53_0 = e3 % 132.24/18.90 | | % 132.24/18.90 | | COMBINE_EQS: (50), (72) imply: % 132.24/18.90 | | (73) e3 = e1 % 132.24/18.90 | | % 132.24/18.90 | | SIMP: (73) implies: % 132.24/18.90 | | (74) e3 = e1 % 132.24/18.90 | | % 132.24/18.90 | | COMBINE_EQS: (68), (74) imply: % 132.24/18.90 | | (75) all_57_0 = e1 % 132.24/18.90 | | % 132.24/18.90 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 132.24/18.90 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 132.24/18.90 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 132.24/18.90 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 132.24/18.90 | | (47), (48), (49), (52), (53), (54), (55), (56), (57), (58), (59), % 132.24/18.90 | | (60), (61), (62), (63), (64), (65), (66), (67), (69), (75) are % 132.24/18.90 | | inconsistent by sub-proof #167. % 132.24/18.90 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #165 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.90 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.90 (3) op(unit, e0) = e0 % 132.24/18.90 (4) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.90 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.90 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.90 (6) ~ (all_53_6 = all_53_7) % 132.24/18.90 (7) ~ (all_53_6 = all_53_14) % 132.24/18.90 (8) all_55_9 = all_53_6 % 132.24/18.90 (9) op(unit, e2) = e2 % 132.24/18.90 (10) ~ (all_53_3 = e0) % 132.24/18.90 (11) ~ (all_53_13 = e0) % 132.24/18.90 (12) ~ (all_53_6 = e3) % 132.24/18.90 (13) ~ (e3 = e0) % 132.24/18.90 (14) ~ (e2 = e0) % 132.24/18.90 (15) op(e1, e1) = e3 % 132.24/18.90 (16) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.24/18.90 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.24/18.90 (17) all_12_2 = e3 % 132.24/18.90 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.90 (19) ~ (e3 = e1) % 132.24/18.90 (20) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.24/18.90 (21) ~ (all_53_6 = all_18_1) % 132.24/18.90 (22) ~ (e2 = e1) % 132.24/18.90 (23) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.90 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.90 (24) op(e3, e3) = all_4_2 % 132.24/18.90 (25) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.90 (26) ~ (e1 = e0) % 132.24/18.90 (27) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 132.24/18.90 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 132.24/18.90 (28) op(e1, unit) = e1 % 132.24/18.90 (29) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.90 (30) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.90 (31) op(e1, e3) = all_18_1 % 132.24/18.90 (32) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.24/18.90 (33) ~ (unit = e1) % 132.24/18.90 (34) ~ (e3 = e2) % 132.24/18.90 (35) all_57_2 = e1 & op(e2, e3) = e1 % 132.24/18.90 (36) ~ (all_53_14 = e0) % 132.24/18.90 (37) ~ (all_4_2 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | ALPHA: (35) implies: % 132.24/18.90 | (38) all_57_2 = e1 % 132.24/18.90 | % 132.24/18.90 | BETA: splitting (27) gives: % 132.24/18.90 | % 132.24/18.90 | Case 1: % 132.24/18.90 | | % 132.24/18.90 | | (39) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 132.24/18.90 | | e0) % 132.24/18.90 | | % 132.24/18.90 | | BETA: splitting (39) gives: % 132.24/18.90 | | % 132.24/18.90 | | Case 1: % 132.24/18.90 | | | % 132.24/18.90 | | | (40) all_57_0 = e0 & op(e3, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (18), (24), (37), (40) are inconsistent by sub-proof #270. % 132.24/18.90 | | | % 132.24/18.90 | | Case 2: % 132.24/18.90 | | | % 132.24/18.90 | | | (41) all_57_2 = e0 & op(e2, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (26), (38), (41) are inconsistent by sub-proof #166. % 132.24/18.90 | | | % 132.24/18.90 | | End of split % 132.24/18.90 | | % 132.24/18.90 | Case 2: % 132.24/18.90 | | % 132.24/18.90 | | (42) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 132.24/18.90 | | e0) % 132.24/18.90 | | % 132.24/18.90 | | BETA: splitting (42) gives: % 132.24/18.90 | | % 132.24/18.90 | | Case 1: % 132.24/18.90 | | | % 132.24/18.90 | | | (43) all_57_6 = e0 & op(e1, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 132.24/18.90 | | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (25), % 132.24/18.90 | | | (26), (28), (29), (30), (31), (32), (33), (34), (36), (43) are % 132.24/18.90 | | | inconsistent by sub-proof #168. % 132.24/18.90 | | | % 132.24/18.90 | | Case 2: % 132.24/18.90 | | | % 132.24/18.90 | | | (44) all_57_12 = e0 & op(e0, e3) = e0 % 132.24/18.90 | | | % 132.24/18.90 | | | REF_CLOSE: (10), (20), (44) are inconsistent by sub-proof #237. % 132.24/18.90 | | | % 132.24/18.90 | | End of split % 132.24/18.90 | | % 132.24/18.90 | End of split % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #166 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_57_2 = e0 & op(e2, e3) = e0 % 132.24/18.90 (2) all_57_2 = e1 % 132.24/18.90 (3) ~ (e1 = e0) % 132.24/18.90 % 132.24/18.90 Begin of proof % 132.24/18.90 | % 132.24/18.90 | ALPHA: (1) implies: % 132.24/18.90 | (4) all_57_2 = e0 % 132.24/18.90 | % 132.24/18.90 | COMBINE_EQS: (2), (4) imply: % 132.24/18.90 | (5) e1 = e0 % 132.24/18.90 | % 132.24/18.90 | REDUCE: (3), (5) imply: % 132.24/18.90 | (6) $false % 132.24/18.90 | % 132.24/18.90 | CLOSE: (6) is inconsistent. % 132.24/18.90 | % 132.24/18.90 End of proof % 132.24/18.90 % 132.24/18.90 Sub-proof #167 shows that the following formulas are inconsistent: % 132.24/18.90 ---------------------------------------------------------------- % 132.24/18.90 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.90 (2) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 132.24/18.90 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 132.24/18.90 (3) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.90 (4) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.90 (5) unit = e2 | unit = e1 | unit = e0 % 132.24/18.90 (6) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.24/18.90 (7) op(unit, e0) = e0 % 132.24/18.90 (8) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.90 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.90 (9) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.90 (10) ~ (all_53_9 = e3) % 132.24/18.90 (11) ~ (all_53_6 = all_53_7) % 132.24/18.90 (12) ~ (all_53_6 = all_53_14) % 132.24/18.90 (13) all_55_9 = all_53_6 % 132.24/18.90 (14) op(unit, e2) = e2 % 132.24/18.90 (15) ~ (all_53_12 = e1) % 132.24/18.90 (16) ~ (all_53_3 = e0) % 132.24/18.90 (17) ~ (op(e1, e3) = e3) % 132.24/18.90 (18) ~ (all_53_6 = e3) % 132.24/18.90 (19) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.24/18.90 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.24/18.90 $i(all_42_0)))) % 132.24/18.90 (20) op(e0, e0) = all_8_2 % 132.24/18.90 (21) ~ (e2 = e0) % 132.24/18.90 (22) op(e1, e1) = e3 % 132.24/18.90 (23) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.90 (24) ~ (all_53_7 = e0) % 132.24/18.90 (25) ~ (all_53_13 = all_6_2) % 132.24/18.90 (26) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.24/18.90 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.24/18.90 (27) op(e2, e1) = all_53_9 % 132.24/18.90 (28) all_12_2 = e3 % 132.24/18.90 (29) all_55_5 = all_6_2 % 132.24/18.90 (30) ~ (all_8_2 = e1) % 132.24/18.90 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.90 (32) ~ (e3 = e1) % 132.24/18.90 (33) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.24/18.90 (34) ~ (all_53_7 = all_6_2) % 132.24/18.90 (35) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.24/18.90 (36) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.24/18.90 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.24/18.90 (37) ~ (all_6_2 = e3) % 132.24/18.90 (38) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.24/18.90 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.24/18.90 (39) ~ (all_53_6 = all_18_1) % 132.24/18.90 (40) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.90 (41) ~ (e2 = e1) % 132.24/18.90 (42) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.90 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.90 (43) op(e2, e2) = all_6_2 % 132.24/18.90 (44) op(e3, e3) = all_4_2 % 132.24/18.90 (45) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.90 (46) ~ (all_6_2 = e1) % 132.24/18.90 (47) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 132.24/18.90 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 132.24/18.91 (48) op(e1, unit) = e1 % 132.24/18.91 (49) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.91 (50) op(e3, e0) = all_53_12 % 132.24/18.91 (51) op(e0, unit) = e0 % 132.24/18.91 (52) ~ (all_53_3 = e1) % 132.24/18.91 (53) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.91 (54) op(e1, e3) = all_18_1 % 132.24/18.91 (55) ~ (all_53_2 = e3) % 132.24/18.91 (56) all_42_2 = all_6_2 % 132.24/18.91 (57) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.24/18.91 (58) ~ (unit = e1) % 132.24/18.91 (59) ~ (all_53_1 = all_53_3) % 132.24/18.91 (60) ~ (e3 = e2) % 132.24/18.91 (61) all_55_13 = all_53_7 % 132.24/18.91 (62) ~ (all_53_6 = all_6_2) % 132.24/18.91 (63) op(unit, e3) = e3 % 132.24/18.91 (64) ~ (all_53_14 = e0) % 132.24/18.91 (65) all_57_0 = e1 % 132.24/18.91 (66) ~ (all_4_2 = e0) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | BETA: splitting (19) gives: % 132.24/18.91 | % 132.24/18.91 | Case 1: % 132.24/18.91 | | % 132.24/18.91 | | (67) ~ (all_42_2 = e0) % 132.24/18.91 | | % 132.24/18.91 | | REDUCE: (56), (67) imply: % 132.24/18.91 | | (68) ~ (all_6_2 = e0) % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (1), (4), (5), (14), (23), (24), (29), (34), (37), (40), (45), % 132.24/18.91 | | (46), (51), (55), (61), (63), (68) are inconsistent by sub-proof % 132.24/18.91 | | #182. % 132.24/18.91 | | % 132.24/18.91 | Case 2: % 132.24/18.91 | | % 132.24/18.91 | | (69) all_42_2 = e0 % 132.24/18.91 | | % 132.24/18.91 | | COMBINE_EQS: (56), (69) imply: % 132.24/18.91 | | (70) all_6_2 = e0 % 132.24/18.91 | | % 132.24/18.91 | | SIMP: (70) implies: % 132.24/18.91 | | (71) all_6_2 = e0 % 132.24/18.91 | | % 132.24/18.91 | | REDUCE: (62), (71) imply: % 132.24/18.91 | | (72) ~ (all_53_6 = e0) % 132.24/18.91 | | % 132.24/18.91 | | REDUCE: (25), (71) imply: % 132.24/18.91 | | (73) ~ (all_53_13 = e0) % 132.24/18.91 | | % 132.24/18.91 | | REDUCE: (37), (71) imply: % 132.24/18.91 | | (74) ~ (e3 = e0) % 132.24/18.91 | | % 132.24/18.91 | | SIMP: (74) implies: % 132.24/18.91 | | (75) ~ (e3 = e0) % 132.24/18.91 | | % 132.24/18.91 | | REDUCE: (46), (71) imply: % 132.24/18.91 | | (76) ~ (e1 = e0) % 132.24/18.91 | | % 132.24/18.91 | | SIMP: (76) implies: % 132.24/18.91 | | (77) ~ (e1 = e0) % 132.24/18.91 | | % 132.24/18.91 | | BETA: splitting (47) gives: % 132.24/18.91 | | % 132.24/18.91 | | Case 1: % 132.24/18.91 | | | % 132.24/18.91 | | | (78) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 132.24/18.91 | | | e0) % 132.24/18.91 | | | % 132.24/18.91 | | | BETA: splitting (78) gives: % 132.24/18.91 | | | % 132.24/18.91 | | | Case 1: % 132.24/18.91 | | | | % 132.24/18.91 | | | | (79) all_57_0 = e0 & op(e3, e3) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | REF_CLOSE: (31), (44), (66), (79) are inconsistent by sub-proof #270. % 132.24/18.91 | | | | % 132.24/18.91 | | | Case 2: % 132.24/18.91 | | | | % 132.24/18.91 | | | | (80) all_57_2 = e0 & op(e2, e3) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | ALPHA: (80) implies: % 132.24/18.91 | | | | (81) all_57_2 = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | BETA: splitting (36) gives: % 132.24/18.91 | | | | % 132.24/18.91 | | | | Case 1: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | (82) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, % 132.24/18.91 | | | | | e3) = e3) % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | BETA: splitting (82) gives: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | Case 1: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (83) all_57_0 = e3 & op(e3, e3) = e3 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (32), (65), (83) are inconsistent by sub-proof #312. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | Case 2: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (84) all_57_2 = e3 & op(e2, e3) = e3 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (75), (81), (84) are inconsistent by sub-proof #192. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | End of split % 132.24/18.91 | | | | | % 132.24/18.91 | | | | Case 2: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | (85) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, % 132.24/18.91 | | | | | e3) = e3) % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | BETA: splitting (85) gives: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | Case 1: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (86) all_57_6 = e3 & op(e1, e3) = e3 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (17), (86) are inconsistent by sub-proof #181. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | Case 2: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (87) all_57_12 = e3 & op(e0, e3) = e3 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | ALPHA: (87) implies: % 132.24/18.91 | | | | | | (88) op(e0, e3) = e3 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | BETA: splitting (6) gives: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | Case 1: % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | (89) ~ (op(e0, e3) = e3) % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | PRED_UNIFY: (88), (89) imply: % 132.24/18.91 | | | | | | | (90) $false % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | CLOSE: (90) is inconsistent. % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | Case 2: % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | (91) all_53_3 = e3 % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | REDUCE: (59), (91) imply: % 132.24/18.91 | | | | | | | (92) ~ (all_53_1 = e3) % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | BETA: splitting (38) gives: % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | | (93) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & % 132.24/18.91 | | | | | | | | op(e2, e2) = e3) % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | | REF_CLOSE: (31), (35), (37), (43), (92), (93) are inconsistent % 132.24/18.91 | | | | | | | | by sub-proof #351. % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | | (94) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & % 132.24/18.91 | | | | | | | | op(e2, e0) = e3) % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | | BETA: splitting (94) gives: % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | (95) all_57_5 = e3 & op(e2, e1) = e3 % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | REF_CLOSE: (10), (27), (31), (95) are inconsistent by % 132.24/18.91 | | | | | | | | | sub-proof #180. % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | (96) all_57_10 = e3 & op(e2, e0) = e3 % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | ALPHA: (96) implies: % 132.24/18.91 | | | | | | | | | (97) all_57_10 = e3 % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | BETA: splitting (2) gives: % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | (98) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 % 132.24/18.91 | | | | | | | | | | & op(e2, e0) = e1) % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | BETA: splitting (98) gives: % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | (99) all_57_9 = e1 & op(e3, e0) = e1 % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | REF_CLOSE: (15), (31), (50), (99) are inconsistent by % 132.24/18.91 | | | | | | | | | | | sub-proof #273. % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | (100) all_57_10 = e1 & op(e2, e0) = e1 % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | REF_CLOSE: (32), (97), (100) are inconsistent by sub-proof % 132.24/18.91 | | | | | | | | | | | #179. % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | (101) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.24/18.91 | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | BETA: splitting (101) gives: % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | (102) all_57_11 = e1 & op(e1, e0) = e1 % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | ALPHA: (102) implies: % 132.24/18.91 | | | | | | | | | | | (103) op(e1, e0) = e1 % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | BETA: splitting (3) gives: % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | (104) ~ (op(e1, e0) = e1) % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | PRED_UNIFY: (103), (104) imply: % 132.24/18.91 | | | | | | | | | | | | (105) $false % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | CLOSE: (105) is inconsistent. % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | (106) all_53_14 = e1 % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | REDUCE: (12), (106) imply: % 132.24/18.91 | | | | | | | | | | | | (107) ~ (all_53_6 = e1) % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | BETA: splitting (53) gives: % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | (108) all_55_9 = e3 % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | COMBINE_EQS: (13), (108) imply: % 132.24/18.91 | | | | | | | | | | | | | (109) all_53_6 = e3 % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | REDUCE: (18), (109) imply: % 132.24/18.91 | | | | | | | | | | | | | (110) $false % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | CLOSE: (110) is inconsistent. % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | (111) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | BETA: splitting (111) gives: % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | Case 1: % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | (112) all_55_9 = e2 % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | COMBINE_EQS: (13), (112) imply: % 132.24/18.91 | | | | | | | | | | | | | | (113) all_53_6 = e2 % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | REDUCE: (11), (113) imply: % 132.24/18.91 | | | | | | | | | | | | | | (114) ~ (all_53_7 = e2) % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | SIMP: (114) implies: % 132.24/18.91 | | | | | | | | | | | | | | (115) ~ (all_53_7 = e2) % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (14), (23), (24), (45), (51), (55), % 132.24/18.91 | | | | | | | | | | | | | | (61), (63), (115) are inconsistent by sub-proof % 132.24/18.91 | | | | | | | | | | | | | | #183. % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | (116) all_55_9 = e1 | all_55_9 = e0 % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | | REF_CLOSE: (13), (72), (107), (116) are inconsistent by % 132.24/18.91 | | | | | | | | | | | | | | sub-proof #178. % 132.24/18.91 | | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | Case 2: % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | (117) all_57_15 = e1 & op(e0, e0) = e1 % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | | REF_CLOSE: (20), (30), (31), (117) are inconsistent by % 132.24/18.91 | | | | | | | | | | | sub-proof #294. % 132.24/18.91 | | | | | | | | | | | % 132.24/18.91 | | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | | % 132.24/18.91 | | | | | | | | | End of split % 132.24/18.91 | | | | | | | | | % 132.24/18.91 | | | | | | | | End of split % 132.24/18.91 | | | | | | | | % 132.24/18.91 | | | | | | | End of split % 132.24/18.91 | | | | | | | % 132.24/18.91 | | | | | | End of split % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | End of split % 132.24/18.91 | | | | | % 132.24/18.91 | | | | End of split % 132.24/18.91 | | | | % 132.24/18.91 | | | End of split % 132.24/18.91 | | | % 132.24/18.91 | | Case 2: % 132.24/18.91 | | | % 132.24/18.91 | | | (118) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) % 132.24/18.91 | | | = e0) % 132.24/18.91 | | | % 132.24/18.91 | | | BETA: splitting (118) gives: % 132.24/18.91 | | | % 132.24/18.91 | | | Case 1: % 132.24/18.91 | | | | % 132.24/18.91 | | | | (119) all_57_6 = e0 & op(e1, e3) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | REF_CLOSE: (3), (5), (7), (8), (9), (11), (12), (13), (14), (18), (21), % 132.24/18.91 | | | | (22), (26), (28), (31), (32), (39), (41), (42), (45), (48), % 132.24/18.91 | | | | (49), (53), (54), (57), (58), (60), (64), (73), (75), (77), % 132.24/18.91 | | | | (119) are inconsistent by sub-proof #168. % 132.24/18.91 | | | | % 132.24/18.91 | | | Case 2: % 132.24/18.91 | | | | % 132.24/18.91 | | | | (120) all_57_12 = e0 & op(e0, e3) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | REF_CLOSE: (16), (33), (120) are inconsistent by sub-proof #237. % 132.24/18.91 | | | | % 132.24/18.91 | | | End of split % 132.24/18.91 | | | % 132.24/18.91 | | End of split % 132.24/18.91 | | % 132.24/18.91 | End of split % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #168 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.91 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.91 (3) op(unit, e0) = e0 % 132.24/18.91 (4) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.24/18.91 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.91 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.24/18.91 (6) ~ (all_53_6 = all_53_7) % 132.24/18.91 (7) ~ (all_53_6 = all_53_14) % 132.24/18.91 (8) all_55_9 = all_53_6 % 132.24/18.91 (9) op(unit, e2) = e2 % 132.24/18.91 (10) ~ (all_53_13 = e0) % 132.24/18.91 (11) ~ (all_53_6 = e3) % 132.24/18.91 (12) ~ (e3 = e0) % 132.24/18.91 (13) ~ (e2 = e0) % 132.24/18.91 (14) op(e1, e1) = e3 % 132.24/18.91 (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.24/18.91 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.24/18.91 (16) all_12_2 = e3 % 132.24/18.91 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.91 (18) ~ (e3 = e1) % 132.24/18.91 (19) ~ (all_53_6 = all_18_1) % 132.24/18.91 (20) ~ (e2 = e1) % 132.24/18.91 (21) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.91 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.91 (22) all_57_6 = e0 & op(e1, e3) = e0 % 132.24/18.91 (23) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.91 (24) ~ (e1 = e0) % 132.24/18.91 (25) op(e1, unit) = e1 % 132.24/18.91 (26) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.91 (27) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.91 (28) op(e1, e3) = all_18_1 % 132.24/18.91 (29) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.24/18.91 (30) ~ (unit = e1) % 132.24/18.91 (31) ~ (e3 = e2) % 132.24/18.91 (32) ~ (all_53_14 = e0) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | ALPHA: (22) implies: % 132.24/18.91 | (33) all_57_6 = e0 % 132.24/18.91 | % 132.24/18.91 | BETA: splitting (5) gives: % 132.24/18.91 | % 132.24/18.91 | Case 1: % 132.24/18.91 | | % 132.24/18.91 | | (34) ~ (op(e2, e0) = e0) % 132.24/18.91 | | % 132.24/18.91 | | BETA: splitting (4) gives: % 132.24/18.91 | | % 132.24/18.91 | | Case 1: % 132.24/18.91 | | | % 132.24/18.91 | | | (35) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = % 132.24/18.91 | | | e0) % 132.24/18.91 | | | % 132.24/18.91 | | | BETA: splitting (35) gives: % 132.24/18.91 | | | % 132.24/18.91 | | | Case 1: % 132.24/18.91 | | | | % 132.24/18.91 | | | | % 132.24/18.91 | | | | ALPHA: (22) implies: % 132.24/18.91 | | | | (36) op(e1, e3) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | GROUND_INST: instantiating (17) with all_18_1, e0, e3, e1, simplifying % 132.24/18.91 | | | | with (28), (36) gives: % 132.24/18.91 | | | | (37) all_18_1 = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | PRED_UNIFY: (3), (34) imply: % 132.24/18.91 | | | | (38) ~ (unit = e2) % 132.24/18.91 | | | | % 132.24/18.91 | | | | REDUCE: (19), (37) imply: % 132.24/18.91 | | | | (39) ~ (all_53_6 = e0) % 132.24/18.91 | | | | % 132.24/18.91 | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (11), (23), (25), (27), (30), % 132.24/18.91 | | | | (38), (39) are inconsistent by sub-proof #176. % 132.24/18.91 | | | | % 132.24/18.91 | | | Case 2: % 132.24/18.91 | | | | % 132.24/18.91 | | | | (40) all_57_7 = e0 & op(e1, e2) = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | ALPHA: (40) implies: % 132.24/18.91 | | | | (41) all_57_7 = e0 % 132.24/18.91 | | | | % 132.24/18.91 | | | | BETA: splitting (15) gives: % 132.24/18.91 | | | | % 132.24/18.91 | | | | Case 1: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | (42) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, % 132.24/18.91 | | | | | e2) = e1) % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | BETA: splitting (42) gives: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | Case 1: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (43) all_57_6 = e1 & op(e1, e3) = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (24), (33), (43) are inconsistent by sub-proof #343. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | Case 2: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (44) all_57_7 = e1 & op(e1, e2) = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | ALPHA: (44) implies: % 132.24/18.91 | | | | | | (45) all_57_7 = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (24), (41), (45) are inconsistent by sub-proof #175. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | End of split % 132.24/18.91 | | | | | % 132.24/18.91 | | | | Case 2: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | (46) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, % 132.24/18.91 | | | | | e0) = e1) % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | BETA: splitting (46) gives: % 132.24/18.91 | | | | | % 132.24/18.91 | | | | | Case 1: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (47) all_57_8 = e1 & op(e1, e1) = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | ALPHA: (47) implies: % 132.24/18.91 | | | | | | (48) op(e1, e1) = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (16), (18), (26), (48) are inconsistent by sub-proof % 132.24/18.91 | | | | | | #174. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | Case 2: % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | (49) all_57_11 = e1 & op(e1, e0) = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | ALPHA: (49) implies: % 132.24/18.91 | | | | | | (50) all_57_11 = e1 % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | | REF_CLOSE: (13), (14), (17), (20), (21), (31), (33), (41), (50) are % 132.24/18.91 | | | | | | inconsistent by sub-proof #170. % 132.24/18.91 | | | | | | % 132.24/18.91 | | | | | End of split % 132.24/18.91 | | | | | % 132.24/18.91 | | | | End of split % 132.24/18.91 | | | | % 132.24/18.91 | | | End of split % 132.24/18.91 | | | % 132.24/18.91 | | Case 2: % 132.24/18.91 | | | % 132.24/18.91 | | | (51) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = % 132.24/18.91 | | | e0) % 132.24/18.91 | | | % 132.24/18.91 | | | REF_CLOSE: (12), (14), (17), (29), (32), (51) are inconsistent by % 132.24/18.91 | | | sub-proof #169. % 132.24/18.91 | | | % 132.24/18.91 | | End of split % 132.24/18.91 | | % 132.24/18.91 | Case 2: % 132.24/18.91 | | % 132.24/18.91 | | (52) op(e2, e0) = e0 % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (5), (10), (52) are inconsistent by sub-proof #356. % 132.24/18.91 | | % 132.24/18.91 | End of split % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #169 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.24/18.91 (2) ~ (e3 = e0) % 132.24/18.91 (3) op(e1, e1) = e3 % 132.24/18.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.91 (5) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.24/18.91 (6) ~ (all_53_14 = e0) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | BETA: splitting (1) gives: % 132.24/18.91 | % 132.24/18.91 | Case 1: % 132.24/18.91 | | % 132.24/18.91 | | (7) all_57_8 = e0 & op(e1, e1) = e0 % 132.24/18.91 | | % 132.24/18.91 | | ALPHA: (7) implies: % 132.24/18.91 | | (8) op(e1, e1) = e0 % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #320. % 132.24/18.91 | | % 132.24/18.91 | Case 2: % 132.24/18.91 | | % 132.24/18.91 | | (9) all_57_11 = e0 & op(e1, e0) = e0 % 132.24/18.91 | | % 132.24/18.91 | | ALPHA: (9) implies: % 132.24/18.91 | | (10) op(e1, e0) = e0 % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #355. % 132.24/18.91 | | % 132.24/18.91 | End of split % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #170 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) all_57_7 = e0 % 132.24/18.91 (2) ~ (e2 = e0) % 132.24/18.91 (3) op(e1, e1) = e3 % 132.24/18.91 (4) all_57_11 = e1 % 132.24/18.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.91 (6) all_57_6 = e0 % 132.24/18.91 (7) ~ (e2 = e1) % 132.24/18.91 (8) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.24/18.91 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.91 (9) ~ (e3 = e2) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | BETA: splitting (8) gives: % 132.24/18.91 | % 132.24/18.91 | Case 1: % 132.24/18.91 | | % 132.24/18.91 | | (10) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 132.24/18.91 | | e2) % 132.24/18.91 | | % 132.24/18.91 | | BETA: splitting (10) gives: % 132.24/18.91 | | % 132.24/18.91 | | Case 1: % 132.24/18.91 | | | % 132.24/18.91 | | | (11) all_57_6 = e2 & op(e1, e3) = e2 % 132.24/18.91 | | | % 132.24/18.91 | | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #263. % 132.24/18.91 | | | % 132.24/18.91 | | Case 2: % 132.24/18.91 | | | % 132.24/18.91 | | | (12) all_57_7 = e2 & op(e1, e2) = e2 % 132.24/18.91 | | | % 132.24/18.91 | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #318. % 132.24/18.91 | | | % 132.24/18.91 | | End of split % 132.24/18.91 | | % 132.24/18.91 | Case 2: % 132.24/18.91 | | % 132.24/18.91 | | (13) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 132.24/18.91 | | e2) % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (3), (4), (5), (7), (9), (13) are inconsistent by sub-proof #171. % 132.24/18.91 | | % 132.24/18.91 | End of split % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #171 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) op(e1, e1) = e3 % 132.24/18.91 (2) all_57_11 = e1 % 132.24/18.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.91 (4) ~ (e2 = e1) % 132.24/18.91 (5) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.24/18.91 (6) ~ (e3 = e2) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | BETA: splitting (5) gives: % 132.24/18.91 | % 132.24/18.91 | Case 1: % 132.24/18.91 | | % 132.24/18.91 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 132.24/18.91 | | % 132.24/18.91 | | ALPHA: (7) implies: % 132.24/18.91 | | (8) op(e1, e1) = e2 % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #173. % 132.24/18.91 | | % 132.24/18.91 | Case 2: % 132.24/18.91 | | % 132.24/18.91 | | (9) all_57_11 = e2 & op(e1, e0) = e2 % 132.24/18.91 | | % 132.24/18.91 | | ALPHA: (9) implies: % 132.24/18.91 | | (10) all_57_11 = e2 % 132.24/18.91 | | % 132.24/18.91 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #172. % 132.24/18.91 | | % 132.24/18.91 | End of split % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #172 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) all_57_11 = e2 % 132.24/18.91 (2) all_57_11 = e1 % 132.24/18.91 (3) ~ (e2 = e1) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | COMBINE_EQS: (1), (2) imply: % 132.24/18.91 | (4) e2 = e1 % 132.24/18.91 | % 132.24/18.91 | SIMP: (4) implies: % 132.24/18.91 | (5) e2 = e1 % 132.24/18.91 | % 132.24/18.91 | REDUCE: (3), (5) imply: % 132.24/18.91 | (6) $false % 132.24/18.91 | % 132.24/18.91 | CLOSE: (6) is inconsistent. % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #173 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.91 (2) op(e1, e1) = e3 % 132.24/18.91 (3) op(e1, e1) = e2 % 132.24/18.91 (4) ~ (e3 = e2) % 132.24/18.91 % 132.24/18.91 Begin of proof % 132.24/18.91 | % 132.24/18.91 | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3) % 132.24/18.91 | gives: % 132.24/18.91 | (5) e3 = e2 % 132.24/18.91 | % 132.24/18.91 | REDUCE: (4), (5) imply: % 132.24/18.91 | (6) $false % 132.24/18.91 | % 132.24/18.91 | CLOSE: (6) is inconsistent. % 132.24/18.91 | % 132.24/18.91 End of proof % 132.24/18.91 % 132.24/18.91 Sub-proof #174 shows that the following formulas are inconsistent: % 132.24/18.91 ---------------------------------------------------------------- % 132.24/18.91 (1) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.92 (2) op(e1, e1) = e1 % 132.24/18.92 (3) all_12_2 = e3 % 132.24/18.92 (4) ~ (e3 = e1) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (1) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (5) ~ (op(e1, e1) = e1) % 132.24/18.92 | | % 132.24/18.92 | | PRED_UNIFY: (2), (5) imply: % 132.24/18.92 | | (6) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (6) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (7) all_12_2 = e1 % 132.24/18.92 | | % 132.24/18.92 | | COMBINE_EQS: (3), (7) imply: % 132.24/18.92 | | (8) e3 = e1 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (4), (8) imply: % 132.24/18.92 | | (9) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (9) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #175 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_57_7 = e1 % 132.24/18.92 (2) all_57_7 = e0 % 132.24/18.92 (3) ~ (e1 = e0) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | COMBINE_EQS: (1), (2) imply: % 132.24/18.92 | (4) e1 = e0 % 132.24/18.92 | % 132.24/18.92 | SIMP: (4) implies: % 132.24/18.92 | (5) e1 = e0 % 132.24/18.92 | % 132.24/18.92 | REDUCE: (3), (5) imply: % 132.24/18.92 | (6) $false % 132.24/18.92 | % 132.24/18.92 | CLOSE: (6) is inconsistent. % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #176 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.24/18.92 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.92 (3) ~ (all_53_6 = all_53_7) % 132.24/18.92 (4) ~ (all_53_6 = all_53_14) % 132.24/18.92 (5) all_55_9 = all_53_6 % 132.24/18.92 (6) ~ (unit = e2) % 132.24/18.92 (7) op(unit, e2) = e2 % 132.24/18.92 (8) ~ (all_53_6 = e3) % 132.24/18.92 (9) ~ (all_53_6 = e0) % 132.24/18.92 (10) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.92 (11) op(e1, unit) = e1 % 132.24/18.92 (12) all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.92 (13) ~ (unit = e1) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (2) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (14) unit = e2 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (6), (14) imply: % 132.24/18.92 | | (15) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (15) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (16) unit = e1 | unit = e0 % 132.24/18.92 | | % 132.24/18.92 | | BETA: splitting (16) gives: % 132.24/18.92 | | % 132.24/18.92 | | Case 1: % 132.24/18.92 | | | % 132.24/18.92 | | | (17) unit = e1 % 132.24/18.92 | | | % 132.24/18.92 | | | REDUCE: (13), (17) imply: % 132.24/18.92 | | | (18) $false % 132.24/18.92 | | | % 132.24/18.92 | | | CLOSE: (18) is inconsistent. % 132.24/18.92 | | | % 132.24/18.92 | | Case 2: % 132.24/18.92 | | | % 132.24/18.92 | | | (19) unit = e0 % 132.24/18.92 | | | % 132.24/18.92 | | | REDUCE: (7), (19) imply: % 132.24/18.92 | | | (20) op(e0, e2) = e2 % 132.24/18.92 | | | % 132.24/18.92 | | | REDUCE: (11), (19) imply: % 132.24/18.92 | | | (21) op(e1, e0) = e1 % 132.24/18.92 | | | % 132.24/18.92 | | | BETA: splitting (1) gives: % 132.24/18.92 | | | % 132.24/18.92 | | | Case 1: % 132.24/18.92 | | | | % 132.24/18.92 | | | | (22) ~ (op(e1, e0) = e1) % 132.24/18.92 | | | | % 132.24/18.92 | | | | PRED_UNIFY: (21), (22) imply: % 132.24/18.92 | | | | (23) $false % 132.24/18.92 | | | | % 132.24/18.92 | | | | CLOSE: (23) is inconsistent. % 132.24/18.92 | | | | % 132.24/18.92 | | | Case 2: % 132.24/18.92 | | | | % 132.24/18.92 | | | | (24) all_53_14 = e1 % 132.24/18.92 | | | | % 132.24/18.92 | | | | REDUCE: (4), (24) imply: % 132.24/18.92 | | | | (25) ~ (all_53_6 = e1) % 132.24/18.92 | | | | % 132.24/18.92 | | | | BETA: splitting (10) gives: % 132.24/18.92 | | | | % 132.24/18.92 | | | | Case 1: % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | (26) ~ (op(e0, e2) = e2) % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | PRED_UNIFY: (20), (26) imply: % 132.24/18.92 | | | | | (27) $false % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | CLOSE: (27) is inconsistent. % 132.24/18.92 | | | | | % 132.24/18.92 | | | | Case 2: % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | (28) all_53_7 = e2 % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | REDUCE: (3), (28) imply: % 132.24/18.92 | | | | | (29) ~ (all_53_6 = e2) % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | BETA: splitting (12) gives: % 132.24/18.92 | | | | | % 132.24/18.92 | | | | | Case 1: % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | (30) all_55_9 = e3 % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | COMBINE_EQS: (5), (30) imply: % 132.24/18.92 | | | | | | (31) all_53_6 = e3 % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | REDUCE: (8), (31) imply: % 132.24/18.92 | | | | | | (32) $false % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | CLOSE: (32) is inconsistent. % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | Case 2: % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | (33) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | | REF_CLOSE: (5), (9), (25), (29), (33) are inconsistent by sub-proof % 132.24/18.92 | | | | | | #177. % 132.24/18.92 | | | | | | % 132.24/18.92 | | | | | End of split % 132.24/18.92 | | | | | % 132.24/18.92 | | | | End of split % 132.24/18.92 | | | | % 132.24/18.92 | | | End of split % 132.24/18.92 | | | % 132.24/18.92 | | End of split % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #177 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_55_9 = all_53_6 % 132.24/18.92 (2) ~ (all_53_6 = e0) % 132.24/18.92 (3) ~ (all_53_6 = e1) % 132.24/18.92 (4) ~ (all_53_6 = e2) % 132.24/18.92 (5) all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0 % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (5) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (6) all_55_9 = e2 % 132.24/18.92 | | % 132.24/18.92 | | COMBINE_EQS: (1), (6) imply: % 132.24/18.92 | | (7) all_53_6 = e2 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (4), (7) imply: % 132.24/18.92 | | (8) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (8) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (9) all_55_9 = e1 | all_55_9 = e0 % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #178. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #178 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_55_9 = e1 | all_55_9 = e0 % 132.24/18.92 (2) all_55_9 = all_53_6 % 132.24/18.92 (3) ~ (all_53_6 = e1) % 132.24/18.92 (4) ~ (all_53_6 = e0) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (1) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (5) all_55_9 = e1 % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #342. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (6) all_55_9 = e0 % 132.24/18.92 | | % 132.24/18.92 | | COMBINE_EQS: (2), (6) imply: % 132.24/18.92 | | (7) all_53_6 = e0 % 132.24/18.92 | | % 132.24/18.92 | | SIMP: (7) implies: % 132.24/18.92 | | (8) all_53_6 = e0 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (4), (8) imply: % 132.24/18.92 | | (9) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (9) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #179 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_57_10 = e1 & op(e2, e0) = e1 % 132.24/18.92 (2) all_57_10 = e3 % 132.24/18.92 (3) ~ (e3 = e1) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | ALPHA: (1) implies: % 132.24/18.92 | (4) all_57_10 = e1 % 132.24/18.92 | % 132.24/18.92 | COMBINE_EQS: (2), (4) imply: % 132.24/18.92 | (5) e3 = e1 % 132.24/18.92 | % 132.24/18.92 | REDUCE: (3), (5) imply: % 132.24/18.92 | (6) $false % 132.24/18.92 | % 132.24/18.92 | CLOSE: (6) is inconsistent. % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #180 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_57_5 = e3 & op(e2, e1) = e3 % 132.24/18.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.24/18.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.24/18.92 (3) op(e2, e1) = all_53_9 % 132.24/18.92 (4) ~ (all_53_9 = e3) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | ALPHA: (1) implies: % 132.24/18.92 | (5) op(e2, e1) = e3 % 132.24/18.92 | % 132.24/18.92 | GROUND_INST: instantiating (2) with all_53_9, e3, e1, e2, simplifying with % 132.24/18.92 | (3), (5) gives: % 132.24/18.92 | (6) all_53_9 = e3 % 132.24/18.92 | % 132.24/18.92 | REDUCE: (4), (6) imply: % 132.24/18.92 | (7) $false % 132.24/18.92 | % 132.24/18.92 | CLOSE: (7) is inconsistent. % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #181 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_57_6 = e3 & op(e1, e3) = e3 % 132.24/18.92 (2) ~ (op(e1, e3) = e3) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | ALPHA: (1) implies: % 132.24/18.92 | (3) op(e1, e3) = e3 % 132.24/18.92 | % 132.24/18.92 | PRED_UNIFY: (2), (3) imply: % 132.24/18.92 | (4) $false % 132.24/18.92 | % 132.24/18.92 | CLOSE: (4) is inconsistent. % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #182 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.92 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.92 (3) unit = e2 | unit = e1 | unit = e0 % 132.24/18.92 (4) op(unit, e2) = e2 % 132.24/18.92 (5) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.92 (6) ~ (all_53_7 = e0) % 132.24/18.92 (7) all_55_5 = all_6_2 % 132.24/18.92 (8) ~ (all_6_2 = e0) % 132.24/18.92 (9) ~ (all_53_7 = all_6_2) % 132.24/18.92 (10) ~ (all_6_2 = e3) % 132.24/18.92 (11) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.92 (12) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.92 (13) ~ (all_6_2 = e1) % 132.24/18.92 (14) op(e0, unit) = e0 % 132.24/18.92 (15) ~ (all_53_2 = e3) % 132.24/18.92 (16) all_55_13 = all_53_7 % 132.24/18.92 (17) op(unit, e3) = e3 % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (11) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (18) all_55_5 = e3 % 132.24/18.92 | | % 132.24/18.92 | | COMBINE_EQS: (7), (18) imply: % 132.24/18.92 | | (19) all_6_2 = e3 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (10), (19) imply: % 132.24/18.92 | | (20) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (20) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (21) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.24/18.92 | | % 132.24/18.92 | | BETA: splitting (21) gives: % 132.24/18.92 | | % 132.24/18.92 | | Case 1: % 132.24/18.92 | | | % 132.24/18.92 | | | (22) all_55_5 = e2 % 132.24/18.92 | | | % 132.24/18.92 | | | COMBINE_EQS: (7), (22) imply: % 132.24/18.92 | | | (23) all_6_2 = e2 % 132.24/18.92 | | | % 132.24/18.92 | | | REDUCE: (9), (23) imply: % 132.24/18.92 | | | (24) ~ (all_53_7 = e2) % 132.24/18.92 | | | % 132.24/18.92 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (12), (14), (15), (16), (17), % 132.24/18.92 | | | (24) are inconsistent by sub-proof #183. % 132.24/18.92 | | | % 132.24/18.92 | | Case 2: % 132.24/18.92 | | | % 132.24/18.92 | | | (25) all_55_5 = e1 | all_55_5 = e0 % 132.24/18.92 | | | % 132.24/18.92 | | | REF_CLOSE: (7), (8), (13), (25) are inconsistent by sub-proof #251. % 132.24/18.92 | | | % 132.24/18.92 | | End of split % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #183 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_53_7 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.92 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.92 (3) unit = e2 | unit = e1 | unit = e0 % 132.24/18.92 (4) op(unit, e2) = e2 % 132.24/18.92 (5) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.92 (6) ~ (all_53_7 = e0) % 132.24/18.92 (7) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.24/18.92 (8) op(e0, unit) = e0 % 132.24/18.92 (9) ~ (all_53_7 = e2) % 132.24/18.92 (10) ~ (all_53_2 = e3) % 132.24/18.92 (11) all_55_13 = all_53_7 % 132.24/18.92 (12) op(unit, e3) = e3 % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (1) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (13) ~ (op(e0, e2) = e0) % 132.24/18.92 | | % 132.24/18.92 | | PRED_UNIFY: (8), (13) imply: % 132.24/18.92 | | (14) ~ (unit = e2) % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (12), (14) are inconsistent by % 132.24/18.92 | | sub-proof #222. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (15) op(e0, e2) = e0 % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (5), (6), (11), (15) are inconsistent by sub-proof #292. