%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG130+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 : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:36:33 EDT 2023 % Result : Unsatisfiable 10.28s 3.69s % Output : Proof 56.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.23 % Problem : ALG130+1 : TPTP v8.1.2. Released v2.7.0. % 0.08/0.24 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.46 % Computer : n002.cluster.edu % 0.09/0.46 % Model : x86_64 x86_64 % 0.09/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.46 % Memory : 8042.1875MB % 0.09/0.46 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.46 % CPULimit : 300 % 0.09/0.46 % WCLimit : 300 % 0.09/0.46 % DateTime : Mon Aug 28 03:21:19 EDT 2023 % 0.13/0.47 % CPUTime : % 0.45/0.87 ________ _____ % 0.45/0.87 ___ __ \_________(_)________________________________ % 0.45/0.87 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.45/0.87 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.45/0.87 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.45/0.87 % 0.45/0.87 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.45/0.87 (2023-06-19) % 0.45/0.87 % 0.45/0.87 (c) Philipp Rümmer, 2009-2023 % 0.45/0.87 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.45/0.87 Amanda Stjerna. % 0.45/0.87 Free software under BSD-3-Clause. % 0.45/0.87 % 0.45/0.87 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.45/0.87 % 0.45/0.87 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.90 Running up to 7 provers in parallel. % 0.57/0.96 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.96 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.96 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.96 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.96 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.96 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.90 Prover 1: Preprocessing ... % 3.08/1.90 Prover 4: Preprocessing ... % 3.35/1.98 Prover 6: Preprocessing ... % 3.35/1.98 Prover 5: Preprocessing ... % 3.35/1.98 Prover 3: Preprocessing ... % 3.35/1.98 Prover 0: Preprocessing ... % 3.35/1.99 Prover 2: Preprocessing ... % 6.15/2.81 Prover 2: Constructing countermodel ... % 6.15/2.82 Prover 3: Constructing countermodel ... % 6.58/2.84 Prover 6: Constructing countermodel ... % 6.58/2.85 Prover 0: Constructing countermodel ... % 6.58/2.85 Prover 1: Constructing countermodel ... % 6.58/2.89 Prover 4: Constructing countermodel ... % 8.89/3.34 Prover 5: Constructing countermodel ... % 10.28/3.68 Prover 0: proved (2769ms) % 10.28/3.68 % 10.28/3.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.28/3.69 % 10.50/3.71 Prover 2: stopped % 10.50/3.72 Prover 5: stopped % 10.50/3.73 Prover 6: stopped % 10.50/3.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.50/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.50/3.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.50/3.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.50/3.75 Prover 3: stopped % 10.69/3.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.88/4.02 Prover 10: Preprocessing ... % 11.88/4.04 Prover 8: Preprocessing ... % 11.88/4.05 Prover 11: Preprocessing ... % 12.15/4.08 Prover 7: Preprocessing ... % 12.15/4.12 Prover 13: Preprocessing ... % 13.29/4.33 Prover 8: Constructing countermodel ... % 13.90/4.45 Prover 7: Constructing countermodel ... % 13.90/4.45 Prover 11: Constructing countermodel ... % 14.18/4.47 Prover 10: Constructing countermodel ... % 14.18/4.54 Prover 13: Constructing countermodel ... % 36.54/9.52 Prover 13: stopped % 36.96/9.54 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 37.46/9.64 Prover 16: Preprocessing ... % 38.80/9.97 Prover 16: Constructing countermodel ... % 51.44/12.63 Prover 7: Found proof (size 2395) % 51.44/12.63 Prover 7: proved (8843ms) % 51.44/12.63 Prover 4: stopped % 51.44/12.63 Prover 8: stopped % 51.44/12.63 Prover 10: stopped % 51.44/12.63 Prover 16: stopped % 51.44/12.63 Prover 11: stopped % 51.44/12.64 Prover 1: stopped % 51.44/12.64 % 51.44/12.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 51.44/12.64 % 53.30/13.28 % SZS output start Proof for theBenchmark % 53.36/13.32 Assumptions after simplification: % 53.36/13.32 --------------------------------- % 53.36/13.32 % 53.36/13.32 (ax1) % 53.61/13.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 53.61/13.43 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 53.61/13.43 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 53.61/13.43 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 53.61/13.43 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 53.61/13.43 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 53.61/13.43 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 53.61/13.43 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 53.61/13.43 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 53.61/13.43 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 53.61/13.43 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 53.61/13.43 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 53.61/13.43 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 53.61/13.43 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 53.61/13.43 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 53.61/13.43 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 53.61/13.43 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 53.61/13.43 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 53.61/13.43 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 53.61/13.43 % 53.61/13.43 (ax10) % 53.61/13.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e3) = % 53.61/13.43 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 53.61/13.43 % 53.61/13.43 (ax11) % 53.61/13.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e3) = % 53.61/13.43 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 53.61/13.43 % 53.61/13.43 (ax12) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e0) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 53.61/13.44 % 53.61/13.44 (ax13) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e0) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 53.61/13.44 % 53.61/13.44 (ax14) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e2) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 53.61/13.44 % 53.61/13.44 (ax15) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e2) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 53.61/13.44 % 53.61/13.44 (ax16) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e3) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 53.61/13.44 % 53.61/13.44 (ax17) % 53.61/13.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e3) = % 53.61/13.44 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 53.61/13.45 % 53.61/13.45 (ax18) % 53.61/13.45 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e0) = % 53.61/13.45 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 53.61/13.45 % 53.61/13.45 (ax19) % 53.61/13.45 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e0) = % 53.61/13.45 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 53.61/13.45 % 53.61/13.45 (ax2) % 53.82/13.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 53.82/13.48 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 53.82/13.48 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 53.82/13.48 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = % 53.82/13.48 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, % 53.82/13.48 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) = % 53.82/13.48 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15 % 53.82/13.48 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 & % 53.82/13.48 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3, % 53.82/13.48 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2) % 53.82/13.48 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1 % 53.82/13.48 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3, % 53.82/13.48 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = % 53.82/13.48 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 % 53.82/13.48 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 & % 53.82/13.48 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3, % 53.82/13.48 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0) % 53.82/13.48 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3 % 53.82/13.48 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) % 53.82/13.48 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 53.82/13.48 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 & % 53.82/13.48 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2) % 53.82/13.48 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) | % 53.82/13.48 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 53.82/13.48 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2, % 53.82/13.48 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = % 53.82/13.48 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 53.82/13.48 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 & % 53.82/13.48 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1) % 53.82/13.48 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) | % 53.82/13.48 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 & % 53.82/13.48 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2, % 53.82/13.48 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) % 53.82/13.48 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 & % 53.82/13.48 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3, % 53.82/13.48 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1) % 53.82/13.48 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0 % 53.82/13.48 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) % 53.82/13.48 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | % 53.82/13.48 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 & % 53.82/13.48 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) = % 53.82/13.48 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8 % 53.82/13.48 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 & % 53.82/13.48 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) % 53.82/13.48 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & % 53.82/13.48 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 & % 53.82/13.48 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0) % 53.82/13.48 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0 % 53.82/13.48 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 & % 53.82/13.48 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = % 53.82/13.48 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 53.82/13.48 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 & % 53.82/13.48 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = % 53.82/13.48 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2 % 53.82/13.48 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 53.82/13.48 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3, % 53.82/13.48 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = % 53.82/13.48 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | % 53.82/13.48 (v1 = e0 & op(e0, e1) = e0))))) % 53.82/13.48 % 53.82/13.48 (ax20) % 53.82/13.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e1) = % 53.82/13.48 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 53.82/13.48 % 53.82/13.48 (ax21) % 53.82/13.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e1) = % 53.82/13.49 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 53.82/13.49 % 53.82/13.49 (ax22) % 53.82/13.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e3) = % 53.82/13.49 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 53.82/13.49 % 53.82/13.49 (ax23) % 53.82/13.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e3) = % 53.82/13.50 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 53.82/13.50 % 53.82/13.50 (ax24) % 53.82/13.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e0) = % 53.82/13.50 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 53.82/13.50 % 53.82/13.50 (ax25) % 53.82/13.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e0) = % 53.82/13.50 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 53.82/13.50 % 53.82/13.50 (ax26) % 53.82/13.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e1) = % 53.82/13.50 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 53.82/13.50 % 53.82/13.50 (ax27) % 53.82/13.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e1) = % 53.82/13.51 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 53.82/13.51 % 53.82/13.51 (ax28) % 53.82/13.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e0, e2) = % 53.82/13.51 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 53.82/13.51 % 53.82/13.51 (ax29) % 53.82/13.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e2) = % 53.82/13.51 v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 53.82/13.51 % 53.82/13.51 (ax3) % 53.82/13.