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #184 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) ~ (all_53_1 = e3) % 132.24/18.92 (2) unit = e2 | unit = e1 | unit = e0 % 132.24/18.92 (3) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.24/18.92 (4) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.92 (5) ~ (all_53_12 = e3) % 132.24/18.92 (6) ~ (unit = e1) % 132.24/18.92 (7) op(unit, e3) = e3 % 132.24/18.92 (8) op(e3, unit) = e3 % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (3) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (9) ~ (op(e2, e3) = e3) % 132.24/18.92 | | % 132.24/18.92 | | PRED_UNIFY: (7), (9) imply: % 132.24/18.92 | | (10) ~ (unit = e2) % 132.24/18.92 | | % 132.24/18.92 | | BETA: splitting (2) gives: % 132.24/18.92 | | % 132.24/18.92 | | Case 1: % 132.24/18.92 | | | % 132.24/18.92 | | | (11) unit = e2 % 132.24/18.92 | | | % 132.24/18.92 | | | REDUCE: (10), (11) imply: % 132.24/18.92 | | | (12) $false % 132.24/18.92 | | | % 132.24/18.92 | | | CLOSE: (12) is inconsistent. % 132.24/18.92 | | | % 132.24/18.92 | | Case 2: % 132.24/18.92 | | | % 132.24/18.92 | | | (13) unit = e1 | unit = e0 % 132.24/18.92 | | | % 132.24/18.92 | | | REF_CLOSE: (4), (5), (6), (8), (13) are inconsistent by sub-proof #185. % 132.24/18.92 | | | % 132.24/18.92 | | End of split % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (14) op(e2, e3) = e3 % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #353. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #185 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.92 (2) ~ (all_53_12 = e3) % 132.24/18.92 (3) ~ (unit = e1) % 132.24/18.92 (4) op(e3, unit) = e3 % 132.24/18.92 (5) unit = e1 | unit = e0 % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (5) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (6) unit = e1 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (3), (6) imply: % 132.24/18.92 | | (7) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (7) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (8) unit = e0 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (4), (8) imply: % 132.24/18.92 | | (9) op(e3, e0) = e3 % 132.24/18.92 | | % 132.24/18.92 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #186. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #186 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.24/18.92 (2) op(e3, e0) = e3 % 132.24/18.92 (3) ~ (all_53_12 = e3) % 132.24/18.92 % 132.24/18.92 Begin of proof % 132.24/18.92 | % 132.24/18.92 | BETA: splitting (1) gives: % 132.24/18.92 | % 132.24/18.92 | Case 1: % 132.24/18.92 | | % 132.24/18.92 | | (4) ~ (op(e3, e0) = e3) % 132.24/18.92 | | % 132.24/18.92 | | PRED_UNIFY: (2), (4) imply: % 132.24/18.92 | | (5) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (5) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | Case 2: % 132.24/18.92 | | % 132.24/18.92 | | (6) all_53_12 = e3 % 132.24/18.92 | | % 132.24/18.92 | | REDUCE: (3), (6) imply: % 132.24/18.92 | | (7) $false % 132.24/18.92 | | % 132.24/18.92 | | CLOSE: (7) is inconsistent. % 132.24/18.92 | | % 132.24/18.92 | End of split % 132.24/18.92 | % 132.24/18.92 End of proof % 132.24/18.92 % 132.24/18.92 Sub-proof #187 shows that the following formulas are inconsistent: % 132.24/18.92 ---------------------------------------------------------------- % 132.24/18.92 (1) all_40_2 = all_6_2 % 132.24/18.92 (2) op(e2, e1) = all_26_1 % 132.24/18.92 (3) ~ (all_53_2 = all_53_3) % 132.24/18.92 (4) ~ (all_53_12 = all_22_1) % 132.24/18.92 (5) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.24/18.92 (6) unit = e2 | unit = e1 | unit = e0 % 132.24/18.92 (7) ~ (all_53_3 = all_53_7) % 132.24/18.92 (8) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.24/18.92 (9) ~ (all_53_3 = all_8_2) % 132.24/18.92 (10) ~ (all_53_7 = all_8_2) % 132.24/18.92 (11) ~ (all_53_11 = all_8_2) % 132.24/18.92 (12) ~ (all_53_6 = all_53_7) % 132.24/18.92 (13) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.24/18.92 (14) ~ (all_53_8 = all_53_12) % 132.24/18.92 (15) ~ (all_53_9 = e0) % 132.24/18.92 (16) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.24/18.92 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.24/18.92 (17) op(e2, unit) = e2 % 132.24/18.92 (18) all_55_9 = all_53_6 % 132.24/18.92 (19) ~ (all_53_1 = all_53_13) % 132.24/18.92 (20) op(unit, e2) = e2 % 132.24/18.92 (21) ~ (all_53_2 = all_22_1) % 132.24/18.92 (22) all_55_1 = all_53_4 % 132.24/18.92 (23) all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0 % 132.24/18.92 (24) all_55_6 = all_53_9 % 132.24/18.92 (25) ~ (all_53_9 = all_53_13) % 132.24/18.92 (26) all_22_2 = e0 % 132.24/18.92 (27) op(e0, e2) = all_53_7 % 132.24/18.92 (28) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.24/18.92 (29) all_36_2 = all_8_2 % 132.24/18.92 (30) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 132.24/18.92 (31) op(e1, e1) = e0 % 132.24/18.92 (32) ~ (all_53_8 = e0) % 132.24/18.92 (33) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.24/18.92 (34) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 132.24/18.92 (35) ~ (all_53_12 = all_53_13) % 132.24/18.92 (36) ~ (all_53_13 = all_6_2) % 132.24/18.92 (37) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.24/18.92 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.24/18.92 (38) op(e2, e1) = all_53_9 % 132.54/18.92 (39) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 132.54/18.92 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 132.54/18.92 (40) ~ (all_8_2 = e1) % 132.54/18.92 (41) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.54/18.92 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.92 (43) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 132.54/18.92 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 132.54/18.92 (44) all_55_2 = all_53_8 % 132.54/18.92 (45) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.54/18.92 (46) all_50_2 = all_6_2 % 132.54/18.92 (47) ~ (all_53_7 = all_6_2) % 132.54/18.92 (48) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.54/18.92 (49) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 132.54/18.92 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 132.54/18.92 (50) ~ (all_40_2 = e1) | (op(e2, e1) = all_40_1 & $i(all_40_1) & ( ~ % 132.54/18.92 (all_40_1 = e0) | ( ~ (all_40_0 = e3) & op(e2, e0) = all_40_0 & % 132.54/18.92 $i(all_40_0)))) % 132.54/18.92 (51) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.54/18.92 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.54/18.92 (52) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 132.54/18.92 (53) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.54/18.92 (54) ~ (all_6_2 = e3) % 132.54/18.92 (55) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.54/18.92 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.54/18.92 (56) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.54/18.92 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.54/18.92 (57) all_38_1 = e1 | ~ (op(e1, e0) = e1) % 132.54/18.92 (58) all_38_1 = all_22_1 % 132.54/18.92 (59) ~ (all_53_3 = all_4_2) % 132.54/18.92 (60) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 132.54/18.92 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 132.54/18.92 (61) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.54/18.92 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.54/18.92 (62) op(e2, e2) = all_6_2 % 132.54/18.92 (63) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.54/18.92 (64) all_6_2 = e1 % 132.54/18.92 (65) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 132.54/18.92 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 132.54/18.92 (66) op(e1, unit) = e1 % 132.54/18.92 (67) ~ (all_53_8 = all_53_11) % 132.54/18.92 (68) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.54/18.92 (69) op(e0, unit) = e0 % 132.54/18.92 (70) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.54/18.92 (71) all_53_12 = e3 | ~ (op(e3, e0) = e3) % 132.54/18.92 (72) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 132.54/18.92 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 132.54/18.92 (73) ~ (all_53_9 = all_6_2) % 132.54/18.93 (74) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 132.54/18.93 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 132.54/18.93 (75) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 132.54/18.93 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 132.54/18.93 (76) ~ (all_53_13 = all_8_2) % 132.54/18.93 (77) ~ (unit = e1) % 132.54/18.93 (78) all_36_2 = e0 | ~ (op(e0, e0) = e0) % 132.54/18.93 (79) all_55_4 = all_53_1 % 132.54/18.93 (80) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 132.54/18.93 (81) ~ (all_53_1 = all_53_3) % 132.54/18.93 (82) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.93 (83) all_14_2 = all_4_2 % 132.54/18.93 (84) all_55_13 = all_53_7 % 132.54/18.93 (85) all_53_8 = e3 | ~ (op(e3, e1) = e3) % 132.54/18.93 (86) ~ (all_53_6 = all_6_2) % 132.54/18.93 (87) ~ (all_22_1 = all_8_2) % 132.54/18.93 (88) op(unit, e3) = e3 % 132.54/18.93 (89) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.54/18.93 (90) op(unit, e1) = e1 % 132.54/18.93 (91) op(e3, unit) = e3 % 132.54/18.93 (92) ~ (all_53_4 = all_53_12) % 132.54/18.93 (93) ~ (all_26_1 = e3) | ( ~ (all_26_0 = e0) & op(e2, e3) = all_26_0 & % 132.54/18.93 $i(all_26_0)) % 132.54/18.93 (94) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 132.54/18.93 (95) ~ (all_53_3 = all_53_11) % 132.54/18.93 % 132.54/18.93 Begin of proof % 132.54/18.93 | % 132.54/18.93 | COMBINE_EQS: (1), (64) imply: % 132.54/18.93 | (96) all_40_2 = e1 % 132.54/18.93 | % 132.54/18.93 | COMBINE_EQS: (46), (64) imply: % 132.54/18.93 | (97) all_50_2 = e1 % 132.54/18.93 | % 132.54/18.93 | REDUCE: (64), (86) imply: % 132.54/18.93 | (98) ~ (all_53_6 = e1) % 132.54/18.93 | % 132.54/18.93 | REDUCE: (47), (64) imply: % 132.54/18.93 | (99) ~ (all_53_7 = e1) % 132.54/18.93 | % 132.54/18.93 | REDUCE: (64), (73) imply: % 132.54/18.93 | (100) ~ (all_53_9 = e1) % 132.54/18.93 | % 132.54/18.93 | REDUCE: (36), (64) imply: % 132.54/18.93 | (101) ~ (all_53_13 = e1) % 132.54/18.93 | % 132.54/18.93 | REDUCE: (54), (64) imply: % 132.54/18.93 | (102) ~ (e3 = e1) % 132.54/18.93 | % 132.54/18.93 | SIMP: (102) implies: % 132.54/18.93 | (103) ~ (e3 = e1) % 132.54/18.93 | % 132.54/18.93 | REDUCE: (62), (64) imply: % 132.54/18.93 | (104) op(e2, e2) = e1 % 132.54/18.93 | % 132.54/18.93 | BETA: splitting (50) gives: % 132.54/18.93 | % 132.54/18.93 | Case 1: % 132.54/18.93 | | % 132.54/18.93 | | (105) ~ (all_40_2 = e1) % 132.54/18.93 | | % 132.54/18.93 | | REDUCE: (96), (105) imply: % 132.54/18.93 | | (106) $false % 132.54/18.93 | | % 132.54/18.93 | | CLOSE: (106) is inconsistent. % 132.54/18.93 | | % 132.54/18.93 | Case 2: % 132.54/18.93 | | % 132.54/18.93 | | (107) op(e2, e1) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e0) | ( ~ % 132.54/18.93 | | (all_40_0 = e3) & op(e2, e0) = all_40_0 & $i(all_40_0))) % 132.54/18.93 | | % 132.54/18.93 | | ALPHA: (107) implies: % 132.54/18.93 | | (108) op(e2, e1) = all_40_1 % 132.54/18.93 | | % 132.54/18.93 | | BETA: splitting (89) gives: % 132.54/18.93 | | % 132.54/18.93 | | Case 1: % 132.54/18.93 | | | % 132.54/18.93 | | | (109) ~ (op(e2, e1) = e1) % 132.54/18.93 | | | % 132.54/18.93 | | | GROUND_INST: instantiating (42) with all_53_9, all_26_1, e1, e2, % 132.54/18.93 | | | simplifying with (2), (38) gives: % 132.54/18.93 | | | (110) all_53_9 = all_26_1 % 132.54/18.93 | | | % 132.54/18.93 | | | GROUND_INST: instantiating (42) with all_53_9, all_40_1, e1, e2, % 132.54/18.93 | | | simplifying with (38), (108) gives: % 132.54/18.93 | | | (111) all_53_9 = all_40_1 % 132.54/18.93 | | | % 132.54/18.93 | | | PRED_UNIFY: (90), (109) imply: % 132.54/18.93 | | | (112) ~ (unit = e2) % 132.54/18.93 | | | % 132.54/18.93 | | | PRED_UNIFY: (108), (109) imply: % 132.54/18.93 | | | (113) ~ (all_40_1 = e1) % 132.54/18.93 | | | % 132.54/18.93 | | | COMBINE_EQS: (110), (111) imply: % 132.54/18.93 | | | (114) all_40_1 = all_26_1 % 132.54/18.93 | | | % 132.54/18.93 | | | SIMP: (114) implies: % 132.54/18.93 | | | (115) all_40_1 = all_26_1 % 132.54/18.93 | | | % 132.54/18.93 | | | COMBINE_EQS: (24), (110) imply: % 132.54/18.93 | | | (116) all_55_6 = all_26_1 % 132.54/18.93 | | | % 132.54/18.93 | | | REDUCE: (25), (110) imply: % 132.54/18.93 | | | (117) ~ (all_53_13 = all_26_1) % 132.54/18.93 | | | % 132.54/18.93 | | | SIMP: (117) implies: % 132.54/18.93 | | | (118) ~ (all_53_13 = all_26_1) % 132.54/18.93 | | | % 132.54/18.93 | | | REDUCE: (15), (110) imply: % 132.54/18.93 | | | (119) ~ (all_26_1 = e0) % 132.54/18.93 | | | % 132.54/18.93 | | | REDUCE: (113), (115) imply: % 132.54/18.93 | | | (120) ~ (all_26_1 = e1) % 132.54/18.93 | | | % 132.54/18.93 | | | BETA: splitting (6) gives: % 132.54/18.93 | | | % 132.54/18.93 | | | Case 1: % 132.54/18.93 | | | | % 132.54/18.93 | | | | (121) unit = e2 % 132.54/18.93 | | | | % 132.54/18.93 | | | | REDUCE: (112), (121) imply: % 132.54/18.93 | | | | (122) $false % 132.54/18.93 | | | | % 132.54/18.93 | | | | CLOSE: (122) is inconsistent. % 132.54/18.93 | | | | % 132.54/18.93 | | | Case 2: % 132.54/18.93 | | | | % 132.54/18.93 | | | | (123) unit = e1 | unit = e0 % 132.54/18.93 | | | | % 132.54/18.93 | | | | BETA: splitting (123) gives: % 132.54/18.93 | | | | % 132.54/18.93 | | | | Case 1: % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | (124) unit = e1 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (77), (124) imply: % 132.54/18.93 | | | | | (125) $false % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | CLOSE: (125) is inconsistent. % 132.54/18.93 | | | | | % 132.54/18.93 | | | | Case 2: % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | (126) unit = e0 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (88), (126) imply: % 132.54/18.93 | | | | | (127) op(e0, e3) = e3 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (20), (126) imply: % 132.54/18.93 | | | | | (128) op(e0, e2) = e2 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (90), (126) imply: % 132.54/18.93 | | | | | (129) op(e0, e1) = e1 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (91), (126) imply: % 132.54/18.93 | | | | | (130) op(e3, e0) = e3 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (17), (126) imply: % 132.54/18.93 | | | | | (131) op(e2, e0) = e2 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (66), (126) imply: % 132.54/18.93 | | | | | (132) op(e1, e0) = e1 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | REDUCE: (69), (126) imply: % 132.54/18.93 | | | | | (133) op(e0, e0) = e0 % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | BETA: splitting (78) gives: % 132.54/18.93 | | | | | % 132.54/18.93 | | | | | Case 1: % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | (134) ~ (op(e0, e0) = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | PRED_UNIFY: (133), (134) imply: % 132.54/18.93 | | | | | | (135) $false % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | CLOSE: (135) is inconsistent. % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | Case 2: % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | (136) all_36_2 = e0 % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | COMBINE_EQS: (29), (136) imply: % 132.54/18.93 | | | | | | (137) all_8_2 = e0 % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | SIMP: (137) implies: % 132.54/18.93 | | | | | | (138) all_8_2 = e0 % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (9), (138) imply: % 132.54/18.93 | | | | | | (139) ~ (all_53_3 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (10), (138) imply: % 132.54/18.93 | | | | | | (140) ~ (all_53_7 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (11), (138) imply: % 132.54/18.93 | | | | | | (141) ~ (all_53_11 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (76), (138) imply: % 132.54/18.93 | | | | | | (142) ~ (all_53_13 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (87), (138) imply: % 132.54/18.93 | | | | | | (143) ~ (all_22_1 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | REDUCE: (40), (138) imply: % 132.54/18.93 | | | | | | (144) ~ (e1 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | SIMP: (144) implies: % 132.54/18.93 | | | | | | (145) ~ (e1 = e0) % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | BETA: splitting (71) gives: % 132.54/18.93 | | | | | | % 132.54/18.93 | | | | | | Case 1: % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | (146) ~ (op(e3, e0) = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | PRED_UNIFY: (130), (146) imply: % 132.54/18.93 | | | | | | | (147) $false % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | CLOSE: (147) is inconsistent. % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | Case 2: % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | (148) all_53_12 = e3 % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | REDUCE: (92), (148) imply: % 132.54/18.93 | | | | | | | (149) ~ (all_53_4 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | REDUCE: (14), (148) imply: % 132.54/18.93 | | | | | | | (150) ~ (all_53_8 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | REDUCE: (35), (148) imply: % 132.54/18.93 | | | | | | | (151) ~ (all_53_13 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | SIMP: (151) implies: % 132.54/18.93 | | | | | | | (152) ~ (all_53_13 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | REDUCE: (4), (148) imply: % 132.54/18.93 | | | | | | | (153) ~ (all_22_1 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | SIMP: (153) implies: % 132.54/18.93 | | | | | | | (154) ~ (all_22_1 = e3) % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | BETA: splitting (8) gives: % 132.54/18.93 | | | | | | | % 132.54/18.93 | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | (155) ~ (op(e0, e3) = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | PRED_UNIFY: (127), (155) imply: % 132.54/18.93 | | | | | | | | (156) $false % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | CLOSE: (156) is inconsistent. % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | (157) all_53_3 = e3 % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (81), (157) imply: % 132.54/18.93 | | | | | | | | (158) ~ (all_53_1 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (3), (157) imply: % 132.54/18.93 | | | | | | | | (159) ~ (all_53_2 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (7), (157) imply: % 132.54/18.93 | | | | | | | | (160) ~ (all_53_7 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | SIMP: (160) implies: % 132.54/18.93 | | | | | | | | (161) ~ (all_53_7 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (95), (157) imply: % 132.54/18.93 | | | | | | | | (162) ~ (all_53_11 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | SIMP: (162) implies: % 132.54/18.93 | | | | | | | | (163) ~ (all_53_11 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (59), (157) imply: % 132.54/18.93 | | | | | | | | (164) ~ (all_4_2 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | SIMP: (164) implies: % 132.54/18.93 | | | | | | | | (165) ~ (all_4_2 = e3) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | REDUCE: (139), (157) imply: % 132.54/18.93 | | | | | | | | (166) ~ (e3 = e0) % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | BETA: splitting (63) gives: % 132.54/18.93 | | | | | | | | % 132.54/18.93 | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | (167) ~ (op(e0, e2) = e2) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | PRED_UNIFY: (128), (167) imply: % 132.54/18.93 | | | | | | | | | (168) $false % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | CLOSE: (168) is inconsistent. % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | (169) all_53_7 = e2 % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | REDUCE: (12), (169) imply: % 132.54/18.93 | | | | | | | | | (170) ~ (all_53_6 = e2) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | REDUCE: (161), (169) imply: % 132.54/18.93 | | | | | | | | | (171) ~ (e3 = e2) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | SIMP: (171) implies: % 132.54/18.93 | | | | | | | | | (172) ~ (e3 = e2) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | REDUCE: (99), (169) imply: % 132.54/18.93 | | | | | | | | | (173) ~ (e2 = e1) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | REDUCE: (140), (169) imply: % 132.54/18.93 | | | | | | | | | (174) ~ (e2 = e0) % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | BETA: splitting (65) gives: % 132.54/18.93 | | | | | | | | | % 132.54/18.93 | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | (175) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 132.54/18.93 | | | | | | | | | | & op(e2, e3) = e0) % 132.54/18.93 | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | BETA: splitting (175) gives: % 132.54/18.93 | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | (176) all_57_0 = e0 & op(e3, e3) = e0 % 132.54/18.93 | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | ALPHA: (176) implies: % 132.54/18.93 | | | | | | | | | | | (177) all_57_0 = e0 % 132.54/18.93 | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | BETA: splitting (68) gives: % 132.54/18.93 | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | (178) ~ (op(e0, e1) = e1) % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | PRED_UNIFY: (129), (178) imply: % 132.54/18.93 | | | | | | | | | | | | (179) $false % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | (180) all_53_11 = e1 % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | REDUCE: (67), (180) imply: % 132.54/18.93 | | | | | | | | | | | | (181) ~ (all_53_8 = e1) % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | BETA: splitting (53) gives: % 132.54/18.93 | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | (182) ~ (op(e2, e0) = e2) % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | PRED_UNIFY: (131), (182) imply: % 132.54/18.93 | | | | | | | | | | | | | (183) $false % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | CLOSE: (183) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | (184) all_53_13 = e2 % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | REDUCE: (19), (184) imply: % 132.54/18.93 | | | | | | | | | | | | | (185) ~ (all_53_1 = e2) % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | BETA: splitting (13) gives: % 132.54/18.93 | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | (186) all_55_2 = e3 % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | COMBINE_EQS: (44), (186) imply: % 132.54/18.93 | | | | | | | | | | | | | | (187) all_53_8 = e3 % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | REDUCE: (150), (187) imply: % 132.54/18.93 | | | | | | | | | | | | | | (188) $false % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | (189) ~ (all_55_2 = e3) % 132.54/18.93 | | | | | | | | | | | | | | (190) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | BETA: splitting (55) gives: % 132.54/18.93 | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | (191) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | REF_CLOSE: (42), (48), (54), (62), (158), (191) are % 132.54/18.93 | | | | | | | | | | | | | | | inconsistent by sub-proof #351. % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | (192) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.54/18.93 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 132.54/18.93 | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | (193) all_57_5 = e3 & op(e2, e1) = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | ALPHA: (193) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | (194) all_57_5 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | (195) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (109), (181), (195) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | sub-proof #207. % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | (196) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 132.54/18.93 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | (197) all_57_8 = e1 & op(e1, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | (198) op(e1, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (145), (198) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | | sub-proof #269. % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | (199) all_57_14 = e1 & op(e0, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | (200) all_57_14 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | (201) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (202) all_57_4 = e2 & op(e3, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (203) all_57_4 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (204) ~ (op(e1, e0) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (132), (204) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (205) $false % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (206) all_38_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (206) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (207) all_22_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (208) all_22_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (208) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (209) ~ (all_53_2 = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (18), (22), (26), (28), (30), (31), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (33), (37), (39), (41), (42), (48), (51), (56), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (70), (74), (80), (82), (83), (84), (98), (103), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (104), (140), (145), (149), (158), (159), (165), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (166), (172), (177), (181), (203), (209) are % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #198. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (210) all_57_5 = e2 & op(e2, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (194), (210) are inconsistent by sub-proof % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | #303. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | (211) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.54/18.93 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (212) all_57_8 = e2 & op(e1, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (213) op(e1, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (42), (174), (213) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | sub-proof #324. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (214) all_57_14 = e2 & op(e0, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (200), (214) are inconsistent by sub-proof % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | #197. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | (215) all_57_10 = e3 & op(e2, e0) = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | (216) all_57_10 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | (217) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (109), (181), (217) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | sub-proof #207. % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | (218) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 132.54/18.93 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | (219) all_57_8 = e1 & op(e1, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | (220) op(e1, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (145), (220) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | | sub-proof #269. % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | (221) all_57_14 = e1 & op(e0, e1) = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | (222) all_57_14 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | (223) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (224) all_57_4 = e3 & op(e3, e1) = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (225) all_57_4 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (226) op(e3, e1) = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (227) ~ (op(e1, e0) = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (132), (227) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (228) $false % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (229) all_38_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (229) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (230) all_22_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (231) all_22_1 = e1 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (231) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_53_2 = e1) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (233) all_55_2 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (233) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (234) all_53_8 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (235) all_53_8 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (op(e3, e1) = e3) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (226), (236) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (237) $false % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (238) all_53_8 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (235), (238) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (239) e3 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (240) e3 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (240) imply: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (241) all_57_4 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (18), (22), (26), (28), (30), (31), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (33), (37), (39), (41), (42), (48), (51), (56), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (70), (74), (80), (82), (83), (84), (98), (103), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (104), (140), (145), (149), (158), (159), (165), % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | (166), (172), (177), (181), (232), (241) are % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #198. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (242) all_55_2 = e1 | all_55_2 = e0 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (44), (181), (242) are inconsistent by % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | sub-proof #213. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (243) all_57_5 = e3 & op(e2, e1) = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | (244) all_57_5 = e3 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (245) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (79), (94), (97), (173), (185), (245) are % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195. % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | (246) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (247) all_57_5 = e2 & op(e2, e1) = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | (248) all_57_5 = e2 % 132.54/18.93 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (244), (248) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | #194. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (249) all_57_10 = e2 & op(e2, e0) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (216), (249) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | #193. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | (250) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.54/18.94 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (251) all_57_8 = e3 & op(e1, e1) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (252) op(e1, e1) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (42), (166), (252) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | sub-proof #320. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (253) all_57_14 = e3 & op(e0, e1) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (254) all_57_14 = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (222), (254) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (255) e3 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | SIMP: (255) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (256) e3 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (256) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | (257) all_57_10 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | (258) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (259) all_57_2 = e0 & op(e2, e3) = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (260) all_57_2 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | (261) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_57_2 = e3 & op(e2, e3) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (260), (262) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | #192. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_57_3 = e3 & op(e2, e2) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (54), (62), (263) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #352. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (264) all_57_5 = e3 & op(e2, e1) = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (265) all_57_5 = e3 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (266) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_57_2 = e2 & op(e2, e3) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (174), (260), (267) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | #349. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_57_3 = e2 & op(e2, e2) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (269) op(e2, e2) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (97), (173), (269) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_57_5 = e2 & op(e2, e1) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (265), (271) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | #303. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_57_10 = e2 & op(e2, e0) = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_57_10 = e2 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (273) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (274) e2 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (274) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (275) $false % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (215), (257) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | #284. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (276) all_57_3 = e0 & op(e2, e2) = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (277) op(e2, e2) = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (104), (145), (277) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | sub-proof #199. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | (278) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (279) all_57_5 = e0 & op(e2, e1) = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (42), (279) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | sub-proof #241. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (280) all_57_10 = e0 & op(e2, e0) = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (281) all_57_10 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (281) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (282) e1 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (282) imply: % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | (283) $false % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | (284) all_57_2 = e0 & op(e2, e3) = e0 % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | ALPHA: (284) implies: % 132.54/18.94 | | | | | | | | | | | (285) op(e2, e3) = e0 % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | BETA: splitting (53) gives: % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | (286) ~ (op(e2, e0) = e2) % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | PRED_UNIFY: (131), (286) imply: % 132.54/18.94 | | | | | | | | | | | | (287) $false % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | (288) all_53_13 = e2 % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | REDUCE: (118), (288) imply: % 132.54/18.94 | | | | | | | | | | | | (289) ~ (all_26_1 = e2) % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | SIMP: (289) implies: % 132.54/18.94 | | | | | | | | | | | | (290) ~ (all_26_1 = e2) % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | BETA: splitting (23) gives: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (291) all_55_6 = e3 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | COMBINE_EQS: (116), (291) imply: % 132.54/18.94 | | | | | | | | | | | | | (292) all_26_1 = e3 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | SIMP: (292) implies: % 132.54/18.94 | | | | | | | | | | | | | (293) all_26_1 = e3 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | BETA: splitting (93) gives: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (294) ~ (all_26_1 = e3) % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | REDUCE: (293), (294) imply: % 132.54/18.94 | | | | | | | | | | | | | | (295) $false % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (296) ~ (all_26_0 = e0) & op(e2, e3) = all_26_0 & % 132.54/18.94 | | | | | | | | | | | | | | $i(all_26_0) % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | ALPHA: (296) implies: % 132.54/18.94 | | | | | | | | | | | | | | (297) ~ (all_26_0 = e0) % 132.54/18.94 | | | | | | | | | | | | | | (298) op(e2, e3) = all_26_0 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | GROUND_INST: instantiating (42) with e0, all_26_0, e3, e2, % 132.54/18.94 | | | | | | | | | | | | | | simplifying with (285), (298) gives: % 132.54/18.94 | | | | | | | | | | | | | | (299) all_26_0 = e0 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | REDUCE: (297), (299) imply: % 132.54/18.94 | | | | | | | | | | | | | | (300) $false % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (301) all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | BETA: splitting (301) gives: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (302) all_55_6 = e2 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | COMBINE_EQS: (116), (302) imply: % 132.54/18.94 | | | | | | | | | | | | | | (303) all_26_1 = e2 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | SIMP: (303) implies: % 132.54/18.94 | | | | | | | | | | | | | | (304) all_26_1 = e2 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | REDUCE: (290), (304) imply: % 132.54/18.94 | | | | | | | | | | | | | | (305) $false % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (306) all_55_6 = e1 | all_55_6 = e0 % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | BETA: splitting (306) gives: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (307) all_55_6 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | COMBINE_EQS: (116), (307) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (308) all_26_1 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | SIMP: (308) implies: % 132.54/18.94 | | | | | | | | | | | | | | | (309) all_26_1 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REDUCE: (120), (309) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (310) $false % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (311) all_55_6 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | COMBINE_EQS: (116), (311) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (312) all_26_1 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | SIMP: (312) implies: % 132.54/18.94 | | | | | | | | | | | | | | | (313) all_26_1 = e0 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REDUCE: (119), (313) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (314) $false % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | % 132.54/18.94 | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | (315) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 % 132.54/18.94 | | | | | | | | | | & op(e0, e3) = e0) % 132.54/18.94 | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | BETA: splitting (315) gives: % 132.54/18.94 | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | (316) all_57_6 = e0 & op(e1, e3) = e0 % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | ALPHA: (316) implies: % 132.54/18.94 | | | | | | | | | | | (317) all_57_6 = e0 % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | BETA: splitting (61) gives: % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | (318) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.54/18.94 | | | | | | | | | | | | & op(e1, e2) = e2) % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | BETA: splitting (318) gives: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (319) all_57_6 = e2 & op(e1, e3) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | ALPHA: (319) implies: % 132.54/18.94 | | | | | | | | | | | | | (320) all_57_6 = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | COMBINE_EQS: (317), (320) imply: % 132.54/18.94 | | | | | | | | | | | | | (321) e2 = e0 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | SIMP: (321) implies: % 132.54/18.94 | | | | | | | | | | | | | (322) e2 = e0 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | COMBINE_EQS: (169), (322) imply: % 132.54/18.94 | | | | | | | | | | | | | (323) all_53_7 = e0 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | REF_CLOSE: (63), (128), (174), (323) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | sub-proof #191. % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (324) all_57_7 = e2 & op(e1, e2) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | ALPHA: (324) implies: % 132.54/18.94 | | | | | | | | | | | | | (325) op(e1, e2) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | REF_CLOSE: (34), (170), (325) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | #326. % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | (326) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.54/18.94 | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | BETA: splitting (326) gives: % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (327) all_57_8 = e2 & op(e1, e1) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | ALPHA: (327) implies: % 132.54/18.94 | | | | | | | | | | | | | (328) op(e1, e1) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | REF_CLOSE: (31), (42), (174), (328) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | sub-proof #324. % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | (329) all_57_11 = e2 & op(e1, e0) = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | ALPHA: (329) implies: % 132.54/18.94 | | | | | | | | | | | | | (330) all_57_11 = e2 % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | BETA: splitting (37) gives: % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (331) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 132.54/18.94 | | | | | | | | | | | | | | & op(e1, e2) = e1) % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | BETA: splitting (331) gives: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (332) all_57_6 = e1 & op(e1, e3) = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REF_CLOSE: (145), (317), (332) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | | | | | #343. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (333) all_57_7 = e1 & op(e1, e2) = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | ALPHA: (333) implies: % 132.54/18.94 | | | | | | | | | | | | | | | (334) all_57_7 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REF_CLOSE: (16), (31), (42), (103), (166), (172), (317), % 132.54/18.94 | | | | | | | | | | | | | | | (330), (334) are inconsistent by sub-proof #188. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | (335) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 132.54/18.94 | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | BETA: splitting (335) gives: % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 1: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (336) all_57_8 = e1 & op(e1, e1) = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | ALPHA: (336) implies: % 132.54/18.94 | | | | | | | | | | | | | | | (337) op(e1, e1) = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REF_CLOSE: (26), (28), (145), (337) are inconsistent by % 132.54/18.94 | | | | | | | | | | | | | | | sub-proof #269. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | (338) all_57_11 = e1 & op(e1, e0) = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | ALPHA: (338) implies: % 132.54/18.94 | | | | | | | | | | | | | | | (339) all_57_11 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | COMBINE_EQS: (330), (339) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (340) e2 = e1 % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | REDUCE: (173), (340) imply: % 132.54/18.94 | | | | | | | | | | | | | | | (341) $false % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | | CLOSE: (341) is inconsistent. % 132.54/18.94 | | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | Case 2: % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | (342) all_57_12 = e0 & op(e0, e3) = e0 % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | | REF_CLOSE: (45), (139), (342) are inconsistent by sub-proof % 132.54/18.94 | | | | | | | | | | | #237. % 132.54/18.94 | | | | | | | | | | | % 132.54/18.94 | | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | | % 132.54/18.94 | | | | | | | | | End of split % 132.54/18.94 | | | | | | | | | % 132.54/18.94 | | | | | | | | End of split % 132.54/18.94 | | | | | | | | % 132.54/18.94 | | | | | | | End of split % 132.54/18.94 | | | | | | | % 132.54/18.94 | | | | | | End of split % 132.54/18.94 | | | | | | % 132.54/18.94 | | | | | End of split % 132.54/18.94 | | | | | % 132.54/18.94 | | | | End of split % 132.54/18.94 | | | | % 132.54/18.94 | | | End of split % 132.54/18.94 | | | % 132.54/18.94 | | Case 2: % 132.54/18.94 | | | % 132.54/18.94 | | | (343) op(e2, e1) = e1 % 132.54/18.94 | | | % 132.54/18.94 | | | REF_CLOSE: (89), (100), (343) are inconsistent by sub-proof #334. % 132.54/18.94 | | | % 132.54/18.94 | | End of split % 132.54/18.94 | | % 132.54/18.94 | End of split % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #188 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.54/18.94 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.54/18.94 (2) ~ (e3 = e0) % 132.54/18.94 (3) op(e1, e1) = e0 % 132.54/18.94 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.94 (5) ~ (e3 = e1) % 132.54/18.94 (6) all_57_6 = e0 % 132.54/18.94 (7) all_57_7 = e1 % 132.54/18.94 (8) all_57_11 = e2 % 132.54/18.94 (9) ~ (e3 = e2) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | BETA: splitting (1) gives: % 132.54/18.94 | % 132.54/18.94 | Case 1: % 132.54/18.94 | | % 132.54/18.94 | | (10) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 132.54/18.94 | | e3) % 132.54/18.94 | | % 132.54/18.94 | | BETA: splitting (10) gives: % 132.54/18.94 | | % 132.54/18.94 | | Case 1: % 132.54/18.94 | | | % 132.54/18.94 | | | (11) all_57_6 = e3 & op(e1, e3) = e3 % 132.54/18.94 | | | % 132.54/18.94 | | | ALPHA: (11) implies: % 132.54/18.94 | | | (12) all_57_6 = e3 % 132.54/18.94 | | | % 132.54/18.94 | | | COMBINE_EQS: (6), (12) imply: % 132.54/18.94 | | | (13) e3 = e0 % 132.54/18.94 | | | % 132.54/18.94 | | | SIMP: (13) implies: % 132.54/18.94 | | | (14) e3 = e0 % 132.54/18.94 | | | % 132.54/18.94 | | | REDUCE: (2), (14) imply: % 132.54/18.94 | | | (15) $false % 132.54/18.94 | | | % 132.54/18.94 | | | CLOSE: (15) is inconsistent. % 132.54/18.94 | | | % 132.54/18.94 | | Case 2: % 132.54/18.94 | | | % 132.54/18.94 | | | (16) all_57_7 = e3 & op(e1, e2) = e3 % 132.54/18.94 | | | % 132.54/18.94 | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #190. % 132.54/18.94 | | | % 132.54/18.94 | | End of split % 132.54/18.94 | | % 132.54/18.94 | Case 2: % 132.54/18.94 | | % 132.54/18.94 | | (17) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 132.54/18.94 | | e3) % 132.54/18.94 | | % 132.54/18.94 | | REF_CLOSE: (2), (3), (4), (8), (9), (17) are inconsistent by sub-proof #189. % 132.54/18.94 | | % 132.54/18.94 | End of split % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #189 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.54/18.94 (2) ~ (e3 = e0) % 132.54/18.94 (3) op(e1, e1) = e0 % 132.54/18.94 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.94 (5) all_57_11 = e2 % 132.54/18.94 (6) ~ (e3 = e2) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | BETA: splitting (1) gives: % 132.54/18.94 | % 132.54/18.94 | Case 1: % 132.54/18.94 | | % 132.54/18.94 | | (7) all_57_8 = e3 & op(e1, e1) = e3 % 132.54/18.94 | | % 132.54/18.94 | | ALPHA: (7) implies: % 132.54/18.94 | | (8) op(e1, e1) = e3 % 132.54/18.94 | | % 132.54/18.94 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #320. % 132.54/18.94 | | % 132.54/18.94 | Case 2: % 132.54/18.94 | | % 132.54/18.94 | | (9) all_57_11 = e3 & op(e1, e0) = e3 % 132.54/18.94 | | % 132.54/18.94 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #260. % 132.54/18.94 | | % 132.54/18.94 | End of split % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #190 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_57_7 = e3 & op(e1, e2) = e3 % 132.54/18.94 (2) all_57_7 = e1 % 132.54/18.94 (3) ~ (e3 = e1) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | ALPHA: (1) implies: % 132.54/18.94 | (4) all_57_7 = e3 % 132.54/18.94 | % 132.54/18.94 | COMBINE_EQS: (2), (4) imply: % 132.54/18.94 | (5) e3 = e1 % 132.54/18.94 | % 132.54/18.94 | SIMP: (5) implies: % 132.54/18.94 | (6) e3 = e1 % 132.54/18.94 | % 132.54/18.94 | REDUCE: (3), (6) imply: % 132.54/18.94 | (7) $false % 132.54/18.94 | % 132.54/18.94 | CLOSE: (7) is inconsistent. % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #191 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.54/18.94 (2) op(e0, e2) = e2 % 132.54/18.94 (3) all_53_7 = e0 % 132.54/18.94 (4) ~ (e2 = e0) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | BETA: splitting (1) gives: % 132.54/18.94 | % 132.54/18.94 | Case 1: % 132.54/18.94 | | % 132.54/18.94 | | (5) ~ (op(e0, e2) = e2) % 132.54/18.94 | | % 132.54/18.94 | | PRED_UNIFY: (2), (5) imply: % 132.54/18.94 | | (6) $false % 132.54/18.94 | | % 132.54/18.94 | | CLOSE: (6) is inconsistent. % 132.54/18.94 | | % 132.54/18.94 | Case 2: % 132.54/18.94 | | % 132.54/18.94 | | (7) all_53_7 = e2 % 132.54/18.94 | | % 132.54/18.94 | | COMBINE_EQS: (3), (7) imply: % 132.54/18.94 | | (8) e2 = e0 % 132.54/18.94 | | % 132.54/18.94 | | REDUCE: (4), (8) imply: % 132.54/18.94 | | (9) $false % 132.54/18.94 | | % 132.54/18.94 | | CLOSE: (9) is inconsistent. % 132.54/18.94 | | % 132.54/18.94 | End of split % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #192 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_57_2 = e3 & op(e2, e3) = e3 % 132.54/18.94 (2) all_57_2 = e0 % 132.54/18.94 (3) ~ (e3 = e0) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | ALPHA: (1) implies: % 132.54/18.94 | (4) all_57_2 = e3 % 132.54/18.94 | % 132.54/18.94 | COMBINE_EQS: (2), (4) imply: % 132.54/18.94 | (5) e3 = e0 % 132.54/18.94 | % 132.54/18.94 | SIMP: (5) implies: % 132.54/18.94 | (6) e3 = e0 % 132.54/18.94 | % 132.54/18.94 | REDUCE: (3), (6) imply: % 132.54/18.94 | (7) $false % 132.54/18.94 | % 132.54/18.94 | CLOSE: (7) is inconsistent. % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #193 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_57_10 = e2 & op(e2, e0) = e2 % 132.54/18.94 (2) all_57_10 = e3 % 132.54/18.94 (3) ~ (e3 = e2) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | ALPHA: (1) implies: % 132.54/18.94 | (4) all_57_10 = e2 % 132.54/18.94 | % 132.54/18.94 | COMBINE_EQS: (2), (4) imply: % 132.54/18.94 | (5) e3 = e2 % 132.54/18.94 | % 132.54/18.94 | REDUCE: (3), (5) imply: % 132.54/18.94 | (6) $false % 132.54/18.94 | % 132.54/18.94 | CLOSE: (6) is inconsistent. % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #194 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_57_5 = e3 % 132.54/18.94 (2) all_57_5 = e2 % 132.54/18.94 (3) ~ (e3 = e2) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | COMBINE_EQS: (1), (2) imply: % 132.54/18.94 | (4) e3 = e2 % 132.54/18.94 | % 132.54/18.94 | SIMP: (4) implies: % 132.54/18.94 | (5) e3 = e2 % 132.54/18.94 | % 132.54/18.94 | REDUCE: (3), (5) imply: % 132.54/18.94 | (6) $false % 132.54/18.94 | % 132.54/18.94 | CLOSE: (6) is inconsistent. % 132.54/18.94 | % 132.54/18.94 End of proof % 132.54/18.94 % 132.54/18.94 Sub-proof #195 shows that the following formulas are inconsistent: % 132.54/18.94 ---------------------------------------------------------------- % 132.54/18.94 (1) all_50_2 = e1 % 132.54/18.94 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 132.54/18.94 (3) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 132.54/18.94 (4) ~ (all_53_1 = e2) % 132.54/18.94 (5) ~ (e2 = e1) % 132.54/18.94 (6) all_55_4 = all_53_1 % 132.54/18.94 (7) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 132.54/18.94 % 132.54/18.94 Begin of proof % 132.54/18.94 | % 132.54/18.94 | BETA: splitting (2) gives: % 132.54/18.94 | % 132.54/18.94 | Case 1: % 132.54/18.94 | | % 132.54/18.94 | | (8) all_57_2 = e2 & op(e2, e3) = e2 % 132.54/18.94 | | % 132.54/18.94 | | ALPHA: (8) implies: % 132.54/18.94 | | (9) op(e2, e3) = e2 % 132.54/18.94 | | % 132.54/18.94 | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #346. % 132.54/18.94 | | % 132.54/18.94 | Case 2: % 132.54/18.94 | | % 132.54/18.96 | | (10) all_57_3 = e2 & op(e2, e2) = e2 % 132.54/18.96 | | % 132.54/18.96 | | ALPHA: (10) implies: % 132.54/18.96 | | (11) op(e2, e2) = e2 % 132.54/18.96 | | % 132.54/18.96 | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #196. % 132.54/18.96 | | % 132.54/18.96 | End of split % 132.54/18.96 | % 132.54/18.96 End of proof % 132.54/18.96 % 132.54/18.96 Sub-proof #196 shows that the following formulas are inconsistent: % 132.54/18.96 ---------------------------------------------------------------- % 132.54/18.96 (1) all_50_2 = e2 | ~ (op(e2, e2) = e2) % 132.54/18.96 (2) op(e2, e2) = e2 % 132.54/18.96 (3) all_50_2 = e1 % 132.54/18.96 (4) ~ (e2 = e1) % 132.54/18.96 % 132.54/18.96 Begin of proof % 132.54/18.96 | % 132.54/18.96 | BETA: splitting (1) gives: % 132.54/18.96 | % 132.54/18.96 | Case 1: % 132.54/18.96 | | % 132.54/18.96 | | (5) ~ (op(e2, e2) = e2) % 132.54/18.96 | | % 132.54/18.96 | | PRED_UNIFY: (2), (5) imply: % 132.54/18.96 | | (6) $false % 132.54/18.96 | | % 132.54/18.96 | | CLOSE: (6) is inconsistent. % 132.54/18.96 | | % 132.54/18.96 | Case 2: % 132.54/18.96 | | % 132.54/18.96 | | (7) all_50_2 = e2 % 132.54/18.96 | | % 132.54/18.96 | | COMBINE_EQS: (3), (7) imply: % 132.54/18.96 | | (8) e2 = e1 % 132.54/18.96 | | % 132.54/18.96 | | REDUCE: (4), (8) imply: % 132.54/18.96 | | (9) $false % 132.54/18.96 | | % 132.54/18.96 | | CLOSE: (9) is inconsistent. % 132.54/18.96 | | % 132.54/18.96 | End of split % 132.54/18.96 | % 132.54/18.96 End of proof % 132.54/18.96 % 132.54/18.96 Sub-proof #197 shows that the following formulas are inconsistent: % 132.54/18.96 ---------------------------------------------------------------- % 132.54/18.96 (1) all_57_14 = e2 & op(e0, e1) = e2 % 132.54/18.96 (2) all_57_14 = e1 % 132.54/18.96 (3) ~ (e2 = e1) % 132.54/18.96 % 132.54/18.96 Begin of proof % 132.54/18.96 | % 132.54/18.96 | ALPHA: (1) implies: % 132.54/18.96 | (4) all_57_14 = e2 % 132.54/18.96 | % 132.54/18.96 | COMBINE_EQS: (2), (4) imply: % 132.54/18.96 | (5) e2 = e1 % 132.54/18.96 | % 132.54/18.96 | SIMP: (5) implies: % 132.54/18.96 | (6) e2 = e1 % 132.54/18.96 | % 132.54/18.96 | REDUCE: (3), (6) imply: % 132.54/18.96 | (7) $false % 132.54/18.96 | % 132.54/18.96 | CLOSE: (7) is inconsistent. % 132.54/18.96 | % 132.54/18.96 End of proof % 132.54/18.96 % 132.54/18.96 Sub-proof #198 shows that the following formulas are inconsistent: % 132.54/18.96 ---------------------------------------------------------------- % 132.54/18.96 (1) ~ (all_53_1 = e3) % 132.54/18.96 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.54/18.96 (3) op(e2, e2) = e1 % 132.54/18.96 (4) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.54/18.96 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.54/18.96 (5) all_55_9 = all_53_6 % 132.54/18.96 (6) all_55_1 = all_53_4 % 132.54/18.96 (7) all_22_2 = e0 % 132.54/18.96 (8) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.54/18.96 (9) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 132.54/18.96 (10) ~ (e3 = e0) % 132.54/18.96 (11) op(e1, e1) = e0 % 132.54/18.96 (12) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.54/18.96 (13) ~ (all_53_7 = e0) % 132.54/18.96 (14) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.54/18.96 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.54/18.96 (15) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 132.54/18.96 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 132.54/18.96 (16) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.54/18.96 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.96 (18) ~ (e3 = e1) % 132.54/18.96 (19) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.54/18.96 (20) ~ (all_53_4 = e3) % 132.54/18.96 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.54/18.96 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.54/18.96 (22) all_57_0 = e0 % 132.54/18.96 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.54/18.96 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.54/18.96 (24) ~ (e1 = e0) % 132.54/18.96 (25) ~ (all_53_6 = e1) % 132.54/18.96 (26) ~ (all_4_2 = e3) % 132.54/18.96 (27) ~ (all_53_2 = e1) % 132.54/18.96 (28) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.54/18.96 (29) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 132.54/18.96 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 132.54/18.96 (30) ~ (all_53_2 = e3) % 132.54/18.96 (31) all_57_4 = e2 % 132.54/18.96 (32) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 132.54/18.96 (33) ~ (e3 = e2) % 132.54/18.96 (34) ~ (all_53_8 = e1) % 132.54/18.96 (35) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.96 (36) all_14_2 = all_4_2 % 132.54/18.96 (37) all_55_13 = all_53_7 % 132.54/18.96 % 132.54/18.96 Begin of proof % 132.54/18.96 | % 132.54/18.96 | BETA: splitting (14) gives: % 132.54/18.96 | % 132.54/18.96 | Case 1: % 132.54/18.96 | | % 132.54/18.96 | | (38) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = % 132.54/18.96 | | e1) % 132.54/18.96 | | % 132.54/18.96 | | REF_CLOSE: (5), (25), (27), (28), (32), (38) are inconsistent by sub-proof % 132.54/18.96 | | #279. % 132.54/18.96 | | % 132.54/18.96 | Case 2: % 132.54/18.96 | | % 132.54/18.96 | | (39) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = % 132.54/18.96 | | e1) % 132.54/18.96 | | % 132.54/18.96 | | BETA: splitting (39) gives: % 132.54/18.96 | | % 132.54/18.96 | | Case 1: % 132.54/18.96 | | | % 132.54/18.96 | | | (40) all_57_8 = e1 & op(e1, e1) = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | ALPHA: (40) implies: % 132.54/18.96 | | | (41) op(e1, e1) = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | REF_CLOSE: (7), (8), (24), (41) are inconsistent by sub-proof #269. % 132.54/18.96 | | | % 132.54/18.96 | | Case 2: % 132.54/18.96 | | | % 132.54/18.96 | | | (42) all_57_11 = e1 & op(e1, e0) = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | ALPHA: (42) implies: % 132.54/18.96 | | | (43) all_57_11 = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | BETA: splitting (15) gives: % 132.54/18.96 | | | % 132.54/18.96 | | | Case 1: % 132.54/18.96 | | | | % 132.54/18.96 | | | | (44) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) % 132.54/18.96 | | | | = e0) % 132.54/18.96 | | | | % 132.54/18.96 | | | | BETA: splitting (44) gives: % 132.54/18.96 | | | | % 132.54/18.96 | | | | Case 1: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | (45) all_57_1 = e0 & op(e3, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | ALPHA: (45) implies: % 132.54/18.96 | | | | | (46) all_57_1 = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | BETA: splitting (21) gives: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | Case 1: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | (47) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, % 132.54/18.96 | | | | | | e3) = e3) % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | REF_CLOSE: (1), (19), (26), (35), (36), (47) are inconsistent by % 132.54/18.96 | | | | | | sub-proof #205. % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | Case 2: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | (48) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, % 132.54/18.96 | | | | | | e3) = e3) % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | BETA: splitting (48) gives: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | Case 1: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (49) all_57_6 = e3 & op(e1, e3) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (49) implies: % 132.54/18.96 | | | | | | | (50) op(e1, e3) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | REF_CLOSE: (2), (30), (50) are inconsistent by sub-proof #323. % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | Case 2: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (51) all_57_12 = e3 & op(e0, e3) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (51) implies: % 132.54/18.96 | | | | | | | (52) all_57_12 = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | BETA: splitting (23) gives: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | Case 1: % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | (53) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & % 132.54/18.96 | | | | | | | | op(e3, e2) = e3) % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | BETA: splitting (53) gives: % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | Case 1: % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | (54) all_57_0 = e3 & op(e3, e3) = e3 % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | REF_CLOSE: (26), (35), (36), (54) are inconsistent by % 132.54/18.96 | | | | | | | | | sub-proof #206. % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | Case 2: % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | (55) all_57_1 = e3 & op(e3, e2) = e3 % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | REF_CLOSE: (6), (9), (20), (55) are inconsistent by sub-proof % 132.54/18.96 | | | | | | | | | #328. % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | End of split % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | Case 2: % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | (56) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & % 132.54/18.96 | | | | | | | | op(e3, e0) = e3) % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | BETA: splitting (56) gives: % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | | Case 1: % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | (57) all_57_4 = e3 & op(e3, e1) = e3 % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | REF_CLOSE: (1), (2), (19), (21), (26), (30), (31), (33), (35), % 132.54/18.96 | | | | | | | | | (36), (52), (57) are inconsistent by sub-proof % 132.54/18.96 | | | | | | | | | #202. % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | Case 2: % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | (58) all_57_9 = e3 & op(e3, e0) = e3 % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | ALPHA: (58) implies: % 132.54/18.96 | | | | | | | | | (59) all_57_9 = e3 % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | | REF_CLOSE: (16), (18), (22), (24), (29), (34), (46), (59) are % 132.54/18.96 | | | | | | | | | inconsistent by sub-proof #200. % 132.54/18.96 | | | | | | | | | % 132.54/18.96 | | | | | | | | End of split % 132.54/18.96 | | | | | | | | % 132.54/18.96 | | | | | | | End of split % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | End of split % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | End of split % 132.54/18.96 | | | | | % 132.54/18.96 | | | | Case 2: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | (60) all_57_3 = e0 & op(e2, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | ALPHA: (60) implies: % 132.54/18.96 | | | | | (61) op(e2, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | REF_CLOSE: (3), (17), (24), (61) are inconsistent by sub-proof #199. % 132.54/18.96 | | | | | % 132.54/18.96 | | | | End of split % 132.54/18.96 | | | | % 132.54/18.96 | | | Case 2: % 132.54/18.96 | | | | % 132.54/18.96 | | | | (62) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) % 132.54/18.96 | | | | = e0) % 132.54/18.96 | | | | % 132.54/18.96 | | | | BETA: splitting (62) gives: % 132.54/18.96 | | | | % 132.54/18.96 | | | | Case 1: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | (63) all_57_7 = e0 & op(e1, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | ALPHA: (63) implies: % 132.54/18.96 | | | | | (64) all_57_7 = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | BETA: splitting (4) gives: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | Case 1: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | (65) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, % 132.54/18.96 | | | | | | e2) = e3) % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | BETA: splitting (65) gives: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | Case 1: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (66) all_57_6 = e3 & op(e1, e3) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (66) implies: % 132.54/18.96 | | | | | | | (67) op(e1, e3) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | REF_CLOSE: (2), (30), (67) are inconsistent by sub-proof #323. % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | Case 2: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (68) all_57_7 = e3 & op(e1, e2) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (68) implies: % 132.54/18.96 | | | | | | | (69) all_57_7 = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | COMBINE_EQS: (64), (69) imply: % 132.54/18.96 | | | | | | | (70) e3 = e0 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | REDUCE: (10), (70) imply: % 132.54/18.96 | | | | | | | (71) $false % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | CLOSE: (71) is inconsistent. % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | End of split % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | Case 2: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | (72) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, % 132.54/18.96 | | | | | | e0) = e3) % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | BETA: splitting (72) gives: % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | | Case 1: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (73) all_57_8 = e3 & op(e1, e1) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (73) implies: % 132.54/18.96 | | | | | | | (74) op(e1, e1) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | REF_CLOSE: (10), (11), (17), (74) are inconsistent by sub-proof % 132.54/18.96 | | | | | | | #320. % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | Case 2: % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | (75) all_57_11 = e3 & op(e1, e0) = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | ALPHA: (75) implies: % 132.54/18.96 | | | | | | | (76) all_57_11 = e3 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | COMBINE_EQS: (43), (76) imply: % 132.54/18.96 | | | | | | | (77) e3 = e1 % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | REDUCE: (18), (77) imply: % 132.54/18.96 | | | | | | | (78) $false % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | | CLOSE: (78) is inconsistent. % 132.54/18.96 | | | | | | | % 132.54/18.96 | | | | | | End of split % 132.54/18.96 | | | | | | % 132.54/18.96 | | | | | End of split % 132.54/18.96 | | | | | % 132.54/18.96 | | | | Case 2: % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | (79) all_57_13 = e0 & op(e0, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | ALPHA: (79) implies: % 132.54/18.96 | | | | | (80) op(e0, e2) = e0 % 132.54/18.96 | | | | | % 132.54/18.96 | | | | | REF_CLOSE: (12), (13), (37), (80) are inconsistent by sub-proof #292. % 132.54/18.96 | | | | | % 132.54/18.96 | | | | End of split % 132.54/18.96 | | | | % 132.54/18.96 | | | End of split % 132.54/18.96 | | | % 132.54/18.96 | | End of split % 132.54/18.96 | | % 132.54/18.96 | End of split % 132.54/18.96 | % 132.54/18.96 End of proof % 132.54/18.96 % 132.54/18.96 Sub-proof #199 shows that the following formulas are inconsistent: % 132.54/18.96 ---------------------------------------------------------------- % 132.54/18.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.96 (2) op(e2, e2) = e1 % 132.54/18.96 (3) op(e2, e2) = e0 % 132.54/18.96 (4) ~ (e1 = e0) % 132.54/18.96 % 132.54/18.96 Begin of proof % 132.54/18.96 | % 132.54/18.96 | GROUND_INST: instantiating (1) with e0, e1, e2, e2, simplifying with (2), (3) % 132.54/18.96 | gives: % 132.54/18.96 | (5) e1 = e0 % 132.54/18.96 | % 132.54/18.96 | REDUCE: (4), (5) imply: % 132.54/18.96 | (6) $false % 132.54/18.96 | % 132.54/18.96 | CLOSE: (6) is inconsistent. % 132.54/18.96 | % 132.54/18.96 End of proof % 132.54/18.96 % 132.54/18.96 Sub-proof #200 shows that the following formulas are inconsistent: % 132.54/18.96 ---------------------------------------------------------------- % 132.54/18.96 (1) all_57_9 = e3 % 132.54/18.96 (2) all_57_1 = e0 % 132.54/18.96 (3) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.54/18.96 (4) ~ (e3 = e1) % 132.54/18.96 (5) all_57_0 = e0 % 132.54/18.96 (6) ~ (e1 = e0) % 132.54/18.96 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 132.54/18.96 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 132.54/18.96 (8) ~ (all_53_8 = e1) % 132.54/18.96 % 132.54/18.96 Begin of proof % 132.54/18.96 | % 132.54/18.96 | BETA: splitting (7) gives: % 132.54/18.96 | % 132.54/18.96 | Case 1: % 132.54/18.96 | | % 132.54/18.96 | | (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 132.54/18.96 | | % 132.54/18.96 | | BETA: splitting (9) gives: % 132.54/18.96 | | % 132.54/18.96 | | Case 1: % 132.54/18.96 | | | % 132.54/18.96 | | | (10) all_57_0 = e1 & op(e3, e3) = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | ALPHA: (10) implies: % 132.54/18.96 | | | (11) all_57_0 = e1 % 132.54/18.96 | | | % 132.54/18.96 | | | COMBINE_EQS: (5), (11) imply: % 132.54/18.96 | | | (12) e1 = e0 % 132.54/18.97 | | | % 132.54/18.97 | | | SIMP: (12) implies: % 132.54/18.97 | | | (13) e1 = e0 % 132.54/18.97 | | | % 132.54/18.97 | | | REDUCE: (6), (13) imply: % 132.54/18.97 | | | (14) $false % 132.54/18.97 | | | % 132.54/18.97 | | | CLOSE: (14) is inconsistent. % 132.54/18.97 | | | % 132.54/18.97 | | Case 2: % 132.54/18.97 | | | % 132.54/18.97 | | | (15) all_57_1 = e1 & op(e3, e2) = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #201. % 132.54/18.97 | | | % 132.54/18.97 | | End of split % 132.54/18.97 | | % 132.54/18.97 | Case 2: % 132.54/18.97 | | % 132.54/18.97 | | (16) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 132.54/18.97 | | e1) % 132.54/18.97 | | % 132.54/18.97 | | BETA: splitting (16) gives: % 132.54/18.97 | | % 132.54/18.97 | | Case 1: % 132.54/18.97 | | | % 132.54/18.97 | | | (17) all_57_4 = e1 & op(e3, e1) = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | ALPHA: (17) implies: % 132.54/18.97 | | | (18) op(e3, e1) = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | REF_CLOSE: (3), (8), (18) are inconsistent by sub-proof #238. % 132.54/18.97 | | | % 132.54/18.97 | | Case 2: % 132.54/18.97 | | | % 132.54/18.97 | | | (19) all_57_9 = e1 & op(e3, e0) = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | ALPHA: (19) implies: % 132.54/18.97 | | | (20) all_57_9 = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | COMBINE_EQS: (1), (20) imply: % 132.54/18.97 | | | (21) e3 = e1 % 132.54/18.97 | | | % 132.54/18.97 | | | REDUCE: (4), (21) imply: % 132.54/18.97 | | | (22) $false % 132.54/18.97 | | | % 132.54/18.97 | | | CLOSE: (22) is inconsistent. % 132.54/18.97 | | | % 132.54/18.97 | | End of split % 132.54/18.97 | | % 132.54/18.97 | End of split % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #201 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) all_57_1 = e1 & op(e3, e2) = e1 % 132.54/18.97 (2) all_57_1 = e0 % 132.54/18.97 (3) ~ (e1 = e0) % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | ALPHA: (1) implies: % 132.54/18.97 | (4) all_57_1 = e1 % 132.54/18.97 | % 132.54/18.97 | COMBINE_EQS: (2), (4) imply: % 132.54/18.97 | (5) e1 = e0 % 132.54/18.97 | % 132.54/18.97 | SIMP: (5) implies: % 132.54/18.97 | (6) e1 = e0 % 132.54/18.97 | % 132.54/18.97 | REDUCE: (3), (6) imply: % 132.54/18.97 | (7) $false % 132.54/18.97 | % 132.54/18.97 | CLOSE: (7) is inconsistent. % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #202 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) ~ (all_53_1 = e3) % 132.54/18.97 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.54/18.97 (3) all_57_12 = e3 % 132.54/18.97 (4) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.54/18.97 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.54/18.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.54/18.97 (6) ~ (all_4_2 = e3) % 132.54/18.97 (7) ~ (all_53_2 = e3) % 132.54/18.97 (8) all_57_4 = e2 % 132.54/18.97 (9) ~ (e3 = e2) % 132.54/18.97 (10) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.97 (11) all_14_2 = all_4_2 % 132.54/18.97 (12) all_57_4 = e3 & op(e3, e1) = e3 % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | ALPHA: (12) implies: % 132.54/18.97 | (13) all_57_4 = e3 % 132.54/18.97 | % 132.54/18.97 | COMBINE_EQS: (8), (13) imply: % 132.54/18.97 | (14) e3 = e2 % 132.54/18.97 | % 132.54/18.97 | SIMP: (14) implies: % 132.54/18.97 | (15) e3 = e2 % 132.54/18.97 | % 132.54/18.97 | COMBINE_EQS: (3), (15) imply: % 132.54/18.97 | (16) all_57_12 = e2 % 132.54/18.97 | % 132.54/18.97 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (16) are % 132.54/18.97 | inconsistent by sub-proof #203. % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #203 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) ~ (all_53_1 = e3) % 132.54/18.97 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.54/18.97 (3) all_57_12 = e2 % 132.54/18.97 (4) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.54/18.97 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.54/18.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.54/18.97 (6) ~ (all_4_2 = e3) % 132.54/18.97 (7) ~ (all_53_2 = e3) % 132.54/18.97 (8) ~ (e3 = e2) % 132.54/18.97 (9) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.97 (10) all_14_2 = all_4_2 % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | BETA: splitting (5) gives: % 132.54/18.97 | % 132.54/18.97 | Case 1: % 132.54/18.97 | | % 132.54/18.97 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 132.54/18.97 | | e3) % 132.54/18.97 | | % 132.54/18.97 | | REF_CLOSE: (1), (4), (6), (9), (10), (11) are inconsistent by sub-proof % 132.54/18.97 | | #205. % 132.54/18.97 | | % 132.54/18.97 | Case 2: % 132.54/18.97 | | % 132.54/18.97 | | (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 132.54/18.97 | | e3) % 132.54/18.97 | | % 132.54/18.97 | | BETA: splitting (12) gives: % 132.54/18.97 | | % 132.54/18.97 | | Case 1: % 132.54/18.97 | | | % 132.54/18.97 | | | (13) all_57_6 = e3 & op(e1, e3) = e3 % 132.54/18.97 | | | % 132.54/18.97 | | | ALPHA: (13) implies: % 132.54/18.97 | | | (14) op(e1, e3) = e3 % 132.54/18.97 | | | % 132.54/18.97 | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #323. % 132.54/18.97 | | | % 132.54/18.97 | | Case 2: % 132.54/18.97 | | | % 132.54/18.97 | | | (15) all_57_12 = e3 & op(e0, e3) = e3 % 132.54/18.97 | | | % 132.54/18.97 | | | REF_CLOSE: (3), (8), (15) are inconsistent by sub-proof #204. % 132.54/18.97 | | | % 132.54/18.97 | | End of split % 132.54/18.97 | | % 132.54/18.97 | End of split % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #204 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) all_57_12 = e3 & op(e0, e3) = e3 % 132.54/18.97 (2) all_57_12 = e2 % 132.54/18.97 (3) ~ (e3 = e2) % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | ALPHA: (1) implies: % 132.54/18.97 | (4) all_57_12 = e3 % 132.54/18.97 | % 132.54/18.97 | COMBINE_EQS: (2), (4) imply: % 132.54/18.97 | (5) e3 = e2 % 132.54/18.97 | % 132.54/18.97 | REDUCE: (3), (5) imply: % 132.54/18.97 | (6) $false % 132.54/18.97 | % 132.54/18.97 | CLOSE: (6) is inconsistent. % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #205 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) ~ (all_53_1 = e3) % 132.54/18.97 (2) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 132.54/18.97 (3) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.54/18.97 (4) ~ (all_4_2 = e3) % 132.54/18.97 (5) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.97 (6) all_14_2 = all_4_2 % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | BETA: splitting (2) gives: % 132.54/18.97 | % 132.54/18.97 | Case 1: % 132.54/18.97 | | % 132.54/18.97 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 132.54/18.97 | | % 132.54/18.97 | | REF_CLOSE: (4), (5), (6), (7) are inconsistent by sub-proof #206. % 132.54/18.97 | | % 132.54/18.97 | Case 2: % 132.54/18.97 | | % 132.54/18.97 | | (8) all_57_2 = e3 & op(e2, e3) = e3 % 132.54/18.97 | | % 132.54/18.97 | | ALPHA: (8) implies: % 132.54/18.97 | | (9) op(e2, e3) = e3 % 132.54/18.97 | | % 132.54/18.97 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #353. % 132.54/18.97 | | % 132.54/18.97 | End of split % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #206 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) all_57_0 = e3 & op(e3, e3) = e3 % 132.54/18.97 (2) all_14_2 = e3 | ~ (op(e3, e3) = e3) % 132.54/18.97 (3) all_14_2 = all_4_2 % 132.54/18.97 (4) ~ (all_4_2 = e3) % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | ALPHA: (1) implies: % 132.54/18.97 | (5) op(e3, e3) = e3 % 132.54/18.97 | % 132.54/18.97 | BETA: splitting (2) gives: % 132.54/18.97 | % 132.54/18.97 | Case 1: % 132.54/18.97 | | % 132.54/18.97 | | (6) ~ (op(e3, e3) = e3) % 132.54/18.97 | | % 132.54/18.97 | | PRED_UNIFY: (5), (6) imply: % 132.54/18.97 | | (7) $false % 132.54/18.97 | | % 132.54/18.97 | | CLOSE: (7) is inconsistent. % 132.54/18.97 | | % 132.54/18.97 | Case 2: % 132.54/18.97 | | % 132.54/18.97 | | (8) all_14_2 = e3 % 132.54/18.97 | | % 132.54/18.97 | | COMBINE_EQS: (3), (8) imply: % 132.54/18.97 | | (9) all_4_2 = e3 % 132.54/18.97 | | % 132.54/18.97 | | REDUCE: (4), (9) imply: % 132.54/18.97 | | (10) $false % 132.54/18.97 | | % 132.54/18.97 | | CLOSE: (10) is inconsistent. % 132.54/18.97 | | % 132.54/18.97 | End of split % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #207 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 132.54/18.97 (2) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.54/18.97 (3) ~ (all_53_8 = e1) % 132.54/18.97 (4) ~ (op(e2, e1) = e1) % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | BETA: splitting (1) gives: % 132.54/18.97 | % 132.54/18.97 | Case 1: % 132.54/18.97 | | % 132.54/18.97 | | (5) all_57_4 = e1 & op(e3, e1) = e1 % 132.54/18.97 | | % 132.54/18.97 | | ALPHA: (5) implies: % 132.54/18.97 | | (6) op(e3, e1) = e1 % 132.54/18.97 | | % 132.54/18.97 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #238. % 132.54/18.97 | | % 132.54/18.97 | Case 2: % 132.54/18.97 | | % 132.54/18.97 | | (7) all_57_5 = e1 & op(e2, e1) = e1 % 132.54/18.97 | | % 132.54/18.97 | | ALPHA: (7) implies: % 132.54/18.97 | | (8) op(e2, e1) = e1 % 132.54/18.97 | | % 132.54/18.97 | | PRED_UNIFY: (4), (8) imply: % 132.54/18.97 | | (9) $false % 132.54/18.97 | | % 132.54/18.97 | | CLOSE: (9) is inconsistent. % 132.54/18.97 | | % 132.54/18.97 | End of split % 132.54/18.97 | % 132.54/18.97 End of proof % 132.54/18.97 % 132.54/18.97 Sub-proof #208 shows that the following formulas are inconsistent: % 132.54/18.97 ---------------------------------------------------------------- % 132.54/18.97 (1) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.54/18.97 (2) ~ (all_53_8 = all_4_2) % 132.54/18.97 (3) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 132.54/18.97 (4) unit = e2 | unit = e1 | unit = e0 % 132.54/18.97 (5) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.54/18.97 (6) ~ (all_34_2 = e1) | (op(e3, e1) = all_34_1 & $i(all_34_1) & ( ~ % 132.54/18.97 (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e3, e2) = all_34_0 & % 132.54/18.97 $i(all_34_0)))) % 132.54/18.97 (7) ~ (all_53_8 = all_53_12) % 132.54/18.97 (8) op(e2, unit) = e2 % 132.54/18.97 (9) all_55_9 = all_53_6 % 132.54/18.97 (10) all_55_11 = all_22_1 % 132.54/18.97 (11) ~ (all_53_2 = all_22_1) % 132.54/18.97 (12) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 132.54/18.97 (13) ~ (all_53_3 = e0) % 132.54/18.97 (14) ~ (all_53_2 = e0) % 132.54/18.97 (15) ~ (all_53_8 = e0) % 132.54/18.97 (16) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 132.54/18.97 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.54/18.97 (17) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.54/18.97 (18) ~ (all_53_13 = all_6_2) % 132.54/18.97 (19) all_55_5 = all_6_2 % 132.54/18.97 (20) ~ (all_53_4 = all_53_8) % 132.54/18.97 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.54/18.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.54/18.97 (22) all_55_3 = all_53_12 % 132.54/18.97 (23) all_55_2 = all_53_8 % 132.54/18.97 (24) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.54/18.97 (25) ~ (all_53_4 = all_4_2) % 132.54/18.97 (26) ~ (all_53_1 = all_53_2) % 132.54/18.97 (27) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.54/18.97 (28) all_55_8 = all_53_2 % 132.54/18.97 (29) op(e2, e3) = all_53_1 % 132.54/18.97 (30) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 132.54/18.97 $i(all_22_0)) % 132.54/18.97 (31) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.54/18.97 (32) ~ (all_6_2 = e3) % 132.54/18.97 (33) op(e1, e3) = all_53_2 % 132.54/18.97 (34) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.54/18.97 (35) all_53_4 = e3 | ~ (op(e3, e2) = e3) % 132.54/18.97 (36) op(e3, e3) = all_4_2 % 132.54/18.97 (37) ~ (all_6_2 = e1) % 132.54/18.97 (38) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 132.54/18.97 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 132.54/18.97 (39) op(e1, unit) = e1 % 132.54/18.97 (40) ~ (all_53_2 = all_53_6) % 132.54/18.97 (41) ~ (all_53_2 = all_4_2) % 132.54/18.97 (42) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.54/18.97 (43) ~ (all_53_12 = e0) % 132.54/18.97 (44) ~ (all_4_2 = e2) % 132.54/18.97 (45) ~ (unit = e1) % 132.54/18.97 (46) all_34_2 = all_4_2 % 132.54/18.97 (47) op(e3, e1) = all_53_8 % 132.54/18.97 (48) ~ (all_53_6 = all_22_1) % 132.54/18.97 (49) ~ (all_53_12 = all_4_2) % 132.54/18.97 (50) op(e3, unit) = e3 % 132.54/18.97 (51) ~ (all_53_4 = all_6_2) % 132.54/18.97 (52) op(e3, e2) = all_53_4 % 132.54/18.97 (53) ~ (all_53_4 = all_53_12) % 132.54/18.97 (54) ~ (all_22_1 = e0) % 132.54/18.97 (55) ~ (all_4_2 = e0) % 132.54/18.97 (56) all_55_0 = all_4_2 % 132.54/18.97 % 132.54/18.97 Begin of proof % 132.54/18.97 | % 132.54/18.97 | BETA: splitting (16) gives: % 132.54/18.97 | % 132.54/18.97 | Case 1: % 132.54/18.97 | | % 132.54/18.97 | | (57) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 132.54/18.97 | | e0) % 132.54/18.97 | | % 132.54/18.97 | | BETA: splitting (57) gives: % 132.54/18.97 | | % 132.54/18.97 | | Case 1: % 132.54/18.97 | | | % 132.54/18.97 | | | (58) all_57_0 = e0 & op(e3, e3) = e0 % 132.54/18.97 | | | % 132.54/18.97 | | | REF_CLOSE: (21), (36), (55), (58) are inconsistent by sub-proof #270. % 132.54/18.97 | | | % 132.54/18.97 | | Case 2: % 132.54/18.97 | | | % 132.54/18.97 | | | (59) all_57_1 = e0 & op(e3, e2) = e0 % 132.54/18.97 | | | % 132.54/18.97 | | | ALPHA: (59) implies: % 132.54/18.97 | | | (60) op(e3, e2) = e0 % 132.54/18.97 | | | % 132.54/18.97 | | | BETA: splitting (38) gives: % 132.54/18.97 | | | % 132.54/18.97 | | | Case 1: % 132.54/18.97 | | | | % 132.54/18.97 | | | | (61) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) % 132.54/18.97 | | | | = e0) % 132.54/18.97 | | | | % 132.54/18.97 | | | | BETA: splitting (61) gives: % 132.54/18.97 | | | | % 132.54/18.97 | | | | Case 1: % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | (62) all_57_0 = e0 & op(e3, e3) = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | ALPHA: (62) implies: % 132.54/18.97 | | | | | (63) op(e3, e3) = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | GROUND_INST: instantiating (21) with all_4_2, e0, e3, e3, simplifying % 132.54/18.97 | | | | | with (36), (63) gives: % 132.54/18.97 | | | | | (64) all_4_2 = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | REDUCE: (55), (64) imply: % 132.54/18.97 | | | | | (65) $false % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | CLOSE: (65) is inconsistent. % 132.54/18.97 | | | | | % 132.54/18.97 | | | | Case 2: % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | (66) all_57_2 = e0 & op(e2, e3) = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | ALPHA: (66) implies: % 132.54/18.97 | | | | | (67) op(e2, e3) = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | GROUND_INST: instantiating (21) with all_53_1, e0, e3, e2, simplifying % 132.54/18.97 | | | | | with (29), (67) gives: % 132.54/18.97 | | | | | (68) all_53_1 = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | GROUND_INST: instantiating (21) with all_53_4, e0, e2, e3, simplifying % 132.54/18.97 | | | | | with (52), (60) gives: % 132.54/18.97 | | | | | (69) all_53_4 = e0 % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | GROUND_INST: instantiating (21) with e3, e0, e2, e3, simplifying with % 132.54/18.97 | | | | | (60) gives: % 132.54/18.97 | | | | | (70) e3 = e0 | ~ (op(e3, e2) = e3) % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | REDUCE: (26), (68) imply: % 132.54/18.97 | | | | | (71) ~ (all_53_2 = e0) % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | REDUCE: (20), (69) imply: % 132.54/18.97 | | | | | (72) ~ (all_53_8 = e0) % 132.54/18.97 | | | | | % 132.54/18.97 | | | | | REDUCE: (53), (69) imply: % 132.78/18.97 | | | | | (73) ~ (all_53_12 = e0) % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | REDUCE: (51), (69) imply: % 132.78/18.97 | | | | | (74) ~ (all_6_2 = e0) % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | SIMP: (74) implies: % 132.78/18.97 | | | | | (75) ~ (all_6_2 = e0) % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | REDUCE: (25), (69) imply: % 132.78/18.97 | | | | | (76) ~ (all_4_2 = e0) % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | BETA: splitting (34) gives: % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | Case 1: % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | (77) all_55_5 = e3 % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | COMBINE_EQS: (19), (77) imply: % 132.78/18.97 | | | | | | (78) all_6_2 = e3 % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | REDUCE: (32), (78) imply: % 132.78/18.97 | | | | | | (79) $false % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | CLOSE: (79) is inconsistent. % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | Case 2: % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | (80) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | BETA: splitting (80) gives: % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | | Case 1: % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | (81) all_55_5 = e2 % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | COMBINE_EQS: (19), (81) imply: % 132.78/18.97 | | | | | | | (82) all_6_2 = e2 % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | REDUCE: (18), (82) imply: % 132.78/18.97 | | | | | | | (83) ~ (all_53_13 = e2) % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | BETA: splitting (6) gives: % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | Case 1: % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | (84) ~ (all_34_2 = e1) % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | REDUCE: (46), (84) imply: % 132.78/18.97 | | | | | | | | (85) ~ (all_4_2 = e1) % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | BETA: splitting (1) gives: % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | Case 1: % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | (86) all_55_0 = e3 % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | COMBINE_EQS: (56), (86) imply: % 132.78/18.97 | | | | | | | | | (87) all_4_2 = e3 % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | REDUCE: (41), (87) imply: % 132.78/18.97 | | | | | | | | | (88) ~ (all_53_2 = e3) % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | REF_CLOSE: (4), (8), (9), (10), (11), (14), (17), (21), (27), % 132.78/18.97 | | | | | | | | | (28), (30), (31), (33), (39), (40), (42), (45), % 132.78/18.97 | | | | | | | | | (48), (54), (83), (88) are inconsistent by % 132.78/18.97 | | | | | | | | | sub-proof #214. % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | Case 2: % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | (89) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | REF_CLOSE: (44), (55), (56), (85), (89) are inconsistent by % 132.78/18.97 | | | | | | | | | sub-proof #274. % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | End of split % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | Case 2: % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | (90) all_34_2 = e1 % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | COMBINE_EQS: (46), (90) imply: % 132.78/18.97 | | | | | | | | (91) all_4_2 = e1 % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | SIMP: (91) implies: % 132.78/18.97 | | | | | | | | (92) all_4_2 = e1 % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | REDUCE: (2), (92) imply: % 132.78/18.97 | | | | | | | | (93) ~ (all_53_8 = e1) % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | REDUCE: (49), (92) imply: % 132.78/18.97 | | | | | | | | (94) ~ (all_53_12 = e1) % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | BETA: splitting (70) gives: % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | | Case 1: % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | (95) ~ (op(e3, e2) = e3) % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | PRED_UNIFY: (50), (95) imply: % 132.78/18.97 | | | | | | | | | (96) ~ (unit = e2) % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | REF_CLOSE: (4), (8), (31), (45), (83), (96) are inconsistent % 132.78/18.97 | | | | | | | | | by sub-proof #217. % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | Case 2: % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | (97) op(e3, e2) = e3 % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | | REF_CLOSE: (5), (7), (12), (15), (20), (22), (23), (35), (43), % 132.78/18.97 | | | | | | | | | (53), (93), (94), (97) are inconsistent by % 132.78/18.97 | | | | | | | | | sub-proof #211. % 132.78/18.97 | | | | | | | | | % 132.78/18.97 | | | | | | | | End of split % 132.78/18.97 | | | | | | | | % 132.78/18.97 | | | | | | | End of split % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | Case 2: % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | (98) all_55_5 = e1 | all_55_5 = e0 % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | | REF_CLOSE: (19), (37), (75), (98) are inconsistent by sub-proof % 132.78/18.97 | | | | | | | #251. % 132.78/18.97 | | | | | | | % 132.78/18.97 | | | | | | End of split % 132.78/18.97 | | | | | | % 132.78/18.97 | | | | | End of split % 132.78/18.97 | | | | | % 132.78/18.97 | | | | End of split % 132.78/18.97 | | | | % 132.78/18.97 | | | Case 2: % 132.78/18.97 | | | | % 132.78/18.97 | | | | (99) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) % 132.78/18.97 | | | | = e0) % 132.78/18.97 | | | | % 132.78/18.97 | | | | BETA: splitting (99) gives: % 132.78/18.97 | | | | % 132.78/18.97 | | | | Case 1: % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | (100) all_57_6 = e0 & op(e1, e3) = e0 % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | ALPHA: (100) implies: % 132.78/18.97 | | | | | (101) op(e1, e3) = e0 % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | GROUND_INST: instantiating (21) with all_53_2, e0, e3, e1, simplifying % 132.78/18.97 | | | | | with (33), (101) gives: % 132.78/18.97 | | | | | (102) all_53_2 = e0 % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | REDUCE: (14), (102) imply: % 132.78/18.97 | | | | | (103) $false % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | CLOSE: (103) is inconsistent. % 132.78/18.97 | | | | | % 132.78/18.97 | | | | Case 2: % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | (104) all_57_12 = e0 & op(e0, e3) = e0 % 132.78/18.97 | | | | | % 132.78/18.97 | | | | | REF_CLOSE: (13), (24), (104) are inconsistent by sub-proof #237. % 132.78/18.97 | | | | | % 132.78/18.97 | | | | End of split % 132.78/18.97 | | | | % 132.78/18.97 | | | End of split % 132.78/18.97 | | | % 132.78/18.97 | | End of split % 132.78/18.97 | | % 132.78/18.97 | Case 2: % 132.78/18.97 | | % 132.78/18.97 | | (105) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 132.78/18.97 | | e0) % 132.78/18.97 | | % 132.78/18.97 | | REF_CLOSE: (3), (15), (21), (43), (47), (105) are inconsistent by sub-proof % 132.78/18.97 | | #209. % 132.78/18.97 | | % 132.78/18.97 | End of split % 132.78/18.97 | % 132.78/18.97 End of proof % 132.78/18.97 % 132.78/18.97 Sub-proof #209 shows that the following formulas are inconsistent: % 132.78/18.97 ---------------------------------------------------------------- % 132.78/18.97 (1) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 132.78/18.97 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.78/18.97 (3) ~ (all_53_8 = e0) % 132.78/18.97 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.97 (5) ~ (all_53_12 = e0) % 132.78/18.97 (6) op(e3, e1) = all_53_8 % 132.78/18.97 % 132.78/18.97 Begin of proof % 132.78/18.97 | % 132.78/18.97 | BETA: splitting (2) gives: % 132.78/18.97 | % 132.78/18.97 | Case 1: % 132.78/18.97 | | % 132.78/18.97 | | (7) all_57_4 = e0 & op(e3, e1) = e0 % 132.78/18.97 | | % 132.78/18.97 | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #210. % 132.78/18.97 | | % 132.78/18.97 | Case 2: % 132.78/18.97 | | % 132.78/18.97 | | (8) all_57_9 = e0 & op(e3, e0) = e0 % 132.78/18.97 | | % 132.78/18.97 | | ALPHA: (8) implies: % 132.78/18.97 | | (9) op(e3, e0) = e0 % 132.78/18.97 | | % 132.78/18.97 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #256. % 132.78/18.97 | | % 132.78/18.97 | End of split % 132.78/18.97 | % 132.78/18.97 End of proof % 132.78/18.97 % 132.78/18.97 Sub-proof #210 shows that the following formulas are inconsistent: % 132.78/18.97 ---------------------------------------------------------------- % 132.78/18.97 (1) all_57_4 = e0 & op(e3, e1) = e0 % 132.78/18.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.97 (3) op(e3, e1) = all_53_8 % 132.78/18.97 (4) ~ (all_53_8 = e0) % 132.78/18.97 % 132.78/18.97 Begin of proof % 132.78/18.97 | % 132.78/18.97 | ALPHA: (1) implies: % 132.78/18.97 | (5) op(e3, e1) = e0 % 132.78/18.97 | % 132.78/18.97 | GROUND_INST: instantiating (2) with all_53_8, e0, e1, e3, simplifying with % 132.78/18.97 | (3), (5) gives: % 132.78/18.97 | (6) all_53_8 = e0 % 132.78/18.97 | % 132.78/18.97 | REDUCE: (4), (6) imply: % 132.78/18.97 | (7) $false % 132.78/18.97 | % 132.78/18.97 | CLOSE: (7) is inconsistent. % 132.78/18.97 | % 132.78/18.97 End of proof % 132.78/18.97 % 132.78/18.97 Sub-proof #211 shows that the following formulas are inconsistent: % 132.78/18.97 ---------------------------------------------------------------- % 132.78/18.97 (1) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.78/18.97 (2) ~ (all_53_8 = all_53_12) % 132.78/18.97 (3) ~ (all_53_12 = e1) % 132.78/18.97 (4) all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 132.78/18.97 (5) ~ (all_53_8 = e0) % 132.78/18.97 (6) ~ (all_53_4 = all_53_8) % 132.78/18.97 (7) all_55_3 = all_53_12 % 132.78/18.97 (8) all_55_2 = all_53_8 % 132.78/18.97 (9) all_53_4 = e3 | ~ (op(e3, e2) = e3) % 132.78/18.97 (10) ~ (all_53_12 = e0) % 132.78/18.97 (11) ~ (all_53_8 = e1) % 132.78/18.98 (12) op(e3, e2) = e3 % 132.78/18.98 (13) ~ (all_53_4 = all_53_12) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (9) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (14) ~ (op(e3, e2) = e3) % 132.78/18.98 | | % 132.78/18.98 | | PRED_UNIFY: (12), (14) imply: % 132.78/18.98 | | (15) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (15) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (16) all_53_4 = e3 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (6), (16) imply: % 132.78/18.98 | | (17) ~ (all_53_8 = e3) % 132.78/18.98 | | % 132.78/18.98 | | SIMP: (17) implies: % 132.78/18.98 | | (18) ~ (all_53_8 = e3) % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (13), (16) imply: % 132.78/18.98 | | (19) ~ (all_53_12 = e3) % 132.78/18.98 | | % 132.78/18.98 | | SIMP: (19) implies: % 132.78/18.98 | | (20) ~ (all_53_12 = e3) % 132.78/18.98 | | % 132.78/18.98 | | BETA: splitting (4) gives: % 132.78/18.98 | | % 132.78/18.98 | | Case 1: % 132.78/18.98 | | | % 132.78/18.98 | | | (21) all_55_3 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | COMBINE_EQS: (7), (21) imply: % 132.78/18.98 | | | (22) all_53_12 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | REDUCE: (20), (22) imply: % 132.78/18.98 | | | (23) $false % 132.78/18.98 | | | % 132.78/18.98 | | | CLOSE: (23) is inconsistent. % 132.78/18.98 | | | % 132.78/18.98 | | Case 2: % 132.78/18.98 | | | % 132.78/18.98 | | | (24) all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0 % 132.78/18.98 | | | % 132.78/18.98 | | | BETA: splitting (24) gives: % 132.78/18.98 | | | % 132.78/18.98 | | | Case 1: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (25) all_55_3 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | COMBINE_EQS: (7), (25) imply: % 132.78/18.98 | | | | (26) all_53_12 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REDUCE: (2), (26) imply: % 132.78/18.98 | | | | (27) ~ (all_53_8 = e2) % 132.78/18.98 | | | | % 132.78/18.98 | | | | REF_CLOSE: (1), (5), (8), (11), (18), (27) are inconsistent by sub-proof % 132.78/18.98 | | | | #212. % 132.78/18.98 | | | | % 132.78/18.98 | | | Case 2: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (28) all_55_3 = e1 | all_55_3 = e0 % 132.78/18.98 | | | | % 132.78/18.98 | | | | BETA: splitting (28) gives: % 132.78/18.98 | | | | % 132.78/18.98 | | | | Case 1: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (29) all_55_3 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (7), (29) imply: % 132.78/18.98 | | | | | (30) all_53_12 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (3), (30) imply: % 132.78/18.98 | | | | | (31) $false % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | CLOSE: (31) is inconsistent. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | Case 2: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (32) all_55_3 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (7), (32) imply: % 132.78/18.98 | | | | | (33) all_53_12 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (10), (33) imply: % 132.78/18.98 | | | | | (34) $false % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | CLOSE: (34) is inconsistent. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | End of split % 132.78/18.98 | | | | % 132.78/18.98 | | | End of split % 132.78/18.98 | | | % 132.78/18.98 | | End of split % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #212 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) ~ (all_53_8 = e3) % 132.78/18.98 (2) all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.78/18.98 (3) ~ (all_53_8 = e2) % 132.78/18.98 (4) ~ (all_53_8 = e0) % 132.78/18.98 (5) all_55_2 = all_53_8 % 132.78/18.98 (6) ~ (all_53_8 = e1) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (2) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (7) all_55_2 = e3 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (5), (7) imply: % 132.78/18.98 | | (8) all_53_8 = e3 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (1), (8) imply: % 132.78/18.98 | | (9) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (9) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (10) all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0 % 132.78/18.98 | | % 132.78/18.98 | | BETA: splitting (10) gives: % 132.78/18.98 | | % 132.78/18.98 | | Case 1: % 132.78/18.98 | | | % 132.78/18.98 | | | (11) all_55_2 = e2 % 132.78/18.98 | | | % 132.78/18.98 | | | COMBINE_EQS: (5), (11) imply: % 132.78/18.98 | | | (12) all_53_8 = e2 % 132.78/18.98 | | | % 132.78/18.98 | | | REDUCE: (3), (12) imply: % 132.78/18.98 | | | (13) $false % 132.78/18.98 | | | % 132.78/18.98 | | | CLOSE: (13) is inconsistent. % 132.78/18.98 | | | % 132.78/18.98 | | Case 2: % 132.78/18.98 | | | % 132.78/18.98 | | | (14) all_55_2 = e1 | all_55_2 = e0 % 132.78/18.98 | | | % 132.78/18.98 | | | REF_CLOSE: (4), (5), (6), (14) are inconsistent by sub-proof #213. % 132.78/18.98 | | | % 132.78/18.98 | | End of split % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #213 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_55_2 = e1 | all_55_2 = e0 % 132.78/18.98 (2) all_55_2 = all_53_8 % 132.78/18.98 (3) ~ (all_53_8 = e1) % 132.78/18.98 (4) ~ (all_53_8 = e0) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (1) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (5) all_55_2 = e1 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (2), (5) imply: % 132.78/18.98 | | (6) all_53_8 = e1 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (3), (6) imply: % 132.78/18.98 | | (7) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (7) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (8) all_55_2 = e0 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (2), (8) imply: % 132.78/18.98 | | (9) all_53_8 = e0 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (4), (9) imply: % 132.78/18.98 | | (10) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (10) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #214 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) unit = e2 | unit = e1 | unit = e0 % 132.78/18.98 (2) op(e2, unit) = e2 % 132.78/18.98 (3) all_55_9 = all_53_6 % 132.78/18.98 (4) all_55_11 = all_22_1 % 132.78/18.98 (5) ~ (all_53_2 = all_22_1) % 132.78/18.98 (6) ~ (all_53_2 = e0) % 132.78/18.98 (7) ~ (all_53_13 = e2) % 132.78/18.98 (8) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.78/18.98 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.98 (10) all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.78/18.98 (11) all_55_8 = all_53_2 % 132.78/18.98 (12) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 132.78/18.98 $i(all_22_0)) % 132.78/18.98 (13) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.78/18.98 (14) op(e1, e3) = all_53_2 % 132.78/18.98 (15) op(e1, unit) = e1 % 132.78/18.98 (16) ~ (all_53_2 = all_53_6) % 132.78/18.98 (17) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/18.98 (18) ~ (all_53_2 = e3) % 132.78/18.98 (19) ~ (unit = e1) % 132.78/18.98 (20) ~ (all_53_6 = all_22_1) % 132.78/18.98 (21) ~ (all_22_1 = e0) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (17) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (22) ~ (op(e1, e2) = e1) % 132.78/18.98 | | % 132.78/18.98 | | PRED_UNIFY: (15), (22) imply: % 132.78/18.98 | | (23) ~ (unit = e2) % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (1), (2), (7), (13), (19), (23) are inconsistent by sub-proof % 132.78/18.98 | | #217. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (24) all_55_9 = e1 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (3), (24) imply: % 132.78/18.98 | | (25) all_53_6 = e1 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (16), (25) imply: % 132.78/18.98 | | (26) ~ (all_53_2 = e1) % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (20), (25) imply: % 132.78/18.98 | | (27) ~ (all_22_1 = e1) % 132.78/18.98 | | % 132.78/18.98 | | SIMP: (27) implies: % 132.78/18.98 | | (28) ~ (all_22_1 = e1) % 132.78/18.98 | | % 132.78/18.98 | | BETA: splitting (10) gives: % 132.78/18.98 | | % 132.78/18.98 | | Case 1: % 132.78/18.98 | | | % 132.78/18.98 | | | (29) all_55_8 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | COMBINE_EQS: (11), (29) imply: % 132.78/18.98 | | | (30) all_53_2 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | SIMP: (30) implies: % 132.78/18.98 | | | (31) all_53_2 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | REDUCE: (18), (31) imply: % 132.78/18.98 | | | (32) $false % 132.78/18.98 | | | % 132.78/18.98 | | | CLOSE: (32) is inconsistent. % 132.78/18.98 | | | % 132.78/18.98 | | Case 2: % 132.78/18.98 | | | % 132.78/18.98 | | | (33) all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0 % 132.78/18.98 | | | % 132.78/18.98 | | | BETA: splitting (33) gives: % 132.78/18.98 | | | % 132.78/18.98 | | | Case 1: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (34) all_55_8 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | COMBINE_EQS: (11), (34) imply: % 132.78/18.98 | | | | (35) all_53_2 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | SIMP: (35) implies: % 132.78/18.98 | | | | (36) all_53_2 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REDUCE: (5), (36) imply: % 132.78/18.98 | | | | (37) ~ (all_22_1 = e2) % 132.78/18.98 | | | | % 132.78/18.98 | | | | SIMP: (37) implies: % 132.78/18.98 | | | | (38) ~ (all_22_1 = e2) % 132.78/18.98 | | | | % 132.78/18.98 | | | | REDUCE: (14), (36) imply: % 132.78/18.98 | | | | (39) op(e1, e3) = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REF_CLOSE: (4), (8), (9), (12), (21), (28), (38), (39) are inconsistent % 132.78/18.98 | | | | by sub-proof #216. % 132.78/18.98 | | | | % 132.78/18.98 | | | Case 2: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (40) all_55_8 = e1 | all_55_8 = e0 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REF_CLOSE: (6), (11), (26), (40) are inconsistent by sub-proof #215. % 132.78/18.98 | | | | % 132.78/18.98 | | | End of split % 132.78/18.98 | | | % 132.78/18.98 | | End of split % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #215 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_55_8 = e1 | all_55_8 = e0 % 132.78/18.98 (2) all_55_8 = all_53_2 % 132.78/18.98 (3) ~ (all_53_2 = e1) % 132.78/18.98 (4) ~ (all_53_2 = e0) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (1) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (5) all_55_8 = e1 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (2), (5) imply: % 132.78/18.98 | | (6) all_53_2 = e1 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (3), (6) imply: % 132.78/18.98 | | (7) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (7) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (8) all_55_8 = e0 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (2), (8) imply: % 132.78/18.98 | | (9) all_53_2 = e0 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (4), (9) imply: % 132.78/18.98 | | (10) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (10) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #216 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) ~ (all_22_1 = e1) % 132.78/18.98 (2) all_55_11 = all_22_1 % 132.78/18.98 (3) op(e1, e3) = e2 % 132.78/18.98 (4) all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.78/18.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.98 (6) ~ (all_22_1 = e3) | ( ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & % 132.78/18.98 $i(all_22_0)) % 132.78/18.98 (7) ~ (all_22_1 = e2) % 132.78/18.98 (8) ~ (all_22_1 = e0) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (6) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (9) ~ (all_22_1 = e3) % 132.78/18.98 | | % 132.78/18.98 | | BETA: splitting (4) gives: % 132.78/18.98 | | % 132.78/18.98 | | Case 1: % 132.78/18.98 | | | % 132.78/18.98 | | | (10) all_55_11 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | COMBINE_EQS: (2), (10) imply: % 132.78/18.98 | | | (11) all_22_1 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | SIMP: (11) implies: % 132.78/18.98 | | | (12) all_22_1 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | REDUCE: (9), (12) imply: % 132.78/18.98 | | | (13) $false % 132.78/18.98 | | | % 132.78/18.98 | | | CLOSE: (13) is inconsistent. % 132.78/18.98 | | | % 132.78/18.98 | | Case 2: % 132.78/18.98 | | | % 132.78/18.98 | | | (14) all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0 % 132.78/18.98 | | | % 132.78/18.98 | | | BETA: splitting (14) gives: % 132.78/18.98 | | | % 132.78/18.98 | | | Case 1: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (15) all_55_11 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | COMBINE_EQS: (2), (15) imply: % 132.78/18.98 | | | | (16) all_22_1 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | SIMP: (16) implies: % 132.78/18.98 | | | | (17) all_22_1 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REDUCE: (7), (17) imply: % 132.78/18.98 | | | | (18) $false % 132.78/18.98 | | | | % 132.78/18.98 | | | | CLOSE: (18) is inconsistent. % 132.78/18.98 | | | | % 132.78/18.98 | | | Case 2: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (19) all_55_11 = e1 | all_55_11 = e0 % 132.78/18.98 | | | | % 132.78/18.98 | | | | BETA: splitting (19) gives: % 132.78/18.98 | | | | % 132.78/18.98 | | | | Case 1: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (20) all_55_11 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (2), (20) imply: % 132.78/18.98 | | | | | (21) all_22_1 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | SIMP: (21) implies: % 132.78/18.98 | | | | | (22) all_22_1 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (1), (22) imply: % 132.78/18.98 | | | | | (23) $false % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | CLOSE: (23) is inconsistent. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | Case 2: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (24) all_55_11 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (2), (24) imply: % 132.78/18.98 | | | | | (25) all_22_1 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | SIMP: (25) implies: % 132.78/18.98 | | | | | (26) all_22_1 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (8), (26) imply: % 132.78/18.98 | | | | | (27) $false % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | CLOSE: (27) is inconsistent. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | End of split % 132.78/18.98 | | | | % 132.78/18.98 | | | End of split % 132.78/18.98 | | | % 132.78/18.98 | | End of split % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (28) ~ (all_22_0 = e2) & op(e1, e3) = all_22_0 & $i(all_22_0) % 132.78/18.98 | | % 132.78/18.98 | | ALPHA: (28) implies: % 132.78/18.98 | | (29) ~ (all_22_0 = e2) % 132.78/18.98 | | (30) op(e1, e3) = all_22_0 % 132.78/18.98 | | % 132.78/18.98 | | GROUND_INST: instantiating (5) with e2, all_22_0, e3, e1, simplifying with % 132.78/18.98 | | (3), (30) gives: % 132.78/18.98 | | (31) all_22_0 = e2 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (29), (31) imply: % 132.78/18.98 | | (32) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (32) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #217 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) unit = e2 | unit = e1 | unit = e0 % 132.78/18.98 (2) op(e2, unit) = e2 % 132.78/18.98 (3) ~ (unit = e2) % 132.78/18.98 (4) ~ (all_53_13 = e2) % 132.78/18.98 (5) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.78/18.98 (6) ~ (unit = e1) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (1) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (7) unit = e2 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (3), (7) imply: % 132.78/18.98 | | (8) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (8) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (9) unit = e1 | unit = e0 % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (2), (4), (5), (6), (9) are inconsistent by sub-proof #218. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #218 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) op(e2, unit) = e2 % 132.78/18.98 (2) ~ (all_53_13 = e2) % 132.78/18.98 (3) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.78/18.98 (4) ~ (unit = e1) % 132.78/18.98 (5) unit = e1 | unit = e0 % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (5) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (6) unit = e1 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (4), (6) imply: % 132.78/18.98 | | (7) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (7) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (8) unit = e0 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (1), (8) imply: % 132.78/18.98 | | (9) op(e2, e0) = e2 % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #225. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #219 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_55_10 = all_12_2 % 132.78/18.98 (2) all_55_10 = e0 % 132.78/18.98 (3) ~ (all_12_2 = e0) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | COMBINE_EQS: (1), (2) imply: % 132.78/18.98 | (4) all_12_2 = e0 % 132.78/18.98 | % 132.78/18.98 | SIMP: (4) implies: % 132.78/18.98 | (5) all_12_2 = e0 % 132.78/18.98 | % 132.78/18.98 | REDUCE: (3), (5) imply: % 132.78/18.98 | (6) $false % 132.78/18.98 | % 132.78/18.98 | CLOSE: (6) is inconsistent. % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #220 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_57_10 = e1 & op(e2, e0) = e1 % 132.78/18.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.98 (3) op(e2, e0) = all_53_13 % 132.78/18.98 (4) ~ (all_53_13 = e1) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | ALPHA: (1) implies: % 132.78/18.98 | (5) op(e2, e0) = e1 % 132.78/18.98 | % 132.78/18.98 | GROUND_INST: instantiating (2) with all_53_13, e1, e0, e2, simplifying with % 132.78/18.98 | (3), (5) gives: % 132.78/18.98 | (6) all_53_13 = e1 % 132.78/18.98 | % 132.78/18.98 | REDUCE: (4), (6) imply: % 132.78/18.98 | (7) $false % 132.78/18.98 | % 132.78/18.98 | CLOSE: (7) is inconsistent. % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #221 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/18.98 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.98 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/18.98 (4) op(unit, e0) = e0 % 132.78/18.98 (5) ~ (all_8_2 = e3) % 132.78/18.98 (6) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.98 (7) ~ (all_53_7 = all_8_2) % 132.78/18.98 (8) ~ (unit = e2) % 132.78/18.98 (9) op(unit, e2) = e2 % 132.78/18.98 (10) all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.78/18.98 (11) ~ (all_28_2 = e2) | (op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ % 132.78/18.98 (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 132.78/18.98 $i(all_28_0)))) % 132.78/18.98 (12) ~ (all_8_2 = e1) % 132.78/18.98 (13) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.78/18.98 (14) op(e1, unit) = e1 % 132.78/18.98 (15) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.98 (16) all_55_15 = all_8_2 % 132.78/18.98 (17) ~ (all_53_14 = e1) % 132.78/18.98 (18) ~ (all_53_2 = e3) % 132.78/18.98 (19) ~ (all_53_13 = all_8_2) % 132.78/18.98 (20) all_28_2 = all_8_2 % 132.78/18.98 (21) op(unit, e3) = e3 % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (11) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (22) ~ (all_28_2 = e2) % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (20), (22) imply: % 132.78/18.98 | | (23) ~ (all_8_2 = e2) % 132.78/18.98 | | % 132.78/18.98 | | BETA: splitting (10) gives: % 132.78/18.98 | | % 132.78/18.98 | | Case 1: % 132.78/18.98 | | | % 132.78/18.98 | | | (24) all_55_15 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | COMBINE_EQS: (16), (24) imply: % 132.78/18.98 | | | (25) all_8_2 = e3 % 132.78/18.98 | | | % 132.78/18.98 | | | REDUCE: (5), (25) imply: % 132.78/18.98 | | | (26) $false % 132.78/18.98 | | | % 132.78/18.98 | | | CLOSE: (26) is inconsistent. % 132.78/18.98 | | | % 132.78/18.98 | | Case 2: % 132.78/18.98 | | | % 132.78/18.98 | | | (27) all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0 % 132.78/18.98 | | | % 132.78/18.98 | | | BETA: splitting (27) gives: % 132.78/18.98 | | | % 132.78/18.98 | | | Case 1: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (28) all_55_15 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | COMBINE_EQS: (16), (28) imply: % 132.78/18.98 | | | | (29) all_8_2 = e2 % 132.78/18.98 | | | | % 132.78/18.98 | | | | REDUCE: (23), (29) imply: % 132.78/18.98 | | | | (30) $false % 132.78/18.98 | | | | % 132.78/18.98 | | | | CLOSE: (30) is inconsistent. % 132.78/18.98 | | | | % 132.78/18.98 | | | Case 2: % 132.78/18.98 | | | | % 132.78/18.98 | | | | (31) all_55_15 = e1 | all_55_15 = e0 % 132.78/18.98 | | | | % 132.78/18.98 | | | | BETA: splitting (31) gives: % 132.78/18.98 | | | | % 132.78/18.98 | | | | Case 1: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (32) all_55_15 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (16), (32) imply: % 132.78/18.98 | | | | | (33) all_8_2 = e1 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (12), (33) imply: % 132.78/18.98 | | | | | (34) $false % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | CLOSE: (34) is inconsistent. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | Case 2: % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | (35) all_55_15 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | COMBINE_EQS: (16), (35) imply: % 132.78/18.98 | | | | | (36) all_8_2 = e0 % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REDUCE: (19), (36) imply: % 132.78/18.98 | | | | | (37) ~ (all_53_13 = e0) % 132.78/18.98 | | | | | % 132.78/18.98 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (14), (15), (17), (18), (21), (37) % 132.78/18.98 | | | | | are inconsistent by sub-proof #275. % 132.78/18.98 | | | | | % 132.78/18.98 | | | | End of split % 132.78/18.98 | | | | % 132.78/18.98 | | | End of split % 132.78/18.98 | | | % 132.78/18.98 | | End of split % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (38) all_28_2 = e2 % 132.78/18.98 | | % 132.78/18.98 | | COMBINE_EQS: (20), (38) imply: % 132.78/18.98 | | (39) all_8_2 = e2 % 132.78/18.98 | | % 132.78/18.98 | | SIMP: (39) implies: % 132.78/18.98 | | (40) all_8_2 = e2 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (7), (40) imply: % 132.78/18.98 | | (41) ~ (all_53_7 = e2) % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (2), (3), (8), (9), (13), (18), (21), (41) are inconsistent by % 132.78/18.98 | | sub-proof #222. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #222 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.98 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/18.98 (3) ~ (unit = e2) % 132.78/18.98 (4) op(unit, e2) = e2 % 132.78/18.98 (5) all_53_7 = e2 | ~ (op(e0, e2) = e2) % 132.78/18.98 (6) ~ (all_53_7 = e2) % 132.78/18.98 (7) ~ (all_53_2 = e3) % 132.78/18.98 (8) op(unit, e3) = e3 % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (5) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (9) ~ (op(e0, e2) = e2) % 132.78/18.98 | | % 132.78/18.98 | | PRED_UNIFY: (4), (9) imply: % 132.78/18.98 | | (10) ~ (unit = e0) % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (1), (2), (3), (7), (8), (10) are inconsistent by sub-proof #223. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (11) all_53_7 = e2 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (6), (11) imply: % 132.78/18.98 | | (12) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (12) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #223 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) ~ (unit = e0) % 132.78/18.98 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.98 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/18.98 (4) ~ (unit = e2) % 132.78/18.98 (5) ~ (all_53_2 = e3) % 132.78/18.98 (6) op(unit, e3) = e3 % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | BETA: splitting (3) gives: % 132.78/18.98 | % 132.78/18.98 | Case 1: % 132.78/18.98 | | % 132.78/18.98 | | (7) unit = e2 % 132.78/18.98 | | % 132.78/18.98 | | REDUCE: (4), (7) imply: % 132.78/18.98 | | (8) $false % 132.78/18.98 | | % 132.78/18.98 | | CLOSE: (8) is inconsistent. % 132.78/18.98 | | % 132.78/18.98 | Case 2: % 132.78/18.98 | | % 132.78/18.98 | | (9) unit = e1 | unit = e0 % 132.78/18.98 | | % 132.78/18.98 | | REF_CLOSE: (1), (2), (5), (6), (9) are inconsistent by sub-proof #277. % 132.78/18.98 | | % 132.78/18.98 | End of split % 132.78/18.98 | % 132.78/18.98 End of proof % 132.78/18.98 % 132.78/18.98 Sub-proof #224 shows that the following formulas are inconsistent: % 132.78/18.98 ---------------------------------------------------------------- % 132.78/18.98 (1) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/18.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.98 (3) op(e1, e0) = all_53_14 % 132.78/18.98 (4) ~ (all_53_14 = e2) % 132.78/18.98 % 132.78/18.98 Begin of proof % 132.78/18.98 | % 132.78/18.98 | ALPHA: (1) implies: % 132.78/18.98 | (5) op(e1, e0) = e2 % 132.78/18.98 | % 132.78/18.98 | GROUND_INST: instantiating (2) with all_53_14, e2, e0, e1, simplifying with % 132.78/18.98 | (3), (5) gives: % 132.78/18.98 | (6) all_53_14 = e2 % 132.78/18.98 | % 132.78/18.98 | REDUCE: (4), (6) imply: % 132.78/18.99 | (7) $false % 132.78/18.99 | % 132.78/18.99 | CLOSE: (7) is inconsistent. % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #225 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) all_53_13 = e2 | ~ (op(e2, e0) = e2) % 132.78/18.99 (2) op(e2, e0) = e2 % 132.78/18.99 (3) ~ (all_53_13 = e2) % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | BETA: splitting (1) gives: % 132.78/18.99 | % 132.78/18.99 | Case 1: % 132.78/18.99 | | % 132.78/18.99 | | (4) ~ (op(e2, e0) = e2) % 132.78/18.99 | | % 132.78/18.99 | | PRED_UNIFY: (2), (4) imply: % 132.78/18.99 | | (5) $false % 132.78/18.99 | | % 132.78/18.99 | | CLOSE: (5) is inconsistent. % 132.78/18.99 | | % 132.78/18.99 | Case 2: % 132.78/18.99 | | % 132.78/18.99 | | (6) all_53_13 = e2 % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (3), (6) imply: % 132.78/18.99 | | (7) $false % 132.78/18.99 | | % 132.78/18.99 | | CLOSE: (7) is inconsistent. % 132.78/18.99 | | % 132.78/18.99 | End of split % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #226 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.78/18.99 (2) ~ (all_53_2 = all_53_3) % 132.78/18.99 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.99 (4) unit = e2 | unit = e1 | unit = e0 % 132.78/18.99 (5) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/18.99 (6) op(unit, e0) = e0 % 132.78/18.99 (7) op(e1, e1) = e1 % 132.78/18.99 (8) all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 132.78/18.99 (9) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.99 (10) ~ (all_53_6 = all_53_7) % 132.78/18.99 (11) ~ (all_34_2 = e1) | (op(e3, e1) = all_34_1 & $i(all_34_1) & ( ~ % 132.78/18.99 (all_34_1 = e2) | ( ~ (all_34_0 = e0) & op(e3, e2) = all_34_0 & % 132.78/18.99 $i(all_34_0)))) % 132.78/18.99 (12) op(e2, unit) = e2 % 132.78/18.99 (13) all_55_9 = all_53_6 % 132.78/18.99 (14) op(e0, e3) = all_53_3 % 132.78/18.99 (15) op(unit, e2) = e2 % 132.78/18.99 (16) ~ (all_53_11 = e2) % 132.78/18.99 (17) ~ (all_28_1 = e1) | ( ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & % 132.78/18.99 $i(all_28_0)) % 132.78/18.99 (18) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.78/18.99 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.78/18.99 $i(all_42_0)))) % 132.78/18.99 (19) all_22_2 = e1 % 132.78/18.99 (20) op(e0, e2) = all_53_7 % 132.78/18.99 (21) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/18.99 (22) ~ (e3 = e0) % 132.78/18.99 (23) op(e0, e1) = all_53_11 % 132.78/18.99 (24) op(e0, e0) = all_8_2 % 132.78/18.99 (25) ~ (e2 = e0) % 132.78/18.99 (26) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 132.78/18.99 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 132.78/18.99 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 132.78/18.99 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 132.78/18.99 (27) ~ (all_53_13 = all_6_2) % 132.78/18.99 (28) all_55_5 = all_6_2 % 132.78/18.99 (29) ~ (all_8_2 = e1) % 132.78/18.99 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/18.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/18.99 (31) ~ (e3 = e1) % 132.78/18.99 (32) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/18.99 (33) all_55_14 = all_53_11 % 132.78/18.99 (34) ~ (all_53_7 = all_6_2) % 132.78/18.99 (35) ~ (all_6_2 = e3) % 132.78/18.99 (36) ~ (op(e0, e2) = e2) % 132.78/18.99 (37) all_53_7 = all_28_1 % 132.78/18.99 (38) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/18.99 (39) ~ (all_53_3 = all_4_2) % 132.78/18.99 (40) ~ (all_6_2 = e1) % 132.78/18.99 (41) op(e1, unit) = e1 % 132.78/18.99 (42) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/18.99 (43) ~ (all_53_6 = e1) % 132.78/18.99 (44) ~ (all_53_2 = all_4_2) % 132.78/18.99 (45) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/18.99 (46) ~ (all_53_7 = all_53_11) % 132.78/18.99 (47) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 132.78/18.99 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 132.78/18.99 e1) % 132.78/18.99 (48) all_57_15 = e2 % 132.78/18.99 (49) op(e0, e2) = all_36_1 % 132.78/18.99 (50) ~ (all_53_9 = all_6_2) % 132.78/18.99 (51) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 132.78/18.99 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 132.78/18.99 e3) % 132.78/18.99 (52) all_42_2 = all_6_2 % 132.78/18.99 (53) ~ (all_4_2 = e2) % 132.78/18.99 (54) ~ (e3 = e2) % 132.78/18.99 (55) all_34_2 = all_4_2 % 132.78/18.99 (56) op(unit, e3) = e3 % 132.78/18.99 (57) ~ (all_53_11 = e1) % 132.78/18.99 (58) all_55_12 = all_53_3 % 132.78/18.99 (59) all_55_12 = e0 | ~ (op(e0, e3) = e0) % 132.78/18.99 (60) ~ (all_4_2 = e0) % 132.78/18.99 (61) ~ (all_53_3 = all_53_11) % 132.78/18.99 (62) all_55_0 = all_4_2 % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | GROUND_INST: instantiating (30) with all_53_7, all_36_1, e2, e0, simplifying % 132.78/18.99 | with (20), (49) gives: % 132.78/18.99 | (63) all_53_7 = all_36_1 % 132.78/18.99 | % 132.78/18.99 | PRED_UNIFY: (15), (36) imply: % 132.78/18.99 | (64) ~ (unit = e0) % 132.78/18.99 | % 132.78/18.99 | COMBINE_EQS: (37), (63) imply: % 132.78/18.99 | (65) all_36_1 = all_28_1 % 132.78/18.99 | % 132.78/18.99 | SIMP: (65) implies: % 132.78/18.99 | (66) all_36_1 = all_28_1 % 132.78/18.99 | % 132.78/18.99 | REDUCE: (10), (37) imply: % 132.78/18.99 | (67) ~ (all_53_6 = all_28_1) % 132.78/18.99 | % 132.78/18.99 | REDUCE: (37), (46) imply: % 132.78/18.99 | (68) ~ (all_53_11 = all_28_1) % 132.78/18.99 | % 132.78/18.99 | SIMP: (68) implies: % 132.78/18.99 | (69) ~ (all_53_11 = all_28_1) % 132.78/18.99 | % 132.78/18.99 | REDUCE: (34), (37) imply: % 132.78/18.99 | (70) ~ (all_28_1 = all_6_2) % 132.78/18.99 | % 132.78/18.99 | REDUCE: (49), (66) imply: % 132.78/18.99 | (71) op(e0, e2) = all_28_1 % 132.78/18.99 | % 132.78/18.99 | BETA: splitting (11) gives: % 132.78/18.99 | % 132.78/18.99 | Case 1: % 132.78/18.99 | | % 132.78/18.99 | | (72) ~ (all_34_2 = e1) % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (55), (72) imply: % 132.78/18.99 | | (73) ~ (all_4_2 = e1) % 132.78/18.99 | | % 132.78/18.99 | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (18), (27), (28), (32), % 132.78/18.99 | | (35), (38), (40), (41), (43), (44), (45), (50), (52), (53), (56), % 132.78/18.99 | | (60), (62), (64), (73) are inconsistent by sub-proof #231. % 132.78/18.99 | | % 132.78/18.99 | Case 2: % 132.78/18.99 | | % 132.78/18.99 | | (74) all_34_2 = e1 % 132.78/18.99 | | % 132.78/18.99 | | COMBINE_EQS: (55), (74) imply: % 132.78/18.99 | | (75) all_4_2 = e1 % 132.78/18.99 | | % 132.78/18.99 | | SIMP: (75) implies: % 132.78/18.99 | | (76) all_4_2 = e1 % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (39), (76) imply: % 132.78/18.99 | | (77) ~ (all_53_3 = e1) % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (60), (76) imply: % 132.78/18.99 | | (78) ~ (e1 = e0) % 132.78/18.99 | | % 132.78/18.99 | | BETA: splitting (47) gives: % 132.78/18.99 | | % 132.78/18.99 | | Case 1: % 132.78/18.99 | | | % 132.78/18.99 | | | (79) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) % 132.78/18.99 | | | = e1) % 132.78/18.99 | | | % 132.78/18.99 | | | BETA: splitting (79) gives: % 132.78/18.99 | | | % 132.78/18.99 | | | Case 1: % 132.78/18.99 | | | | % 132.78/18.99 | | | | (80) all_57_12 = e1 & op(e0, e3) = e1 % 132.78/18.99 | | | | % 132.78/18.99 | | | | REF_CLOSE: (14), (30), (77), (80) are inconsistent by sub-proof #272. % 132.78/18.99 | | | | % 132.78/18.99 | | | Case 2: % 132.78/18.99 | | | | % 132.78/18.99 | | | | (81) all_57_13 = e1 & op(e0, e2) = e1 % 132.78/18.99 | | | | % 132.78/18.99 | | | | ALPHA: (81) implies: % 132.78/18.99 | | | | (82) all_57_13 = e1 % 132.78/18.99 | | | | (83) op(e0, e2) = e1 % 132.78/18.99 | | | | % 132.78/18.99 | | | | GROUND_INST: instantiating (30) with all_28_1, e1, e2, e0, simplifying % 132.78/18.99 | | | | with (71), (83) gives: % 132.78/18.99 | | | | (84) all_28_1 = e1 % 132.78/18.99 | | | | % 132.78/18.99 | | | | REDUCE: (70), (84) imply: % 132.78/18.99 | | | | (85) ~ (all_6_2 = e1) % 132.78/18.99 | | | | % 132.78/18.99 | | | | BETA: splitting (17) gives: % 132.78/18.99 | | | | % 132.78/18.99 | | | | Case 1: % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | (86) ~ (all_28_1 = e1) % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | REDUCE: (84), (86) imply: % 132.78/18.99 | | | | | (87) $false % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | CLOSE: (87) is inconsistent. % 132.78/18.99 | | | | | % 132.78/18.99 | | | | Case 2: % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | (88) ~ (all_28_0 = e3) & op(e0, e1) = all_28_0 & $i(all_28_0) % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | ALPHA: (88) implies: % 132.78/18.99 | | | | | (89) ~ (all_28_0 = e3) % 132.78/18.99 | | | | | (90) op(e0, e1) = all_28_0 % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | GROUND_INST: instantiating (30) with all_53_11, all_28_0, e1, e0, % 132.78/18.99 | | | | | simplifying with (23), (90) gives: % 132.78/18.99 | | | | | (91) all_53_11 = all_28_0 % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | COMBINE_EQS: (33), (91) imply: % 132.78/18.99 | | | | | (92) all_55_14 = all_28_0 % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | REDUCE: (61), (91) imply: % 132.78/18.99 | | | | | (93) ~ (all_53_3 = all_28_0) % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | REDUCE: (16), (91) imply: % 132.78/18.99 | | | | | (94) ~ (all_28_0 = e2) % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | REDUCE: (57), (91) imply: % 132.78/18.99 | | | | | (95) ~ (all_28_0 = e1) % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | BETA: splitting (8) gives: % 132.78/18.99 | | | | | % 132.78/18.99 | | | | | Case 1: % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | (96) all_55_14 = e3 % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | COMBINE_EQS: (92), (96) imply: % 132.78/18.99 | | | | | | (97) all_28_0 = e3 % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | REDUCE: (89), (97) imply: % 132.78/18.99 | | | | | | (98) $false % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | CLOSE: (98) is inconsistent. % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | Case 2: % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | (99) all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0 % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | BETA: splitting (51) gives: % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | | Case 1: % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | (100) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & % 132.78/18.99 | | | | | | | op(e0, e2) = e3) % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | BETA: splitting (100) gives: % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | (101) all_57_12 = e3 & op(e0, e3) = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | ALPHA: (101) implies: % 132.78/18.99 | | | | | | | | (102) op(e0, e3) = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (12), (13), (18), (27), % 132.78/18.99 | | | | | | | | (28), (32), (35), (38), (40), (41), (43), (45), (50), % 132.78/18.99 | | | | | | | | (52), (56), (64), (102) are inconsistent by sub-proof % 132.78/18.99 | | | | | | | | #230. % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | (103) all_57_13 = e3 & op(e0, e2) = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | REF_CLOSE: (31), (82), (103) are inconsistent by sub-proof #297. % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | End of split % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | Case 2: % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | (104) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & % 132.78/18.99 | | | | | | | op(e0, e0) = e3) % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | BETA: splitting (104) gives: % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | (105) all_57_14 = e3 & op(e0, e1) = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | ALPHA: (105) implies: % 132.78/18.99 | | | | | | | | (106) all_57_14 = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | BETA: splitting (26) gives: % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | (107) all_57_15 = e0 & op(e0, e0) = e0 % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | REF_CLOSE: (25), (48), (107) are inconsistent by sub-proof % 132.78/18.99 | | | | | | | | | #229. % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | (108) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 % 132.78/18.99 | | | | | | | | | & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 132.78/18.99 | | | | | | | | | = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | % 132.78/18.99 | | | | | | | | | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 132.78/18.99 | | | | | | | | | e0 & op(e0, e1) = e0)) % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | ALPHA: (108) implies: % 132.78/18.99 | | | | | | | | | (109) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 % 132.78/18.99 | | | | | | | | | & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 132.78/18.99 | | | | | | | | | e0) % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | BETA: splitting (109) gives: % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | (110) all_57_12 = e0 & op(e0, e3) = e0 % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | ALPHA: (110) implies: % 132.78/18.99 | | | | | | | | | | (111) op(e0, e3) = e0 % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | BETA: splitting (59) gives: % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | (112) ~ (op(e0, e3) = e0) % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | PRED_UNIFY: (111), (112) imply: % 132.78/18.99 | | | | | | | | | | | (113) $false % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | CLOSE: (113) is inconsistent. % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | (114) all_55_12 = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | COMBINE_EQS: (58), (114) imply: % 132.78/18.99 | | | | | | | | | | | (115) all_53_3 = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | REDUCE: (93), (115) imply: % 132.78/18.99 | | | | | | | | | | | (116) ~ (all_28_0 = e0) % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | SIMP: (116) implies: % 132.78/18.99 | | | | | | | | | | | (117) ~ (all_28_0 = e0) % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | BETA: splitting (99) gives: % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | (118) all_55_14 = e2 % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | COMBINE_EQS: (92), (118) imply: % 132.78/18.99 | | | | | | | | | | | | (119) all_28_0 = e2 % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | REDUCE: (94), (119) imply: % 132.78/18.99 | | | | | | | | | | | | (120) $false % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | CLOSE: (120) is inconsistent. % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | (121) all_55_14 = e1 | all_55_14 = e0 % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | BETA: splitting (121) gives: % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | (122) all_55_14 = e1 % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | COMBINE_EQS: (92), (122) imply: % 132.78/18.99 | | | | | | | | | | | | | (123) all_28_0 = e1 % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | REDUCE: (95), (123) imply: % 132.78/18.99 | | | | | | | | | | | | | (124) $false % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | (125) all_55_14 = e0 % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | COMBINE_EQS: (92), (125) imply: % 132.78/18.99 | | | | | | | | | | | | | (126) all_28_0 = e0 % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | REDUCE: (117), (126) imply: % 132.78/18.99 | | | | | | | | | | | | | (127) $false % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | | CLOSE: (127) is inconsistent. % 132.78/18.99 | | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | | End of split % 132.78/18.99 | | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | End of split % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | End of split % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | (128) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 132.78/18.99 | | | | | | | | | | e0 & op(e0, e1) = e0) % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | BETA: splitting (128) gives: % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | Case 1: % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | (129) all_57_13 = e0 & op(e0, e2) = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (78), (82), (129) are % 132.78/18.99 | | | | | | | | | | | inconsistent by sub-proof #228. % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | (130) all_57_14 = e0 & op(e0, e1) = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | ALPHA: (130) implies: % 132.78/18.99 | | | | | | | | | | | (131) all_57_14 = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | COMBINE_EQS: (106), (131) imply: % 132.78/18.99 | | | | | | | | | | | (132) e3 = e0 % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | REDUCE: (22), (132) imply: % 132.78/18.99 | | | | | | | | | | | (133) $false % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | | CLOSE: (133) is inconsistent. % 132.78/18.99 | | | | | | | | | | | % 132.78/18.99 | | | | | | | | | | End of split % 132.78/18.99 | | | | | | | | | | % 132.78/18.99 | | | | | | | | | End of split % 132.78/18.99 | | | | | | | | | % 132.78/18.99 | | | | | | | | End of split % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | Case 2: % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | (134) all_57_15 = e3 & op(e0, e0) = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | ALPHA: (134) implies: % 132.78/18.99 | | | | | | | | (135) all_57_15 = e3 % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | | REF_CLOSE: (48), (54), (135) are inconsistent by sub-proof #227. % 132.78/18.99 | | | | | | | | % 132.78/18.99 | | | | | | | End of split % 132.78/18.99 | | | | | | | % 132.78/18.99 | | | | | | End of split % 132.78/18.99 | | | | | | % 132.78/18.99 | | | | | End of split % 132.78/18.99 | | | | | % 132.78/18.99 | | | | End of split % 132.78/18.99 | | | | % 132.78/18.99 | | | End of split % 132.78/18.99 | | | % 132.78/18.99 | | Case 2: % 132.78/18.99 | | | % 132.78/18.99 | | | (136) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) % 132.78/18.99 | | | = e1) % 132.78/18.99 | | | % 132.78/18.99 | | | REF_CLOSE: (24), (29), (30), (42), (57), (136) are inconsistent by % 132.78/18.99 | | | sub-proof #293. % 132.78/18.99 | | | % 132.78/18.99 | | End of split % 132.78/18.99 | | % 132.78/18.99 | End of split % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #227 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) all_57_15 = e3 % 132.78/18.99 (2) all_57_15 = e2 % 132.78/18.99 (3) ~ (e3 = e2) % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | COMBINE_EQS: (1), (2) imply: % 132.78/18.99 | (4) e3 = e2 % 132.78/18.99 | % 132.78/18.99 | SIMP: (4) implies: % 132.78/18.99 | (5) e3 = e2 % 132.78/18.99 | % 132.78/18.99 | REDUCE: (3), (5) imply: % 132.78/18.99 | (6) $false % 132.78/18.99 | % 132.78/18.99 | CLOSE: (6) is inconsistent. % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #228 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) op(e1, e1) = e1 % 132.78/18.99 (2) all_57_13 = e1 % 132.78/18.99 (3) all_22_2 = e1 % 132.78/18.99 (4) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/18.99 (5) all_57_13 = e0 & op(e0, e2) = e0 % 132.78/18.99 (6) ~ (e1 = e0) % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | ALPHA: (5) implies: % 132.78/18.99 | (7) all_57_13 = e0 % 132.78/18.99 | % 132.78/18.99 | COMBINE_EQS: (2), (7) imply: % 132.78/18.99 | (8) e1 = e0 % 132.78/18.99 | % 132.78/18.99 | COMBINE_EQS: (3), (8) imply: % 132.78/18.99 | (9) all_22_2 = e0 % 132.78/18.99 | % 132.78/18.99 | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #269. % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #229 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) all_57_15 = e0 & op(e0, e0) = e0 % 132.78/18.99 (2) all_57_15 = e2 % 132.78/18.99 (3) ~ (e2 = e0) % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | ALPHA: (1) implies: % 132.78/18.99 | (4) all_57_15 = e0 % 132.78/18.99 | % 132.78/18.99 | COMBINE_EQS: (2), (4) imply: % 132.78/18.99 | (5) e2 = e0 % 132.78/18.99 | % 132.78/18.99 | REDUCE: (3), (5) imply: % 132.78/18.99 | (6) $false % 132.78/18.99 | % 132.78/18.99 | CLOSE: (6) is inconsistent. % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #230 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) ~ (all_53_2 = all_53_3) % 132.78/18.99 (2) ~ (unit = e0) % 132.78/18.99 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.99 (4) unit = e2 | unit = e1 | unit = e0 % 132.78/18.99 (5) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/18.99 (6) op(unit, e0) = e0 % 132.78/18.99 (7) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.99 (8) op(e2, unit) = e2 % 132.78/18.99 (9) all_55_9 = all_53_6 % 132.78/18.99 (10) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.78/18.99 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.78/18.99 $i(all_42_0)))) % 132.78/18.99 (11) op(e0, e3) = e3 % 132.78/18.99 (12) ~ (all_53_13 = all_6_2) % 132.78/18.99 (13) all_55_5 = all_6_2 % 132.78/18.99 (14) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/18.99 (15) ~ (all_6_2 = e3) % 132.78/18.99 (16) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/18.99 (17) ~ (all_6_2 = e1) % 132.78/18.99 (18) op(e1, unit) = e1 % 132.78/18.99 (19) ~ (all_53_6 = e1) % 132.78/18.99 (20) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/18.99 (21) ~ (all_53_9 = all_6_2) % 132.78/18.99 (22) all_42_2 = all_6_2 % 132.78/18.99 (23) op(unit, e3) = e3 % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | BETA: splitting (5) gives: % 132.78/18.99 | % 132.78/18.99 | Case 1: % 132.78/18.99 | | % 132.78/18.99 | | (24) ~ (op(e0, e3) = e3) % 132.78/18.99 | | % 132.78/18.99 | | PRED_UNIFY: (11), (24) imply: % 132.78/18.99 | | (25) $false % 132.78/18.99 | | % 132.78/18.99 | | CLOSE: (25) is inconsistent. % 132.78/18.99 | | % 132.78/18.99 | Case 2: % 132.78/18.99 | | % 132.78/18.99 | | (26) all_53_3 = e3 % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (1), (26) imply: % 132.78/18.99 | | (27) ~ (all_53_2 = e3) % 132.78/18.99 | | % 132.78/18.99 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15), % 132.78/18.99 | | (16), (17), (18), (19), (20), (21), (22), (23), (27) are % 132.78/18.99 | | inconsistent by sub-proof #232. % 132.78/18.99 | | % 132.78/18.99 | End of split % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #231 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.78/18.99 (2) ~ (unit = e0) % 132.78/18.99 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.99 (4) unit = e2 | unit = e1 | unit = e0 % 132.78/18.99 (5) op(unit, e0) = e0 % 132.78/18.99 (6) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.99 (7) op(e2, unit) = e2 % 132.78/18.99 (8) all_55_9 = all_53_6 % 132.78/18.99 (9) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.78/18.99 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.78/18.99 $i(all_42_0)))) % 132.78/18.99 (10) ~ (all_4_2 = e1) % 132.78/18.99 (11) ~ (all_53_13 = all_6_2) % 132.78/18.99 (12) all_55_5 = all_6_2 % 132.78/18.99 (13) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/18.99 (14) ~ (all_6_2 = e3) % 132.78/18.99 (15) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/18.99 (16) ~ (all_6_2 = e1) % 132.78/18.99 (17) op(e1, unit) = e1 % 132.78/18.99 (18) ~ (all_53_6 = e1) % 132.78/18.99 (19) ~ (all_53_2 = all_4_2) % 132.78/18.99 (20) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/18.99 (21) ~ (all_53_9 = all_6_2) % 132.78/18.99 (22) all_42_2 = all_6_2 % 132.78/18.99 (23) ~ (all_4_2 = e2) % 132.78/18.99 (24) op(unit, e3) = e3 % 132.78/18.99 (25) ~ (all_4_2 = e0) % 132.78/18.99 (26) all_55_0 = all_4_2 % 132.78/18.99 % 132.78/18.99 Begin of proof % 132.78/18.99 | % 132.78/18.99 | BETA: splitting (1) gives: % 132.78/18.99 | % 132.78/18.99 | Case 1: % 132.78/18.99 | | % 132.78/18.99 | | (27) all_55_0 = e3 % 132.78/18.99 | | % 132.78/18.99 | | COMBINE_EQS: (26), (27) imply: % 132.78/18.99 | | (28) all_4_2 = e3 % 132.78/18.99 | | % 132.78/18.99 | | SIMP: (28) implies: % 132.78/18.99 | | (29) all_4_2 = e3 % 132.78/18.99 | | % 132.78/18.99 | | REDUCE: (19), (29) imply: % 132.78/18.99 | | (30) ~ (all_53_2 = e3) % 132.78/18.99 | | % 132.78/18.99 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 132.78/18.99 | | (15), (16), (17), (18), (20), (21), (22), (24), (30) are % 132.78/18.99 | | inconsistent by sub-proof #232. % 132.78/18.99 | | % 132.78/18.99 | Case 2: % 132.78/18.99 | | % 132.78/18.99 | | (31) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.78/18.99 | | % 132.78/18.99 | | REF_CLOSE: (10), (23), (25), (26), (31) are inconsistent by sub-proof #274. % 132.78/18.99 | | % 132.78/18.99 | End of split % 132.78/18.99 | % 132.78/18.99 End of proof % 132.78/18.99 % 132.78/18.99 Sub-proof #232 shows that the following formulas are inconsistent: % 132.78/18.99 ---------------------------------------------------------------- % 132.78/18.99 (1) ~ (unit = e0) % 132.78/18.99 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/18.99 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/18.99 (4) op(unit, e0) = e0 % 132.78/18.99 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/18.99 (6) op(e2, unit) = e2 % 132.78/18.99 (7) all_55_9 = all_53_6 % 132.78/19.00 (8) ~ (all_42_2 = e0) | (op(e2, e0) = all_42_1 & $i(all_42_1) & ( ~ % 132.78/19.00 (all_42_1 = e1) | ( ~ (all_42_0 = e3) & op(e2, e1) = all_42_0 & % 132.78/19.00 $i(all_42_0)))) % 132.78/19.00 (9) ~ (all_53_13 = all_6_2) % 132.78/19.00 (10) all_55_5 = all_6_2 % 132.78/19.00 (11) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.00 (12) ~ (all_6_2 = e3) % 132.78/19.00 (13) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 (14) ~ (all_6_2 = e1) % 132.78/19.00 (15) op(e1, unit) = e1 % 132.78/19.00 (16) ~ (all_53_6 = e1) % 132.78/19.00 (17) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.00 (18) ~ (all_53_9 = all_6_2) % 132.78/19.00 (19) ~ (all_53_2 = e3) % 132.78/19.00 (20) all_42_2 = all_6_2 % 132.78/19.00 (21) op(unit, e3) = e3 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (8) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (22) ~ (all_42_2 = e0) % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (20), (22) imply: % 132.78/19.00 | | (23) ~ (all_6_2 = e0) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (3), (6), (7), (10), (11), (12), (13), (14), (15), (16), % 132.78/19.00 | | (17), (18), (23) are inconsistent by sub-proof #234. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (24) all_42_2 = e0 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (20), (24) imply: % 132.78/19.00 | | (25) all_6_2 = e0 % 132.78/19.00 | | % 132.78/19.00 | | SIMP: (25) implies: % 132.78/19.00 | | (26) all_6_2 = e0 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (9), (26) imply: % 132.78/19.00 | | (27) ~ (all_53_13 = e0) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (2), (3), (4), (5), (19), (21), (27) are inconsistent by % 132.78/19.00 | | sub-proof #233. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #233 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ~ (unit = e0) % 132.78/19.00 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.00 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (4) op(unit, e0) = e0 % 132.78/19.00 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.00 (6) ~ (all_53_13 = e0) % 132.78/19.00 (7) ~ (all_53_2 = e3) % 132.78/19.00 (8) op(unit, e3) = e3 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (5) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (9) ~ (op(e2, e0) = e0) % 132.78/19.00 | | % 132.78/19.00 | | PRED_UNIFY: (4), (9) imply: % 132.78/19.00 | | (10) ~ (unit = e2) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (2), (3), (7), (8), (10) are inconsistent by sub-proof #276. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (11) op(e2, e0) = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #356. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #234 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ~ (unit = e0) % 132.78/19.00 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (3) op(e2, unit) = e2 % 132.78/19.00 (4) all_55_9 = all_53_6 % 132.78/19.00 (5) all_55_5 = all_6_2 % 132.78/19.00 (6) ~ (all_6_2 = e0) % 132.78/19.00 (7) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.00 (8) ~ (all_6_2 = e3) % 132.78/19.00 (9) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 (10) ~ (all_6_2 = e1) % 132.78/19.00 (11) op(e1, unit) = e1 % 132.78/19.00 (12) ~ (all_53_6 = e1) % 132.78/19.00 (13) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.00 (14) ~ (all_53_9 = all_6_2) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (9) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (15) all_55_5 = e3 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (5), (15) imply: % 132.78/19.00 | | (16) all_6_2 = e3 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (8), (16) imply: % 132.78/19.00 | | (17) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (17) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (18) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), % 132.78/19.00 | | (18) are inconsistent by sub-proof #250. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #235 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_10_2 = e0 | ~ (op(e0, e0) = e0) % 132.78/19.00 (2) op(e0, e0) = e0 % 132.78/19.00 (3) all_10_2 = e2 % 132.78/19.00 (4) ~ (e2 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (1) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (5) ~ (op(e0, e0) = e0) % 132.78/19.00 | | % 132.78/19.00 | | PRED_UNIFY: (2), (5) imply: % 132.78/19.00 | | (6) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (6) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (7) all_10_2 = e0 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (3), (7) imply: % 132.78/19.00 | | (8) e2 = e0 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (4), (8) imply: % 132.78/19.00 | | (9) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (9) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #236 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) | % 132.78/19.00 (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = % 132.78/19.00 e0) | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 132.78/19.00 e1) = e0)) % 132.78/19.00 (2) ~ (all_53_11 = e0) % 132.78/19.00 (3) ~ (all_53_3 = e0) % 132.78/19.00 (4) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.78/19.00 (5) ~ (all_53_7 = e0) % 132.78/19.00 (6) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.78/19.00 (7) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.00 (8) all_55_13 = all_53_7 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (9) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 132.78/19.00 | | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (9) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (10) all_57_12 = e0 & op(e0, e3) = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #237. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (11) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 132.78/19.00 | | e0) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (2), (4), (5), (7), (8), (11) are inconsistent by sub-proof #291. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #237 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_12 = e0 & op(e0, e3) = e0 % 132.78/19.00 (2) all_53_3 = e0 | ~ (op(e0, e3) = e0) % 132.78/19.00 (3) ~ (all_53_3 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (4) op(e0, e3) = e0 % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (2) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (5) ~ (op(e0, e3) = e0) % 132.78/19.00 | | % 132.78/19.00 | | PRED_UNIFY: (4), (5) imply: % 132.78/19.00 | | (6) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (6) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (7) all_53_3 = e0 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (3), (7) imply: % 132.78/19.00 | | (8) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (8) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #238 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.78/19.00 (2) op(e3, e1) = e1 % 132.78/19.00 (3) ~ (all_53_8 = e1) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (1) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (4) ~ (op(e3, e1) = e1) % 132.78/19.00 | | % 132.78/19.00 | | PRED_UNIFY: (2), (4) imply: % 132.78/19.00 | | (5) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (5) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (6) all_53_8 = e1 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (3), (6) imply: % 132.78/19.00 | | (7) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (7) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #239 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_4 = e1 & op(e3, e1) = e1 % 132.78/19.00 (2) ~ (op(e3, e1) = e1) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (3) op(e3, e1) = e1 % 132.78/19.00 | % 132.78/19.00 | PRED_UNIFY: (2), (3) imply: % 132.78/19.00 | (4) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (4) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #240 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.00 (2) ~ (all_53_11 = e0) % 132.78/19.00 (3) op(e1, e1) = e1 % 132.78/19.00 (4) all_22_2 = e1 % 132.78/19.00 (5) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.00 (6) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.00 (7) ~ (e1 = e0) % 132.78/19.00 (8) all_57_8 = e1 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (1) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (9) all_57_8 = e0 & op(e1, e1) = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (3), (4), (5), (7), (8), (9) are inconsistent by sub-proof #257. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (10) all_57_14 = e0 & op(e0, e1) = e0 % 132.78/19.00 | | % 132.78/19.00 | | ALPHA: (10) implies: % 132.78/19.00 | | (11) op(e0, e1) = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #296. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #241 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_5 = e0 & op(e2, e1) = e0 % 132.78/19.00 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.00 (3) op(e2, e1) = all_53_9 % 132.78/19.00 (4) ~ (all_53_9 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (5) op(e2, e1) = e0 % 132.78/19.00 | % 132.78/19.00 | GROUND_INST: instantiating (2) with all_53_9, e0, e1, e2, simplifying with % 132.78/19.00 | (3), (5) gives: % 132.78/19.00 | (6) all_53_9 = e0 % 132.78/19.00 | % 132.78/19.00 | REDUCE: (4), (6) imply: % 132.78/19.00 | (7) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (7) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #242 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ~ (unit = e0) % 132.78/19.00 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (3) ~ (all_53_11 = e0) % 132.78/19.00 (4) all_55_6 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.00 (5) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.00 (6) op(e0, unit) = e0 % 132.78/19.00 (7) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.00 (8) op(unit, e1) = e1 % 132.78/19.00 (9) ~ (all_53_9 = e1) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (4) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (10) ~ (op(e2, e1) = e1) % 132.78/19.00 | | % 132.78/19.00 | | PRED_UNIFY: (8), (10) imply: % 132.78/19.00 | | (11) ~ (unit = e2) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (2), (3), (5), (6), (11) are inconsistent by sub-proof #243. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (12) op(e2, e1) = e1 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #334. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #243 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ~ (unit = e0) % 132.78/19.00 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (3) ~ (all_53_11 = e0) % 132.78/19.00 (4) ~ (unit = e2) % 132.78/19.00 (5) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.00 (6) op(e0, unit) = e0 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (2) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (7) unit = e2 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (4), (7) imply: % 132.78/19.00 | | (8) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (8) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (9) unit = e1 | unit = e0 % 132.78/19.00 | | % 132.78/19.00 | | BETA: splitting (9) gives: % 132.78/19.00 | | % 132.78/19.00 | | Case 1: % 132.78/19.00 | | | % 132.78/19.00 | | | (10) unit = e1 % 132.78/19.00 | | | % 132.78/19.00 | | | REDUCE: (6), (10) imply: % 132.78/19.00 | | | (11) op(e0, e1) = e0 % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #296. % 132.78/19.00 | | | % 132.78/19.00 | | Case 2: % 132.78/19.00 | | | % 132.78/19.00 | | | (12) ~ (unit = e1) % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (1), (9), (12) are inconsistent by sub-proof #278. % 132.78/19.00 | | | % 132.78/19.00 | | End of split % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #244 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) op(e3, e3) = e1 % 132.78/19.00 (2) ~ (e3 = e0) % 132.78/19.00 (3) ~ (e2 = e0) % 132.78/19.00 (4) all_57_4 = e0 % 132.78/19.00 (5) all_57_1 = e0 % 132.78/19.00 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.00 (7) ~ (e3 = e1) % 132.78/19.00 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 132.78/19.00 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 132.78/19.00 (9) ~ (e2 = e1) % 132.78/19.00 (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 132.78/19.00 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 132.78/19.00 (11) ~ (e3 = e2) % 132.78/19.00 (12) all_57_0 = e1 % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (8) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 132.78/19.00 | | e3) % 132.78/19.00 | | % 132.78/19.00 | | BETA: splitting (13) gives: % 132.78/19.00 | | % 132.78/19.00 | | Case 1: % 132.78/19.00 | | | % 132.78/19.00 | | | (14) all_57_0 = e3 & op(e3, e3) = e3 % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (7), (12), (14) are inconsistent by sub-proof #312. % 132.78/19.00 | | | % 132.78/19.00 | | Case 2: % 132.78/19.00 | | | % 132.78/19.00 | | | (15) all_57_1 = e3 & op(e3, e2) = e3 % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #248. % 132.78/19.00 | | | % 132.78/19.00 | | End of split % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 132.78/19.00 | | e3) % 132.78/19.00 | | % 132.78/19.00 | | BETA: splitting (16) gives: % 132.78/19.00 | | % 132.78/19.00 | | Case 1: % 132.78/19.00 | | | % 132.78/19.00 | | | (17) all_57_4 = e3 & op(e3, e1) = e3 % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (2), (4), (17) are inconsistent by sub-proof #247. % 132.78/19.00 | | | % 132.78/19.00 | | Case 2: % 132.78/19.00 | | | % 132.78/19.00 | | | (18) all_57_9 = e3 & op(e3, e0) = e3 % 132.78/19.00 | | | % 132.78/19.00 | | | ALPHA: (18) implies: % 132.78/19.00 | | | (19) all_57_9 = e3 % 132.78/19.00 | | | % 132.78/19.00 | | | BETA: splitting (10) gives: % 132.78/19.00 | | | % 132.78/19.00 | | | Case 1: % 132.78/19.00 | | | | % 132.78/19.00 | | | | (20) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) % 132.78/19.00 | | | | = e2) % 132.78/19.00 | | | | % 132.78/19.00 | | | | BETA: splitting (20) gives: % 132.78/19.00 | | | | % 132.78/19.00 | | | | Case 1: % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | (21) all_57_0 = e2 & op(e3, e3) = e2 % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | ALPHA: (21) implies: % 132.78/19.00 | | | | | (22) op(e3, e3) = e2 % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | REF_CLOSE: (1), (6), (9), (22) are inconsistent by sub-proof #267. % 132.78/19.00 | | | | | % 132.78/19.00 | | | | Case 2: % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | (23) all_57_1 = e2 & op(e3, e2) = e2 % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | REF_CLOSE: (3), (5), (23) are inconsistent by sub-proof #246. % 132.78/19.00 | | | | | % 132.78/19.00 | | | | End of split % 132.78/19.00 | | | | % 132.78/19.00 | | | Case 2: % 132.78/19.00 | | | | % 132.78/19.00 | | | | (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) % 132.78/19.00 | | | | = e2) % 132.78/19.00 | | | | % 132.78/19.00 | | | | BETA: splitting (24) gives: % 132.78/19.00 | | | | % 132.78/19.00 | | | | Case 1: % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | (25) all_57_4 = e2 & op(e3, e1) = e2 % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | REF_CLOSE: (3), (4), (25) are inconsistent by sub-proof #264. % 132.78/19.00 | | | | | % 132.78/19.00 | | | | Case 2: % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | (26) all_57_9 = e2 & op(e3, e0) = e2 % 132.78/19.00 | | | | | % 132.78/19.00 | | | | | REF_CLOSE: (11), (19), (26) are inconsistent by sub-proof #245. % 132.78/19.00 | | | | | % 132.78/19.00 | | | | End of split % 132.78/19.00 | | | | % 132.78/19.00 | | | End of split % 132.78/19.00 | | | % 132.78/19.00 | | End of split % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #245 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_9 = e2 & op(e3, e0) = e2 % 132.78/19.00 (2) all_57_9 = e3 % 132.78/19.00 (3) ~ (e3 = e2) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (4) all_57_9 = e2 % 132.78/19.00 | % 132.78/19.00 | COMBINE_EQS: (2), (4) imply: % 132.78/19.00 | (5) e3 = e2 % 132.78/19.00 | % 132.78/19.00 | REDUCE: (3), (5) imply: % 132.78/19.00 | (6) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (6) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #246 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_1 = e2 & op(e3, e2) = e2 % 132.78/19.00 (2) all_57_1 = e0 % 132.78/19.00 (3) ~ (e2 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (4) all_57_1 = e2 % 132.78/19.00 | % 132.78/19.00 | COMBINE_EQS: (2), (4) imply: % 132.78/19.00 | (5) e2 = e0 % 132.78/19.00 | % 132.78/19.00 | SIMP: (5) implies: % 132.78/19.00 | (6) e2 = e0 % 132.78/19.00 | % 132.78/19.00 | REDUCE: (3), (6) imply: % 132.78/19.00 | (7) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (7) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #247 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_4 = e3 & op(e3, e1) = e3 % 132.78/19.00 (2) all_57_4 = e0 % 132.78/19.00 (3) ~ (e3 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (4) all_57_4 = e3 % 132.78/19.00 | % 132.78/19.00 | COMBINE_EQS: (2), (4) imply: % 132.78/19.00 | (5) e3 = e0 % 132.78/19.00 | % 132.78/19.00 | SIMP: (5) implies: % 132.78/19.00 | (6) e3 = e0 % 132.78/19.00 | % 132.78/19.00 | REDUCE: (3), (6) imply: % 132.78/19.00 | (7) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (7) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #248 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_57_1 = e3 & op(e3, e2) = e3 % 132.78/19.00 (2) all_57_1 = e0 % 132.78/19.00 (3) ~ (e3 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | ALPHA: (1) implies: % 132.78/19.00 | (4) all_57_1 = e3 % 132.78/19.00 | % 132.78/19.00 | COMBINE_EQS: (2), (4) imply: % 132.78/19.00 | (5) e3 = e0 % 132.78/19.00 | % 132.78/19.00 | SIMP: (5) implies: % 132.78/19.00 | (6) e3 = e0 % 132.78/19.00 | % 132.78/19.00 | REDUCE: (3), (6) imply: % 132.78/19.00 | (7) $false % 132.78/19.00 | % 132.78/19.00 | CLOSE: (7) is inconsistent. % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #249 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (2) op(e2, unit) = e2 % 132.78/19.00 (3) all_55_9 = all_53_6 % 132.78/19.00 (4) all_55_5 = all_6_2 % 132.78/19.00 (5) ~ (all_6_2 = e0) % 132.78/19.00 (6) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.00 (7) ~ (all_6_2 = e3) % 132.78/19.00 (8) all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 (9) ~ (all_6_2 = e1) % 132.78/19.00 (10) op(e1, unit) = e1 % 132.78/19.00 (11) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.00 (12) ~ (all_53_6 = e1) % 132.78/19.00 (13) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.00 (14) ~ (all_53_9 = all_6_2) % 132.78/19.00 (15) op(unit, e1) = e1 % 132.78/19.00 (16) ~ (all_53_11 = e1) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (8) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (17) all_55_5 = e3 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (4), (17) imply: % 132.78/19.00 | | (18) all_6_2 = e3 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (7), (18) imply: % 132.78/19.00 | | (19) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (19) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (20) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 | | % 132.78/19.00 | | BETA: splitting (11) gives: % 132.78/19.00 | | % 132.78/19.00 | | Case 1: % 132.78/19.00 | | | % 132.78/19.00 | | | (21) ~ (op(e0, e1) = e1) % 132.78/19.00 | | | % 132.78/19.00 | | | PRED_UNIFY: (15), (21) imply: % 132.78/19.00 | | | (22) ~ (unit = e0) % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (13), (14), % 132.78/19.00 | | | (20), (22) are inconsistent by sub-proof #250. % 132.78/19.00 | | | % 132.78/19.00 | | Case 2: % 132.78/19.00 | | | % 132.78/19.00 | | | (23) op(e0, e1) = e1 % 132.78/19.00 | | | % 132.78/19.00 | | | REF_CLOSE: (11), (16), (23) are inconsistent by sub-proof #333. % 132.78/19.00 | | | % 132.78/19.00 | | End of split % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #250 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) ~ (unit = e0) % 132.78/19.00 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.00 (3) op(e2, unit) = e2 % 132.78/19.00 (4) all_55_9 = all_53_6 % 132.78/19.00 (5) all_55_5 = all_6_2 % 132.78/19.00 (6) ~ (all_6_2 = e0) % 132.78/19.00 (7) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.00 (8) all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 (9) ~ (all_6_2 = e1) % 132.78/19.00 (10) op(e1, unit) = e1 % 132.78/19.00 (11) ~ (all_53_6 = e1) % 132.78/19.00 (12) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.00 (13) ~ (all_53_9 = all_6_2) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (8) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (14) all_55_5 = e2 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (5), (14) imply: % 132.78/19.00 | | (15) all_6_2 = e2 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (13), (15) imply: % 132.78/19.00 | | (16) ~ (all_53_9 = e2) % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (1), (2), (3), (4), (7), (10), (11), (12), (16) are inconsistent % 132.78/19.00 | | by sub-proof #252. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (17) all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 | | % 132.78/19.00 | | REF_CLOSE: (5), (6), (9), (17) are inconsistent by sub-proof #251. % 132.78/19.00 | | % 132.78/19.00 | End of split % 132.78/19.00 | % 132.78/19.00 End of proof % 132.78/19.00 % 132.78/19.00 Sub-proof #251 shows that the following formulas are inconsistent: % 132.78/19.00 ---------------------------------------------------------------- % 132.78/19.00 (1) all_55_5 = e1 | all_55_5 = e0 % 132.78/19.00 (2) all_55_5 = all_6_2 % 132.78/19.00 (3) ~ (all_6_2 = e1) % 132.78/19.00 (4) ~ (all_6_2 = e0) % 132.78/19.00 % 132.78/19.00 Begin of proof % 132.78/19.00 | % 132.78/19.00 | BETA: splitting (1) gives: % 132.78/19.00 | % 132.78/19.00 | Case 1: % 132.78/19.00 | | % 132.78/19.00 | | (5) all_55_5 = e1 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (2), (5) imply: % 132.78/19.00 | | (6) all_6_2 = e1 % 132.78/19.00 | | % 132.78/19.00 | | SIMP: (6) implies: % 132.78/19.00 | | (7) all_6_2 = e1 % 132.78/19.00 | | % 132.78/19.00 | | REDUCE: (3), (7) imply: % 132.78/19.00 | | (8) $false % 132.78/19.00 | | % 132.78/19.00 | | CLOSE: (8) is inconsistent. % 132.78/19.00 | | % 132.78/19.00 | Case 2: % 132.78/19.00 | | % 132.78/19.00 | | (9) all_55_5 = e0 % 132.78/19.00 | | % 132.78/19.00 | | COMBINE_EQS: (2), (9) imply: % 132.78/19.01 | | (10) all_6_2 = e0 % 132.78/19.01 | | % 132.78/19.01 | | SIMP: (10) implies: % 132.78/19.01 | | (11) all_6_2 = e0 % 132.78/19.01 | | % 132.78/19.01 | | REDUCE: (4), (11) imply: % 132.78/19.01 | | (12) $false % 132.78/19.01 | | % 132.78/19.01 | | CLOSE: (12) is inconsistent. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #252 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) ~ (unit = e0) % 132.78/19.01 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.01 (3) op(e2, unit) = e2 % 132.78/19.01 (4) all_55_9 = all_53_6 % 132.78/19.01 (5) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.01 (6) op(e1, unit) = e1 % 132.78/19.01 (7) ~ (all_53_9 = e2) % 132.78/19.01 (8) ~ (all_53_6 = e1) % 132.78/19.01 (9) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (5) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (10) ~ (op(e2, e1) = e2) % 132.78/19.01 | | % 132.78/19.01 | | PRED_UNIFY: (3), (10) imply: % 132.78/19.01 | | (11) ~ (unit = e1) % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (11) are inconsistent by sub-proof % 132.78/19.01 | | #253. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (12) op(e2, e1) = e2 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #347. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #253 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) ~ (unit = e0) % 132.78/19.01 (2) unit = e2 | unit = e1 | unit = e0 % 132.78/19.01 (3) all_55_9 = all_53_6 % 132.78/19.01 (4) op(e1, unit) = e1 % 132.78/19.01 (5) ~ (all_53_6 = e1) % 132.78/19.01 (6) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.01 (7) ~ (unit = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (2) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (8) unit = e2 % 132.78/19.01 | | % 132.78/19.01 | | REDUCE: (4), (8) imply: % 132.78/19.01 | | (9) op(e1, e2) = e1 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #341. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (10) unit = e1 | unit = e0 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (1), (7), (10) are inconsistent by sub-proof #278. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #254 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_3 = e1 & op(e2, e2) = e1 % 132.78/19.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.01 (3) op(e2, e2) = all_6_2 % 132.78/19.01 (4) ~ (all_6_2 = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (5) op(e2, e2) = e1 % 132.78/19.01 | % 132.78/19.01 | GROUND_INST: instantiating (2) with all_6_2, e1, e2, e2, simplifying with (3), % 132.78/19.01 | (5) gives: % 132.78/19.01 | (6) all_6_2 = e1 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (4), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #255 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 132.78/19.01 (2) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.78/19.01 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.78/19.01 (3) op(e1, e1) = e1 % 132.78/19.01 (4) op(e3, e3) = e1 % 132.78/19.01 (5) all_57_15 = e0 % 132.78/19.01 (6) all_57_13 = e1 % 132.78/19.01 (7) all_22_2 = e1 % 132.78/19.01 (8) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.01 (9) ~ (e3 = e0) % 132.78/19.01 (10) ~ (e2 = e0) % 132.78/19.01 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 132.78/19.01 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 132.78/19.01 (12) all_57_10 = e1 % 132.78/19.01 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.01 (14) ~ (e3 = e1) % 132.78/19.01 (15) ~ (all_6_2 = e3) % 132.78/19.01 (16) ~ (e2 = e1) % 132.78/19.01 (17) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.78/19.01 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.78/19.01 (18) op(e2, e2) = all_6_2 % 132.78/19.01 (19) op(e3, e3) = all_4_2 % 132.78/19.01 (20) ~ (e1 = e0) % 132.78/19.01 (21) all_57_8 = e1 % 132.78/19.01 (22) ~ (all_53_12 = e0) % 132.78/19.01 (23) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 132.78/19.01 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 132.78/19.01 (24) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 132.78/19.01 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 132.78/19.01 (25) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 132.78/19.01 (26) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.78/19.01 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 132.78/19.01 (27) ~ (e3 = e2) % 132.78/19.01 (28) all_57_1 = e1 % 132.78/19.01 (29) ~ (all_53_14 = e0) % 132.78/19.01 (30) ~ (all_4_2 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (26) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (31) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = % 132.78/19.01 | | e3) % 132.78/19.01 | | % 132.78/19.01 | | BETA: splitting (31) gives: % 132.78/19.01 | | % 132.78/19.01 | | Case 1: % 132.78/19.01 | | | % 132.78/19.01 | | | (32) all_57_1 = e3 & op(e3, e2) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | REF_CLOSE: (14), (28), (32) are inconsistent by sub-proof #271. % 132.78/19.01 | | | % 132.78/19.01 | | Case 2: % 132.78/19.01 | | | % 132.78/19.01 | | | (33) all_57_3 = e3 & op(e2, e2) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | REF_CLOSE: (13), (15), (18), (33) are inconsistent by sub-proof #352. % 132.78/19.01 | | | % 132.78/19.01 | | End of split % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (34) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = % 132.78/19.01 | | e3) % 132.78/19.01 | | % 132.78/19.01 | | BETA: splitting (34) gives: % 132.78/19.01 | | % 132.78/19.01 | | Case 1: % 132.78/19.01 | | | % 132.78/19.01 | | | (35) all_57_7 = e3 & op(e1, e2) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | ALPHA: (35) implies: % 132.78/19.01 | | | (36) all_57_7 = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | BETA: splitting (11) gives: % 132.78/19.01 | | | % 132.78/19.01 | | | Case 1: % 132.78/19.01 | | | | % 132.78/19.01 | | | | (37) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) % 132.78/19.01 | | | | = e0) % 132.78/19.01 | | | | % 132.78/19.01 | | | | BETA: splitting (37) gives: % 132.78/19.01 | | | | % 132.78/19.01 | | | | Case 1: % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | (38) all_57_0 = e0 & op(e3, e3) = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | REF_CLOSE: (13), (19), (30), (38) are inconsistent by sub-proof #270. % 132.78/19.01 | | | | | % 132.78/19.01 | | | | Case 2: % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | (39) all_57_1 = e0 & op(e3, e2) = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | REF_CLOSE: (3), (7), (8), (20), (28), (39) are inconsistent by % 132.78/19.01 | | | | | sub-proof #268. % 132.78/19.01 | | | | | % 132.78/19.01 | | | | End of split % 132.78/19.01 | | | | % 132.78/19.01 | | | Case 2: % 132.78/19.01 | | | | % 132.78/19.01 | | | | (40) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) % 132.78/19.01 | | | | = e0) % 132.78/19.01 | | | | % 132.78/19.01 | | | | BETA: splitting (40) gives: % 132.78/19.01 | | | | % 132.78/19.01 | | | | Case 1: % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | (41) all_57_4 = e0 & op(e3, e1) = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | ALPHA: (41) implies: % 132.78/19.01 | | | | | (42) all_57_4 = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | BETA: splitting (2) gives: % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | Case 1: % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | (43) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, % 132.78/19.01 | | | | | | e2) = e0) % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | BETA: splitting (43) gives: % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | Case 1: % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | (44) all_57_6 = e0 & op(e1, e3) = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | ALPHA: (44) implies: % 132.78/19.01 | | | | | | | (45) all_57_6 = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | BETA: splitting (24) gives: % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | Case 1: % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | | (46) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & % 132.78/19.01 | | | | | | | | op(e3, e2) = e2) % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | | REF_CLOSE: (4), (13), (16), (28), (46) are inconsistent by % 132.78/19.01 | | | | | | | | sub-proof #265. % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | Case 2: % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | | (47) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & % 132.78/19.01 | | | | | | | | op(e3, e0) = e2) % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | | BETA: splitting (47) gives: % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | | Case 1: % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | (48) all_57_4 = e2 & op(e3, e1) = e2 % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | REF_CLOSE: (10), (42), (48) are inconsistent by sub-proof % 132.78/19.01 | | | | | | | | | #264. % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | Case 2: % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | (49) all_57_9 = e2 & op(e3, e0) = e2 % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | ALPHA: (49) implies: % 132.78/19.01 | | | | | | | | | (50) all_57_9 = e2 % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | BETA: splitting (17) gives: % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | | Case 1: % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | (51) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & % 132.78/19.01 | | | | | | | | | | op(e1, e2) = e2) % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | BETA: splitting (51) gives: % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | Case 1: % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | (52) all_57_6 = e2 & op(e1, e3) = e2 % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | REF_CLOSE: (10), (45), (52) are inconsistent by sub-proof % 132.78/19.01 | | | | | | | | | | | #263. % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | Case 2: % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | (53) all_57_7 = e2 & op(e1, e2) = e2 % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | REF_CLOSE: (27), (36), (53) are inconsistent by sub-proof % 132.78/19.01 | | | | | | | | | | | #306. % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | End of split % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | Case 2: % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | (54) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 % 132.78/19.01 | | | | | | | | | | & op(e1, e0) = e2) % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | BETA: splitting (54) gives: % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | Case 1: % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | (55) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | REF_CLOSE: (16), (21), (55) are inconsistent by sub-proof % 132.78/19.01 | | | | | | | | | | | #262. % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | Case 2: % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | (56) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | ALPHA: (56) implies: % 132.78/19.01 | | | | | | | | | | | (57) all_57_11 = e2 % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | | REF_CLOSE: (5), (9), (12), (14), (23), (27), (50), (57) are % 132.78/19.01 | | | | | | | | | | | inconsistent by sub-proof #258. % 132.78/19.01 | | | | | | | | | | | % 132.78/19.01 | | | | | | | | | | End of split % 132.78/19.01 | | | | | | | | | | % 132.78/19.01 | | | | | | | | | End of split % 132.78/19.01 | | | | | | | | | % 132.78/19.01 | | | | | | | | End of split % 132.78/19.01 | | | | | | | | % 132.78/19.01 | | | | | | | End of split % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | Case 2: % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | (58) all_57_7 = e0 & op(e1, e2) = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | REF_CLOSE: (9), (36), (58) are inconsistent by sub-proof #307. % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | End of split % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | Case 2: % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | (59) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, % 132.78/19.01 | | | | | | e0) = e0) % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | BETA: splitting (59) gives: % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | | Case 1: % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | (60) all_57_8 = e0 & op(e1, e1) = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | REF_CLOSE: (3), (7), (8), (20), (21), (60) are inconsistent by % 132.78/19.01 | | | | | | | sub-proof #257. % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | Case 2: % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | (61) all_57_11 = e0 & op(e1, e0) = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | ALPHA: (61) implies: % 132.78/19.01 | | | | | | | (62) op(e1, e0) = e0 % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | | REF_CLOSE: (25), (29), (62) are inconsistent by sub-proof #355. % 132.78/19.01 | | | | | | | % 132.78/19.01 | | | | | | End of split % 132.78/19.01 | | | | | | % 132.78/19.01 | | | | | End of split % 132.78/19.01 | | | | | % 132.78/19.01 | | | | Case 2: % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | (63) all_57_9 = e0 & op(e3, e0) = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | ALPHA: (63) implies: % 132.78/19.01 | | | | | (64) op(e3, e0) = e0 % 132.78/19.01 | | | | | % 132.78/19.01 | | | | | REF_CLOSE: (1), (22), (64) are inconsistent by sub-proof #256. % 132.78/19.01 | | | | | % 132.78/19.01 | | | | End of split % 132.78/19.01 | | | | % 132.78/19.01 | | | End of split % 132.78/19.01 | | | % 132.78/19.01 | | Case 2: % 132.78/19.01 | | | % 132.78/19.01 | | | (65) all_57_13 = e3 & op(e0, e2) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | REF_CLOSE: (6), (14), (65) are inconsistent by sub-proof #297. % 132.78/19.01 | | | % 132.78/19.01 | | End of split % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #256 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_53_12 = e0 | ~ (op(e3, e0) = e0) % 132.78/19.01 (2) op(e3, e0) = e0 % 132.78/19.01 (3) ~ (all_53_12 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (1) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (4) ~ (op(e3, e0) = e0) % 132.78/19.01 | | % 132.78/19.01 | | PRED_UNIFY: (2), (4) imply: % 132.78/19.01 | | (5) $false % 132.78/19.01 | | % 132.78/19.01 | | CLOSE: (5) is inconsistent. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (6) all_53_12 = e0 % 132.78/19.01 | | % 132.78/19.01 | | REDUCE: (3), (6) imply: % 132.78/19.01 | | (7) $false % 132.78/19.01 | | % 132.78/19.01 | | CLOSE: (7) is inconsistent. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #257 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) op(e1, e1) = e1 % 132.78/19.01 (2) all_22_2 = e1 % 132.78/19.01 (3) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.01 (4) all_57_8 = e0 & op(e1, e1) = e0 % 132.78/19.01 (5) ~ (e1 = e0) % 132.78/19.01 (6) all_57_8 = e1 % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (4) implies: % 132.78/19.01 | (7) all_57_8 = e0 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (6), (7) imply: % 132.78/19.01 | (8) e1 = e0 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (8) imply: % 132.78/19.01 | (9) all_22_2 = e0 % 132.78/19.01 | % 132.78/19.01 | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #269. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #258 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_15 = e0 % 132.78/19.01 (2) ~ (e3 = e0) % 132.78/19.01 (3) all_57_10 = e1 % 132.78/19.01 (4) ~ (e3 = e1) % 132.78/19.01 (5) all_57_9 = e2 % 132.78/19.01 (6) all_57_11 = e2 % 132.78/19.01 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 132.78/19.01 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 132.78/19.01 (8) ~ (e3 = e2) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (7) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (9) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 132.78/19.01 | | e3) % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (3), (4), (5), (8), (9) are inconsistent by sub-proof #261. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (10) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 132.78/19.01 | | e3) % 132.78/19.01 | | % 132.78/19.01 | | BETA: splitting (10) gives: % 132.78/19.01 | | % 132.78/19.01 | | Case 1: % 132.78/19.01 | | | % 132.78/19.01 | | | (11) all_57_11 = e3 & op(e1, e0) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #260. % 132.78/19.01 | | | % 132.78/19.01 | | Case 2: % 132.78/19.01 | | | % 132.78/19.01 | | | (12) all_57_15 = e3 & op(e0, e0) = e3 % 132.78/19.01 | | | % 132.78/19.01 | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #259. % 132.78/19.01 | | | % 132.78/19.01 | | End of split % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #259 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_15 = e3 & op(e0, e0) = e3 % 132.78/19.01 (2) all_57_15 = e0 % 132.78/19.01 (3) ~ (e3 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_15 = e3 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e3 = e0 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e3 = e0 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #260 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_11 = e3 & op(e1, e0) = e3 % 132.78/19.01 (2) all_57_11 = e2 % 132.78/19.01 (3) ~ (e3 = e2) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_11 = e3 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e3 = e2 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e3 = e2 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #261 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 132.78/19.01 (2) all_57_10 = e1 % 132.78/19.01 (3) ~ (e3 = e1) % 132.78/19.01 (4) all_57_9 = e2 % 132.78/19.01 (5) ~ (e3 = e2) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (1) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (6) all_57_9 = e3 & op(e3, e0) = e3 % 132.78/19.01 | | % 132.78/19.01 | | ALPHA: (6) implies: % 132.78/19.01 | | (7) all_57_9 = e3 % 132.78/19.01 | | % 132.78/19.01 | | COMBINE_EQS: (4), (7) imply: % 132.78/19.01 | | (8) e3 = e2 % 132.78/19.01 | | % 132.78/19.01 | | SIMP: (8) implies: % 132.78/19.01 | | (9) e3 = e2 % 132.78/19.01 | | % 132.78/19.01 | | REDUCE: (5), (9) imply: % 132.78/19.01 | | (10) $false % 132.78/19.01 | | % 132.78/19.01 | | CLOSE: (10) is inconsistent. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (11) all_57_10 = e3 & op(e2, e0) = e3 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #284. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #262 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.01 (2) all_57_8 = e1 % 132.78/19.01 (3) ~ (e2 = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_8 = e2 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e2 = e1 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e2 = e1 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #263 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_6 = e2 & op(e1, e3) = e2 % 132.78/19.01 (2) all_57_6 = e0 % 132.78/19.01 (3) ~ (e2 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_6 = e2 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e2 = e0 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e2 = e0 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #264 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_4 = e2 & op(e3, e1) = e2 % 132.78/19.01 (2) all_57_4 = e0 % 132.78/19.01 (3) ~ (e2 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_4 = e2 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e2 = e0 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e2 = e0 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #265 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) op(e3, e3) = e1 % 132.78/19.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.01 (3) ~ (e2 = e1) % 132.78/19.01 (4) all_57_1 = e1 % 132.78/19.01 (5) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (5) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (6) all_57_0 = e2 & op(e3, e3) = e2 % 132.78/19.01 | | % 132.78/19.01 | | ALPHA: (6) implies: % 132.78/19.01 | | (7) op(e3, e3) = e2 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #267. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (8) all_57_1 = e2 & op(e3, e2) = e2 % 132.78/19.01 | | % 132.78/19.01 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #266. % 132.78/19.01 | | % 132.78/19.01 | End of split % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #266 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_57_1 = e2 & op(e3, e2) = e2 % 132.78/19.01 (2) all_57_1 = e1 % 132.78/19.01 (3) ~ (e2 = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (1) implies: % 132.78/19.01 | (4) all_57_1 = e2 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (2), (4) imply: % 132.78/19.01 | (5) e2 = e1 % 132.78/19.01 | % 132.78/19.01 | SIMP: (5) implies: % 132.78/19.01 | (6) e2 = e1 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (3), (6) imply: % 132.78/19.01 | (7) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (7) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #267 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.01 (2) op(e3, e3) = e2 % 132.78/19.01 (3) op(e3, e3) = e1 % 132.78/19.01 (4) ~ (e2 = e1) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3) % 132.78/19.01 | gives: % 132.78/19.01 | (5) e2 = e1 % 132.78/19.01 | % 132.78/19.01 | REDUCE: (4), (5) imply: % 132.78/19.01 | (6) $false % 132.78/19.01 | % 132.78/19.01 | CLOSE: (6) is inconsistent. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #268 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) op(e1, e1) = e1 % 132.78/19.01 (2) all_57_1 = e0 & op(e3, e2) = e0 % 132.78/19.01 (3) all_22_2 = e1 % 132.78/19.01 (4) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.01 (5) ~ (e1 = e0) % 132.78/19.01 (6) all_57_1 = e1 % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | ALPHA: (2) implies: % 132.78/19.01 | (7) all_57_1 = e0 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (6), (7) imply: % 132.78/19.01 | (8) e1 = e0 % 132.78/19.01 | % 132.78/19.01 | COMBINE_EQS: (3), (8) imply: % 132.78/19.01 | (9) all_22_2 = e0 % 132.78/19.01 | % 132.78/19.01 | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #269. % 132.78/19.01 | % 132.78/19.01 End of proof % 132.78/19.01 % 132.78/19.01 Sub-proof #269 shows that the following formulas are inconsistent: % 132.78/19.01 ---------------------------------------------------------------- % 132.78/19.01 (1) all_22_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.01 (2) op(e1, e1) = e1 % 132.78/19.01 (3) all_22_2 = e0 % 132.78/19.01 (4) ~ (e1 = e0) % 132.78/19.01 % 132.78/19.01 Begin of proof % 132.78/19.01 | % 132.78/19.01 | BETA: splitting (1) gives: % 132.78/19.01 | % 132.78/19.01 | Case 1: % 132.78/19.01 | | % 132.78/19.01 | | (5) ~ (op(e1, e1) = e1) % 132.78/19.01 | | % 132.78/19.01 | | PRED_UNIFY: (2), (5) imply: % 132.78/19.01 | | (6) $false % 132.78/19.01 | | % 132.78/19.01 | | CLOSE: (6) is inconsistent. % 132.78/19.01 | | % 132.78/19.01 | Case 2: % 132.78/19.01 | | % 132.78/19.01 | | (7) all_22_2 = e1 % 132.78/19.02 | | % 132.78/19.02 | | COMBINE_EQS: (3), (7) imply: % 132.78/19.02 | | (8) e1 = e0 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (4), (8) imply: % 132.78/19.02 | | (9) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (9) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #270 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_0 = e0 & op(e3, e3) = e0 % 132.78/19.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.02 (3) op(e3, e3) = all_4_2 % 132.78/19.02 (4) ~ (all_4_2 = e0) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (5) op(e3, e3) = e0 % 132.78/19.02 | % 132.78/19.02 | GROUND_INST: instantiating (2) with all_4_2, e0, e3, e3, simplifying with (3), % 132.78/19.02 | (5) gives: % 132.78/19.02 | (6) all_4_2 = e0 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (4), (6) imply: % 132.78/19.02 | (7) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (7) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #271 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_1 = e3 & op(e3, e2) = e3 % 132.78/19.02 (2) all_57_1 = e1 % 132.78/19.02 (3) ~ (e3 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (4) all_57_1 = e3 % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (2), (4) imply: % 132.78/19.02 | (5) e3 = e1 % 132.78/19.02 | % 132.78/19.02 | SIMP: (5) implies: % 132.78/19.02 | (6) e3 = e1 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (6) imply: % 132.78/19.02 | (7) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (7) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #272 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_12 = e1 & op(e0, e3) = e1 % 132.78/19.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.02 (3) op(e0, e3) = all_53_3 % 132.78/19.02 (4) ~ (all_53_3 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (5) op(e0, e3) = e1 % 132.78/19.02 | % 132.78/19.02 | GROUND_INST: instantiating (2) with all_53_3, e1, e3, e0, simplifying with % 132.78/19.02 | (3), (5) gives: % 132.78/19.02 | (6) all_53_3 = e1 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (4), (6) imply: % 132.78/19.02 | (7) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (7) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #273 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_9 = e1 & op(e3, e0) = e1 % 132.78/19.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.02 (3) op(e3, e0) = all_53_12 % 132.78/19.02 (4) ~ (all_53_12 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (5) op(e3, e0) = e1 % 132.78/19.02 | % 132.78/19.02 | GROUND_INST: instantiating (2) with all_53_12, e1, e0, e3, simplifying with % 132.78/19.02 | (3), (5) gives: % 132.78/19.02 | (6) all_53_12 = e1 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (4), (6) imply: % 132.78/19.02 | (7) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (7) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #274 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) ~ (all_4_2 = e1) % 132.78/19.02 (2) ~ (all_4_2 = e2) % 132.78/19.02 (3) all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0 % 132.78/19.02 (4) ~ (all_4_2 = e0) % 132.78/19.02 (5) all_55_0 = all_4_2 % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (3) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (6) all_55_0 = e2 % 132.78/19.02 | | % 132.78/19.02 | | COMBINE_EQS: (5), (6) imply: % 132.78/19.02 | | (7) all_4_2 = e2 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (2), (7) imply: % 132.78/19.02 | | (8) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (8) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (9) all_55_0 = e1 | all_55_0 = e0 % 132.78/19.02 | | % 132.78/19.02 | | BETA: splitting (9) gives: % 132.78/19.02 | | % 132.78/19.02 | | Case 1: % 132.78/19.02 | | | % 132.78/19.02 | | | (10) all_55_0 = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | COMBINE_EQS: (5), (10) imply: % 132.78/19.02 | | | (11) all_4_2 = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | REDUCE: (1), (11) imply: % 132.78/19.02 | | | (12) $false % 132.78/19.02 | | | % 132.78/19.02 | | | CLOSE: (12) is inconsistent. % 132.78/19.02 | | | % 132.78/19.02 | | Case 2: % 132.78/19.02 | | | % 132.78/19.02 | | | (13) all_55_0 = e0 % 132.78/19.02 | | | % 132.78/19.02 | | | COMBINE_EQS: (5), (13) imply: % 132.78/19.02 | | | (14) all_4_2 = e0 % 132.78/19.02 | | | % 132.78/19.02 | | | REDUCE: (4), (14) imply: % 132.78/19.02 | | | (15) $false % 132.78/19.02 | | | % 132.78/19.02 | | | CLOSE: (15) is inconsistent. % 132.78/19.02 | | | % 132.78/19.02 | | End of split % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #275 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/19.02 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.02 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/19.02 (4) op(unit, e0) = e0 % 132.78/19.02 (5) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.02 (6) ~ (all_53_13 = e0) % 132.78/19.02 (7) op(e1, unit) = e1 % 132.78/19.02 (8) all_55_7 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.02 (9) ~ (all_53_14 = e1) % 132.78/19.02 (10) ~ (all_53_2 = e3) % 132.78/19.02 (11) op(unit, e3) = e3 % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (8) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (12) ~ (op(e2, e0) = e0) % 132.78/19.02 | | % 132.78/19.02 | | BETA: splitting (1) gives: % 132.78/19.02 | | % 132.78/19.02 | | Case 1: % 132.78/19.02 | | | % 132.78/19.02 | | | (13) ~ (op(e1, e0) = e1) % 132.78/19.02 | | | % 132.78/19.02 | | | PRED_UNIFY: (7), (13) imply: % 132.78/19.02 | | | (14) ~ (unit = e0) % 132.78/19.02 | | | % 132.78/19.02 | | | PRED_UNIFY: (4), (12) imply: % 132.78/19.02 | | | (15) ~ (unit = e2) % 132.78/19.02 | | | % 132.78/19.02 | | | REF_CLOSE: (2), (3), (10), (11), (14), (15) are inconsistent by sub-proof % 132.78/19.02 | | | #276. % 132.78/19.02 | | | % 132.78/19.02 | | Case 2: % 132.78/19.02 | | | % 132.78/19.02 | | | (16) op(e1, e0) = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #339. % 132.78/19.02 | | | % 132.78/19.02 | | End of split % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (17) op(e2, e0) = e0 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #356. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #276 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) ~ (unit = e0) % 132.78/19.02 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.02 (3) unit = e2 | unit = e1 | unit = e0 % 132.78/19.02 (4) ~ (unit = e2) % 132.78/19.02 (5) ~ (all_53_2 = e3) % 132.78/19.02 (6) op(unit, e3) = e3 % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (3) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (7) unit = e2 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (4), (7) imply: % 132.78/19.02 | | (8) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (8) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (9) unit = e1 | unit = e0 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (1), (2), (5), (6), (9) are inconsistent by sub-proof #277. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #277 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) ~ (unit = e0) % 132.78/19.02 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.02 (3) ~ (all_53_2 = e3) % 132.78/19.02 (4) op(unit, e3) = e3 % 132.78/19.02 (5) unit = e1 | unit = e0 % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (5) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (6) unit = e1 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (4), (6) imply: % 132.78/19.02 | | (7) op(e1, e3) = e3 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #323. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (8) ~ (unit = e1) % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #278. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #278 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) unit = e1 | unit = e0 % 132.78/19.02 (2) ~ (unit = e1) % 132.78/19.02 (3) ~ (unit = e0) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (1) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (4) unit = e1 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (2), (4) imply: % 132.78/19.02 | | (5) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (5) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (6) unit = e0 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (3), (6) imply: % 132.78/19.02 | | (7) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (7) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #279 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_55_9 = all_53_6 % 132.78/19.02 (2) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) % 132.78/19.02 (3) ~ (all_53_6 = e1) % 132.78/19.02 (4) ~ (all_53_2 = e1) % 132.78/19.02 (5) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.02 (6) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (2) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (7) all_57_6 = e1 & op(e1, e3) = e1 % 132.78/19.02 | | % 132.78/19.02 | | ALPHA: (7) implies: % 132.78/19.02 | | (8) op(e1, e3) = e1 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #280. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (9) all_57_7 = e1 & op(e1, e2) = e1 % 132.78/19.02 | | % 132.78/19.02 | | ALPHA: (9) implies: % 132.78/19.02 | | (10) op(e1, e2) = e1 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #341. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #280 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_53_2 = e1 | ~ (op(e1, e3) = e1) % 132.78/19.02 (2) op(e1, e3) = e1 % 132.78/19.02 (3) ~ (all_53_2 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (1) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (4) ~ (op(e1, e3) = e1) % 132.78/19.02 | | % 132.78/19.02 | | PRED_UNIFY: (2), (4) imply: % 132.78/19.02 | | (5) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (5) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (6) all_53_2 = e1 % 132.78/19.02 | | % 132.78/19.02 | | REDUCE: (3), (6) imply: % 132.78/19.02 | | (7) $false % 132.78/19.02 | | % 132.78/19.02 | | CLOSE: (7) is inconsistent. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #281 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_55_10 = all_12_2 % 132.78/19.02 (2) all_55_10 = e2 % 132.78/19.02 (3) ~ (all_12_2 = e2) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (1), (2) imply: % 132.78/19.02 | (4) all_12_2 = e2 % 132.78/19.02 | % 132.78/19.02 | SIMP: (4) implies: % 132.78/19.02 | (5) all_12_2 = e2 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (5) imply: % 132.78/19.02 | (6) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (6) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #282 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_55_10 = all_12_2 % 132.78/19.02 (2) all_55_10 = e3 % 132.78/19.02 (3) ~ (all_12_2 = e3) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (1), (2) imply: % 132.78/19.02 | (4) all_12_2 = e3 % 132.78/19.02 | % 132.78/19.02 | SIMP: (4) implies: % 132.78/19.02 | (5) all_12_2 = e3 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (5) imply: % 132.78/19.02 | (6) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (6) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #283 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/19.02 (2) op(e0, e0) = all_8_2 % 132.78/19.02 (3) ~ (all_8_2 = e1) % 132.78/19.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.02 (5) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 132.78/19.02 (6) ~ (all_53_14 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (5) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (7) all_57_11 = e1 & op(e1, e0) = e1 % 132.78/19.02 | | % 132.78/19.02 | | ALPHA: (7) implies: % 132.78/19.02 | | (8) op(e1, e0) = e1 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #339. % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (9) all_57_15 = e1 & op(e0, e0) = e1 % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #294. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #284 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_10 = e3 & op(e2, e0) = e3 % 132.78/19.02 (2) all_57_10 = e1 % 132.78/19.02 (3) ~ (e3 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (4) all_57_10 = e3 % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (2), (4) imply: % 132.78/19.02 | (5) e3 = e1 % 132.78/19.02 | % 132.78/19.02 | SIMP: (5) implies: % 132.78/19.02 | (6) e3 = e1 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (6) imply: % 132.78/19.02 | (7) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (7) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #285 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_9 = e0 & op(e3, e0) = e0 % 132.78/19.02 (2) all_57_9 = e2 % 132.78/19.02 (3) ~ (e2 = e0) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (4) all_57_9 = e0 % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (2), (4) imply: % 132.78/19.02 | (5) e2 = e0 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (5) imply: % 132.78/19.02 | (6) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (6) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #286 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_1 = e0 & op(e3, e2) = e0 % 132.78/19.02 (2) all_57_1 = e1 % 132.78/19.02 (3) ~ (e1 = e0) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (4) all_57_1 = e0 % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (2), (4) imply: % 132.78/19.02 | (5) e1 = e0 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (5) imply: % 132.78/19.02 | (6) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (6) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #287 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) ~ (all_12_2 = e1) % 132.78/19.02 (2) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 132.78/19.02 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 132.78/19.02 (3) ~ (e2 = e1) % 132.78/19.02 (4) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.02 (5) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.02 (6) all_57_4 = e2 % 132.78/19.02 (7) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.02 (8) ~ (all_53_11 = e1) % 132.78/19.02 (9) ~ (all_53_9 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | BETA: splitting (2) gives: % 132.78/19.02 | % 132.78/19.02 | Case 1: % 132.78/19.02 | | % 132.78/19.02 | | (10) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = % 132.78/19.02 | | e1) % 132.78/19.02 | | % 132.78/19.02 | | BETA: splitting (10) gives: % 132.78/19.02 | | % 132.78/19.02 | | Case 1: % 132.78/19.02 | | | % 132.78/19.02 | | | (11) all_57_4 = e1 & op(e3, e1) = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #288. % 132.78/19.02 | | | % 132.78/19.02 | | Case 2: % 132.78/19.02 | | | % 132.78/19.02 | | | (12) all_57_5 = e1 & op(e2, e1) = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | ALPHA: (12) implies: % 132.78/19.02 | | | (13) op(e2, e1) = e1 % 132.78/19.02 | | | % 132.78/19.02 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #334. % 132.78/19.02 | | | % 132.78/19.02 | | End of split % 132.78/19.02 | | % 132.78/19.02 | Case 2: % 132.78/19.02 | | % 132.78/19.02 | | (14) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 132.78/19.02 | | e1) % 132.78/19.02 | | % 132.78/19.02 | | REF_CLOSE: (1), (4), (5), (8), (14) are inconsistent by sub-proof #332. % 132.78/19.02 | | % 132.78/19.02 | End of split % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #288 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) all_57_4 = e1 & op(e3, e1) = e1 % 132.78/19.02 (2) all_57_4 = e2 % 132.78/19.02 (3) ~ (e2 = e1) % 132.78/19.02 % 132.78/19.02 Begin of proof % 132.78/19.02 | % 132.78/19.02 | ALPHA: (1) implies: % 132.78/19.02 | (4) all_57_4 = e1 % 132.78/19.02 | % 132.78/19.02 | COMBINE_EQS: (2), (4) imply: % 132.78/19.02 | (5) e2 = e1 % 132.78/19.02 | % 132.78/19.02 | REDUCE: (3), (5) imply: % 132.78/19.02 | (6) $false % 132.78/19.02 | % 132.78/19.02 | CLOSE: (6) is inconsistent. % 132.78/19.02 | % 132.78/19.02 End of proof % 132.78/19.02 % 132.78/19.02 Sub-proof #289 shows that the following formulas are inconsistent: % 132.78/19.02 ---------------------------------------------------------------- % 132.78/19.02 (1) ~ (all_53_1 = e3) % 132.78/19.02 (2) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/19.02 (3) op(e1, e1) = all_12_2 % 132.78/19.02 (4) all_57_5 = e3 % 132.78/19.02 (5) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.02 (6) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.02 (7) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.78/19.02 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.78/19.02 (8) ~ (all_53_11 = e0) % 132.78/19.02 (9) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.02 (10) ~ (all_53_8 = e3) % 132.78/19.02 (11) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 132.78/19.02 | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.02 (12) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 132.78/19.02 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.02 (13) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.78/19.02 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.78/19.02 (14) all_55_9 = all_53_6 % 132.78/19.02 (15) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.78/19.02 (16) ~ (all_53_1 = all_53_13) % 132.78/19.02 (17) ~ (all_53_8 = all_12_2) % 132.78/19.02 (18) all_55_7 = all_53_13 % 132.78/19.02 (19) op(e2, e3) = e2 % 132.78/19.02 (20) ~ (all_53_8 = e2) % 132.78/19.02 (21) all_55_1 = all_53_4 % 132.78/19.02 (22) all_53_3 = e0 % 132.78/19.02 (23) ~ (all_53_13 = e0) % 132.78/19.02 (24) op(e3, e1) = e1 % 132.78/19.02 (25) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 132.78/19.02 (26) ~ (all_53_8 = all_53_9) % 132.78/19.02 (27) ~ (e3 = e0) % 132.78/19.02 (28) op(e0, e0) = all_8_2 % 132.78/19.02 (29) ~ (e2 = e0) % 132.78/19.02 (30) op(e1, e2) = all_53_6 % 132.78/19.02 (31) ~ (all_53_8 = e0) % 132.78/19.02 (32) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.78/19.02 (33) op(e1, e0) = all_53_14 % 132.78/19.02 (34) ~ (all_53_7 = e0) % 132.78/19.02 (35) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 132.78/19.02 (36) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.78/19.02 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.78/19.02 (37) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 132.78/19.02 (38) ~ (all_8_2 = e1) % 132.78/19.02 (39) all_53_8 = e1 | ~ (op(e3, e1) = e1) % 132.78/19.02 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.02 (41) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 132.78/19.02 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 132.78/19.02 (42) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.02 (43) ~ (all_6_2 = e2) % 132.78/19.02 (44) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.78/19.02 (45) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 132.78/19.02 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 132.78/19.02 (46) ~ (all_53_4 = e3) % 132.78/19.02 (47) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.78/19.02 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.78/19.02 (48) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.02 (49) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.02 (50) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 132.78/19.02 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 132.78/19.02 (51) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.78/19.02 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.78/19.02 (52) op(e3, e3) = e3 % 132.78/19.02 (53) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.02 (54) ~ (all_53_8 = all_53_11) % 132.78/19.02 (55) ~ (all_53_9 = e2) % 132.78/19.02 (56) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.02 (57) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 132.78/19.02 (58) ~ (all_53_3 = e3) % 132.78/19.02 (59) ~ (all_53_6 = e1) % 132.78/19.02 (60) all_4_2 = e3 % 132.78/19.02 (61) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.02 (62) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 132.78/19.02 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 132.78/19.02 e1) % 132.78/19.02 (63) ~ (all_53_14 = e1) % 132.78/19.02 (64) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 132.78/19.02 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 132.78/19.02 (65) ~ (all_53_6 = e2) % 132.78/19.02 (66) all_38_2 = all_12_2 % 132.78/19.02 (67) ~ (all_38_2 = e0) | (op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 132.78/19.02 (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 132.78/19.02 $i(all_38_0)))) % 132.78/19.02 (68) ~ (all_53_2 = e3) % 132.78/19.02 (69) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 132.78/19.02 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 132.78/19.02 (70) all_42_2 = all_6_2 % 132.78/19.03 (71) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.78/19.03 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 132.78/19.03 (72) all_55_4 = all_53_1 % 132.78/19.03 (73) ~ (e3 = e2) % 132.78/19.03 (74) all_55_13 = all_53_7 % 132.78/19.03 (75) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.03 (76) all_57_4 = e1 % 132.78/19.03 (77) all_55_12 = all_53_3 % 132.78/19.03 (78) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (39) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (79) ~ (op(e3, e1) = e1) % 132.78/19.03 | | % 132.78/19.03 | | PRED_UNIFY: (24), (79) imply: % 132.78/19.03 | | (80) $false % 132.78/19.03 | | % 132.78/19.03 | | CLOSE: (80) is inconsistent. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (81) all_53_8 = e1 % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (26), (81) imply: % 132.78/19.03 | | (82) ~ (all_53_9 = e1) % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (82) implies: % 132.78/19.03 | | (83) ~ (all_53_9 = e1) % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (54), (81) imply: % 132.78/19.03 | | (84) ~ (all_53_11 = e1) % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (84) implies: % 132.78/19.03 | | (85) ~ (all_53_11 = e1) % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (17), (81) imply: % 132.78/19.03 | | (86) ~ (all_12_2 = e1) % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (86) implies: % 132.78/19.03 | | (87) ~ (all_12_2 = e1) % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (10), (81) imply: % 132.78/19.03 | | (88) ~ (e3 = e1) % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (88) implies: % 132.78/19.03 | | (89) ~ (e3 = e1) % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (20), (81) imply: % 132.78/19.03 | | (90) ~ (e2 = e1) % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (90) implies: % 132.78/19.03 | | (91) ~ (e2 = e1) % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (31), (81) imply: % 132.78/19.03 | | (92) ~ (e1 = e0) % 132.78/19.03 | | % 132.78/19.03 | | BETA: splitting (62) gives: % 132.78/19.03 | | % 132.78/19.03 | | Case 1: % 132.78/19.03 | | | % 132.78/19.03 | | | (93) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) % 132.78/19.03 | | | = e1) % 132.78/19.03 | | | % 132.78/19.03 | | | BETA: splitting (93) gives: % 132.78/19.03 | | | % 132.78/19.03 | | | Case 1: % 132.78/19.03 | | | | % 132.78/19.03 | | | | (94) all_57_12 = e1 & op(e0, e3) = e1 % 132.78/19.03 | | | | % 132.78/19.03 | | | | ALPHA: (94) implies: % 132.78/19.03 | | | | (95) all_57_12 = e1 % 132.78/19.03 | | | | % 132.78/19.03 | | | | REF_CLOSE: (8), (11), (32), (34), (41), (48), (53), (56), (74), (75), % 132.78/19.03 | | | | (76), (83), (85), (87), (92), (95) are inconsistent by % 132.78/19.03 | | | | sub-proof #290. % 132.78/19.03 | | | | % 132.78/19.03 | | | Case 2: % 132.78/19.03 | | | | % 132.78/19.03 | | | | (96) all_57_13 = e1 & op(e0, e2) = e1 % 132.78/19.03 | | | | % 132.78/19.03 | | | | ALPHA: (96) implies: % 132.78/19.03 | | | | (97) all_57_13 = e1 % 132.78/19.03 | | | | % 132.78/19.03 | | | | BETA: splitting (36) gives: % 132.78/19.03 | | | | % 132.78/19.03 | | | | Case 1: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | (98) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, % 132.78/19.03 | | | | | e2) = e1) % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | BETA: splitting (98) gives: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | Case 1: % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | (99) all_57_6 = e1 & op(e1, e3) = e1 % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | ALPHA: (99) implies: % 132.78/19.03 | | | | | | (100) all_57_6 = e1 % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), % 132.78/19.03 | | | | | | (14), (15), (16), (18), (19), (21), (22), (23), (25), % 132.78/19.03 | | | | | | (27), (29), (30), (33), (35), (36), (37), (40), (41), % 132.78/19.03 | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), % 132.78/19.03 | | | | | | (51), (52), (53), (55), (56), (57), (58), (59), (60), % 132.78/19.03 | | | | | | (61), (63), (64), (65), (66), (67), (68), (69), (70), % 132.78/19.03 | | | | | | (71), (72), (73), (75), (76), (77), (78), (83), (85), % 132.78/19.03 | | | | | | (87), (89), (91), (92), (97), (100) are inconsistent by % 132.78/19.03 | | | | | | sub-proof #295. % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | Case 2: % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | (101) all_57_7 = e1 & op(e1, e2) = e1 % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | ALPHA: (101) implies: % 132.78/19.03 | | | | | | (102) op(e1, e2) = e1 % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | REF_CLOSE: (14), (59), (61), (102) are inconsistent by sub-proof % 132.78/19.03 | | | | | | #341. % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | End of split % 132.78/19.03 | | | | | % 132.78/19.03 | | | | Case 2: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | (103) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, % 132.78/19.03 | | | | | e0) = e1) % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | REF_CLOSE: (2), (53), (63), (87), (103) are inconsistent by sub-proof % 132.78/19.03 | | | | | #338. % 132.78/19.03 | | | | | % 132.78/19.03 | | | | End of split % 132.78/19.03 | | | | % 132.78/19.03 | | | End of split % 132.78/19.03 | | | % 132.78/19.03 | | Case 2: % 132.78/19.03 | | | % 132.78/19.03 | | | (104) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) % 132.78/19.03 | | | = e1) % 132.78/19.03 | | | % 132.78/19.03 | | | REF_CLOSE: (28), (38), (40), (56), (85), (104) are inconsistent by % 132.78/19.03 | | | sub-proof #293. % 132.78/19.03 | | | % 132.78/19.03 | | End of split % 132.78/19.03 | | % 132.78/19.03 | End of split % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #290 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) ~ (all_53_11 = e0) % 132.78/19.03 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 132.78/19.03 (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.03 (3) ~ (all_12_2 = e1) % 132.78/19.03 (4) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.78/19.03 (5) ~ (all_53_7 = e0) % 132.78/19.03 (6) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 132.78/19.03 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 132.78/19.03 (7) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.03 (8) ~ (e1 = e0) % 132.78/19.03 (9) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.03 (10) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.03 (11) all_57_12 = e1 % 132.78/19.03 (12) all_55_13 = all_53_7 % 132.78/19.03 (13) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.03 (14) ~ (all_53_11 = e1) % 132.78/19.03 (15) all_57_4 = e1 % 132.78/19.03 (16) ~ (all_53_9 = e1) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (2) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (17) all_57_12 = e0 & op(e0, e3) = e0 % 132.78/19.03 | | % 132.78/19.03 | | ALPHA: (17) implies: % 132.78/19.03 | | (18) all_57_12 = e0 % 132.78/19.03 | | % 132.78/19.03 | | COMBINE_EQS: (11), (18) imply: % 132.78/19.03 | | (19) e1 = e0 % 132.78/19.03 | | % 132.78/19.03 | | COMBINE_EQS: (15), (19) imply: % 132.78/19.03 | | (20) all_57_4 = e0 % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (3), (6), (8), (9), (10), (13), (14), (16), (20) are inconsistent % 132.78/19.03 | | by sub-proof #331. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (21) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 132.78/19.03 | | e0) % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (1), (4), (5), (7), (12), (21) are inconsistent by sub-proof % 132.78/19.03 | | #291. % 132.78/19.03 | | % 132.78/19.03 | End of split % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #291 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) ~ (all_53_11 = e0) % 132.78/19.03 (2) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.78/19.03 (3) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.03 (4) ~ (all_53_7 = e0) % 132.78/19.03 (5) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.03 (6) all_55_13 = all_53_7 % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (3) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (7) all_57_13 = e0 & op(e0, e2) = e0 % 132.78/19.03 | | % 132.78/19.03 | | ALPHA: (7) implies: % 132.78/19.03 | | (8) op(e0, e2) = e0 % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #292. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (9) all_57_14 = e0 & op(e0, e1) = e0 % 132.78/19.03 | | % 132.78/19.03 | | ALPHA: (9) implies: % 132.78/19.03 | | (10) op(e0, e1) = e0 % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #296. % 132.78/19.03 | | % 132.78/19.03 | End of split % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #292 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) all_55_13 = e0 | ~ (op(e0, e2) = e0) % 132.78/19.03 (2) op(e0, e2) = e0 % 132.78/19.03 (3) all_55_13 = all_53_7 % 132.78/19.03 (4) ~ (all_53_7 = e0) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (1) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (5) ~ (op(e0, e2) = e0) % 132.78/19.03 | | % 132.78/19.03 | | PRED_UNIFY: (2), (5) imply: % 132.78/19.03 | | (6) $false % 132.78/19.03 | | % 132.78/19.03 | | CLOSE: (6) is inconsistent. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (7) all_55_13 = e0 % 132.78/19.03 | | % 132.78/19.03 | | COMBINE_EQS: (3), (7) imply: % 132.78/19.03 | | (8) all_53_7 = e0 % 132.78/19.03 | | % 132.78/19.03 | | SIMP: (8) implies: % 132.78/19.03 | | (9) all_53_7 = e0 % 132.78/19.03 | | % 132.78/19.03 | | REDUCE: (4), (9) imply: % 132.78/19.03 | | (10) $false % 132.78/19.03 | | % 132.78/19.03 | | CLOSE: (10) is inconsistent. % 132.78/19.03 | | % 132.78/19.03 | End of split % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #293 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 132.78/19.03 (2) op(e0, e0) = all_8_2 % 132.78/19.03 (3) ~ (all_8_2 = e1) % 132.78/19.03 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.03 (5) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.03 (6) ~ (all_53_11 = e1) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (1) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (7) all_57_14 = e1 & op(e0, e1) = e1 % 132.78/19.03 | | % 132.78/19.03 | | ALPHA: (7) implies: % 132.78/19.03 | | (8) op(e0, e1) = e1 % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #333. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (9) all_57_15 = e1 & op(e0, e0) = e1 % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #294. % 132.78/19.03 | | % 132.78/19.03 | End of split % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #294 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) all_57_15 = e1 & op(e0, e0) = e1 % 132.78/19.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.03 (3) op(e0, e0) = all_8_2 % 132.78/19.03 (4) ~ (all_8_2 = e1) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | ALPHA: (1) implies: % 132.78/19.03 | (5) op(e0, e0) = e1 % 132.78/19.03 | % 132.78/19.03 | GROUND_INST: instantiating (2) with all_8_2, e1, e0, e0, simplifying with (3), % 132.78/19.03 | (5) gives: % 132.78/19.03 | (6) all_8_2 = e1 % 132.78/19.03 | % 132.78/19.03 | REDUCE: (4), (6) imply: % 132.78/19.03 | (7) $false % 132.78/19.03 | % 132.78/19.03 | CLOSE: (7) is inconsistent. % 132.78/19.03 | % 132.78/19.03 End of proof % 132.78/19.03 % 132.78/19.03 Sub-proof #295 shows that the following formulas are inconsistent: % 132.78/19.03 ---------------------------------------------------------------- % 132.78/19.03 (1) ~ (all_53_1 = e3) % 132.78/19.03 (2) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/19.03 (3) op(e1, e1) = all_12_2 % 132.78/19.03 (4) all_57_5 = e3 % 132.78/19.03 (5) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.03 (6) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.03 (7) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.78/19.03 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.78/19.03 (8) ~ (all_53_11 = e0) % 132.78/19.03 (9) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.03 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 132.78/19.03 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 132.78/19.03 (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.78/19.