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 53.82/13.52 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 53.82/13.53 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 53.82/13.53 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 53.82/13.53 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 53.82/13.53 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 53.82/13.53 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 53.82/13.53 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 53.82/13.53 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 53.82/13.53 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 53.82/13.53 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 53.82/13.53 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 53.82/13.53 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 53.82/13.53 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 53.82/13.53 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 53.82/13.53 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 53.82/13.53 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 53.82/13.53 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 53.82/13.53 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 53.82/13.53 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 53.82/13.53 % 53.82/13.53 (ax4) % 53.82/13.53 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 53.82/13.53 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 53.82/13.53 % 53.82/13.53 (ax5) % 53.82/13.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 53.82/13.54 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 53.82/13.54 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 53.82/13.54 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: % 53.82/13.54 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 53.82/13.54 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 53.82/13.54 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(v15, e3) = e3 & % 53.82/13.54 op(v14, e3) = e2 & op(v13, e3) = e1 & op(v12, e3) = e0 & op(v11, e2) = e3 & % 53.82/13.54 op(v10, e2) = e2 & op(v9, e2) = e1 & op(v8, e2) = e0 & op(v7, e1) = e3 & % 53.82/13.54 op(v6, e1) = e2 & op(v5, e1) = e1 & op(v4, e1) = e0 & op(v3, e0) = e3 & % 53.82/13.54 op(v2, e0) = e2 & op(v1, e0) = e1 & op(v0, e0) = e0 & op(e3, e3) = v15 & % 53.82/13.54 op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & % 53.82/13.54 op(e2, e2) = v10 & op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & % 53.82/13.54 op(e1, e2) = v6 & op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & % 53.82/13.54 op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 53.82/13.54 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 53.82/13.54 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v31 = v15 & v30 = % 53.82/13.54 v11 & v29 = v7 & v28 = v3 & op(e3, v15) = v15 & op(e3, v11) = v11 & % 53.82/13.54 op(e3, v7) = v7 & op(e3, v3) = v3) | (v27 = v14 & v26 = v10 & v25 = v6 & % 53.82/13.54 v24 = v2 & op(e2, v14) = v14 & op(e2, v10) = v10 & op(e2, v6) = v6 & % 53.82/13.54 op(e2, v2) = v2) | (v23 = v13 & v22 = v9 & v21 = v5 & v20 = v1 & op(e1, % 53.82/13.54 v13) = v13 & op(e1, v9) = v9 & op(e1, v5) = v5 & op(e1, v1) = v1) | % 53.82/13.54 (v19 = v12 & v18 = v8 & v17 = v4 & v16 = v0 & op(e0, v12) = v12 & op(e0, % 53.82/13.54 v8) = v8 & op(e0, v4) = v4 & op(e0, v0) = v0))) % 53.82/13.54 % 53.82/13.54 (ax6) % 53.82/13.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e2, e1) = % 53.82/13.54 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 53.82/13.54 % 53.82/13.54 (ax7) % 53.82/13.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e1) = % 53.82/13.54 v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 53.82/13.54 % 53.82/13.54 (ax8) % 53.82/13.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e1, e2) = % 53.82/13.54 v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 53.82/13.54 % 53.82/13.54 (ax9) % 53.82/13.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : (op(e3, e2) = % 53.82/13.55 v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 53.82/13.55 % 53.82/13.55 (function-axioms) % 53.82/13.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 53.82/13.55 v2) = v1) | ~ (op(v3, v2) = v0)) % 53.82/13.55 % 53.82/13.55 Those formulas are unsatisfiable: % 53.82/13.55 --------------------------------- % 53.82/13.55 % 53.82/13.55 Begin of proof % 53.82/13.55 | % 53.82/13.55 | ALPHA: (ax1) implies: % 53.82/13.56 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 53.82/13.56 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 53.82/13.56 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 53.82/13.56 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 53.82/13.56 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 53.82/13.56 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 53.82/13.56 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 53.82/13.56 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 53.82/13.56 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 53.82/13.56 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 53.82/13.56 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 53.82/13.56 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 53.82/13.56 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 53.82/13.56 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 53.82/13.56 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 53.82/13.56 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 53.82/13.56 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 53.82/13.56 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 53.82/13.56 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 53.82/13.56 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 53.82/13.56 | = e0)) % 53.82/13.56 | % 53.82/13.56 | ALPHA: (ax2) implies: % 54.17/13.58 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 54.17/13.58 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 54.17/13.58 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 54.17/13.58 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2) % 54.17/13.58 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) = % 54.17/13.58 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) = % 54.17/13.58 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) % 54.17/13.58 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 % 54.17/13.58 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = % 54.17/13.58 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & % 54.17/13.58 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & % 54.17/13.58 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 & % 54.17/13.58 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 & % 54.17/13.58 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 & % 54.17/13.58 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 & % 54.17/13.58 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 & % 54.17/13.58 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & % 54.17/13.58 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & % 54.17/13.58 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & % 54.17/13.58 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 & % 54.17/13.58 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 & % 54.17/13.58 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 & % 54.17/13.58 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 & % 54.17/13.58 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & % 54.17/13.58 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & % 54.17/13.58 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & % 54.17/13.58 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 & % 54.17/13.58 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 54.17/13.58 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 & % 54.17/13.58 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 & % 54.17/13.58 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 & % 54.17/13.58 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & % 54.17/13.58 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & % 54.17/13.58 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & % 54.17/13.58 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 & % 54.17/13.58 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 & % 54.17/13.58 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 & % 54.17/13.58 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 & % 54.17/13.58 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & % 54.17/13.58 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & % 54.17/13.58 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & % 54.17/13.58 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 & % 54.17/13.58 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 & % 54.17/13.58 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 & % 54.17/13.58 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 & % 54.17/13.58 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & % 54.17/13.58 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & % 54.17/13.58 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 & % 54.17/13.59 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 & % 54.17/13.59 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 & % 54.17/13.59 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 & % 54.17/13.59 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 & % 54.17/13.59 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & % 54.17/13.59 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & % 54.17/13.59 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & % 54.17/13.59 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 & % 54.17/13.59 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 & % 54.17/13.59 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 & % 54.17/13.59 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 & % 54.17/13.59 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & % 54.17/13.59 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & % 54.17/13.59 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 & % 54.17/13.59 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 & % 54.17/13.59 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 & % 54.17/13.59 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 & % 54.17/13.59 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & % 54.17/13.59 | op(e0, e1) = e0))))) % 54.17/13.59 | % 54.17/13.59 | ALPHA: (ax3) implies: % 54.17/13.59 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 54.17/13.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 54.17/13.59 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 54.17/13.59 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 54.17/13.59 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 54.17/13.59 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 54.17/13.59 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 54.17/13.59 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 54.17/13.59 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 54.17/13.59 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 54.17/13.59 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 54.17/13.59 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 54.17/13.59 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 54.17/13.59 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 54.17/13.59 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 54.17/13.59 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 54.17/13.59 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 54.17/13.59 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 54.17/13.59 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 54.17/13.59 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 54.17/13.59 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 54.17/13.59 | % 54.17/13.59 | ALPHA: (ax4) implies: % 54.25/13.59 | (4) ~ (e1 = e0) % 54.25/13.59 | (5) ~ (e2 = e0) % 54.25/13.59 | (6) ~ (e2 = e1) % 54.25/13.60 | (7) ~ (e3 = e0) % 54.25/13.60 | (8) ~ (e3 = e1) % 54.25/13.60 | (9) ~ (e3 = e2) % 54.25/13.60 | % 54.25/13.60 | ALPHA: (ax5) implies: % 54.25/13.60 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 54.25/13.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 54.25/13.60 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 54.25/13.60 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 54.25/13.60 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 54.25/13.60 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 54.25/13.60 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(v15, e3) = e3 % 54.25/13.60 | & op(v14, e3) = e2 & op(v13, e3) = e1 & op(v12, e3) = e0 & op(v11, % 54.25/13.60 | e2) = e3 & op(v10, e2) = e2 & op(v9, e2) = e1 & op(v8, e2) = e0 & % 54.25/13.60 | op(v7, e1) = e3 & op(v6, e1) = e2 & op(v5, e1) = e1 & op(v4, e1) = % 54.25/13.60 | e0 & op(v3, e0) = e3 & op(v2, e0) = e2 & op(v1, e0) = e1 & op(v0, % 54.25/13.60 | e0) = e0 & op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 54.25/13.60 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, % 54.25/13.60 | e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 54.25/13.60 | op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = % 54.25/13.60 | v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) % 54.25/13.60 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 54.25/13.60 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v31 = v15 & % 54.25/13.60 | v30 = v11 & v29 = v7 & v28 = v3 & op(e3, v15) = v15 & op(e3, % 54.25/13.60 | v11) = v11 & op(e3, v7) = v7 & op(e3, v3) = v3) | (v27 = v14 & % 54.25/13.60 | v26 = v10 & v25 = v6 & v24 = v2 & op(e2, v14) = v14 & op(e2, % 54.25/13.60 | v10) = v10 & op(e2, v6) = v6 & op(e2, v2) = v2) | (v23 = v13 & % 54.25/13.60 | v22 = v9 & v21 = v5 & v20 = v1 & op(e1, v13) = v13 & op(e1, v9) % 54.25/13.60 | = v9 & op(e1, v5) = v5 & op(e1, v1) = v1) | (v19 = v12 & v18 = % 54.25/13.60 | v8 & v17 = v4 & v16 = v0 & op(e0, v12) = v12 & op(e0, v8) = v8 & % 54.25/13.60 | op(e0, v4) = v4 & op(e0, v0) = v0))) % 54.25/13.60 | % 54.25/13.60 | ALPHA: (ax6) implies: % 54.25/13.61 | (11) ? [v0: $i] : ? [v1: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax7) implies: % 54.25/13.61 | (12) ? [v0: $i] : ? [v1: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax8) implies: % 54.25/13.61 | (13) ? [v0: $i] : ? [v1: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax9) implies: % 54.25/13.61 | (14) ? [v0: $i] : ? [v1: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax10) implies: % 54.25/13.61 | (15) ? [v0: $i] : ? [v1: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax11) implies: % 54.25/13.61 | (16) ? [v0: $i] : ? [v1: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.25/13.61 | | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax12) implies: % 54.25/13.61 | (17) ? [v0: $i] : ? [v1: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.25/13.61 | | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax13) implies: % 54.25/13.61 | (18) ? [v0: $i] : ? [v1: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.25/13.61 | | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 54.25/13.61 | % 54.25/13.61 | ALPHA: (ax14) implies: % 54.25/13.62 | (19) ? [v0: $i] : ? [v1: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.25/13.62 | | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 54.25/13.62 | % 54.25/13.62 | ALPHA: (ax15) implies: % 54.25/13.62 | (20) ? [v0: $i] : ? [v1: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.25/13.62 | | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 54.25/13.62 | % 54.25/13.62 | ALPHA: (ax16) implies: % 54.35/13.62 | (21) ? [v0: $i] : ? [v1: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.35/13.62 | | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 54.35/13.62 | % 54.35/13.62 | ALPHA: (ax17) implies: % 54.35/13.62 | (22) ? [v0: $i] : ? [v1: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.35/13.62 | | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax18) implies: % 54.36/13.63 | (23) ? [v0: $i] : ? [v1: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax19) implies: % 54.36/13.63 | (24) ? [v0: $i] : ? [v1: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax20) implies: % 54.36/13.63 | (25) ? [v0: $i] : ? [v1: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e3) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax21) implies: % 54.36/13.63 | (26) ? [v0: $i] : ? [v1: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax22) implies: % 54.36/13.63 | (27) ? [v0: $i] : ? [v1: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax23) implies: % 54.36/13.63 | (28) ? [v0: $i] : ? [v1: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.36/13.63 | | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax24) implies: % 54.36/13.63 | (29) ? [v0: $i] : ? [v1: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.36/13.63 | | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 54.36/13.63 | % 54.36/13.63 | ALPHA: (ax25) implies: % 54.36/13.64 | (30) ? [v0: $i] : ? [v1: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.36/13.64 | | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 54.36/13.64 | % 54.36/13.64 | ALPHA: (ax26) implies: % 54.36/13.64 | (31) ? [v0: $i] : ? [v1: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e2) % 54.36/13.64 | | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 54.36/13.64 | % 54.36/13.64 | ALPHA: (ax27) implies: % 54.36/13.64 | (32) ? [v0: $i] : ? [v1: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.36/13.64 | | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 54.36/13.64 | % 54.36/13.64 | ALPHA: (ax28) implies: % 54.36/13.64 | (33) ? [v0: $i] : ? [v1: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e1) % 54.36/13.64 | | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 54.36/13.64 | % 54.36/13.64 | ALPHA: (ax29) implies: % 54.36/13.65 | (34) ? [v0: $i] : ? [v1: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e0) % 54.36/13.65 | | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1 gives: % 54.36/13.65 | (35) op(e3, e2) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e0) | ( ~ (all_4_0 % 54.36/13.65 | = e1) & op(e0, e0) = all_4_0 & $i(all_4_0))) % 54.36/13.65 | % 54.36/13.65 | ALPHA: (35) implies: % 54.36/13.65 | (36) op(e3, e2) = all_4_1 % 54.36/13.65 | (37) ~ (all_4_1 = e0) | ( ~ (all_4_0 = e1) & op(e0, e0) = all_4_0 & % 54.36/13.65 | $i(all_4_0)) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1 gives: % 54.36/13.65 | (38) op(e0, e3) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e1) | ( ~ (all_6_0 % 54.36/13.65 | = e2) & op(e1, e1) = all_6_0 & $i(all_6_0))) % 54.36/13.65 | % 54.36/13.65 | ALPHA: (38) implies: % 54.36/13.65 | (39) op(e0, e3) = all_6_1 % 54.36/13.65 | (40) ~ (all_6_1 = e1) | ( ~ (all_6_0 = e2) & op(e1, e1) = all_6_0 & % 54.36/13.65 | $i(all_6_0)) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1 gives: % 54.36/13.65 | (41) op(e0, e3) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e2) | ( ~ (all_8_0 % 54.36/13.65 | = e1) & op(e2, e2) = all_8_0 & $i(all_8_0))) % 54.36/13.65 | % 54.36/13.65 | ALPHA: (41) implies: % 54.36/13.65 | (42) op(e0, e3) = all_8_1 % 54.36/13.65 | (43) ~ (all_8_1 = e2) | ( ~ (all_8_0 = e1) & op(e2, e2) = all_8_0 & % 54.36/13.65 | $i(all_8_0)) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1 gives: % 54.36/13.65 | (44) op(e2, e1) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e3) | ( ~ % 54.36/13.65 | (all_10_0 = e0) & op(e3, e3) = all_10_0 & $i(all_10_0))) % 54.36/13.65 | % 54.36/13.65 | ALPHA: (44) implies: % 54.36/13.65 | (45) op(e2, e1) = all_10_1 % 54.36/13.65 | (46) ~ (all_10_1 = e3) | ( ~ (all_10_0 = e0) & op(e3, e3) = all_10_0 & % 54.36/13.65 | $i(all_10_0)) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1 gives: % 54.36/13.65 | (47) op(e2, e3) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e0) | ( ~ % 54.36/13.65 | (all_12_0 = e1) & op(e0, e0) = all_12_0 & $i(all_12_0))) % 54.36/13.65 | % 54.36/13.65 | ALPHA: (47) implies: % 54.36/13.65 | (48) op(e2, e3) = all_12_1 % 54.36/13.65 | (49) ~ (all_12_1 = e0) | ( ~ (all_12_0 = e1) & op(e0, e0) = all_12_0 & % 54.36/13.65 | $i(all_12_0)) % 54.36/13.65 | % 54.36/13.65 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1 gives: % 54.36/13.66 | (50) op(e1, e0) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = e2) | ( ~ % 54.36/13.66 | (all_14_0 = e3) & op(e2, e2) = all_14_0 & $i(all_14_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (50) implies: % 54.36/13.66 | (51) op(e1, e0) = all_14_1 % 54.36/13.66 | (52) ~ (all_14_1 = e2) | ( ~ (all_14_0 = e3) & op(e2, e2) = all_14_0 & % 54.36/13.66 | $i(all_14_0)) % 54.36/13.66 | % 54.36/13.66 | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1 gives: % 54.36/13.66 | (53) op(e0, e1) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e2) | ( ~ % 54.36/13.66 | (all_16_0 = e3) & op(e2, e2) = all_16_0 & $i(all_16_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (53) implies: % 54.36/13.66 | (54) op(e0, e1) = all_16_1 % 54.36/13.66 | % 54.36/13.66 | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1 gives: % 54.36/13.66 | (55) op(e1, e0) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 = e3) | ( ~ % 54.36/13.66 | (all_18_0 = e2) & op(e3, e3) = all_18_0 & $i(all_18_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (55) implies: % 54.36/13.66 | (56) op(e1, e0) = all_18_1 % 54.36/13.66 | (57) ~ (all_18_1 = e3) | ( ~ (all_18_0 = e2) & op(e3, e3) = all_18_0 & % 54.36/13.66 | $i(all_18_0)) % 54.36/13.66 | % 54.36/13.66 | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1 gives: % 54.36/13.66 | (58) op(e1, e2) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e3) | ( ~ % 54.36/13.66 | (all_20_0 = e0) & op(e3, e3) = all_20_0 & $i(all_20_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (58) implies: % 54.36/13.66 | (59) op(e1, e2) = all_20_1 % 54.36/13.66 | (60) ~ (all_20_1 = e3) | ( ~ (all_20_0 = e0) & op(e3, e3) = all_20_0 & % 54.36/13.66 | $i(all_20_0)) % 54.36/13.66 | % 54.36/13.66 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1 gives: % 54.36/13.66 | (61) op(e1, e3) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e0) | ( ~ % 54.36/13.66 | (all_22_0 = e2) & op(e0, e0) = all_22_0 & $i(all_22_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (61) implies: % 54.36/13.66 | (62) op(e1, e3) = all_22_1 % 54.36/13.66 | (63) ~ (all_22_1 = e0) | ( ~ (all_22_0 = e2) & op(e0, e0) = all_22_0 & % 54.36/13.66 | $i(all_22_0)) % 54.36/13.66 | % 54.36/13.66 | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1 gives: % 54.36/13.66 | (64) op(e2, e0) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e1) | ( ~ % 54.36/13.66 | (all_24_0 = e3) & op(e1, e1) = all_24_0 & $i(all_24_0))) % 54.36/13.66 | % 54.36/13.66 | ALPHA: (64) implies: % 54.36/13.67 | (65) op(e2, e0) = all_24_1 % 54.36/13.67 | (66) ~ (all_24_1 = e1) | ( ~ (all_24_0 = e3) & op(e1, e1) = all_24_0 & % 54.36/13.67 | $i(all_24_0)) % 54.36/13.67 | % 54.36/13.67 | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1 gives: % 54.36/13.67 | (67) op(e3, e1) = all_26_1 & $i(all_26_1) & ( ~ (all_26_1 = e2) | ( ~ % 54.36/13.67 | (all_26_0 = e0) & op(e2, e2) = all_26_0 & $i(all_26_0))) % 54.36/13.67 | % 54.36/13.67 | ALPHA: (67) implies: % 54.36/13.67 | (68) op(e3, e1) = all_26_1 % 54.36/13.68 | (69) ~ (all_26_1 = e2) | ( ~ (all_26_0 = e0) & op(e2, e2) = all_26_0 & % 54.36/13.68 | $i(all_26_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1 gives: % 54.36/13.68 | (70) op(e0, e2) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e3) | ( ~ % 54.36/13.68 | (all_28_0 = e1) & op(e3, e3) = all_28_0 & $i(all_28_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (70) implies: % 54.36/13.68 | (71) op(e0, e2) = all_28_1 % 54.36/13.68 | (72) ~ (all_28_1 = e3) | ( ~ (all_28_0 = e1) & op(e3, e3) = all_28_0 & % 54.36/13.68 | $i(all_28_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1 gives: % 54.36/13.68 | (73) op(e2, e1) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 = e0) | ( ~ % 54.36/13.68 | (all_30_0 = e3) & op(e0, e0) = all_30_0 & $i(all_30_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (73) implies: % 54.36/13.68 | (74) op(e2, e1) = all_30_1 % 54.36/13.68 | (75) ~ (all_30_1 = e0) | ( ~ (all_30_0 = e3) & op(e0, e0) = all_30_0 & % 54.36/13.68 | $i(all_30_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1 gives: % 54.36/13.68 | (76) op(e1, e2) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 = e0) | ( ~ % 54.36/13.68 | (all_32_0 = e3) & op(e0, e0) = all_32_0 & $i(all_32_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (76) implies: % 54.36/13.68 | (77) op(e1, e2) = all_32_1 % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1 gives: % 54.36/13.68 | (78) op(e3, e0) = all_34_1 & $i(all_34_1) & ( ~ (all_34_1 = e1) | ( ~ % 54.36/13.68 | (all_34_0 = e2) & op(e1, e1) = all_34_0 & $i(all_34_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (78) implies: % 54.36/13.68 | (79) op(e3, e0) = all_34_1 % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1 gives: % 54.36/13.68 | (80) op(e0, e1) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e3) | ( ~ % 54.36/13.68 | (all_36_0 = e2) & op(e3, e3) = all_36_0 & $i(all_36_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (80) implies: % 54.36/13.68 | (81) op(e0, e1) = all_36_1 % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1 gives: % 54.36/13.68 | (82) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e1) | ( ~ % 54.36/13.68 | (all_38_0 = e3) & op(e1, e1) = all_38_0 & $i(all_38_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (82) implies: % 54.36/13.68 | (83) op(e0, e2) = all_38_1 % 54.36/13.68 | (84) ~ (all_38_1 = e1) | ( ~ (all_38_0 = e3) & op(e1, e1) = all_38_0 & % 54.36/13.68 | $i(all_38_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1 gives: % 54.36/13.68 | (85) op(e3, e1) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e0) | ( ~ % 54.36/13.68 | (all_40_0 = e2) & op(e0, e0) = all_40_0 & $i(all_40_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (85) implies: % 54.36/13.68 | (86) op(e3, e1) = all_40_1 % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1 gives: % 54.36/13.68 | (87) op(e3, e2) = all_42_1 & $i(all_42_1) & ( ~ (all_42_1 = e1) | ( ~ % 54.36/13.68 | (all_42_0 = e0) & op(e1, e1) = all_42_0 & $i(all_42_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (87) implies: % 54.36/13.68 | (88) op(e3, e2) = all_42_1 % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1 gives: % 54.36/13.68 | (89) op(e1, e3) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 = e2) | ( ~ % 54.36/13.68 | (all_44_0 = e0) & op(e2, e2) = all_44_0 & $i(all_44_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (89) implies: % 54.36/13.68 | (90) op(e1, e3) = all_44_1 % 54.36/13.68 | (91) ~ (all_44_1 = e2) | ( ~ (all_44_0 = e0) & op(e2, e2) = all_44_0 & % 54.36/13.68 | $i(all_44_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1 gives: % 54.36/13.68 | (92) op(e2, e3) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e1) | ( ~ % 54.36/13.68 | (all_46_0 = e0) & op(e1, e1) = all_46_0 & $i(all_46_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (92) implies: % 54.36/13.68 | (93) op(e2, e3) = all_46_1 % 54.36/13.68 | (94) ~ (all_46_1 = e1) | ( ~ (all_46_0 = e0) & op(e1, e1) = all_46_0 & % 54.36/13.68 | $i(all_46_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1 gives: % 54.36/13.68 | (95) op(e2, e0) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e3) | ( ~ % 54.36/13.68 | (all_48_0 = e1) & op(e3, e3) = all_48_0 & $i(all_48_0))) % 54.36/13.68 | % 54.36/13.68 | ALPHA: (95) implies: % 54.36/13.68 | (96) op(e2, e0) = all_48_1 % 54.36/13.68 | (97) ~ (all_48_1 = e3) | ( ~ (all_48_0 = e1) & op(e3, e3) = all_48_0 & % 54.36/13.68 | $i(all_48_0)) % 54.36/13.68 | % 54.36/13.68 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1 gives: % 54.36/13.69 | (98) op(e3, e0) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e2) | ( ~ % 54.36/13.69 | (all_50_0 = e1) & op(e2, e2) = all_50_0 & $i(all_50_0))) % 54.36/13.69 | % 54.36/13.69 | ALPHA: (98) implies: % 54.36/13.69 | (99) op(e3, e0) = all_50_1 % 54.36/13.69 | % 54.36/13.69 | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2, % 54.36/13.69 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9, % 54.36/13.69 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15, % 54.36/13.69 | all_52_16, all_52_17, all_52_18, all_52_19, all_52_20, all_52_21, % 54.36/13.69 | all_52_22, all_52_23, all_52_24, all_52_25, all_52_26, all_52_27, % 54.36/13.69 | all_52_28, all_52_29, all_52_30, all_52_31 gives: % 54.36/13.69 | (100) op(all_52_16, e3) = e3 & op(all_52_17, e3) = e2 & op(all_52_18, e3) = % 54.36/13.69 | e1 & op(all_52_19, e3) = e0 & op(all_52_20, e2) = e3 & op(all_52_21, % 54.36/13.69 | e2) = e2 & op(all_52_22, e2) = e1 & op(all_52_23, e2) = e0 & % 54.36/13.69 | op(all_52_24, e1) = e3 & op(all_52_25, e1) = e2 & op(all_52_26, e1) = % 54.36/13.69 | e1 & op(all_52_27, e1) = e0 & op(all_52_28, e0) = e3 & op(all_52_29, % 54.36/13.69 | e0) = e2 & op(all_52_30, e0) = e1 & op(all_52_31, e0) = e0 & op(e3, % 54.36/13.69 | e3) = all_52_16 & op(e3, e2) = all_52_17 & op(e3, e1) = all_52_18 & % 54.36/13.69 | op(e3, e0) = all_52_19 & op(e2, e3) = all_52_20 & op(e2, e2) = % 54.36/13.69 | all_52_21 & op(e2, e1) = all_52_22 & op(e2, e0) = all_52_23 & op(e1, % 54.36/13.69 | e3) = all_52_24 & op(e1, e2) = all_52_25 & op(e1, e1) = all_52_26 & % 54.36/13.69 | op(e1, e0) = all_52_27 & op(e0, e3) = all_52_28 & op(e0, e2) = % 54.36/13.69 | all_52_29 & op(e0, e1) = all_52_30 & op(e0, e0) = all_52_31 & % 54.36/13.69 | $i(all_52_16) & $i(all_52_17) & $i(all_52_18) & $i(all_52_19) & % 54.36/13.69 | $i(all_52_20) & $i(all_52_21) & $i(all_52_22) & $i(all_52_23) & % 54.36/13.69 | $i(all_52_24) & $i(all_52_25) & $i(all_52_26) & $i(all_52_27) & % 54.36/13.69 | $i(all_52_28) & $i(all_52_29) & $i(all_52_30) & $i(all_52_31) & % 54.36/13.69 | ((all_52_0 = all_52_16 & all_52_1 = all_52_20 & all_52_2 = all_52_24 % 54.36/13.69 | & all_52_3 = all_52_28 & op(e3, all_52_16) = all_52_16 & op(e3, % 54.36/13.69 | all_52_20) = all_52_20 & op(e3, all_52_24) = all_52_24 & op(e3, % 54.36/13.69 | all_52_28) = all_52_28) | (all_52_4 = all_52_17 & all_52_5 = % 54.36/13.69 | all_52_21 & all_52_6 = all_52_25 & all_52_7 = all_52_29 & op(e2, % 54.36/13.69 | all_52_17) = all_52_17 & op(e2, all_52_21) = all_52_21 & op(e2, % 54.36/13.69 | all_52_25) = all_52_25 & op(e2, all_52_29) = all_52_29) | % 54.36/13.69 | (all_52_8 = all_52_18 & all_52_9 = all_52_22 & all_52_10 = % 54.36/13.69 | all_52_26 & all_52_11 = all_52_30 & op(e1, all_52_18) = all_52_18 % 54.36/13.69 | & op(e1, all_52_22) = all_52_22 & op(e1, all_52_26) = all_52_26 & % 54.36/13.69 | op(e1, all_52_30) = all_52_30) | (all_52_12 = all_52_19 & % 54.36/13.69 | all_52_13 = all_52_23 & all_52_14 = all_52_27 & all_52_15 = % 54.36/13.69 | all_52_31 & op(e0, all_52_19) = all_52_19 & op(e0, all_52_23) = % 54.36/13.69 | all_52_23 & op(e0, all_52_27) = all_52_27 & op(e0, all_52_31) = % 54.36/13.69 | all_52_31)) % 54.36/13.69 | % 54.36/13.69 | ALPHA: (100) implies: % 54.36/13.69 | (101) op(e0, e0) = all_52_31 % 54.56/13.70 | (102) op(e0, e1) = all_52_30 % 54.56/13.70 | (103) op(e0, e2) = all_52_29 % 54.56/13.70 | (104) op(e0, e3) = all_52_28 % 54.56/13.70 | (105) op(e1, e0) = all_52_27 % 54.56/13.70 | (106) op(e1, e1) = all_52_26 % 54.56/13.70 | (107) op(e1, e2) = all_52_25 % 54.56/13.70 | (108) op(e1, e3) = all_52_24 % 54.56/13.70 | (109) op(e2, e0) = all_52_23 % 54.56/13.70 | (110) op(e2, e1) = all_52_22 % 54.56/13.70 | (111) op(e2, e2) = all_52_21 % 54.56/13.70 | (112) op(e2, e3) = all_52_20 % 54.56/13.70 | (113) op(e3, e0) = all_52_19 % 54.56/13.70 | (114) op(e3, e1) = all_52_18 % 54.56/13.70 | (115) op(e3, e2) = all_52_17 % 54.56/13.70 | (116) op(e3, e3) = all_52_16 % 54.56/13.70 | (117) op(all_52_31, e0) = e0 % 54.56/13.70 | (118) op(all_52_30, e0) = e1 % 54.56/13.70 | (119) op(all_52_29, e0) = e2 % 54.56/13.70 | (120) op(all_52_28, e0) = e3 % 54.56/13.70 | (121) op(all_52_27, e1) = e0 % 54.56/13.70 | (122) op(all_52_25, e1) = e2 % 54.56/13.70 | (123) op(all_52_24, e1) = e3 % 54.56/13.70 | (124) op(all_52_23, e2) = e0 % 54.56/13.70 | (125) op(all_52_22, e2) = e1 % 54.56/13.70 | (126) op(all_52_20, e2) = e3 % 54.56/13.70 | (127) op(all_52_19, e3) = e0 % 54.56/13.70 | (128) op(all_52_18, e3) = e1 % 54.56/13.70 | (129) op(all_52_17, e3) = e2 % 54.56/13.72 | (130) (all_52_0 = all_52_16 & all_52_1 = all_52_20 & all_52_2 = all_52_24 & % 54.56/13.72 | all_52_3 = all_52_28 & op(e3, all_52_16) = all_52_16 & op(e3, % 54.56/13.72 | all_52_20) = all_52_20 & op(e3, all_52_24) = all_52_24 & op(e3, % 54.56/13.72 | all_52_28) = all_52_28) | (all_52_4 = all_52_17 & all_52_5 = % 54.56/13.72 | all_52_21 & all_52_6 = all_52_25 & all_52_7 = all_52_29 & op(e2, % 54.56/13.72 | all_52_17) = all_52_17 & op(e2, all_52_21) = all_52_21 & op(e2, % 54.56/13.72 | all_52_25) = all_52_25 & op(e2, all_52_29) = all_52_29) | % 54.56/13.72 | (all_52_8 = all_52_18 & all_52_9 = all_52_22 & all_52_10 = all_52_26 % 54.56/13.72 | & all_52_11 = all_52_30 & op(e1, all_52_18) = all_52_18 & op(e1, % 54.56/13.72 | all_52_22) = all_52_22 & op(e1, all_52_26) = all_52_26 & op(e1, % 54.56/13.72 | all_52_30) = all_52_30) | (all_52_12 = all_52_19 & all_52_13 = % 54.56/13.72 | all_52_23 & all_52_14 = all_52_27 & all_52_15 = all_52_31 & op(e0, % 54.56/13.72 | all_52_19) = all_52_19 & op(e0, all_52_23) = all_52_23 & op(e0, % 54.56/13.72 | all_52_27) = all_52_27 & op(e0, all_52_31) = all_52_31) % 54.56/13.72 | % 54.56/13.72 | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2, % 54.56/13.72 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9, % 54.56/13.72 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives: % 54.56/13.72 | (131) ~ (all_54_0 = all_54_1) & ~ (all_54_0 = all_54_2) & ~ (all_54_0 = % 54.56/13.72 | all_54_3) & ~ (all_54_0 = all_54_4) & ~ (all_54_0 = all_54_8) & % 54.56/13.72 | ~ (all_54_0 = all_54_12) & ~ (all_54_1 = all_54_2) & ~ (all_54_1 = % 54.56/13.72 | all_54_3) & ~ (all_54_1 = all_54_5) & ~ (all_54_1 = all_54_9) & % 54.56/13.72 | ~ (all_54_1 = all_54_13) & ~ (all_54_2 = all_54_3) & ~ (all_54_2 = % 54.56/13.72 | all_54_6) & ~ (all_54_2 = all_54_10) & ~ (all_54_2 = all_54_14) & % 54.56/13.72 | ~ (all_54_3 = all_54_7) & ~ (all_54_3 = all_54_11) & ~ (all_54_3 = % 54.56/13.72 | all_54_15) & ~ (all_54_4 = all_54_5) & ~ (all_54_4 = all_54_6) & % 54.56/13.72 | ~ (all_54_4 = all_54_7) & ~ (all_54_4 = all_54_8) & ~ (all_54_4 = % 54.56/13.72 | all_54_12) & ~ (all_54_5 = all_54_6) & ~ (all_54_5 = all_54_7) & % 54.56/13.72 | ~ (all_54_5 = all_54_9) & ~ (all_54_5 = all_54_13) & ~ (all_54_6 = % 54.56/13.72 | all_54_7) & ~ (all_54_6 = all_54_10) & ~ (all_54_6 = all_54_14) & % 54.56/13.72 | ~ (all_54_7 = all_54_11) & ~ (all_54_7 = all_54_15) & ~ (all_54_8 % 54.56/13.72 | = all_54_9) & ~ (all_54_8 = all_54_10) & ~ (all_54_8 = all_54_11) % 54.56/13.72 | & ~ (all_54_8 = all_54_12) & ~ (all_54_9 = all_54_10) & ~ % 54.56/13.72 | (all_54_9 = all_54_11) & ~ (all_54_9 = all_54_13) & ~ (all_54_10 = % 54.56/13.72 | all_54_11) & ~ (all_54_10 = all_54_14) & ~ (all_54_11 = % 54.56/13.72 | all_54_15) & ~ (all_54_12 = all_54_13) & ~ (all_54_12 = % 54.56/13.72 | all_54_14) & ~ (all_54_12 = all_54_15) & ~ (all_54_13 = % 54.56/13.72 | all_54_14) & ~ (all_54_13 = all_54_15) & ~ (all_54_14 = % 54.56/13.72 | all_54_15) & op(e3, e3) = all_54_0 & op(e3, e2) = all_54_4 & op(e3, % 54.56/13.72 | e1) = all_54_8 & op(e3, e0) = all_54_12 & op(e2, e3) = all_54_1 & % 54.56/13.72 | op(e2, e2) = all_54_5 & op(e2, e1) = all_54_9 & op(e2, e0) = % 54.56/13.72 | all_54_13 & op(e1, e3) = all_54_2 & op(e1, e2) = all_54_6 & op(e1, % 54.56/13.72 | e1) = all_54_10 & op(e1, e0) = all_54_14 & op(e0, e3) = all_54_3 & % 54.56/13.72 | op(e0, e2) = all_54_7 & op(e0, e1) = all_54_11 & op(e0, e0) = % 54.56/13.72 | all_54_15 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3) % 54.56/13.72 | & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & % 54.56/13.72 | $i(all_54_8) & $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & % 54.56/13.72 | $i(all_54_12) & $i(all_54_13) & $i(all_54_14) & $i(all_54_15) % 54.56/13.72 | % 54.56/13.72 | ALPHA: (131) implies: % 54.56/13.72 | (132) ~ (all_54_14 = all_54_15) % 54.56/13.72 | (133) ~ (all_54_13 = all_54_15) % 54.56/13.72 | (134) ~ (all_54_13 = all_54_14) % 54.56/13.72 | (135) ~ (all_54_12 = all_54_14) % 54.56/13.72 | (136) ~ (all_54_11 = all_54_15) % 54.56/13.72 | (137) ~ (all_54_10 = all_54_14) % 54.56/13.72 | (138) ~ (all_54_9 = all_54_13) % 54.56/13.72 | (139) ~ (all_54_9 = all_54_10) % 54.56/13.72 | (140) ~ (all_54_8 = all_54_12) % 54.56/13.72 | (141) ~ (all_54_8 = all_54_10) % 54.56/13.72 | (142) ~ (all_54_8 = all_54_9) % 54.56/13.72 | (143) ~ (all_54_7 = all_54_15) % 54.56/13.72 | (144) ~ (all_54_7 = all_54_11) % 54.56/13.72 | (145) ~ (all_54_6 = all_54_14) % 54.56/13.72 | (146) ~ (all_54_6 = all_54_10) % 54.56/13.72 | (147) ~ (all_54_6 = all_54_7) % 54.56/13.72 | (148) ~ (all_54_5 = all_54_13) % 54.56/13.72 | (149) ~ (all_54_5 = all_54_9) % 54.56/13.72 | (150) ~ (all_54_5 = all_54_7) % 54.56/13.72 | (151) ~ (all_54_4 = all_54_12) % 54.56/13.72 | (152) ~ (all_54_4 = all_54_8) % 54.56/13.72 | (153) ~ (all_54_4 = all_54_7) % 54.56/13.72 | (154) ~ (all_54_4 = all_54_6) % 54.56/13.72 | (155) ~ (all_54_4 = all_54_5) % 54.56/13.72 | (156) ~ (all_54_3 = all_54_15) % 54.56/13.72 | (157) ~ (all_54_3 = all_54_7) % 54.56/13.72 | (158) ~ (all_54_2 = all_54_14) % 54.56/13.72 | (159) ~ (all_54_2 = all_54_10) % 54.56/13.72 | (160) ~ (all_54_2 = all_54_6) % 54.56/13.72 | (161) ~ (all_54_2 = all_54_3) % 54.56/13.72 | (162) ~ (all_54_1 = all_54_13) % 54.56/13.72 | (163) ~ (all_54_1 = all_54_9) % 54.56/13.73 | (164) ~ (all_54_1 = all_54_3) % 54.56/13.73 | (165) ~ (all_54_1 = all_54_2) % 54.56/13.73 | (166) ~ (all_54_0 = all_54_8) % 54.56/13.73 | (167) ~ (all_54_0 = all_54_4) % 54.56/13.73 | (168) ~ (all_54_0 = all_54_3) % 54.56/13.73 | (169) ~ (all_54_0 = all_54_2) % 54.56/13.73 | (170) ~ (all_54_0 = all_54_1) % 54.56/13.73 | (171) op(e0, e0) = all_54_15 % 54.56/13.73 | (172) op(e0, e1) = all_54_11 % 54.56/13.73 | (173) op(e0, e2) = all_54_7 % 54.56/13.73 | (174) op(e0, e3) = all_54_3 % 54.56/13.73 | (175) op(e1, e0) = all_54_14 % 54.56/13.73 | (176) op(e1, e1) = all_54_10 % 54.56/13.74 | (177) op(e1, e2) = all_54_6 % 54.56/13.74 | (178) op(e1, e3) = all_54_2 % 54.56/13.74 | (179) op(e2, e0) = all_54_13 % 54.56/13.74 | (180) op(e2, e1) = all_54_9 % 54.56/13.74 | (181) op(e2, e2) = all_54_5 % 54.56/13.74 | (182) op(e2, e3) = all_54_1 % 54.56/13.74 | (183) op(e3, e0) = all_54_12 % 54.56/13.74 | (184) op(e3, e1) = all_54_8 % 54.56/13.74 | (185) op(e3, e2) = all_54_4 % 54.56/13.74 | (186) op(e3, e3) = all_54_0 % 54.56/13.74 | % 54.56/13.74 | DELTA: instantiating (1) with fresh symbols all_56_0, all_56_1, all_56_2, % 54.56/13.74 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9, % 54.56/13.74 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives: % 54.56/13.75 | (187) op(e3, e3) = all_56_0 & op(e3, e2) = all_56_1 & op(e3, e1) = all_56_2 % 54.56/13.75 | & op(e3, e0) = all_56_3 & op(e2, e3) = all_56_4 & op(e2, e2) = % 54.56/13.75 | all_56_5 & op(e2, e1) = all_56_6 & op(e2, e0) = all_56_7 & op(e1, e3) % 54.56/13.75 | = all_56_8 & op(e1, e2) = all_56_9 & op(e1, e1) = all_56_10 & op(e1, % 54.56/13.75 | e0) = all_56_11 & op(e0, e3) = all_56_12 & op(e0, e2) = all_56_13 & % 54.56/13.75 | op(e0, e1) = all_56_14 & op(e0, e0) = all_56_15 & $i(all_56_0) & % 54.56/13.75 | $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & % 54.56/13.75 | $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & $i(all_56_8) & % 54.56/13.75 | $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & $i(all_56_12) & % 54.56/13.75 | $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & (all_56_0 = e3 | % 54.56/13.75 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0) & (all_56_1 = e3 | % 54.56/13.75 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0) & (all_56_2 = e3 | % 54.56/13.75 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0) & (all_56_3 = e3 | % 54.56/13.75 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0) & (all_56_4 = e3 | % 54.56/13.75 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0) & (all_56_5 = e3 | % 54.56/13.75 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0) & (all_56_6 = e3 | % 54.56/13.75 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0) & (all_56_7 = e3 | % 54.56/13.75 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0) & (all_56_8 = e3 | % 54.56/13.75 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0) & (all_56_9 = e3 | % 54.56/13.75 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0) & (all_56_10 = e3 | % 54.56/13.75 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0) & (all_56_11 = e3 % 54.56/13.75 | | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0) & (all_56_12 = % 54.56/13.75 | e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0) & (all_56_13 % 54.56/13.75 | = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0) & % 54.56/13.75 | (all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0) & % 54.56/13.75 | (all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0) % 54.56/13.75 | % 54.56/13.75 | ALPHA: (187) implies: % 54.56/13.75 | (188) op(e0, e0) = all_56_15 % 54.56/13.75 | (189) op(e0, e1) = all_56_14 % 54.56/13.75 | (190) op(e0, e2) = all_56_13 % 54.56/13.75 | (191) op(e0, e3) = all_56_12 % 54.56/13.75 | (192) op(e1, e0) = all_56_11 % 54.56/13.75 | (193) op(e1, e1) = all_56_10 % 54.56/13.75 | (194) op(e1, e2) = all_56_9 % 54.56/13.75 | (195) op(e1, e3) = all_56_8 % 54.56/13.75 | (196) op(e2, e0) = all_56_7 % 54.56/13.75 | (197) op(e2, e1) = all_56_6 % 54.56/13.76 | (198) op(e2, e2) = all_56_5 % 54.56/13.76 | (199) op(e2, e3) = all_56_4 % 54.56/13.76 | (200) op(e3, e0) = all_56_3 % 54.56/13.76 | (201) op(e3, e1) = all_56_2 % 54.56/13.76 | (202) op(e3, e2) = all_56_1 % 54.56/13.76 | (203) op(e3, e3) = all_56_0 % 54.56/13.76 | (204) all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0 % 54.56/13.76 | (205) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 54.56/13.76 | (206) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 54.56/13.76 | (207) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 54.56/13.76 | (208) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0 % 54.56/13.76 | (209) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0 % 54.56/13.76 | (210) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0 % 54.56/13.76 | (211) all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0 % 54.56/13.76 | (212) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0 % 54.56/13.76 | (213) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 54.56/13.76 | (214) all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0 % 54.56/13.76 | % 54.56/13.76 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2, % 54.56/13.76 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9, % 54.56/13.76 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives: % 54.56/13.77 | (215) ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = % 54.56/13.77 | e3) | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, % 54.56/13.77 | e0) = e3)) & ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = % 54.56/13.77 | e3 & op(e2, e3) = e3) | (all_58_6 = e3 & op(e1, e3) = e3) | % 54.56/13.77 | (all_58_12 = e3 & op(e0, e3) = e3)) & ((all_58_0 = e2 & op(e3, e3) % 54.56/13.77 | = e2) | (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_4 = e2 & % 54.56/13.77 | op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)) & % 54.56/13.77 | ((all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = % 54.56/13.77 | e2) | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & % 54.56/13.77 | op(e0, e3) = e2)) & ((all_58_0 = e1 & op(e3, e3) = e1) | % 54.56/13.77 | (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_4 = e1 & op(e3, e1) = % 54.56/13.77 | e1) | (all_58_9 = e1 & op(e3, e0) = e1)) & ((all_58_0 = e1 & % 54.56/13.77 | op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_6 % 54.56/13.77 | = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)) & % 54.56/13.77 | ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = % 54.56/13.77 | e0) | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, % 54.56/13.77 | e0) = e0)) & ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = % 54.56/13.77 | e0 & op(e2, e3) = e0) | (all_58_6 = e0 & op(e1, e3) = e0) | % 54.56/13.77 | (all_58_12 = e0 & op(e0, e3) = e0)) & ((all_58_1 = e3 & op(e3, e2) % 54.56/13.77 | = e3) | (all_58_3 = e3 & op(e2, e2) = e3) | (all_58_7 = e3 & % 54.56/13.77 | op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)) & % 54.56/13.77 | ((all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = % 54.56/13.77 | e2) | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & % 54.56/13.77 | op(e0, e2) = e2)) & ((all_58_1 = e1 & op(e3, e2) = e1) | % 54.56/13.77 | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_7 = e1 & op(e1, e2) = % 54.56/13.77 | e1) | (all_58_13 = e1 & op(e0, e2) = e1)) & ((all_58_1 = e0 & % 54.56/13.77 | op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) | (all_58_7 % 54.56/13.77 | = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)) & % 54.56/13.77 | ((all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = % 54.56/13.77 | e3) | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & % 54.56/13.77 | op(e2, e0) = e3)) & ((all_58_2 = e2 & op(e2, e3) = e2) | % 54.56/13.77 | (all_58_3 = e2 & op(e2, e2) = e2) | (all_58_5 = e2 & op(e2, e1) = % 54.56/13.77 | e2) | (all_58_10 = e2 & op(e2, e0) = e2)) & ((all_58_2 = e1 & % 54.56/13.77 | op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_5 % 54.56/13.77 | = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)) & % 54.56/13.77 | ((all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = % 54.56/13.77 | e0) | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & % 54.56/13.77 | op(e2, e0) = e0)) & ((all_58_4 = e3 & op(e3, e1) = e3) | % 54.56/13.77 | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_8 = e3 & op(e1, e1) = % 54.56/13.77 | e3) | (all_58_14 = e3 & op(e0, e1) = e3)) & ((all_58_4 = e2 & % 54.56/13.77 | op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_8 % 54.56/13.77 | = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)) & % 54.56/13.77 | ((all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = % 54.56/13.77 | e1) | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & % 54.56/13.77 | op(e0, e1) = e1)) & ((all_58_4 = e0 & op(e3, e1) = e0) | % 54.56/13.77 | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_8 = e0 & op(e1, e1) = % 54.56/13.77 | e0) | (all_58_14 = e0 & op(e0, e1) = e0)) & ((all_58_6 = e3 & % 54.56/13.77 | op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_8 % 54.56/13.77 | = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)) & % 54.56/13.77 | ((all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = % 54.56/13.77 | e2) | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & % 54.56/13.77 | op(e1, e0) = e2)) & ((all_58_6 = e1 & op(e1, e3) = e1) | % 54.56/13.77 | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_8 = e1 & op(e1, e1) = % 54.56/13.77 | e1) | (all_58_11 = e1 & op(e1, e0) = e1)) & ((all_58_6 = e0 & % 54.56/13.77 | op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_8 % 54.56/13.77 | = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & % 54.56/13.77 | ((all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = % 54.56/13.77 | e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & % 54.56/13.78 | op(e0, e0) = e3)) & ((all_58_9 = e2 & op(e3, e0) = e2) | % 54.56/13.78 | (all_58_10 = e2 & op(e2, e0) = e2) | (all_58_11 = e2 & op(e1, e0) = % 54.56/13.78 | e2) | (all_58_15 = e2 & op(e0, e0) = e2)) & ((all_58_9 = e1 & % 54.56/13.78 | op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) | % 54.56/13.78 | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = % 54.56/13.78 | e1)) & ((all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & % 54.56/13.78 | op(e0, e2) = e3) | (all_58_14 = e3 & op(e0, e1) = e3) | % 54.56/13.78 | (all_58_15 = e3 & op(e0, e0) = e3)) & ((all_58_12 = e2 & op(e0, e3) % 54.56/13.78 | = e2) | (all_58_13 = e2 & op(e0, e2) = e2) | (all_58_14 = e2 & % 54.76/13.78 | op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)) & % 54.76/13.78 | ((all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = % 54.76/13.78 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & % 54.76/13.78 | op(e0, e0) = e1)) & ((all_58_15 = e0 & op(e0, e0) = e0) | % 54.76/13.78 | (((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) % 54.76/13.78 | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = % 54.76/13.78 | e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) | % 54.76/13.78 | (all_58_14 = e0 & op(e0, e1) = e0)))) % 54.76/13.78 | % 54.76/13.78 | ALPHA: (215) implies: % 54.76/13.78 | (216) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = % 54.76/13.78 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, % 54.76/13.78 | e0) = e1) % 54.76/13.78 | (217) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = % 54.76/13.78 | e2) | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, % 54.76/13.78 | e0) = e2) % 54.76/13.78 | (218) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = % 54.76/13.78 | e3) | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, % 54.76/13.78 | e0) = e3) % 54.76/13.78 | (219) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = % 54.76/13.78 | e2) | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, % 54.76/13.78 | e0) = e2) % 54.76/13.78 | (220) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) % 54.76/13.78 | | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = % 54.76/13.78 | e1) % 54.76/13.78 | (221) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) % 54.76/13.78 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = % 54.76/13.78 | e2) % 54.76/13.78 | (222) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) % 54.76/13.78 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = % 54.76/13.78 | e3) % 54.76/13.78 | (223) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) % 54.76/13.78 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = % 54.76/13.78 | e2) % 54.76/13.78 | (224) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) % 54.76/13.78 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = % 54.76/13.78 | e3) % 54.76/13.79 | (225) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) % 54.76/13.79 | | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = % 54.76/13.79 | e0) % 54.76/13.79 | (226) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) % 54.76/13.79 | | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = % 54.76/13.79 | e3) % 54.76/13.79 | (227) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) % 54.76/13.79 | | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = % 54.76/13.79 | e0) % 54.76/13.79 | (228) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) % 54.76/13.79 | | (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = % 54.76/13.79 | e0) % 54.76/13.79 | (229) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) % 54.76/13.79 | | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = % 54.76/13.79 | e0) % 54.76/13.79 | (230) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) % 54.76/13.79 | | (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = % 54.76/13.79 | e1) % 54.76/13.79 | (231) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) % 54.76/13.79 | | (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = % 54.76/13.79 | e1) % 54.76/13.79 | (232) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) % 54.76/13.79 | | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = % 54.76/13.79 | e2) % 54.76/13.80 | (233) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) % 54.76/13.80 | | (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = % 54.76/13.80 | e2) % 54.76/13.80 | (234) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) % 54.76/13.80 | | (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = % 54.76/13.80 | e3) % 54.76/13.80 | % 54.76/13.80 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0, % 54.76/13.80 | e0, simplifying with (171), (188) gives: % 54.76/13.80 | (235) all_56_15 = all_54_15 % 54.76/13.80 | % 54.76/13.80 | GROUND_INST: instantiating (function-axioms) with all_52_31, all_56_15, e0, % 54.76/13.80 | e0, simplifying with (101), (188) gives: % 54.76/13.80 | (236) all_56_15 = all_52_31 % 54.76/13.80 | % 54.76/13.80 | GROUND_INST: instantiating (function-axioms) with all_52_30, all_54_11, e1, % 54.76/13.80 | e0, simplifying with (102), (172) gives: % 54.76/13.80 | (237) all_54_11 = all_52_30 % 54.76/13.80 | % 54.76/13.80 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_54_11, e1, e0, % 54.76/13.80 | simplifying with (54), (172) gives: % 54.76/13.80 | (238) all_54_11 = all_16_1 % 54.76/13.80 | % 54.76/13.80 | GROUND_INST: instantiating (function-axioms) with all_52_30, all_56_14, e1, % 54.76/13.80 | e0, simplifying with (102), (189) gives: % 54.76/13.80 | (239) all_56_14 = all_52_30 % 54.76/13.80 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_36_1, all_56_14, e1, e0, % 54.76/13.82 | simplifying with (81), (189) gives: % 54.76/13.82 | (240) all_56_14 = all_36_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_29, all_54_7, e2, e0, % 54.76/13.82 | simplifying with (103), (173) gives: % 54.76/13.82 | (241) all_54_7 = all_52_29 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_54_7, e2, e0, % 54.76/13.82 | simplifying with (83), (173) gives: % 54.76/13.82 | (242) all_54_7 = all_38_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_29, all_56_13, e2, % 54.76/13.82 | e0, simplifying with (103), (190) gives: % 54.76/13.82 | (243) all_56_13 = all_52_29 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_56_13, e2, e0, % 54.76/13.82 | simplifying with (71), (190) gives: % 54.76/13.82 | (244) all_56_13 = all_28_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_52_28, e3, e0, % 54.76/13.82 | simplifying with (42), (104) gives: % 54.76/13.82 | (245) all_52_28 = all_8_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_56_12, e3, e0, % 54.76/13.82 | simplifying with (174), (191) gives: % 54.76/13.82 | (246) all_56_12 = all_54_3 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_28, all_56_12, e3, % 54.76/13.82 | e0, simplifying with (104), (191) gives: % 54.76/13.82 | (247) all_56_12 = all_52_28 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_56_12, e3, e0, % 54.76/13.82 | simplifying with (39), (191) gives: % 54.76/13.82 | (248) all_56_12 = all_6_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_27, all_54_14, e0, % 54.76/13.82 | e1, simplifying with (105), (175) gives: % 54.76/13.82 | (249) all_54_14 = all_52_27 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_18_1, all_54_14, e0, e1, % 54.76/13.82 | simplifying with (56), (175) gives: % 54.76/13.82 | (250) all_54_14 = all_18_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_56_11, e0, % 54.76/13.82 | e1, simplifying with (175), (192) gives: % 54.76/13.82 | (251) all_56_11 = all_54_14 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_56_11, e0, e1, % 54.76/13.82 | simplifying with (51), (192) gives: % 54.76/13.82 | (252) all_56_11 = all_14_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_10, e1, % 54.76/13.82 | e1, simplifying with (176), (193) gives: % 54.76/13.82 | (253) all_56_10 = all_54_10 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_26, all_56_10, e1, % 54.76/13.82 | e1, simplifying with (106), (193) gives: % 54.76/13.82 | (254) all_56_10 = all_52_26 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_25, all_54_6, e2, e1, % 54.76/13.82 | simplifying with (107), (177) gives: % 54.76/13.82 | (255) all_54_6 = all_52_25 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_54_6, e2, e1, % 54.76/13.82 | simplifying with (59), (177) gives: % 54.76/13.82 | (256) all_54_6 = all_20_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_52_25, all_56_9, e2, e1, % 54.76/13.82 | simplifying with (107), (194) gives: % 54.76/13.82 | (257) all_56_9 = all_52_25 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_56_9, e2, e1, % 54.76/13.82 | simplifying with (77), (194) gives: % 54.76/13.82 | (258) all_56_9 = all_32_1 % 54.76/13.82 | % 54.76/13.82 | GROUND_INST: instantiating (function-axioms) with all_44_1, all_52_24, e3, e1, % 54.76/13.84 | simplifying with (90), (108) gives: % 54.76/13.84 | (259) all_52_24 = all_44_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_8, e3, e1, % 54.76/13.84 | simplifying with (178), (195) gives: % 54.76/13.84 | (260) all_56_8 = all_54_2 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_24, all_56_8, e3, e1, % 54.76/13.84 | simplifying with (108), (195) gives: % 54.76/13.84 | (261) all_56_8 = all_52_24 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_56_8, e3, e1, % 54.76/13.84 | simplifying with (62), (195) gives: % 54.76/13.84 | (262) all_56_8 = all_22_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_23, all_54_13, e0, % 54.76/13.84 | e2, simplifying with (109), (179) gives: % 54.76/13.84 | (263) all_54_13 = all_52_23 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_54_13, e0, e2, % 54.76/13.84 | simplifying with (65), (179) gives: % 54.76/13.84 | (264) all_54_13 = all_24_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_56_7, e0, e2, % 54.76/13.84 | simplifying with (179), (196) gives: % 54.76/13.84 | (265) all_56_7 = all_54_13 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_48_1, all_56_7, e0, e2, % 54.76/13.84 | simplifying with (96), (196) gives: % 54.76/13.84 | (266) all_56_7 = all_48_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_54_9, e1, e2, % 54.76/13.84 | simplifying with (74), (180) gives: % 54.76/13.84 | (267) all_54_9 = all_30_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_54_9, e1, e2, % 54.76/13.84 | simplifying with (45), (180) gives: % 54.76/13.84 | (268) all_54_9 = all_10_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_6, e1, e2, % 54.76/13.84 | simplifying with (180), (197) gives: % 54.76/13.84 | (269) all_56_6 = all_54_9 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_22, all_56_6, e1, e2, % 54.76/13.84 | simplifying with (110), (197) gives: % 54.76/13.84 | (270) all_56_6 = all_52_22 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_56_5, e2, e2, % 54.76/13.84 | simplifying with (181), (198) gives: % 54.76/13.84 | (271) all_56_5 = all_54_5 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_21, all_56_5, e2, e2, % 54.76/13.84 | simplifying with (111), (198) gives: % 54.76/13.84 | (272) all_56_5 = all_52_21 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_52_20, e3, e2, % 54.76/13.84 | simplifying with (48), (112) gives: % 54.76/13.84 | (273) all_52_20 = all_12_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_20, all_54_1, e3, e2, % 54.76/13.84 | simplifying with (112), (182) gives: % 54.76/13.84 | (274) all_54_1 = all_52_20 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_4, e3, e2, % 54.76/13.84 | simplifying with (182), (199) gives: % 54.76/13.84 | (275) all_56_4 = all_54_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_46_1, all_56_4, e3, e2, % 54.76/13.84 | simplifying with (93), (199) gives: % 54.76/13.84 | (276) all_56_4 = all_46_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_19, all_54_12, e0, % 54.76/13.84 | e3, simplifying with (113), (183) gives: % 54.76/13.84 | (277) all_54_12 = all_52_19 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_34_1, all_54_12, e0, e3, % 54.76/13.84 | simplifying with (79), (183) gives: % 54.76/13.84 | (278) all_54_12 = all_34_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_19, all_56_3, e0, e3, % 54.76/13.84 | simplifying with (113), (200) gives: % 54.76/13.84 | (279) all_56_3 = all_52_19 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_50_1, all_56_3, e0, e3, % 54.76/13.84 | simplifying with (99), (200) gives: % 54.76/13.84 | (280) all_56_3 = all_50_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_52_18, all_54_8, e1, e3, % 54.76/13.84 | simplifying with (114), (184) gives: % 54.76/13.84 | (281) all_54_8 = all_52_18 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_40_1, all_54_8, e1, e3, % 54.76/13.84 | simplifying with (86), (184) gives: % 54.76/13.84 | (282) all_54_8 = all_40_1 % 54.76/13.84 | % 54.76/13.84 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_56_2, e1, e3, % 54.76/13.84 | simplifying with (184), (201) gives: % 54.76/13.85 | (283) all_56_2 = all_54_8 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_56_2, e1, e3, % 54.76/13.85 | simplifying with (68), (201) gives: % 54.76/13.85 | (284) all_56_2 = all_26_1 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_52_17, e2, e3, % 54.76/13.85 | simplifying with (36), (115) gives: % 54.76/13.85 | (285) all_52_17 = all_4_1 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_17, all_54_4, e2, e3, % 54.76/13.85 | simplifying with (115), (185) gives: % 54.76/13.85 | (286) all_54_4 = all_52_17 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_56_1, e2, e3, % 54.76/13.85 | simplifying with (185), (202) gives: % 54.76/13.85 | (287) all_56_1 = all_54_4 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_56_1, e2, e3, % 54.76/13.85 | simplifying with (88), (202) gives: % 54.76/13.85 | (288) all_56_1 = all_42_1 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_0, e3, e3, % 54.76/13.85 | simplifying with (186), (203) gives: % 54.76/13.85 | (289) all_56_0 = all_54_0 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_16, all_56_0, e3, e3, % 54.76/13.85 | simplifying with (116), (203) gives: % 54.76/13.85 | (290) all_56_0 = all_52_16 % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_34_1, e0, e0, e3, % 54.76/13.85 | simplifying with (79) gives: % 54.76/13.85 | (291) all_34_1 = e0 | ~ (op(e3, e0) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_24_1, e0, e0, e2, % 54.76/13.85 | simplifying with (65) gives: % 54.76/13.85 | (292) all_24_1 = e0 | ~ (op(e2, e0) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_14, e0, e0, e1, % 54.76/13.85 | simplifying with (175) gives: % 54.76/13.85 | (293) all_54_14 = e0 | ~ (op(e1, e0) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_56_3, e1, e0, e3, % 54.76/13.85 | simplifying with (200) gives: % 54.76/13.85 | (294) all_56_3 = e1 | ~ (op(e3, e0) = e1) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_12, e1, e0, e3, % 54.76/13.85 | simplifying with (183) gives: % 54.76/13.85 | (295) all_54_12 = e1 | ~ (op(e3, e0) = e1) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_23, e1, e0, e2, % 54.76/13.85 | simplifying with (109) gives: % 54.76/13.85 | (296) all_52_23 = e1 | ~ (op(e2, e0) = e1) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_31, e1, e0, e0, % 54.76/13.85 | simplifying with (101) gives: % 54.76/13.85 | (297) all_52_31 = e1 | ~ (op(e0, e0) = e1) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_12, e2, e0, e3, % 54.76/13.85 | simplifying with (183) gives: % 54.76/13.85 | (298) all_54_12 = e2 | ~ (op(e3, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_50_1, e2, e0, e3, % 54.76/13.85 | simplifying with (99) gives: % 54.76/13.85 | (299) all_50_1 = e2 | ~ (op(e3, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_34_1, e2, e0, e3, % 54.76/13.85 | simplifying with (79) gives: % 54.76/13.85 | (300) all_34_1 = e2 | ~ (op(e3, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_56_7, e2, e0, e2, % 54.76/13.85 | simplifying with (196) gives: % 54.76/13.85 | (301) all_56_7 = e2 | ~ (op(e2, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_14_1, e2, e0, e1, % 54.76/13.85 | simplifying with (51) gives: % 54.76/13.85 | (302) all_14_1 = e2 | ~ (op(e1, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_31, e2, e0, e0, % 54.76/13.85 | simplifying with (101) gives: % 54.76/13.85 | (303) all_52_31 = e2 | ~ (op(e0, e0) = e2) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_48_1, e3, e0, e2, % 54.76/13.85 | simplifying with (96) gives: % 54.76/13.85 | (304) all_48_1 = e3 | ~ (op(e2, e0) = e3) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_14_1, e3, e0, e1, % 54.76/13.85 | simplifying with (51) gives: % 54.76/13.85 | (305) all_14_1 = e3 | ~ (op(e1, e0) = e3) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_15, e3, e0, e0, % 54.76/13.85 | simplifying with (171) gives: % 54.76/13.85 | (306) all_54_15 = e3 | ~ (op(e0, e0) = e3) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_52_18, e0, e1, e3, % 54.76/13.85 | simplifying with (114) gives: % 54.76/13.85 | (307) all_52_18 = e0 | ~ (op(e3, e1) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_30_1, e0, e1, e2, % 54.76/13.85 | simplifying with (74) gives: % 54.76/13.85 | (308) all_30_1 = e0 | ~ (op(e2, e1) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_56_14, e0, e1, e0, % 54.76/13.85 | simplifying with (189) gives: % 54.76/13.85 | (309) all_56_14 = e0 | ~ (op(e0, e1) = e0) % 54.76/13.85 | % 54.76/13.85 | GROUND_INST: instantiating (function-axioms) with all_54_11, e0, e1, e0, % 54.76/13.85 | simplifying with (172) gives: % 54.76/13.85 | (310) all_54_11 = e0 | ~ (op(e0, e1) = e0) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with e0, e1, e1, all_52_27, % 54.76/13.86 | simplifying with (121) gives: % 54.76/13.86 | (311) e1 = e0 | ~ (op(all_52_27, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_40_1, e1, e1, e3, % 54.76/13.86 | simplifying with (86) gives: % 54.76/13.86 | (312) all_40_1 = e1 | ~ (op(e3, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_26_1, e1, e1, e3, % 54.76/13.86 | simplifying with (68) gives: % 54.76/13.86 | (313) all_26_1 = e1 | ~ (op(e3, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_54_9, e1, e1, e2, % 54.76/13.86 | simplifying with (180) gives: % 54.76/13.86 | (314) all_54_9 = e1 | ~ (op(e2, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_10_1, e1, e1, e2, % 54.76/13.86 | simplifying with (45) gives: % 54.76/13.86 | (315) all_10_1 = e1 | ~ (op(e2, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_36_1, e1, e1, e0, % 54.76/13.86 | simplifying with (81) gives: % 54.76/13.86 | (316) all_36_1 = e1 | ~ (op(e0, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_16_1, e1, e1, e0, % 54.76/13.86 | simplifying with (54) gives: % 54.76/13.86 | (317) all_16_1 = e1 | ~ (op(e0, e1) = e1) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_56_2, e2, e1, e3, % 54.76/13.86 | simplifying with (201) gives: % 54.76/13.86 | (318) all_56_2 = e2 | ~ (op(e3, e1) = e2) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_26_1, e2, e1, e3, % 54.76/13.86 | simplifying with (68) gives: % 54.76/13.86 | (319) all_26_1 = e2 | ~ (op(e3, e1) = e2) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_52_22, e2, e1, e2, % 54.76/13.86 | simplifying with (110) gives: % 54.76/13.86 | (320) all_52_22 = e2 | ~ (op(e2, e1) = e2) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_30_1, e2, e1, e2, % 54.76/13.86 | simplifying with (74) gives: % 54.76/13.86 | (321) all_30_1 = e2 | ~ (op(e2, e1) = e2) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_52_26, e2, e1, e1, % 54.76/13.86 | simplifying with (106) gives: % 