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.78/19.03 (12) all_55_9 = all_53_6 % 132.78/19.03 (13) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.78/19.03 (14) ~ (all_53_1 = all_53_13) % 132.78/19.03 (15) ~ (all_12_2 = e1) % 132.78/19.03 (16) all_57_13 = e1 % 132.78/19.03 (17) all_55_7 = all_53_13 % 132.78/19.03 (18) op(e2, e3) = e2 % 132.78/19.03 (19) all_55_1 = all_53_4 % 132.78/19.03 (20) all_53_3 = e0 % 132.78/19.03 (21) ~ (all_53_13 = e0) % 132.78/19.03 (22) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 132.78/19.03 (23) ~ (e3 = e0) % 132.78/19.03 (24) ~ (e2 = e0) % 132.78/19.03 (25) op(e1, e2) = all_53_6 % 132.78/19.03 (26) op(e1, e0) = all_53_14 % 132.78/19.03 (27) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 132.78/19.03 (28) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 132.78/19.03 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 132.78/19.03 (29) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 132.78/19.03 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.03 (31) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 132.78/19.03 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 132.78/19.03 (32) ~ (e3 = e1) % 132.78/19.03 (33) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 132.78/19.03 (34) ~ (all_6_2 = e2) % 132.78/19.03 (35) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.78/19.03 (36) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 132.78/19.03 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 132.78/19.03 (37) ~ (all_53_4 = e3) % 132.78/19.03 (38) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.78/19.03 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.78/19.03 (39) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.03 (40) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.03 (41) all_57_6 = e1 % 132.78/19.03 (42) ~ (e2 = e1) % 132.78/19.03 (43) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 132.78/19.03 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 132.78/19.03 (44) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.78/19.03 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.78/19.03 (45) ~ (e1 = e0) % 132.78/19.03 (46) op(e3, e3) = e3 % 132.78/19.03 (47) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 132.78/19.03 (48) ~ (all_53_9 = e2) % 132.78/19.03 (49) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 132.78/19.03 (50) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 132.78/19.03 (51) ~ (all_53_3 = e3) % 132.78/19.03 (52) ~ (all_53_6 = e1) % 132.78/19.03 (53) all_4_2 = e3 % 132.78/19.03 (54) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 132.78/19.03 (55) ~ (all_53_14 = e1) % 132.78/19.03 (56) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 132.78/19.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 132.78/19.03 (57) ~ (all_53_6 = e2) % 132.78/19.03 (58) all_38_2 = all_12_2 % 132.78/19.03 (59) ~ (all_38_2 = e0) | (op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 132.78/19.03 (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 132.78/19.03 $i(all_38_0)))) % 132.78/19.03 (60) ~ (all_53_2 = e3) % 132.78/19.03 (61) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 132.78/19.03 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 132.78/19.03 (62) all_42_2 = all_6_2 % 132.78/19.03 (63) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 132.78/19.03 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 132.78/19.03 (64) all_55_4 = all_53_1 % 132.78/19.03 (65) ~ (e3 = e2) % 132.78/19.03 (66) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 132.78/19.03 (67) ~ (all_53_11 = e1) % 132.78/19.03 (68) all_57_4 = e1 % 132.78/19.03 (69) ~ (all_53_9 = e1) % 132.78/19.03 (70) all_55_12 = all_53_3 % 132.78/19.03 (71) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 132.78/19.03 % 132.78/19.03 Begin of proof % 132.78/19.03 | % 132.78/19.03 | BETA: splitting (10) gives: % 132.78/19.03 | % 132.78/19.03 | Case 1: % 132.78/19.03 | | % 132.78/19.03 | | (72) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = % 132.78/19.03 | | e0) % 132.78/19.03 | | % 132.78/19.03 | | REF_CLOSE: (4), (15), (23), (31), (45), (47), (49), (66), (67), (69), (72) % 132.78/19.03 | | are inconsistent by sub-proof #329. % 132.78/19.03 | | % 132.78/19.03 | Case 2: % 132.78/19.03 | | % 132.78/19.03 | | (73) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 132.78/19.03 | | e0) % 132.78/19.03 | | % 132.78/19.03 | | BETA: splitting (73) gives: % 132.78/19.03 | | % 132.78/19.03 | | Case 1: % 132.78/19.03 | | | % 132.78/19.03 | | | (74) all_57_8 = e0 & op(e1, e1) = e0 % 132.78/19.03 | | | % 132.78/19.03 | | | ALPHA: (74) implies: % 132.78/19.03 | | | (75) all_57_8 = e0 % 132.78/19.03 | | | (76) op(e1, e1) = e0 % 132.78/19.03 | | | % 132.78/19.03 | | | BETA: splitting (63) gives: % 132.78/19.03 | | | % 132.78/19.03 | | | Case 1: % 132.78/19.03 | | | | % 132.78/19.03 | | | | (77) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) % 132.78/19.03 | | | | = e3) % 132.78/19.03 | | | | % 132.78/19.03 | | | | BETA: splitting (77) gives: % 132.78/19.03 | | | | % 132.78/19.03 | | | | Case 1: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | (78) all_57_1 = e3 & op(e3, e2) = e3 % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | REF_CLOSE: (19), (22), (37), (78) are inconsistent by sub-proof #328. % 132.78/19.03 | | | | | % 132.78/19.03 | | | | Case 2: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | (79) all_57_3 = e3 & op(e2, e2) = e3 % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | ALPHA: (79) implies: % 132.78/19.03 | | | | | (80) all_57_3 = e3 % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | REF_CLOSE: (2), (4), (5), (9), (11), (12), (13), (14), (15), (17), % 132.78/19.03 | | | | | (18), (21), (23), (24), (27), (28), (29), (30), (32), (33), % 132.78/19.03 | | | | | (34), (36), (41), (42), (44), (46), (47), (48), (50), (52), % 132.78/19.03 | | | | | (53), (54), (55), (57), (60), (61), (62), (64), (65), (71), % 132.78/19.03 | | | | | (75), (76), (80) are inconsistent by sub-proof #313. % 132.78/19.03 | | | | | % 132.78/19.03 | | | | End of split % 132.78/19.03 | | | | % 132.78/19.03 | | | Case 2: % 132.78/19.03 | | | | % 132.78/19.03 | | | | (81) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) % 132.78/19.03 | | | | = e3) % 132.78/19.03 | | | | % 132.78/19.03 | | | | BETA: splitting (81) gives: % 132.78/19.03 | | | | % 132.78/19.03 | | | | Case 1: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | (82) all_57_7 = e3 & op(e1, e2) = e3 % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | ALPHA: (82) implies: % 132.78/19.03 | | | | | (83) all_57_7 = e3 % 132.78/19.03 | | | | | (84) op(e1, e2) = e3 % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | BETA: splitting (44) gives: % 132.78/19.03 | | | | | % 132.78/19.03 | | | | | Case 1: % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | (85) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, % 132.78/19.03 | | | | | | e2) = e2) % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | REF_CLOSE: (2), (12), (15), (27), (28), (42), (47), (52), (54), % 132.78/19.03 | | | | | | (55), (57), (85) are inconsistent by sub-proof #325. % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | Case 2: % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | (86) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, % 132.78/19.03 | | | | | | e0) = e2) % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | BETA: splitting (86) gives: % 132.78/19.03 | | | | | | % 132.78/19.03 | | | | | | Case 1: % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | (87) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | ALPHA: (87) implies: % 132.78/19.03 | | | | | | | (88) op(e1, e1) = e2 % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | REF_CLOSE: (24), (30), (76), (88) are inconsistent by sub-proof % 132.78/19.03 | | | | | | | #324. % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | Case 2: % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | (89) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | ALPHA: (89) implies: % 132.78/19.03 | | | | | | | (90) all_57_11 = e2 % 132.78/19.03 | | | | | | | (91) op(e1, e0) = e2 % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | BETA: splitting (38) gives: % 132.78/19.03 | | | | | | | % 132.78/19.03 | | | | | | | Case 1: % 132.78/19.03 | | | | | | | | % 132.78/19.03 | | | | | | | | (92) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & % 132.78/19.03 | | | | | | | | op(e2, e3) = e3) % 132.78/19.03 | | | | | | | | % 132.78/19.03 | | | | | | | | BETA: splitting (92) gives: % 132.78/19.03 | | | | | | | | % 132.78/19.03 | | | | | | | | Case 1: % 132.78/19.03 | | | | | | | | | % 132.78/19.03 | | | | | | | | | (93) all_57_0 = e3 & op(e3, e3) = e3 % 132.78/19.03 | | | | | | | | | % 132.78/19.03 | | | | | | | | | ALPHA: (93) implies: % 132.78/19.03 | | | | | | | | | (94) all_57_0 = e3 % 132.78/19.03 | | | | | | | | | % 132.78/19.03 | | | | | | | | | BETA: splitting (56) gives: % 132.78/19.03 | | | | | | | | | % 132.78/19.03 | | | | | | | | | Case 1: % 132.78/19.03 | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | (95) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & % 132.78/19.03 | | | | | | | | | | op(e2, e1) = e3) % 132.78/19.03 | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | BETA: splitting (95) gives: % 132.78/19.03 | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | Case 1: % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | (96) all_57_4 = e3 & op(e3, e1) = e3 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | ALPHA: (96) implies: % 132.78/19.03 | | | | | | | | | | | (97) all_57_4 = e3 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | COMBINE_EQS: (68), (97) imply: % 132.78/19.03 | | | | | | | | | | | (98) e3 = e1 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | COMBINE_EQS: (94), (98) imply: % 132.78/19.03 | | | | | | | | | | | (99) all_57_0 = e1 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | REF_CLOSE: (1), (5), (32), (35), (38), (40), (51), (60), % 132.78/19.03 | | | | | | | | | | | (70), (99) are inconsistent by sub-proof #310. % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | Case 2: % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_53_14, e2, e0, e1, % 132.78/19.03 | | | | | | | | | | | simplifying with (26), (91) gives: % 132.78/19.03 | | | | | | | | | | | (100) all_53_14 = e2 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_12_2, e0, e1, e1, % 132.78/19.03 | | | | | | | | | | | simplifying with (3), (76) gives: % 132.78/19.03 | | | | | | | | | | | (101) all_12_2 = e0 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.03 | | | | | | | | | | | GROUND_INST: instantiating (30) with all_53_6, e3, e2, e1, % 132.78/19.03 | | | | | | | | | | | simplifying with (25), (84) gives: % 132.78/19.03 | | | | | | | | | | | (102) all_53_6 = e3 % 132.78/19.03 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | COMBINE_EQS: (58), (101) imply: % 132.78/19.04 | | | | | | | | | | | (103) all_38_2 = e0 % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | REF_CLOSE: (30), (59), (84), (91), (103) are inconsistent by % 132.78/19.04 | | | | | | | | | | | sub-proof #308. % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | | % 132.78/19.04 | | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | (104) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 % 132.78/19.04 | | | | | | | | | | & op(e0, e1) = e3) % 132.78/19.04 | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | BETA: splitting (104) gives: % 132.78/19.04 | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | Case 1: % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | (105) all_57_8 = e3 & op(e1, e1) = e3 % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | ALPHA: (105) implies: % 132.78/19.04 | | | | | | | | | | | (106) op(e1, e1) = e3 % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | REF_CLOSE: (7), (23), (24), (30), (41), (42), (44), (45), % 132.78/19.04 | | | | | | | | | | | (65), (83), (106) are inconsistent by sub-proof % 132.78/19.04 | | | | | | | | | | | #304. % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | (107) all_57_14 = e3 & op(e0, e1) = e3 % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | ALPHA: (107) implies: % 132.78/19.04 | | | | | | | | | | | (108) all_57_14 = e3 % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | BETA: splitting (43) gives: % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | Case 1: % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | (109) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.78/19.04 | | | | | | | | | | | | & op(e2, e1) = e2) % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | BETA: splitting (109) gives: % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | Case 1: % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | (110) all_57_4 = e2 & op(e3, e1) = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | ALPHA: (110) implies: % 132.78/19.04 | | | | | | | | | | | | | (111) all_57_4 = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | COMBINE_EQS: (68), (111) imply: % 132.78/19.04 | | | | | | | | | | | | | (112) e2 = e1 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | SIMP: (112) implies: % 132.78/19.04 | | | | | | | | | | | | | (113) e2 = e1 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | REDUCE: (42), (113) imply: % 132.78/19.04 | | | | | | | | | | | | | (114) $false % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | CLOSE: (114) is inconsistent. % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | (115) all_57_5 = e2 & op(e2, e1) = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | REF_CLOSE: (4), (65), (115) are inconsistent by sub-proof % 132.78/19.04 | | | | | | | | | | | | | #303. % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | (116) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.78/19.04 | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | BETA: splitting (116) gives: % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | Case 1: % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | (117) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | ALPHA: (117) implies: % 132.78/19.04 | | | | | | | | | | | | | (118) all_57_8 = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | COMBINE_EQS: (75), (118) imply: % 132.78/19.04 | | | | | | | | | | | | | (119) e2 = e0 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | REF_CLOSE: (24), (41), (42), (44), (65), (75), (83), (90), % 132.78/19.04 | | | | | | | | | | | | | (119) are inconsistent by sub-proof #301. % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | (120) all_57_14 = e2 & op(e0, e1) = e2 % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | | REF_CLOSE: (65), (108), (120) are inconsistent by sub-proof % 132.78/19.04 | | | | | | | | | | | | | #300. % 132.78/19.04 | | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | | | % 132.78/19.04 | | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | | % 132.78/19.04 | | | | | | | | | End of split % 132.78/19.04 | | | | | | | | | % 132.78/19.04 | | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | | % 132.78/19.04 | | | | | | | | | (121) all_57_2 = e3 & op(e2, e3) = e3 % 132.78/19.04 | | | | | | | | | % 132.78/19.04 | | | | | | | | | ALPHA: (121) implies: % 132.78/19.04 | | | | | | | | | (122) op(e2, e3) = e3 % 132.78/19.04 | | | | | | | | | % 132.78/19.04 | | | | | | | | | REF_CLOSE: (1), (35), (122) are inconsistent by sub-proof % 132.78/19.04 | | | | | | | | | #353. % 132.78/19.04 | | | | | | | | | % 132.78/19.04 | | | | | | | | End of split % 132.78/19.04 | | | | | | | | % 132.78/19.04 | | | | | | | Case 2: % 132.78/19.04 | | | | | | | | % 132.78/19.04 | | | | | | | | (123) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & % 132.78/19.04 | | | | | | | | op(e0, e3) = e3) % 132.78/19.04 | | | | | | | | % 132.78/19.04 | | | | | | | | REF_CLOSE: (5), (6), (20), (23), (60), (123) are inconsistent by % 132.78/19.04 | | | | | | | | sub-proof #298. % 132.78/19.04 | | | | | | | | % 132.78/19.04 | | | | | | | End of split % 132.78/19.04 | | | | | | | % 132.78/19.04 | | | | | | End of split % 132.78/19.04 | | | | | | % 132.78/19.04 | | | | | End of split % 132.78/19.04 | | | | | % 132.78/19.04 | | | | Case 2: % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | (124) all_57_13 = e3 & op(e0, e2) = e3 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | REF_CLOSE: (16), (32), (124) are inconsistent by sub-proof #297. % 132.78/19.04 | | | | | % 132.78/19.04 | | | | End of split % 132.78/19.04 | | | | % 132.78/19.04 | | | End of split % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (125) all_57_14 = e0 & op(e0, e1) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (125) implies: % 132.78/19.04 | | | (126) op(e0, e1) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (8), (39), (126) are inconsistent by sub-proof #296. % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #296 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_53_11 = e0 | ~ (op(e0, e1) = e0) % 132.78/19.04 (2) op(e0, e1) = e0 % 132.78/19.04 (3) ~ (all_53_11 = e0) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (1) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (4) ~ (op(e0, e1) = e0) % 132.78/19.04 | | % 132.78/19.04 | | PRED_UNIFY: (2), (4) imply: % 132.78/19.04 | | (5) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (5) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (6) all_53_11 = e0 % 132.78/19.04 | | % 132.78/19.04 | | REDUCE: (3), (6) imply: % 132.78/19.04 | | (7) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (7) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #297 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_13 = e3 & op(e0, e2) = e3 % 132.78/19.04 (2) all_57_13 = e1 % 132.78/19.04 (3) ~ (e3 = e1) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_13 = e3 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e3 = e1 % 132.78/19.04 | % 132.78/19.04 | SIMP: (5) implies: % 132.78/19.04 | (6) e3 = e1 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (6) imply: % 132.78/19.04 | (7) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (7) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #298 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.04 (2) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.04 (3) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.78/19.04 (4) all_53_3 = e0 % 132.78/19.04 (5) ~ (e3 = e0) % 132.78/19.04 (6) ~ (all_53_2 = e3) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (3) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (7) all_57_6 = e3 & op(e1, e3) = e3 % 132.78/19.04 | | % 132.78/19.04 | | ALPHA: (7) implies: % 132.78/19.04 | | (8) op(e1, e3) = e3 % 132.78/19.04 | | % 132.78/19.04 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #323. % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (9) all_57_12 = e3 & op(e0, e3) = e3 % 132.78/19.04 | | % 132.78/19.04 | | ALPHA: (9) implies: % 132.78/19.04 | | (10) op(e0, e3) = e3 % 132.78/19.04 | | % 132.78/19.04 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #299. % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #299 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_53_3 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.04 (2) op(e0, e3) = e3 % 132.78/19.04 (3) all_53_3 = e0 % 132.78/19.04 (4) ~ (e3 = e0) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (1) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (5) ~ (op(e0, e3) = e3) % 132.78/19.04 | | % 132.78/19.04 | | PRED_UNIFY: (2), (5) imply: % 132.78/19.04 | | (6) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (6) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (7) all_53_3 = e3 % 132.78/19.04 | | % 132.78/19.04 | | COMBINE_EQS: (3), (7) imply: % 132.78/19.04 | | (8) e3 = e0 % 132.78/19.04 | | % 132.78/19.04 | | SIMP: (8) implies: % 132.78/19.04 | | (9) e3 = e0 % 132.78/19.04 | | % 132.78/19.04 | | REDUCE: (4), (9) imply: % 132.78/19.04 | | (10) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (10) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #300 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_14 = e2 & op(e0, e1) = e2 % 132.78/19.04 (2) all_57_14 = e3 % 132.78/19.04 (3) ~ (e3 = e2) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_14 = e2 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e3 = e2 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (5) imply: % 132.78/19.04 | (6) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (6) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #301 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) ~ (e2 = e0) % 132.78/19.04 (2) all_57_8 = e0 % 132.78/19.04 (3) e2 = e0 % 132.78/19.04 (4) all_57_6 = e1 % 132.78/19.04 (5) ~ (e2 = e1) % 132.78/19.04 (6) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.78/19.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.78/19.04 (7) all_57_11 = e2 % 132.78/19.04 (8) ~ (e3 = e2) % 132.78/19.04 (9) all_57_7 = e3 % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | SIMP: (3) implies: % 132.78/19.04 | (10) e2 = e0 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (7), (10) imply: % 132.78/19.04 | (11) all_57_11 = e0 % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (6) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 132.78/19.04 | | e2) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (12) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (13) all_57_6 = e2 & op(e1, e3) = e2 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #319. % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (14) all_57_7 = e2 & op(e1, e2) = e2 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #306. % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (15) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 132.78/19.04 | | e2) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (15) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (16) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (16) implies: % 132.78/19.04 | | | (17) all_57_8 = e2 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #317. % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (18) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (1), (11), (18) are inconsistent by sub-proof #302. % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #302 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.04 (2) all_57_11 = e0 % 132.78/19.04 (3) ~ (e2 = e0) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_11 = e2 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e2 = e0 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (5) imply: % 132.78/19.04 | (6) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (6) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #303 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_5 = e2 & op(e2, e1) = e2 % 132.78/19.04 (2) all_57_5 = e3 % 132.78/19.04 (3) ~ (e3 = e2) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_5 = e2 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e3 = e2 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (5) imply: % 132.78/19.04 | (6) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (6) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #304 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 132.78/19.04 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 132.78/19.04 (2) ~ (e3 = e0) % 132.78/19.04 (3) ~ (e2 = e0) % 132.78/19.04 (4) op(e1, e1) = e3 % 132.78/19.04 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.04 (6) all_57_6 = e1 % 132.78/19.04 (7) ~ (e2 = e1) % 132.78/19.04 (8) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 132.78/19.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 132.78/19.04 (9) ~ (e1 = e0) % 132.78/19.04 (10) ~ (e3 = e2) % 132.78/19.04 (11) all_57_7 = e3 % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (1) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (12) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = % 132.78/19.04 | | e0) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (12) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (13) all_57_6 = e0 & op(e1, e3) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (13) implies: % 132.78/19.04 | | | (14) all_57_6 = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | COMBINE_EQS: (6), (14) imply: % 132.78/19.04 | | | (15) e1 = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | REDUCE: (9), (15) imply: % 132.78/19.04 | | | (16) $false % 132.78/19.04 | | | % 132.78/19.04 | | | CLOSE: (16) is inconsistent. % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (17) all_57_7 = e0 & op(e1, e2) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (2), (11), (17) are inconsistent by sub-proof #307. % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (18) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = % 132.78/19.04 | | e0) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (18) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (19) all_57_8 = e0 & op(e1, e1) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (19) implies: % 132.78/19.04 | | | (20) op(e1, e1) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (2), (4), (5), (20) are inconsistent by sub-proof #320. % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (21) all_57_11 = e0 & op(e1, e0) = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (21) implies: % 132.78/19.04 | | | (22) all_57_11 = e0 % 132.78/19.04 | | | % 132.78/19.04 | | | BETA: splitting (8) gives: % 132.78/19.04 | | | % 132.78/19.04 | | | Case 1: % 132.78/19.04 | | | | % 132.78/19.04 | | | | (23) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) % 132.78/19.04 | | | | = e2) % 132.78/19.04 | | | | % 132.78/19.04 | | | | BETA: splitting (23) gives: % 132.78/19.04 | | | | % 132.78/19.04 | | | | Case 1: % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | (24) all_57_6 = e2 & op(e1, e3) = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | REF_CLOSE: (6), (7), (24) are inconsistent by sub-proof #319. % 132.78/19.04 | | | | | % 132.78/19.04 | | | | Case 2: % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | (25) all_57_7 = e2 & op(e1, e2) = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | REF_CLOSE: (10), (11), (25) are inconsistent by sub-proof #306. % 132.78/19.04 | | | | | % 132.78/19.04 | | | | End of split % 132.78/19.04 | | | | % 132.78/19.04 | | | Case 2: % 132.78/19.04 | | | | % 132.78/19.04 | | | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) % 132.78/19.04 | | | | = e2) % 132.78/19.04 | | | | % 132.78/19.04 | | | | BETA: splitting (26) gives: % 132.78/19.04 | | | | % 132.78/19.04 | | | | Case 1: % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | (27) all_57_8 = e2 & op(e1, e1) = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | ALPHA: (27) implies: % 132.78/19.04 | | | | | (28) op(e1, e1) = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | GROUND_INST: instantiating (5) with e2, e3, e1, e1, simplifying with % 132.78/19.04 | | | | | (4), (28) gives: % 132.78/19.04 | | | | | (29) e3 = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | REDUCE: (10), (29) imply: % 132.78/19.04 | | | | | (30) $false % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | CLOSE: (30) is inconsistent. % 132.78/19.04 | | | | | % 132.78/19.04 | | | | Case 2: % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | (31) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.04 | | | | | % 132.78/19.04 | | | | | REF_CLOSE: (3), (22), (31) are inconsistent by sub-proof #305. % 132.78/19.04 | | | | | % 132.78/19.04 | | | | End of split % 132.78/19.04 | | | | % 132.78/19.04 | | | End of split % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #305 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_11 = e2 & op(e1, e0) = e2 % 132.78/19.04 (2) all_57_11 = e0 % 132.78/19.04 (3) ~ (e2 = e0) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_11 = e2 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e2 = e0 % 132.78/19.04 | % 132.78/19.04 | SIMP: (5) implies: % 132.78/19.04 | (6) e2 = e0 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (6) imply: % 132.78/19.04 | (7) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (7) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #306 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_7 = e2 & op(e1, e2) = e2 % 132.78/19.04 (2) all_57_7 = e3 % 132.78/19.04 (3) ~ (e3 = e2) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_7 = e2 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e3 = e2 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (5) imply: % 132.78/19.04 | (6) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (6) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #307 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_57_7 = e0 & op(e1, e2) = e0 % 132.78/19.04 (2) all_57_7 = e3 % 132.78/19.04 (3) ~ (e3 = e0) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | ALPHA: (1) implies: % 132.78/19.04 | (4) all_57_7 = e0 % 132.78/19.04 | % 132.78/19.04 | COMBINE_EQS: (2), (4) imply: % 132.78/19.04 | (5) e3 = e0 % 132.78/19.04 | % 132.78/19.04 | REDUCE: (3), (5) imply: % 132.78/19.04 | (6) $false % 132.78/19.04 | % 132.78/19.04 | CLOSE: (6) is inconsistent. % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #308 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) all_38_2 = e0 % 132.78/19.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.04 (3) op(e1, e0) = e2 % 132.78/19.04 (4) op(e1, e2) = e3 % 132.78/19.04 (5) ~ (all_38_2 = e0) | (op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ % 132.78/19.04 (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 132.78/19.04 $i(all_38_0)))) % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (5) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (6) ~ (all_38_2 = e0) % 132.78/19.04 | | % 132.78/19.04 | | REDUCE: (1), (6) imply: % 132.78/19.04 | | (7) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (7) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (8) op(e1, e0) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e2) | ( ~ % 132.78/19.04 | | (all_38_0 = e3) & op(e1, e2) = all_38_0 & $i(all_38_0))) % 132.78/19.04 | | % 132.78/19.04 | | ALPHA: (8) implies: % 132.78/19.04 | | (9) op(e1, e0) = all_38_1 % 132.78/19.04 | | (10) ~ (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 132.78/19.04 | | $i(all_38_0)) % 132.78/19.04 | | % 132.78/19.04 | | REF_CLOSE: (2), (3), (4), (9), (10) are inconsistent by sub-proof #309. % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #309 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 132.78/19.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 132.78/19.04 (2) op(e1, e0) = e2 % 132.78/19.04 (3) op(e1, e2) = e3 % 132.78/19.04 (4) ~ (all_38_1 = e2) | ( ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & % 132.78/19.04 $i(all_38_0)) % 132.78/19.04 (5) op(e1, e0) = all_38_1 % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (4) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (6) ~ (all_38_1 = e2) % 132.78/19.04 | | % 132.78/19.04 | | GROUND_INST: instantiating (1) with e2, all_38_1, e0, e1, simplifying with % 132.78/19.04 | | (2), (5) gives: % 132.78/19.04 | | (7) all_38_1 = e2 % 132.78/19.04 | | % 132.78/19.04 | | REDUCE: (6), (7) imply: % 132.78/19.04 | | (8) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (8) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (9) ~ (all_38_0 = e3) & op(e1, e2) = all_38_0 & $i(all_38_0) % 132.78/19.04 | | % 132.78/19.04 | | ALPHA: (9) implies: % 132.78/19.04 | | (10) ~ (all_38_0 = e3) % 132.78/19.04 | | (11) op(e1, e2) = all_38_0 % 132.78/19.04 | | % 132.78/19.04 | | GROUND_INST: instantiating (1) with e3, all_38_0, e2, e1, simplifying with % 132.78/19.04 | | (3), (11) gives: % 132.78/19.04 | | (12) all_38_0 = e3 % 132.78/19.04 | | % 132.78/19.04 | | REDUCE: (10), (12) imply: % 132.78/19.04 | | (13) $false % 132.78/19.04 | | % 132.78/19.04 | | CLOSE: (13) is inconsistent. % 132.78/19.04 | | % 132.78/19.04 | End of split % 132.78/19.04 | % 132.78/19.04 End of proof % 132.78/19.04 % 132.78/19.04 Sub-proof #310 shows that the following formulas are inconsistent: % 132.78/19.04 ---------------------------------------------------------------- % 132.78/19.04 (1) ~ (all_53_1 = e3) % 132.78/19.04 (2) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.04 (3) ~ (e3 = e1) % 132.78/19.04 (4) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 132.78/19.04 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 132.78/19.04 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 132.78/19.04 (6) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.04 (7) ~ (all_53_3 = e3) % 132.78/19.04 (8) ~ (all_53_2 = e3) % 132.78/19.04 (9) all_57_0 = e1 % 132.78/19.04 (10) all_55_12 = all_53_3 % 132.78/19.04 % 132.78/19.04 Begin of proof % 132.78/19.04 | % 132.78/19.04 | BETA: splitting (5) gives: % 132.78/19.04 | % 132.78/19.04 | Case 1: % 132.78/19.04 | | % 132.78/19.04 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 132.78/19.04 | | e3) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (11) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (12) all_57_0 = e3 & op(e3, e3) = e3 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #312. % 132.78/19.04 | | | % 132.78/19.04 | | Case 2: % 132.78/19.04 | | | % 132.78/19.04 | | | (13) all_57_2 = e3 & op(e2, e3) = e3 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (13) implies: % 132.78/19.04 | | | (14) op(e2, e3) = e3 % 132.78/19.04 | | | % 132.78/19.04 | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #353. % 132.78/19.04 | | | % 132.78/19.04 | | End of split % 132.78/19.04 | | % 132.78/19.04 | Case 2: % 132.78/19.04 | | % 132.78/19.04 | | (15) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 132.78/19.04 | | e3) % 132.78/19.04 | | % 132.78/19.04 | | BETA: splitting (15) gives: % 132.78/19.04 | | % 132.78/19.04 | | Case 1: % 132.78/19.04 | | | % 132.78/19.04 | | | (16) all_57_6 = e3 & op(e1, e3) = e3 % 132.78/19.04 | | | % 132.78/19.04 | | | ALPHA: (16) implies: % 132.78/19.04 | | | (17) op(e1, e3) = e3 % 132.78/19.04 | | | % 132.78/19.05 | | | REF_CLOSE: (2), (8), (17) are inconsistent by sub-proof #323. % 132.78/19.05 | | | % 132.78/19.05 | | Case 2: % 132.78/19.05 | | | % 132.78/19.05 | | | (18) all_57_12 = e3 & op(e0, e3) = e3 % 132.78/19.05 | | | % 132.78/19.05 | | | ALPHA: (18) implies: % 132.78/19.05 | | | (19) op(e0, e3) = e3 % 132.78/19.05 | | | % 132.78/19.05 | | | REF_CLOSE: (6), (7), (10), (19) are inconsistent by sub-proof #311. % 132.78/19.05 | | | % 132.78/19.05 | | End of split % 132.78/19.05 | | % 132.78/19.05 | End of split % 132.78/19.05 | % 132.78/19.05 End of proof % 132.78/19.05 % 132.78/19.05 Sub-proof #311 shows that the following formulas are inconsistent: % 132.78/19.05 ---------------------------------------------------------------- % 132.78/19.05 (1) all_55_12 = e3 | ~ (op(e0, e3) = e3) % 132.78/19.05 (2) op(e0, e3) = e3 % 132.78/19.05 (3) all_55_12 = all_53_3 % 132.78/19.05 (4) ~ (all_53_3 = e3) % 132.78/19.05 % 132.78/19.05 Begin of proof % 132.78/19.05 | % 132.78/19.05 | BETA: splitting (1) gives: % 132.78/19.05 | % 132.78/19.05 | Case 1: % 132.78/19.05 | | % 132.78/19.05 | | (5) ~ (op(e0, e3) = e3) % 132.78/19.05 | | % 132.78/19.05 | | PRED_UNIFY: (2), (5) imply: % 132.78/19.05 | | (6) $false % 132.78/19.05 | | % 132.78/19.05 | | CLOSE: (6) is inconsistent. % 132.78/19.05 | | % 132.78/19.05 | Case 2: % 132.78/19.05 | | % 132.78/19.05 | | (7) all_55_12 = e3 % 132.78/19.05 | | % 132.78/19.05 | | COMBINE_EQS: (3), (7) imply: % 132.78/19.05 | | (8) all_53_3 = e3 % 132.78/19.05 | | % 132.78/19.05 | | SIMP: (8) implies: % 132.78/19.05 | | (9) all_53_3 = e3 % 132.78/19.05 | | % 132.78/19.05 | | REDUCE: (4), (9) imply: % 132.78/19.05 | | (10) $false % 132.78/19.05 | | % 132.78/19.05 | | CLOSE: (10) is inconsistent. % 132.78/19.05 | | % 132.78/19.05 | End of split % 132.78/19.05 | % 132.78/19.05 End of proof % 132.78/19.05 % 132.78/19.05 Sub-proof #312 shows that the following formulas are inconsistent: % 132.78/19.05 ---------------------------------------------------------------- % 132.78/19.05 (1) all_57_0 = e3 & op(e3, e3) = e3 % 132.78/19.05 (2) all_57_0 = e1 % 132.78/19.05 (3) ~ (e3 = e1) % 132.78/19.05 % 132.78/19.05 Begin of proof % 132.78/19.05 | % 132.78/19.05 | ALPHA: (1) implies: % 132.78/19.05 | (4) all_57_0 = e3 % 132.78/19.05 | % 132.78/19.05 | COMBINE_EQS: (2), (4) imply: % 132.78/19.05 | (5) e3 = e1 % 132.78/19.05 | % 132.78/19.05 | SIMP: (5) implies: % 132.78/19.05 | (6) e3 = e1 % 132.78/19.05 | % 132.78/19.05 | REDUCE: (3), (6) imply: % 132.78/19.05 | (7) $false % 132.78/19.05 | % 132.78/19.05 | CLOSE: (7) is inconsistent. % 132.78/19.05 | % 132.78/19.05 End of proof % 132.78/19.05 % 132.78/19.05 Sub-proof #313 shows that the following formulas are inconsistent: % 132.78/19.05 ---------------------------------------------------------------- % 132.78/19.05 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 132.78/19.05 (2) all_57_5 = e3 % 132.78/19.05 (3) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 132.78/19.05 (4) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 132.78/19.05 (5) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 132.78/19.05 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 132.78/19.05 (6) all_55_9 = all_53_6 % 132.78/19.05 (7) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 132.78/19.05 (8) ~ (all_53_1 = all_53_13) % 132.78/19.05 (9) ~ (all_12_2 = e1) % 133.09/19.05 (10) all_55_7 = all_53_13 % 133.09/19.05 (11) op(e2, e3) = e2 % 133.09/19.05 (12) ~ (all_53_13 = e0) % 133.09/19.05 (13) ~ (e3 = e0) % 133.09/19.05 (14) ~ (e2 = e0) % 133.09/19.05 (15) op(e1, e1) = e0 % 133.09/19.05 (16) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 133.09/19.05 (17) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 133.09/19.05 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 133.09/19.05 (18) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 133.09/19.05 (19) all_57_8 = e0 % 133.09/19.05 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.05 (21) ~ (e3 = e1) % 133.09/19.05 (22) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 133.09/19.05 (23) ~ (all_6_2 = e2) % 133.09/19.05 (24) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 133.09/19.05 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 133.09/19.05 (25) all_57_6 = e1 % 133.09/19.05 (26) ~ (e2 = e1) % 133.09/19.05 (27) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 133.09/19.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 133.09/19.05 (28) op(e3, e3) = e3 % 133.09/19.05 (29) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.05 (30) ~ (all_53_9 = e2) % 133.09/19.05 (31) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 133.09/19.05 (32) ~ (all_53_6 = e1) % 133.09/19.05 (33) all_4_2 = e3 % 133.09/19.05 (34) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 133.09/19.05 (35) all_57_3 = e3 % 133.09/19.05 (36) ~ (all_53_14 = e1) % 133.09/19.05 (37) ~ (all_53_6 = e2) % 133.09/19.05 (38) ~ (all_53_2 = e3) % 133.09/19.05 (39) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 133.09/19.05 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 133.09/19.05 (40) all_42_2 = all_6_2 % 133.09/19.05 (41) all_55_4 = all_53_1 % 133.09/19.05 (42) ~ (e3 = e2) % 133.09/19.05 (43) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | BETA: splitting (27) gives: % 133.09/19.05 | % 133.09/19.05 | Case 1: % 133.09/19.05 | | % 133.09/19.05 | | (44) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 133.09/19.05 | | e2) % 133.09/19.05 | | % 133.09/19.05 | | REF_CLOSE: (1), (6), (9), (16), (17), (26), (29), (32), (34), (36), (37), % 133.09/19.05 | | (44) are inconsistent by sub-proof #325. % 133.09/19.05 | | % 133.09/19.05 | Case 2: % 133.09/19.05 | | % 133.09/19.05 | | (45) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 133.09/19.05 | | e2) % 133.09/19.05 | | % 133.09/19.05 | | BETA: splitting (45) gives: % 133.09/19.05 | | % 133.09/19.05 | | Case 1: % 133.09/19.05 | | | % 133.09/19.05 | | | (46) all_57_8 = e2 & op(e1, e1) = e2 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (46) implies: % 133.09/19.05 | | | (47) op(e1, e1) = e2 % 133.09/19.05 | | | % 133.09/19.05 | | | REF_CLOSE: (14), (15), (20), (47) are inconsistent by sub-proof #324. % 133.09/19.05 | | | % 133.09/19.05 | | Case 2: % 133.09/19.05 | | | % 133.09/19.05 | | | (48) all_57_11 = e2 & op(e1, e0) = e2 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (48) implies: % 133.09/19.05 | | | (49) all_57_11 = e2 % 133.09/19.05 | | | % 133.09/19.05 | | | BETA: splitting (5) gives: % 133.09/19.05 | | | % 133.09/19.05 | | | Case 1: % 133.09/19.05 | | | | % 133.09/19.05 | | | | (50) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) % 133.09/19.05 | | | | = e3) % 133.09/19.05 | | | | % 133.09/19.05 | | | | BETA: splitting (50) gives: % 133.09/19.05 | | | | % 133.09/19.05 | | | | Case 1: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (51) all_57_6 = e3 & op(e1, e3) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (51) implies: % 133.09/19.05 | | | | | (52) op(e1, e3) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (3), (38), (52) are inconsistent by sub-proof #323. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | Case 2: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (53) all_57_7 = e3 & op(e1, e2) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (53) implies: % 133.09/19.05 | | | | | (54) all_57_7 = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | BETA: splitting (24) gives: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | Case 1: % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | (55) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, % 133.09/19.05 | | | | | | e2) = e0) % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | BETA: splitting (55) gives: % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | Case 1: % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | (56) all_57_2 = e0 & op(e2, e3) = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | REF_CLOSE: (8), (10), (11), (14), (18), (22), (23), (30), (31), % 133.09/19.05 | | | | | | | (39), (40), (41), (43), (56) are inconsistent by % 133.09/19.05 | | | | | | | sub-proof #344. % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | Case 2: % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | (57) all_57_3 = e0 & op(e2, e2) = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | ALPHA: (57) implies: % 133.09/19.05 | | | | | | | (58) all_57_3 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | COMBINE_EQS: (35), (58) imply: % 133.09/19.05 | | | | | | | (59) e3 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | COMBINE_EQS: (54), (59) imply: % 133.09/19.05 | | | | | | | (60) all_57_7 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | REF_CLOSE: (5), (13), (14), (15), (19), (20), (21), (25), (26), % 133.09/19.05 | | | | | | | (27), (42), (60) are inconsistent by sub-proof #316. % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | End of split % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | Case 2: % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | (61) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, % 133.09/19.05 | | | | | | e0) = e0) % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | BETA: splitting (61) gives: % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | | Case 1: % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | (62) all_57_5 = e0 & op(e2, e1) = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | ALPHA: (62) implies: % 133.09/19.05 | | | | | | | (63) all_57_5 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | COMBINE_EQS: (2), (63) imply: % 133.09/19.05 | | | | | | | (64) e3 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | COMBINE_EQS: (54), (64) imply: % 133.09/19.05 | | | | | | | (65) all_57_7 = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | REF_CLOSE: (5), (13), (14), (15), (19), (20), (21), (25), (26), % 133.09/19.05 | | | | | | | (27), (42), (65) are inconsistent by sub-proof #316. % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | Case 2: % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | (66) all_57_10 = e0 & op(e2, e0) = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | ALPHA: (66) implies: % 133.09/19.05 | | | | | | | (67) op(e2, e0) = e0 % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | | REF_CLOSE: (4), (12), (67) are inconsistent by sub-proof #356. % 133.09/19.05 | | | | | | | % 133.09/19.05 | | | | | | End of split % 133.09/19.05 | | | | | | % 133.09/19.05 | | | | | End of split % 133.09/19.05 | | | | | % 133.09/19.05 | | | | End of split % 133.09/19.05 | | | | % 133.09/19.05 | | | Case 2: % 133.09/19.05 | | | | % 133.09/19.05 | | | | (68) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) % 133.09/19.05 | | | | = e3) % 133.09/19.05 | | | | % 133.09/19.05 | | | | BETA: splitting (68) gives: % 133.09/19.05 | | | | % 133.09/19.05 | | | | Case 1: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (69) all_57_8 = e3 & op(e1, e1) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (69) implies: % 133.09/19.05 | | | | | (70) op(e1, e1) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (13), (15), (20), (70) are inconsistent by sub-proof #320. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | Case 2: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (71) all_57_11 = e3 & op(e1, e0) = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (71) implies: % 133.09/19.05 | | | | | (72) all_57_11 = e3 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (7), (28), (33), (42), (49), (72) are inconsistent by % 133.09/19.05 | | | | | sub-proof #314. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | End of split % 133.09/19.05 | | | | % 133.09/19.05 | | | End of split % 133.09/19.05 | | | % 133.09/19.05 | | End of split % 133.09/19.05 | | % 133.09/19.05 | End of split % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #314 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 133.09/19.05 (2) all_57_11 = e3 % 133.09/19.05 (3) op(e3, e3) = e3 % 133.09/19.05 (4) all_57_11 = e2 % 133.09/19.05 (5) all_4_2 = e3 % 133.09/19.05 (6) ~ (e3 = e2) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (2), (4) imply: % 133.09/19.05 | (7) e3 = e2 % 133.09/19.05 | % 133.09/19.05 | SIMP: (7) implies: % 133.09/19.05 | (8) e3 = e2 % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (5), (8) imply: % 133.09/19.05 | (9) all_4_2 = e2 % 133.09/19.05 | % 133.09/19.05 | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #315. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #315 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_4_2 = e3 | ~ (op(e3, e3) = e3) % 133.09/19.05 (2) op(e3, e3) = e3 % 133.09/19.05 (3) all_4_2 = e2 % 133.09/19.05 (4) ~ (e3 = e2) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | BETA: splitting (1) gives: % 133.09/19.05 | % 133.09/19.05 | Case 1: % 133.09/19.05 | | % 133.09/19.05 | | (5) ~ (op(e3, e3) = e3) % 133.09/19.05 | | % 133.09/19.05 | | PRED_UNIFY: (2), (5) imply: % 133.09/19.05 | | (6) $false % 133.09/19.05 | | % 133.09/19.05 | | CLOSE: (6) is inconsistent. % 133.09/19.05 | | % 133.09/19.05 | Case 2: % 133.09/19.05 | | % 133.09/19.05 | | (7) all_4_2 = e3 % 133.09/19.05 | | % 133.09/19.05 | | COMBINE_EQS: (3), (7) imply: % 133.09/19.05 | | (8) e3 = e2 % 133.09/19.05 | | % 133.09/19.05 | | SIMP: (8) implies: % 133.09/19.05 | | (9) e3 = e2 % 133.09/19.05 | | % 133.09/19.05 | | REDUCE: (4), (9) imply: % 133.09/19.05 | | (10) $false % 133.09/19.05 | | % 133.09/19.05 | | CLOSE: (10) is inconsistent. % 133.09/19.05 | | % 133.09/19.05 | End of split % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #316 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_7 = e0 % 133.09/19.05 (2) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 133.09/19.05 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 133.09/19.05 (3) ~ (e3 = e0) % 133.09/19.05 (4) ~ (e2 = e0) % 133.09/19.05 (5) op(e1, e1) = e0 % 133.09/19.05 (6) all_57_8 = e0 % 133.09/19.05 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.05 (8) ~ (e3 = e1) % 133.09/19.05 (9) all_57_6 = e1 % 133.09/19.05 (10) ~ (e2 = e1) % 133.09/19.05 (11) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 133.09/19.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 133.09/19.05 (12) ~ (e3 = e2) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | BETA: splitting (2) gives: % 133.09/19.05 | % 133.09/19.05 | Case 1: % 133.09/19.05 | | % 133.09/19.05 | | (13) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 133.09/19.05 | | e3) % 133.09/19.05 | | % 133.09/19.05 | | BETA: splitting (13) gives: % 133.09/19.05 | | % 133.09/19.05 | | Case 1: % 133.09/19.05 | | | % 133.09/19.05 | | | (14) all_57_6 = e3 & op(e1, e3) = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (14) implies: % 133.09/19.05 | | | (15) all_57_6 = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #322. % 133.09/19.05 | | | % 133.09/19.05 | | Case 2: % 133.09/19.05 | | | % 133.09/19.05 | | | (16) all_57_7 = e3 & op(e1, e2) = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (16) implies: % 133.09/19.05 | | | (17) all_57_7 = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | REF_CLOSE: (1), (3), (17) are inconsistent by sub-proof #321. % 133.09/19.05 | | | % 133.09/19.05 | | End of split % 133.09/19.05 | | % 133.09/19.05 | Case 2: % 133.09/19.05 | | % 133.09/19.05 | | (18) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 133.09/19.05 | | e3) % 133.09/19.05 | | % 133.09/19.05 | | BETA: splitting (18) gives: % 133.09/19.05 | | % 133.09/19.05 | | Case 1: % 133.09/19.05 | | | % 133.09/19.05 | | | (19) all_57_8 = e3 & op(e1, e1) = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (19) implies: % 133.09/19.05 | | | (20) op(e1, e1) = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | REF_CLOSE: (3), (5), (7), (20) are inconsistent by sub-proof #320. % 133.09/19.05 | | | % 133.09/19.05 | | Case 2: % 133.09/19.05 | | | % 133.09/19.05 | | | (21) all_57_11 = e3 & op(e1, e0) = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | ALPHA: (21) implies: % 133.09/19.05 | | | (22) all_57_11 = e3 % 133.09/19.05 | | | % 133.09/19.05 | | | BETA: splitting (11) gives: % 133.09/19.05 | | | % 133.09/19.05 | | | Case 1: % 133.09/19.05 | | | | % 133.09/19.05 | | | | (23) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) % 133.09/19.05 | | | | = e2) % 133.09/19.05 | | | | % 133.09/19.05 | | | | BETA: splitting (23) gives: % 133.09/19.05 | | | | % 133.09/19.05 | | | | Case 1: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (24) all_57_6 = e2 & op(e1, e3) = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (9), (10), (24) are inconsistent by sub-proof #319. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | Case 2: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (25) all_57_7 = e2 & op(e1, e2) = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (1), (4), (25) are inconsistent by sub-proof #318. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | End of split % 133.09/19.05 | | | | % 133.09/19.05 | | | Case 2: % 133.09/19.05 | | | | % 133.09/19.05 | | | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) % 133.09/19.05 | | | | = e2) % 133.09/19.05 | | | | % 133.09/19.05 | | | | BETA: splitting (26) gives: % 133.09/19.05 | | | | % 133.09/19.05 | | | | Case 1: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (27) all_57_8 = e2 & op(e1, e1) = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (27) implies: % 133.09/19.05 | | | | | (28) all_57_8 = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REF_CLOSE: (4), (6), (28) are inconsistent by sub-proof #317. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | Case 2: % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | (29) all_57_11 = e2 & op(e1, e0) = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | ALPHA: (29) implies: % 133.09/19.05 | | | | | (30) all_57_11 = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | COMBINE_EQS: (22), (30) imply: % 133.09/19.05 | | | | | (31) e3 = e2 % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | REDUCE: (12), (31) imply: % 133.09/19.05 | | | | | (32) $false % 133.09/19.05 | | | | | % 133.09/19.05 | | | | | CLOSE: (32) is inconsistent. % 133.09/19.05 | | | | | % 133.09/19.05 | | | | End of split % 133.09/19.05 | | | | % 133.09/19.05 | | | End of split % 133.09/19.05 | | | % 133.09/19.05 | | End of split % 133.09/19.05 | | % 133.09/19.05 | End of split % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #317 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_8 = e2 % 133.09/19.05 (2) all_57_8 = e0 % 133.09/19.05 (3) ~ (e2 = e0) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (1), (2) imply: % 133.09/19.05 | (4) e2 = e0 % 133.09/19.05 | % 133.09/19.05 | SIMP: (4) implies: % 133.09/19.05 | (5) e2 = e0 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (3), (5) imply: % 133.09/19.05 | (6) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (6) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #318 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_7 = e2 & op(e1, e2) = e2 % 133.09/19.05 (2) all_57_7 = e0 % 133.09/19.05 (3) ~ (e2 = e0) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | ALPHA: (1) implies: % 133.09/19.05 | (4) all_57_7 = e2 % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (2), (4) imply: % 133.09/19.05 | (5) e2 = e0 % 133.09/19.05 | % 133.09/19.05 | SIMP: (5) implies: % 133.09/19.05 | (6) e2 = e0 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (3), (6) imply: % 133.09/19.05 | (7) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (7) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #319 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_6 = e2 & op(e1, e3) = e2 % 133.09/19.05 (2) all_57_6 = e1 % 133.09/19.05 (3) ~ (e2 = e1) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | ALPHA: (1) implies: % 133.09/19.05 | (4) all_57_6 = e2 % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (2), (4) imply: % 133.09/19.05 | (5) e2 = e1 % 133.09/19.05 | % 133.09/19.05 | SIMP: (5) implies: % 133.09/19.05 | (6) e2 = e1 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (3), (6) imply: % 133.09/19.05 | (7) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (7) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #320 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.05 (2) op(e1, e1) = e3 % 133.09/19.05 (3) op(e1, e1) = e0 % 133.09/19.05 (4) ~ (e3 = e0) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | GROUND_INST: instantiating (1) with e0, e3, e1, e1, simplifying with (2), (3) % 133.09/19.05 | gives: % 133.09/19.05 | (5) e3 = e0 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (4), (5) imply: % 133.09/19.05 | (6) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (6) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #321 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_7 = e3 % 133.09/19.05 (2) all_57_7 = e0 % 133.09/19.05 (3) ~ (e3 = e0) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (1), (2) imply: % 133.09/19.05 | (4) e3 = e0 % 133.09/19.05 | % 133.09/19.05 | SIMP: (4) implies: % 133.09/19.05 | (5) e3 = e0 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (3), (5) imply: % 133.09/19.05 | (6) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (6) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #322 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_57_6 = e3 % 133.09/19.05 (2) all_57_6 = e1 % 133.09/19.05 (3) ~ (e3 = e1) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | COMBINE_EQS: (1), (2) imply: % 133.09/19.05 | (4) e3 = e1 % 133.09/19.05 | % 133.09/19.05 | SIMP: (4) implies: % 133.09/19.05 | (5) e3 = e1 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (3), (5) imply: % 133.09/19.05 | (6) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (6) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #323 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_53_2 = e3 | ~ (op(e1, e3) = e3) % 133.09/19.05 (2) op(e1, e3) = e3 % 133.09/19.05 (3) ~ (all_53_2 = e3) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | BETA: splitting (1) gives: % 133.09/19.05 | % 133.09/19.05 | Case 1: % 133.09/19.05 | | % 133.09/19.05 | | (4) ~ (op(e1, e3) = e3) % 133.09/19.05 | | % 133.09/19.05 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.05 | | (5) $false % 133.09/19.05 | | % 133.09/19.05 | | CLOSE: (5) is inconsistent. % 133.09/19.05 | | % 133.09/19.05 | Case 2: % 133.09/19.05 | | % 133.09/19.05 | | (6) all_53_2 = e3 % 133.09/19.05 | | % 133.09/19.05 | | REDUCE: (3), (6) imply: % 133.09/19.05 | | (7) $false % 133.09/19.05 | | % 133.09/19.05 | | CLOSE: (7) is inconsistent. % 133.09/19.05 | | % 133.09/19.05 | End of split % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #324 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.05 (2) op(e1, e1) = e2 % 133.09/19.05 (3) op(e1, e1) = e0 % 133.09/19.05 (4) ~ (e2 = e0) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (2), (3) % 133.09/19.05 | gives: % 133.09/19.05 | (5) e2 = e0 % 133.09/19.05 | % 133.09/19.05 | REDUCE: (4), (5) imply: % 133.09/19.05 | (6) $false % 133.09/19.05 | % 133.09/19.05 | CLOSE: (6) is inconsistent. % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #325 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.05 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 133.09/19.05 (2) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) % 133.09/19.05 (3) all_55_9 = all_53_6 % 133.09/19.05 (4) ~ (all_12_2 = e1) % 133.09/19.05 (5) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 133.09/19.05 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 133.09/19.05 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 133.09/19.05 (7) ~ (e2 = e1) % 133.09/19.05 (8) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.05 (9) ~ (all_53_6 = e1) % 133.09/19.05 (10) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 133.09/19.05 (11) ~ (all_53_14 = e1) % 133.09/19.05 (12) ~ (all_53_6 = e2) % 133.09/19.05 % 133.09/19.05 Begin of proof % 133.09/19.05 | % 133.09/19.05 | BETA: splitting (2) gives: % 133.09/19.05 | % 133.09/19.05 | Case 1: % 133.09/19.05 | | % 133.09/19.05 | | (13) all_57_6 = e2 & op(e1, e3) = e2 % 133.09/19.05 | | % 133.09/19.05 | | ALPHA: (13) implies: % 133.09/19.05 | | (14) all_57_6 = e2 % 133.09/19.05 | | % 133.09/19.05 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (14) are % 133.09/19.05 | | inconsistent by sub-proof #327. % 133.09/19.05 | | % 133.09/19.05 | Case 2: % 133.09/19.05 | | % 133.09/19.05 | | (15) all_57_7 = e2 & op(e1, e2) = e2 % 133.09/19.05 | | % 133.09/19.05 | | ALPHA: (15) implies: % 133.09/19.05 | | (16) op(e1, e2) = e2 % 133.09/19.05 | | % 133.09/19.05 | | REF_CLOSE: (5), (12), (16) are inconsistent by sub-proof #326. % 133.09/19.05 | | % 133.09/19.05 | End of split % 133.09/19.05 | % 133.09/19.05 End of proof % 133.09/19.05 % 133.09/19.05 Sub-proof #326 shows that the following formulas are inconsistent: % 133.09/19.05 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_6 = e2 | ~ (op(e1, e2) = e2) % 133.09/19.06 (2) op(e1, e2) = e2 % 133.09/19.06 (3) ~ (all_53_6 = e2) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (4) ~ (op(e1, e2) = e2) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.06 | | (5) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (5) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_53_6 = e2 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (3), (6) imply: % 133.09/19.06 | | (7) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (7) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #327 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 133.09/19.06 (2) all_55_9 = all_53_6 % 133.09/19.06 (3) ~ (all_12_2 = e1) % 133.09/19.06 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 133.09/19.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 133.09/19.06 (5) ~ (e2 = e1) % 133.09/19.06 (6) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (7) ~ (all_53_6 = e1) % 133.09/19.06 (8) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 133.09/19.06 (9) ~ (all_53_14 = e1) % 133.09/19.06 (10) all_57_6 = e2 % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (4) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | BETA: splitting (11) gives: % 133.09/19.06 | | % 133.09/19.06 | | Case 1: % 133.09/19.06 | | | % 133.09/19.06 | | | (12) all_57_6 = e1 & op(e1, e3) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (12) implies: % 133.09/19.06 | | | (13) all_57_6 = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | COMBINE_EQS: (10), (13) imply: % 133.09/19.06 | | | (14) e2 = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REDUCE: (5), (14) imply: % 133.09/19.06 | | | (15) $false % 133.09/19.06 | | | % 133.09/19.06 | | | CLOSE: (15) is inconsistent. % 133.09/19.06 | | | % 133.09/19.06 | | Case 2: % 133.09/19.06 | | | % 133.09/19.06 | | | (16) all_57_7 = e1 & op(e1, e2) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (16) implies: % 133.09/19.06 | | | (17) op(e1, e2) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (2), (7), (8), (17) are inconsistent by sub-proof #341. % 133.09/19.06 | | | % 133.09/19.06 | | End of split % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (18) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (3), (6), (9), (18) are inconsistent by sub-proof #338. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #328 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_1 = e3 & op(e3, e2) = e3 % 133.09/19.06 (2) all_55_1 = e3 | ~ (op(e3, e2) = e3) % 133.09/19.06 (3) all_55_1 = all_53_4 % 133.09/19.06 (4) ~ (all_53_4 = e3) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (5) op(e3, e2) = e3 % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (2) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (6) ~ (op(e3, e2) = e3) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (5), (6) imply: % 133.09/19.06 | | (7) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (7) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (8) all_55_1 = e3 % 133.09/19.06 | | % 133.09/19.06 | | COMBINE_EQS: (3), (8) imply: % 133.09/19.06 | | (9) all_53_4 = e3 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (4), (9) imply: % 133.09/19.06 | | (10) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (10) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #329 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_5 = e3 % 133.09/19.06 (2) ~ (all_12_2 = e1) % 133.09/19.06 (3) ~ (e3 = e0) % 133.09/19.06 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) % 133.09/19.06 (5) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 133.09/19.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 133.09/19.06 (6) ~ (e1 = e0) % 133.09/19.06 (7) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (8) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 133.09/19.06 (9) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 133.09/19.06 (10) ~ (all_53_11 = e1) % 133.09/19.06 (11) ~ (all_53_9 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (4) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (12) all_57_4 = e0 & op(e3, e1) = e0 % 133.09/19.06 | | % 133.09/19.06 | | ALPHA: (12) implies: % 133.09/19.06 | | (13) all_57_4 = e0 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (13) are inconsistent % 133.09/19.06 | | by sub-proof #331. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (14) all_57_5 = e0 & op(e2, e1) = e0 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #330. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #330 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_5 = e0 & op(e2, e1) = e0 % 133.09/19.06 (2) all_57_5 = e3 % 133.09/19.06 (3) ~ (e3 = e0) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (4) all_57_5 = e0 % 133.09/19.06 | % 133.09/19.06 | COMBINE_EQS: (2), (4) imply: % 133.09/19.06 | (5) e3 = e0 % 133.09/19.06 | % 133.09/19.06 | REDUCE: (3), (5) imply: % 133.09/19.06 | (6) $false % 133.09/19.06 | % 133.09/19.06 | CLOSE: (6) is inconsistent. % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #331 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) ~ (all_12_2 = e1) % 133.09/19.06 (2) all_57_4 = e0 % 133.09/19.06 (3) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 133.09/19.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 133.09/19.06 (4) ~ (e1 = e0) % 133.09/19.06 (5) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (6) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 133.09/19.06 (7) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 133.09/19.06 (8) ~ (all_53_11 = e1) % 133.09/19.06 (9) ~ (all_53_9 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (3) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (10) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | BETA: splitting (10) gives: % 133.09/19.06 | | % 133.09/19.06 | | Case 1: % 133.09/19.06 | | | % 133.09/19.06 | | | (11) all_57_4 = e1 & op(e3, e1) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #335. % 133.09/19.06 | | | % 133.09/19.06 | | Case 2: % 133.09/19.06 | | | % 133.09/19.06 | | | (12) all_57_5 = e1 & op(e2, e1) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (12) implies: % 133.09/19.06 | | | (13) op(e2, e1) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #334. % 133.09/19.06 | | | % 133.09/19.06 | | End of split % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (14) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (5), (6), (8), (14) are inconsistent by sub-proof #332. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #332 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) ~ (all_12_2 = e1) % 133.09/19.06 (2) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (3) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 133.09/19.06 (4) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 133.09/19.06 (5) ~ (all_53_11 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (4) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_57_8 = e1 & op(e1, e1) = e1 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #340. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (7) all_57_14 = e1 & op(e0, e1) = e1 % 133.09/19.06 | | % 133.09/19.06 | | ALPHA: (7) implies: % 133.09/19.06 | | (8) op(e0, e1) = e1 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #333. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #333 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_11 = e1 | ~ (op(e0, e1) = e1) % 133.09/19.06 (2) op(e0, e1) = e1 % 133.09/19.06 (3) ~ (all_53_11 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (4) ~ (op(e0, e1) = e1) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.06 | | (5) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (5) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_53_11 = e1 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (3), (6) imply: % 133.09/19.06 | | (7) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (7) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #334 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_9 = e1 | ~ (op(e2, e1) = e1) % 133.09/19.06 (2) op(e2, e1) = e1 % 133.09/19.06 (3) ~ (all_53_9 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (4) ~ (op(e2, e1) = e1) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.06 | | (5) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (5) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_53_9 = e1 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (3), (6) imply: % 133.09/19.06 | | (7) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (7) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #335 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_4 = e1 & op(e3, e1) = e1 % 133.09/19.06 (2) all_57_4 = e0 % 133.09/19.06 (3) ~ (e1 = e0) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (4) all_57_4 = e1 % 133.09/19.06 | % 133.09/19.06 | COMBINE_EQS: (2), (4) imply: % 133.09/19.06 | (5) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | SIMP: (5) implies: % 133.09/19.06 | (6) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | REDUCE: (3), (6) imply: % 133.09/19.06 | (7) $false % 133.09/19.06 | % 133.09/19.06 | CLOSE: (7) is inconsistent. % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #336 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_12 = e1 & op(e0, e3) = e1 % 133.09/19.06 (2) all_57_12 = e0 % 133.09/19.06 (3) ~ (e1 = e0) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (4) all_57_12 = e1 % 133.09/19.06 | % 133.09/19.06 | COMBINE_EQS: (2), (4) imply: % 133.09/19.06 | (5) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | SIMP: (5) implies: % 133.09/19.06 | (6) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | REDUCE: (3), (6) imply: % 133.09/19.06 | (7) $false % 133.09/19.06 | % 133.09/19.06 | CLOSE: (7) is inconsistent. % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #337 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 133.09/19.06 (2) all_55_9 = all_53_6 % 133.09/19.06 (3) ~ (all_12_2 = e1) % 133.09/19.06 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 133.09/19.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 133.09/19.06 (5) all_57_6 = e0 & op(e1, e3) = e0 % 133.09/19.06 (6) ~ (e1 = e0) % 133.09/19.06 (7) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (8) ~ (all_53_6 = e1) % 133.09/19.06 (9) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 133.09/19.06 (10) ~ (all_53_14 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (5) implies: % 133.09/19.06 | (11) all_57_6 = e0 % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (4) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (12) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | BETA: splitting (12) gives: % 133.09/19.06 | | % 133.09/19.06 | | Case 1: % 133.09/19.06 | | | % 133.09/19.06 | | | (13) all_57_6 = e1 & op(e1, e3) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (6), (11), (13) are inconsistent by sub-proof #343. % 133.09/19.06 | | | % 133.09/19.06 | | Case 2: % 133.09/19.06 | | | % 133.09/19.06 | | | (14) all_57_7 = e1 & op(e1, e2) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (14) implies: % 133.09/19.06 | | | (15) op(e1, e2) = e1 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (2), (8), (9), (15) are inconsistent by sub-proof #341. % 133.09/19.06 | | | % 133.09/19.06 | | End of split % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (16) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = % 133.09/19.06 | | e1) % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (3), (7), (10), (16) are inconsistent by sub-proof #338. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #338 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 133.09/19.06 (2) ~ (all_12_2 = e1) % 133.09/19.06 (3) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (4) ~ (all_53_14 = e1) % 133.09/19.06 (5) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (5) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_57_8 = e1 & op(e1, e1) = e1 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #340. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (7) all_57_11 = e1 & op(e1, e0) = e1 % 133.09/19.06 | | % 133.09/19.06 | | ALPHA: (7) implies: % 133.09/19.06 | | (8) op(e1, e0) = e1 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #339. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #339 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_14 = e1 | ~ (op(e1, e0) = e1) % 133.09/19.06 (2) op(e1, e0) = e1 % 133.09/19.06 (3) ~ (all_53_14 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (4) ~ (op(e1, e0) = e1) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.06 | | (5) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (5) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_53_14 = e1 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (3), (6) imply: % 133.09/19.06 | | (7) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (7) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #340 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_8 = e1 & op(e1, e1) = e1 % 133.09/19.06 (2) all_12_2 = e1 | ~ (op(e1, e1) = e1) % 133.09/19.06 (3) ~ (all_12_2 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (4) op(e1, e1) = e1 % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (2) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (5) ~ (op(e1, e1) = e1) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (4), (5) imply: % 133.09/19.06 | | (6) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (6) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (7) all_12_2 = e1 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (3), (7) imply: % 133.09/19.06 | | (8) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (8) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #341 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_55_9 = e1 | ~ (op(e1, e2) = e1) % 133.09/19.06 (2) op(e1, e2) = e1 % 133.09/19.06 (3) all_55_9 = all_53_6 % 133.09/19.06 (4) ~ (all_53_6 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (5) ~ (op(e1, e2) = e1) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (5) imply: % 133.09/19.06 | | (6) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (6) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (7) all_55_9 = e1 % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #342. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #342 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_55_9 = all_53_6 % 133.09/19.06 (2) all_55_9 = e1 % 133.09/19.06 (3) ~ (all_53_6 = e1) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | COMBINE_EQS: (1), (2) imply: % 133.09/19.06 | (4) all_53_6 = e1 % 133.09/19.06 | % 133.09/19.06 | SIMP: (4) implies: % 133.09/19.06 | (5) all_53_6 = e1 % 133.09/19.06 | % 133.09/19.06 | REDUCE: (3), (5) imply: % 133.09/19.06 | (6) $false % 133.09/19.06 | % 133.09/19.06 | CLOSE: (6) is inconsistent. % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #343 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_6 = e1 & op(e1, e3) = e1 % 133.09/19.06 (2) all_57_6 = e0 % 133.09/19.06 (3) ~ (e1 = e0) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (4) all_57_6 = e1 % 133.09/19.06 | % 133.09/19.06 | COMBINE_EQS: (2), (4) imply: % 133.09/19.06 | (5) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | SIMP: (5) implies: % 133.09/19.06 | (6) e1 = e0 % 133.09/19.06 | % 133.09/19.06 | REDUCE: (3), (6) imply: % 133.09/19.06 | (7) $false % 133.09/19.06 | % 133.09/19.06 | CLOSE: (7) is inconsistent. % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #344 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_57_2 = e0 & op(e2, e3) = e0 % 133.09/19.06 (2) ~ (all_53_1 = all_53_13) % 133.09/19.06 (3) all_55_7 = all_53_13 % 133.09/19.06 (4) op(e2, e3) = e2 % 133.09/19.06 (5) ~ (e2 = e0) % 133.09/19.06 (6) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 133.09/19.06 (7) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 133.09/19.06 (8) ~ (all_6_2 = e2) % 133.09/19.06 (9) ~ (all_53_9 = e2) % 133.09/19.06 (10) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 133.09/19.06 (11) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 133.09/19.06 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 133.09/19.06 (12) all_42_2 = all_6_2 % 133.09/19.06 (13) all_55_4 = all_53_1 % 133.09/19.06 (14) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | ALPHA: (1) implies: % 133.09/19.06 | (15) all_57_2 = e0 % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (11) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (16) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = % 133.09/19.06 | | e2) % 133.09/19.06 | | % 133.09/19.06 | | BETA: splitting (16) gives: % 133.09/19.06 | | % 133.09/19.06 | | Case 1: % 133.09/19.06 | | | % 133.09/19.06 | | | (17) all_57_2 = e2 & op(e2, e3) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (5), (15), (17) are inconsistent by sub-proof #349. % 133.09/19.06 | | | % 133.09/19.06 | | Case 2: % 133.09/19.06 | | | % 133.09/19.06 | | | (18) all_57_3 = e2 & op(e2, e2) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (18) implies: % 133.09/19.06 | | | (19) op(e2, e2) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (8), (10), (12), (19) are inconsistent by sub-proof #348. % 133.09/19.06 | | | % 133.09/19.06 | | End of split % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (20) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 133.09/19.06 | | e2) % 133.09/19.06 | | % 133.09/19.06 | | BETA: splitting (20) gives: % 133.09/19.06 | | % 133.09/19.06 | | Case 1: % 133.09/19.06 | | | % 133.09/19.06 | | | (21) all_57_5 = e2 & op(e2, e1) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (21) implies: % 133.09/19.06 | | | (22) op(e2, e1) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (7), (9), (22) are inconsistent by sub-proof #347. % 133.09/19.06 | | | % 133.09/19.06 | | Case 2: % 133.09/19.06 | | | % 133.09/19.06 | | | (23) all_57_10 = e2 & op(e2, e0) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | ALPHA: (23) implies: % 133.09/19.06 | | | (24) op(e2, e0) = e2 % 133.09/19.06 | | | % 133.09/19.06 | | | REF_CLOSE: (2), (3), (4), (6), (13), (14), (24) are inconsistent by % 133.09/19.06 | | | sub-proof #345. % 133.09/19.06 | | | % 133.09/19.06 | | End of split % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #345 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) ~ (all_53_1 = all_53_13) % 133.09/19.06 (2) all_55_7 = all_53_13 % 133.09/19.06 (3) op(e2, e3) = e2 % 133.09/19.06 (4) all_55_7 = e2 | ~ (op(e2, e0) = e2) % 133.09/19.06 (5) op(e2, e0) = e2 % 133.09/19.06 (6) all_55_4 = all_53_1 % 133.09/19.06 (7) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (4) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (8) ~ (op(e2, e0) = e2) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (5), (8) imply: % 133.09/19.06 | | (9) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (9) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (10) all_55_7 = e2 % 133.09/19.06 | | % 133.09/19.06 | | COMBINE_EQS: (2), (10) imply: % 133.09/19.06 | | (11) all_53_13 = e2 % 133.09/19.06 | | % 133.09/19.06 | | SIMP: (11) implies: % 133.09/19.06 | | (12) all_53_13 = e2 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (1), (12) imply: % 133.09/19.06 | | (13) ~ (all_53_1 = e2) % 133.09/19.06 | | % 133.09/19.06 | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #346. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #346 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_55_4 = e2 | ~ (op(e2, e3) = e2) % 133.09/19.06 (2) op(e2, e3) = e2 % 133.09/19.06 (3) all_55_4 = all_53_1 % 133.09/19.06 (4) ~ (all_53_1 = e2) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (5) ~ (op(e2, e3) = e2) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (5) imply: % 133.09/19.06 | | (6) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (6) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (7) all_55_4 = e2 % 133.09/19.06 | | % 133.09/19.06 | | COMBINE_EQS: (3), (7) imply: % 133.09/19.06 | | (8) all_53_1 = e2 % 133.09/19.06 | | % 133.09/19.06 | | SIMP: (8) implies: % 133.09/19.06 | | (9) all_53_1 = e2 % 133.09/19.06 | | % 133.09/19.06 | | REDUCE: (4), (9) imply: % 133.09/19.06 | | (10) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (10) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | End of split % 133.09/19.06 | % 133.09/19.06 End of proof % 133.09/19.06 % 133.09/19.06 Sub-proof #347 shows that the following formulas are inconsistent: % 133.09/19.06 ---------------------------------------------------------------- % 133.09/19.06 (1) all_53_9 = e2 | ~ (op(e2, e1) = e2) % 133.09/19.06 (2) op(e2, e1) = e2 % 133.09/19.06 (3) ~ (all_53_9 = e2) % 133.09/19.06 % 133.09/19.06 Begin of proof % 133.09/19.06 | % 133.09/19.06 | BETA: splitting (1) gives: % 133.09/19.06 | % 133.09/19.06 | Case 1: % 133.09/19.06 | | % 133.09/19.06 | | (4) ~ (op(e2, e1) = e2) % 133.09/19.06 | | % 133.09/19.06 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.06 | | (5) $false % 133.09/19.06 | | % 133.09/19.06 | | CLOSE: (5) is inconsistent. % 133.09/19.06 | | % 133.09/19.06 | Case 2: % 133.09/19.06 | | % 133.09/19.06 | | (6) all_53_9 = e2 % 133.09/19.06 | | % 133.09/19.07 | | REDUCE: (3), (6) imply: % 133.09/19.07 | | (7) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (7) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #348 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_42_2 = e2 | ~ (op(e2, e2) = e2) % 133.09/19.07 (2) op(e2, e2) = e2 % 133.09/19.07 (3) all_42_2 = all_6_2 % 133.09/19.07 (4) ~ (all_6_2 = e2) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (1) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (5) ~ (op(e2, e2) = e2) % 133.09/19.07 | | % 133.09/19.07 | | PRED_UNIFY: (2), (5) imply: % 133.09/19.07 | | (6) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (6) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (7) all_42_2 = e2 % 133.09/19.07 | | % 133.09/19.07 | | COMBINE_EQS: (3), (7) imply: % 133.09/19.07 | | (8) all_6_2 = e2 % 133.09/19.07 | | % 133.09/19.07 | | SIMP: (8) implies: % 133.09/19.07 | | (9) all_6_2 = e2 % 133.09/19.07 | | % 133.09/19.07 | | REDUCE: (4), (9) imply: % 133.09/19.07 | | (10) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (10) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #349 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_57_2 = e2 & op(e2, e3) = e2 % 133.09/19.07 (2) all_57_2 = e0 % 133.09/19.07 (3) ~ (e2 = e0) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | ALPHA: (1) implies: % 133.09/19.07 | (4) all_57_2 = e2 % 133.09/19.07 | % 133.09/19.07 | COMBINE_EQS: (2), (4) imply: % 133.09/19.07 | (5) e2 = e0 % 133.09/19.07 | % 133.09/19.07 | SIMP: (5) implies: % 133.09/19.07 | (6) e2 = e0 % 133.09/19.07 | % 133.09/19.07 | REDUCE: (3), (6) imply: % 133.09/19.07 | (7) $false % 133.09/19.07 | % 133.09/19.07 | CLOSE: (7) is inconsistent. % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #350 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.07 (2) op(e3, e3) = e2 % 133.09/19.07 (3) op(e3, e3) = e0 % 133.09/19.07 (4) ~ (e2 = e0) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3) % 133.09/19.07 | gives: % 133.09/19.07 | (5) e2 = e0 % 133.09/19.07 | % 133.09/19.07 | REDUCE: (4), (5) imply: % 133.09/19.07 | (6) $false % 133.09/19.07 | % 133.09/19.07 | CLOSE: (6) is inconsistent. % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #351 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) ~ (all_53_1 = e3) % 133.09/19.07 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 133.09/19.07 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.07 (4) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 133.09/19.07 (5) ~ (all_6_2 = e3) % 133.09/19.07 (6) op(e2, e2) = all_6_2 % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (2) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (7) all_57_2 = e3 & op(e2, e3) = e3 % 133.09/19.07 | | % 133.09/19.07 | | ALPHA: (7) implies: % 133.09/19.07 | | (8) op(e2, e3) = e3 % 133.09/19.07 | | % 133.09/19.07 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #353. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (9) all_57_3 = e3 & op(e2, e2) = e3 % 133.09/19.07 | | % 133.09/19.07 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #352. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #352 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_57_3 = e3 & op(e2, e2) = e3 % 133.09/19.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 133.09/19.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 133.09/19.07 (3) op(e2, e2) = all_6_2 % 133.09/19.07 (4) ~ (all_6_2 = e3) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | ALPHA: (1) implies: % 133.09/19.07 | (5) op(e2, e2) = e3 % 133.09/19.07 | % 133.09/19.07 | GROUND_INST: instantiating (2) with all_6_2, e3, e2, e2, simplifying with (3), % 133.09/19.07 | (5) gives: % 133.09/19.07 | (6) all_6_2 = e3 % 133.09/19.07 | % 133.09/19.07 | REDUCE: (4), (6) imply: % 133.09/19.07 | (7) $false % 133.09/19.07 | % 133.09/19.07 | CLOSE: (7) is inconsistent. % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #353 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_53_1 = e3 | ~ (op(e2, e3) = e3) % 133.09/19.07 (2) op(e2, e3) = e3 % 133.09/19.07 (3) ~ (all_53_1 = e3) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (1) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (4) ~ (op(e2, e3) = e3) % 133.09/19.07 | | % 133.09/19.07 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.07 | | (5) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (5) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (6) all_53_1 = e3 % 133.09/19.07 | | % 133.09/19.07 | | REDUCE: (3), (6) imply: % 133.09/19.07 | | (7) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (7) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #354 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 133.09/19.07 (2) ~ (all_53_13 = e0) % 133.09/19.07 (3) all_57_9 = e1 & op(e3, e0) = e1 % 133.09/19.07 (4) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) | % 133.09/19.07 (all_57_11 = e0 & op(e1, e0) = e0) % 133.09/19.07 (5) ~ (e1 = e0) % 133.09/19.07 (6) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 133.09/19.07 (7) ~ (all_53_14 = e0) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | ALPHA: (3) implies: % 133.09/19.07 | (8) all_57_9 = e1 % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (4) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (9) all_57_9 = e0 & op(e3, e0) = e0 % 133.09/19.07 | | % 133.09/19.07 | | ALPHA: (9) implies: % 133.09/19.07 | | (10) all_57_9 = e0 % 133.09/19.07 | | % 133.09/19.07 | | COMBINE_EQS: (8), (10) imply: % 133.09/19.07 | | (11) e1 = e0 % 133.09/19.07 | | % 133.09/19.07 | | REDUCE: (5), (11) imply: % 133.09/19.07 | | (12) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (12) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (13) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 133.09/19.07 | | e0) % 133.09/19.07 | | % 133.09/19.07 | | BETA: splitting (13) gives: % 133.09/19.07 | | % 133.09/19.07 | | Case 1: % 133.09/19.07 | | | % 133.09/19.07 | | | (14) all_57_10 = e0 & op(e2, e0) = e0 % 133.09/19.07 | | | % 133.09/19.07 | | | ALPHA: (14) implies: % 133.09/19.07 | | | (15) op(e2, e0) = e0 % 133.09/19.07 | | | % 133.09/19.07 | | | REF_CLOSE: (1), (2), (15) are inconsistent by sub-proof #356. % 133.09/19.07 | | | % 133.09/19.07 | | Case 2: % 133.09/19.07 | | | % 133.09/19.07 | | | (16) all_57_11 = e0 & op(e1, e0) = e0 % 133.09/19.07 | | | % 133.09/19.07 | | | ALPHA: (16) implies: % 133.09/19.07 | | | (17) op(e1, e0) = e0 % 133.09/19.07 | | | % 133.09/19.07 | | | REF_CLOSE: (6), (7), (17) are inconsistent by sub-proof #355. % 133.09/19.07 | | | % 133.09/19.07 | | End of split % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #355 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_53_14 = e0 | ~ (op(e1, e0) = e0) % 133.09/19.07 (2) op(e1, e0) = e0 % 133.09/19.07 (3) ~ (all_53_14 = e0) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (1) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (4) ~ (op(e1, e0) = e0) % 133.09/19.07 | | % 133.09/19.07 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.07 | | (5) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (5) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (6) all_53_14 = e0 % 133.09/19.07 | | % 133.09/19.07 | | REDUCE: (3), (6) imply: % 133.09/19.07 | | (7) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (7) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % 133.09/19.07 Sub-proof #356 shows that the following formulas are inconsistent: % 133.09/19.07 ---------------------------------------------------------------- % 133.09/19.07 (1) all_53_13 = e0 | ~ (op(e2, e0) = e0) % 133.09/19.07 (2) op(e2, e0) = e0 % 133.09/19.07 (3) ~ (all_53_13 = e0) % 133.09/19.07 % 133.09/19.07 Begin of proof % 133.09/19.07 | % 133.09/19.07 | BETA: splitting (1) gives: % 133.09/19.07 | % 133.09/19.07 | Case 1: % 133.09/19.07 | | % 133.09/19.07 | | (4) ~ (op(e2, e0) = e0) % 133.09/19.07 | | % 133.09/19.07 | | PRED_UNIFY: (2), (4) imply: % 133.09/19.07 | | (5) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (5) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | Case 2: % 133.09/19.07 | | % 133.09/19.07 | | (6) all_53_13 = e0 % 133.09/19.07 | | % 133.09/19.07 | | REDUCE: (3), (6) imply: % 133.09/19.07 | | (7) $false % 133.09/19.07 | | % 133.09/19.07 | | CLOSE: (7) is inconsistent. % 133.09/19.07 | | % 133.09/19.07 | End of split % 133.09/19.07 | % 133.09/19.07 End of proof % 133.09/19.07 % SZS output end Proof for theBenchmark % 133.09/19.07 % 133.09/19.07 18443ms %------------------------------------------------------------------------------