54.76/13.86 | (322) all_52_26 = e2 | ~ (op(e1, e1) = e2) % 54.76/13.86 | % 54.76/13.86 | GROUND_INST: instantiating (function-axioms) with all_36_1, e2, e1, e0, % 54.76/13.86 | simplifying with (81) gives: % 54.76/13.87 | (323) all_36_1 = e2 | ~ (op(e0, e1) = e2) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with e2, e3, e1, all_52_25, % 54.76/13.87 | simplifying with (122) gives: % 54.76/13.87 | (324) e3 = e2 | ~ (op(all_52_25, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_52_22, e3, e1, e2, % 54.76/13.87 | simplifying with (110) gives: % 54.76/13.87 | (325) all_52_22 = e3 | ~ (op(e2, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_54_10, e3, e1, e1, % 54.76/13.87 | simplifying with (176) gives: % 54.76/13.87 | (326) all_54_10 = e3 | ~ (op(e1, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_52_26, e3, e1, e1, % 54.76/13.87 | simplifying with (106) gives: % 54.76/13.87 | (327) all_52_26 = e3 | ~ (op(e1, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_52_30, e3, e1, e0, % 54.76/13.87 | simplifying with (102) gives: % 54.76/13.87 | (328) all_52_30 = e3 | ~ (op(e0, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_16_1, e3, e1, e0, % 54.76/13.87 | simplifying with (54) gives: % 54.76/13.87 | (329) all_16_1 = e3 | ~ (op(e0, e1) = e3) % 54.76/13.87 | % 54.76/13.87 | GROUND_INST: instantiating (function-axioms) with all_42_1, e0, e2, e3, % 54.76/13.87 | simplifying with (88) gives: % 55.06/13.87 | (330) all_42_1 = e0 | ~ (op(e3, e2) = e0) % 55.06/13.87 | % 55.06/13.87 | GROUND_INST: instantiating (function-axioms) with all_56_5, e0, e2, e2, % 55.06/13.87 | simplifying with (198) gives: % 55.06/13.87 | (331) all_56_5 = e0 | ~ (op(e2, e2) = e0) % 55.06/13.87 | % 55.06/13.87 | GROUND_INST: instantiating (function-axioms) with all_52_21, e0, e2, e2, % 55.06/13.87 | simplifying with (111) gives: % 55.06/13.87 | (332) all_52_21 = e0 | ~ (op(e2, e2) = e0) % 55.06/13.87 | % 55.06/13.87 | GROUND_INST: instantiating (function-axioms) with all_20_1, e0, e2, e1, % 55.06/13.87 | simplifying with (59) gives: % 55.06/13.87 | (333) all_20_1 = e0 | ~ (op(e1, e2) = e0) % 55.06/13.87 | % 55.06/13.87 | GROUND_INST: instantiating (function-axioms) with all_28_1, e0, e2, e0, % 55.06/13.87 | simplifying with (71) gives: % 55.06/13.87 | (334) all_28_1 = e0 | ~ (op(e0, e2) = e0) % 55.06/13.87 | % 55.06/13.87 | GROUND_INST: instantiating (function-axioms) with all_52_17, e1, e2, e3, % 55.06/13.87 | simplifying with (115) gives: % 55.06/13.87 | (335) all_52_17 = e1 | ~ (op(e3, e2) = e1) % 55.06/13.87 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, e2, e3, % 55.06/13.88 | simplifying with (36) gives: % 55.06/13.88 | (336) all_4_1 = e1 | ~ (op(e3, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_5, e1, e2, e2, % 55.06/13.88 | simplifying with (198) gives: % 55.06/13.88 | (337) all_56_5 = e1 | ~ (op(e2, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_25, e1, e2, e1, % 55.06/13.88 | simplifying with (107) gives: % 55.06/13.88 | (338) all_52_25 = e1 | ~ (op(e1, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_20_1, e1, e2, e1, % 55.06/13.88 | simplifying with (59) gives: % 55.06/13.88 | (339) all_20_1 = e1 | ~ (op(e1, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_13, e1, e2, e0, % 55.06/13.88 | simplifying with (190) gives: % 55.06/13.88 | (340) all_56_13 = e1 | ~ (op(e0, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_7, e1, e2, e0, % 55.06/13.88 | simplifying with (173) gives: % 55.06/13.88 | (341) all_54_7 = e1 | ~ (op(e0, e2) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with e1, e2, e2, all_52_22, % 55.06/13.88 | simplifying with (125) gives: % 55.06/13.88 | (342) e2 = e1 | ~ (op(all_52_22, e2) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_17, e2, e2, e3, % 55.06/13.88 | simplifying with (115) gives: % 55.06/13.88 | (343) all_52_17 = e2 | ~ (op(e3, e2) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_32_1, e2, e2, e1, % 55.06/13.88 | simplifying with (77) gives: % 55.06/13.88 | (344) all_32_1 = e2 | ~ (op(e1, e2) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_21, e3, e2, e2, % 55.06/13.88 | simplifying with (111) gives: % 55.06/13.88 | (345) all_52_21 = e3 | ~ (op(e2, e2) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_25, e3, e2, e1, % 55.06/13.88 | simplifying with (107) gives: % 55.06/13.88 | (346) all_52_25 = e3 | ~ (op(e1, e2) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_13, e3, e2, e0, % 55.06/13.88 | simplifying with (190) gives: % 55.06/13.88 | (347) all_56_13 = e3 | ~ (op(e0, e2) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_7, e3, e2, e0, % 55.06/13.88 | simplifying with (173) gives: % 55.06/13.88 | (348) all_54_7 = e3 | ~ (op(e0, e2) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_0, e0, e3, e3, % 55.06/13.88 | simplifying with (203) gives: % 55.06/13.88 | (349) all_56_0 = e0 | ~ (op(e3, e3) = e0) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_16, e0, e3, e3, % 55.06/13.88 | simplifying with (116) gives: % 55.06/13.88 | (350) all_52_16 = e0 | ~ (op(e3, e3) = e0) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_1, e0, e3, e2, % 55.06/13.88 | simplifying with (182) gives: % 55.06/13.88 | (351) all_54_1 = e0 | ~ (op(e2, e3) = e0) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_22_1, e0, e3, e1, % 55.06/13.88 | simplifying with (62) gives: % 55.06/13.88 | (352) all_22_1 = e0 | ~ (op(e1, e3) = e0) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_0, e1, e3, e3, % 55.06/13.88 | simplifying with (203) gives: % 55.06/13.88 | (353) all_56_0 = e1 | ~ (op(e3, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_0, e1, e3, e3, % 55.06/13.88 | simplifying with (186) gives: % 55.06/13.88 | (354) all_54_0 = e1 | ~ (op(e3, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_20, e1, e3, e2, % 55.06/13.88 | simplifying with (112) gives: % 55.06/13.88 | (355) all_52_20 = e1 | ~ (op(e2, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_2, e1, e3, e1, % 55.06/13.88 | simplifying with (178) gives: % 55.06/13.88 | (356) all_54_2 = e1 | ~ (op(e1, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_44_1, e1, e3, e1, % 55.06/13.88 | simplifying with (90) gives: % 55.06/13.88 | (357) all_44_1 = e1 | ~ (op(e1, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_6_1, e1, e3, e0, % 55.06/13.88 | simplifying with (39) gives: % 55.06/13.88 | (358) all_6_1 = e1 | ~ (op(e0, e3) = e1) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_54_0, e2, e3, e3, % 55.06/13.88 | simplifying with (186) gives: % 55.06/13.88 | (359) all_54_0 = e2 | ~ (op(e3, e3) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_52_20, e2, e3, e2, % 55.06/13.88 | simplifying with (112) gives: % 55.06/13.88 | (360) all_52_20 = e2 | ~ (op(e2, e3) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_22_1, e2, e3, e1, % 55.06/13.88 | simplifying with (62) gives: % 55.06/13.88 | (361) all_22_1 = e2 | ~ (op(e1, e3) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_56_12, e2, e3, e0, % 55.06/13.88 | simplifying with (191) gives: % 55.06/13.88 | (362) all_56_12 = e2 | ~ (op(e0, e3) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_6_1, e2, e3, e0, % 55.06/13.88 | simplifying with (39) gives: % 55.06/13.88 | (363) all_6_1 = e2 | ~ (op(e0, e3) = e2) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with e0, e3, e3, all_52_19, % 55.06/13.88 | simplifying with (127) gives: % 55.06/13.88 | (364) e3 = e0 | ~ (op(all_52_19, e3) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_12_1, e3, e3, e2, % 55.06/13.88 | simplifying with (48) gives: % 55.06/13.88 | (365) all_12_1 = e3 | ~ (op(e2, e3) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_44_1, e3, e3, e1, % 55.06/13.88 | simplifying with (90) gives: % 55.06/13.88 | (366) all_44_1 = e3 | ~ (op(e1, e3) = e3) % 55.06/13.88 | % 55.06/13.88 | GROUND_INST: instantiating (function-axioms) with all_8_1, e3, e3, e0, % 55.06/13.88 | simplifying with (42) gives: % 55.06/13.88 | (367) all_8_1 = e3 | ~ (op(e0, e3) = e3) % 55.06/13.88 | % 55.06/13.88 | COMBINE_EQS: (289), (290) imply: % 55.06/13.88 | (368) all_54_0 = all_52_16 % 55.06/13.88 | % 55.06/13.88 | SIMP: (368) implies: % 55.06/13.88 | (369) all_54_0 = all_52_16 % 55.06/13.88 | % 55.06/13.88 | COMBINE_EQS: (287), (288) imply: % 55.06/13.88 | (370) all_54_4 = all_42_1 % 55.06/13.88 | % 55.06/13.88 | SIMP: (370) implies: % 55.06/13.88 | (371) all_54_4 = all_42_1 % 55.06/13.88 | % 55.06/13.88 | COMBINE_EQS: (283), (284) imply: % 55.06/13.88 | (372) all_54_8 = all_26_1 % 55.06/13.88 | % 55.06/13.88 | SIMP: (372) implies: % 55.06/13.88 | (373) all_54_8 = all_26_1 % 55.06/13.88 | % 55.06/13.88 | COMBINE_EQS: (279), (280) imply: % 55.06/13.88 | (374) all_52_19 = all_50_1 % 55.06/13.89 | % 55.06/13.89 | SIMP: (374) implies: % 55.06/13.89 | (375) all_52_19 = all_50_1 % 55.06/13.89 | % 55.06/13.89 | COMBINE_EQS: (275), (276) imply: % 55.06/13.89 | (376) all_54_1 = all_46_1 % 55.06/13.89 | % 55.06/13.89 | SIMP: (376) implies: % 55.06/13.89 | (377) all_54_1 = all_46_1 % 55.06/13.89 | % 55.06/13.89 | COMBINE_EQS: (271), (272) imply: % 55.06/13.90 | (378) all_54_5 = all_52_21 % 55.06/13.90 | % 55.06/13.90 | COMBINE_EQS: (269), (270) imply: % 55.06/13.90 | (379) all_54_9 = all_52_22 % 55.06/13.90 | % 55.06/13.90 | SIMP: (379) implies: % 55.06/13.90 | (380) all_54_9 = all_52_22 % 55.06/13.90 | % 55.06/13.90 | COMBINE_EQS: (265), (266) imply: % 55.06/13.90 | (381) all_54_13 = all_48_1 % 55.06/13.90 | % 55.06/13.90 | SIMP: (381) implies: % 55.06/13.90 | (382) all_54_13 = all_48_1 % 55.06/13.90 | % 55.06/13.90 | COMBINE_EQS: (260), (261) imply: % 55.06/13.90 | (383) all_54_2 = all_52_24 % 55.06/13.90 | % 55.06/13.90 | COMBINE_EQS: (260), (262) imply: % 55.13/13.90 | (384) all_54_2 = all_22_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (257), (258) imply: % 55.13/13.90 | (385) all_52_25 = all_32_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (385) implies: % 55.13/13.90 | (386) all_52_25 = all_32_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (253), (254) imply: % 55.13/13.90 | (387) all_54_10 = all_52_26 % 55.13/13.90 | % 55.13/13.90 | SIMP: (387) implies: % 55.13/13.90 | (388) all_54_10 = all_52_26 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (251), (252) imply: % 55.13/13.90 | (389) all_54_14 = all_14_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (389) implies: % 55.13/13.90 | (390) all_54_14 = all_14_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (246), (248) imply: % 55.13/13.90 | (391) all_54_3 = all_6_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (246), (247) imply: % 55.13/13.90 | (392) all_54_3 = all_52_28 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (243), (244) imply: % 55.13/13.90 | (393) all_52_29 = all_28_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (393) implies: % 55.13/13.90 | (394) all_52_29 = all_28_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (239), (240) imply: % 55.13/13.90 | (395) all_52_30 = all_36_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (395) implies: % 55.13/13.90 | (396) all_52_30 = all_36_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (235), (236) imply: % 55.13/13.90 | (397) all_54_15 = all_52_31 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (274), (377) imply: % 55.13/13.90 | (398) all_52_20 = all_46_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (398) implies: % 55.13/13.90 | (399) all_52_20 = all_46_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (383), (384) imply: % 55.13/13.90 | (400) all_52_24 = all_22_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (400) implies: % 55.13/13.90 | (401) all_52_24 = all_22_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (391), (392) imply: % 55.13/13.90 | (402) all_52_28 = all_6_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (402) implies: % 55.13/13.90 | (403) all_52_28 = all_6_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (286), (371) imply: % 55.13/13.90 | (404) all_52_17 = all_42_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (404) implies: % 55.13/13.90 | (405) all_52_17 = all_42_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (255), (256) imply: % 55.13/13.90 | (406) all_52_25 = all_20_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (406) implies: % 55.13/13.90 | (407) all_52_25 = all_20_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (241), (242) imply: % 55.13/13.90 | (408) all_52_29 = all_38_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (408) implies: % 55.13/13.90 | (409) all_52_29 = all_38_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (281), (282) imply: % 55.13/13.90 | (410) all_52_18 = all_40_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (281), (373) imply: % 55.13/13.90 | (411) all_52_18 = all_26_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (268), (380) imply: % 55.13/13.90 | (412) all_52_22 = all_10_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (267), (380) imply: % 55.13/13.90 | (413) all_52_22 = all_30_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (237), (238) imply: % 55.13/13.90 | (414) all_52_30 = all_16_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (414) implies: % 55.13/13.90 | (415) all_52_30 = all_16_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (277), (278) imply: % 55.13/13.90 | (416) all_52_19 = all_34_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (416) implies: % 55.13/13.90 | (417) all_52_19 = all_34_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (263), (264) imply: % 55.13/13.90 | (418) all_52_23 = all_24_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (263), (382) imply: % 55.13/13.90 | (419) all_52_23 = all_48_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (249), (390) imply: % 55.13/13.90 | (420) all_52_27 = all_14_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (249), (250) imply: % 55.13/13.90 | (421) all_52_27 = all_18_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (285), (405) imply: % 55.13/13.90 | (422) all_42_1 = all_4_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (422) implies: % 55.13/13.90 | (423) all_42_1 = all_4_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (410), (411) imply: % 55.13/13.90 | (424) all_40_1 = all_26_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (424) implies: % 55.13/13.90 | (425) all_40_1 = all_26_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (375), (417) imply: % 55.13/13.90 | (426) all_50_1 = all_34_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (273), (399) imply: % 55.13/13.90 | (427) all_46_1 = all_12_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (427) implies: % 55.13/13.90 | (428) all_46_1 = all_12_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (412), (413) imply: % 55.13/13.90 | (429) all_30_1 = all_10_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (429) implies: % 55.13/13.90 | (430) all_30_1 = all_10_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (418), (419) imply: % 55.13/13.90 | (431) all_48_1 = all_24_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (431) implies: % 55.13/13.90 | (432) all_48_1 = all_24_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (259), (401) imply: % 55.13/13.90 | (433) all_44_1 = all_22_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (386), (407) imply: % 55.13/13.90 | (434) all_32_1 = all_20_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (420), (421) imply: % 55.13/13.90 | (435) all_18_1 = all_14_1 % 55.13/13.90 | % 55.13/13.90 | SIMP: (435) implies: % 55.13/13.90 | (436) all_18_1 = all_14_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (245), (403) imply: % 55.13/13.90 | (437) all_8_1 = all_6_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (394), (409) imply: % 55.13/13.90 | (438) all_38_1 = all_28_1 % 55.13/13.90 | % 55.13/13.90 | COMBINE_EQS: (396), (415) imply: % 55.13/13.90 | (439) all_36_1 = all_16_1 % 55.13/13.90 | % 55.13/13.91 | SIMP: (439) implies: % 55.13/13.91 | (440) all_36_1 = all_16_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (242), (438) imply: % 55.13/13.91 | (441) all_54_7 = all_28_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (371), (423) imply: % 55.13/13.91 | (442) all_54_4 = all_4_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (377), (428) imply: % 55.13/13.91 | (443) all_54_1 = all_12_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (240), (440) imply: % 55.13/13.91 | (444) all_56_14 = all_16_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (266), (432) imply: % 55.13/13.91 | (445) all_56_7 = all_24_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (270), (412) imply: % 55.13/13.91 | (446) all_56_6 = all_10_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (276), (428) imply: % 55.13/13.91 | (447) all_56_4 = all_12_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (280), (426) imply: % 55.13/13.91 | (448) all_56_3 = all_34_1 % 55.13/13.91 | % 55.13/13.91 | COMBINE_EQS: (288), (423) imply: % 55.13/13.91 | (449) all_56_1 = all_4_1 % 55.13/13.91 | % 55.13/13.91 | REDUCE: (170), (369), (443) imply: % 55.13/13.91 | (450) ~ (all_52_16 = all_12_1) % 55.13/13.91 | % 55.13/13.91 | REDUCE: (169), (369), (384) imply: % 55.13/13.91 | (451) ~ (all_52_16 = all_22_1) % 55.13/13.91 | % 55.13/13.91 | REDUCE: (168), (369), (391) imply: % 55.13/13.91 | (452) ~ (all_52_16 = all_6_1) % 55.13/13.91 | % 55.13/13.91 | REDUCE: (167), (369), (442) imply: % 55.13/13.91 | (453) ~ (all_52_16 = all_4_1) % 55.13/13.91 | % 55.13/13.91 | REDUCE: (166), (369), (373) imply: % 55.13/13.91 | (454) ~ (all_52_16 = all_26_1) % 55.13/13.91 | % 55.13/13.91 | REDUCE: (165), (384), (443) imply: % 55.13/13.91 | (455) ~ (all_22_1 = all_12_1) % 55.13/13.91 | % 55.13/13.91 | SIMP: (455) implies: % 55.13/13.91 | (456) ~ (all_22_1 = all_12_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (164), (391), (443) imply: % 55.13/13.92 | (457) ~ (all_12_1 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (163), (268), (443) imply: % 55.13/13.92 | (458) ~ (all_12_1 = all_10_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (162), (264), (443) imply: % 55.13/13.92 | (459) ~ (all_24_1 = all_12_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (459) implies: % 55.13/13.92 | (460) ~ (all_24_1 = all_12_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (161), (384), (391) imply: % 55.13/13.92 | (461) ~ (all_22_1 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (160), (256), (384) imply: % 55.13/13.92 | (462) ~ (all_22_1 = all_20_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (159), (384), (388) imply: % 55.13/13.92 | (463) ~ (all_52_26 = all_22_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (463) implies: % 55.13/13.92 | (464) ~ (all_52_26 = all_22_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (158), (384), (390) imply: % 55.13/13.92 | (465) ~ (all_22_1 = all_14_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (157), (391), (441) imply: % 55.13/13.92 | (466) ~ (all_28_1 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (466) implies: % 55.13/13.92 | (467) ~ (all_28_1 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (156), (391), (397) imply: % 55.13/13.92 | (468) ~ (all_52_31 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (468) implies: % 55.13/13.92 | (469) ~ (all_52_31 = all_6_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (155), (378), (442) imply: % 55.13/13.92 | (470) ~ (all_52_21 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (470) implies: % 55.13/13.92 | (471) ~ (all_52_21 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (154), (256), (442) imply: % 55.13/13.92 | (472) ~ (all_20_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (472) implies: % 55.13/13.92 | (473) ~ (all_20_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (153), (441), (442) imply: % 55.13/13.92 | (474) ~ (all_28_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (474) implies: % 55.13/13.92 | (475) ~ (all_28_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (152), (373), (442) imply: % 55.13/13.92 | (476) ~ (all_26_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (476) implies: % 55.13/13.92 | (477) ~ (all_26_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (151), (278), (442) imply: % 55.13/13.92 | (478) ~ (all_34_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (478) implies: % 55.13/13.92 | (479) ~ (all_34_1 = all_4_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (150), (378), (441) imply: % 55.13/13.92 | (480) ~ (all_52_21 = all_28_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (149), (268), (378) imply: % 55.13/13.92 | (481) ~ (all_52_21 = all_10_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (148), (264), (378) imply: % 55.13/13.92 | (482) ~ (all_52_21 = all_24_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (147), (256), (441) imply: % 55.13/13.92 | (483) ~ (all_28_1 = all_20_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (483) implies: % 55.13/13.92 | (484) ~ (all_28_1 = all_20_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (146), (256), (388) imply: % 55.13/13.92 | (485) ~ (all_52_26 = all_20_1) % 55.13/13.92 | % 55.13/13.92 | SIMP: (485) implies: % 55.13/13.92 | (486) ~ (all_52_26 = all_20_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (145), (256), (390) imply: % 55.13/13.92 | (487) ~ (all_20_1 = all_14_1) % 55.13/13.92 | % 55.13/13.92 | REDUCE: (144), (238), (441) imply: % 55.13/13.92 | (488) ~ (all_28_1 = all_16_1) % 55.13/13.92 | % 55.13/13.93 | REDUCE: (143), (397), (441) imply: % 55.13/13.93 | (489) ~ (all_52_31 = all_28_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (489) implies: % 55.13/13.93 | (490) ~ (all_52_31 = all_28_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (142), (268), (373) imply: % 55.13/13.93 | (491) ~ (all_26_1 = all_10_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (141), (373), (388) imply: % 55.13/13.93 | (492) ~ (all_52_26 = all_26_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (492) implies: % 55.13/13.93 | (493) ~ (all_52_26 = all_26_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (140), (278), (373) imply: % 55.13/13.93 | (494) ~ (all_34_1 = all_26_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (494) implies: % 55.13/13.93 | (495) ~ (all_34_1 = all_26_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (139), (268), (388) imply: % 55.13/13.93 | (496) ~ (all_52_26 = all_10_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (496) implies: % 55.13/13.93 | (497) ~ (all_52_26 = all_10_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (138), (264), (268) imply: % 55.13/13.93 | (498) ~ (all_24_1 = all_10_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (498) implies: % 55.13/13.93 | (499) ~ (all_24_1 = all_10_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (137), (388), (390) imply: % 55.13/13.93 | (500) ~ (all_52_26 = all_14_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (136), (238), (397) imply: % 55.13/13.93 | (501) ~ (all_52_31 = all_16_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (501) implies: % 55.13/13.93 | (502) ~ (all_52_31 = all_16_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (135), (278), (390) imply: % 55.13/13.93 | (503) ~ (all_34_1 = all_14_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (134), (264), (390) imply: % 55.13/13.93 | (504) ~ (all_24_1 = all_14_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (133), (264), (397) imply: % 55.13/13.93 | (505) ~ (all_52_31 = all_24_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (505) implies: % 55.13/13.93 | (506) ~ (all_52_31 = all_24_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (132), (390), (397) imply: % 55.13/13.93 | (507) ~ (all_52_31 = all_14_1) % 55.13/13.93 | % 55.13/13.93 | SIMP: (507) implies: % 55.13/13.93 | (508) ~ (all_52_31 = all_14_1) % 55.13/13.93 | % 55.13/13.93 | REDUCE: (129), (285) imply: % 55.13/13.93 | (509) op(all_4_1, e3) = e2 % 55.13/13.93 | % 55.13/13.94 | REDUCE: (128), (411) imply: % 55.13/13.94 | (510) op(all_26_1, e3) = e1 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (126), (273) imply: % 55.13/13.94 | (511) op(all_12_1, e2) = e3 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (125), (412) imply: % 55.13/13.94 | (512) op(all_10_1, e2) = e1 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (124), (418) imply: % 55.13/13.94 | (513) op(all_24_1, e2) = e0 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (123), (401) imply: % 55.13/13.94 | (514) op(all_22_1, e1) = e3 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (122), (407) imply: % 55.13/13.94 | (515) op(all_20_1, e1) = e2 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (121), (420) imply: % 55.13/13.94 | (516) op(all_14_1, e1) = e0 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (120), (403) imply: % 55.13/13.94 | (517) op(all_6_1, e0) = e3 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (119), (394) imply: % 55.13/13.94 | (518) op(all_28_1, e0) = e2 % 55.13/13.94 | % 55.13/13.94 | REDUCE: (118), (415) imply: % 55.13/13.94 | (519) op(all_16_1, e0) = e1 % 55.13/13.95 | % 55.13/13.95 | BETA: splitting (37) gives: % 55.13/13.95 | % 55.13/13.95 | Case 1: % 55.13/13.95 | | % 55.13/13.95 | | (520) ~ (all_4_1 = e0) % 55.13/13.95 | | % 55.13/13.95 | | BETA: splitting (40) gives: % 55.13/13.95 | | % 55.13/13.95 | | Case 1: % 55.13/13.95 | | | % 55.13/13.95 | | | (521) ~ (all_6_1 = e1) % 55.13/13.95 | | | % 55.13/13.95 | | | BETA: splitting (43) gives: % 55.13/13.95 | | | % 55.13/13.95 | | | Case 1: % 55.13/13.95 | | | | % 55.13/13.95 | | | | (522) ~ (all_8_1 = e2) % 55.13/13.95 | | | | % 55.13/13.95 | | | | REDUCE: (437), (522) imply: % 55.13/13.95 | | | | (523) ~ (all_6_1 = e2) % 55.13/13.95 | | | | % 55.13/13.95 | | | | BETA: splitting (46) gives: % 55.13/13.95 | | | | % 55.13/13.95 | | | | Case 1: % 55.13/13.95 | | | | | % 55.13/13.95 | | | | | (524) ~ (all_10_1 = e3) % 55.13/13.96 | | | | | % 55.13/13.96 | | | | | BETA: splitting (49) gives: % 55.13/13.96 | | | | | % 55.13/13.96 | | | | | Case 1: % 55.13/13.96 | | | | | | % 55.13/13.96 | | | | | | (525) ~ (all_12_1 = e0) % 55.13/13.96 | | | | | | % 55.13/13.96 | | | | | | BETA: splitting (52) gives: % 55.13/13.96 | | | | | | % 55.13/13.96 | | | | | | Case 1: % 55.13/13.96 | | | | | | | % 55.13/13.96 | | | | | | | (526) ~ (all_14_1 = e2) % 55.13/13.96 | | | | | | | % 55.13/13.96 | | | | | | | BETA: splitting (57) gives: % 55.13/13.96 | | | | | | | % 55.13/13.96 | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | % 55.13/13.96 | | | | | | | | (527) ~ (all_18_1 = e3) % 55.13/13.96 | | | | | | | | % 55.13/13.96 | | | | | | | | REDUCE: (436), (527) imply: % 55.13/13.96 | | | | | | | | (528) ~ (all_14_1 = e3) % 55.13/13.96 | | | | | | | | % 55.13/13.96 | | | | | | | | BETA: splitting (60) gives: % 55.13/13.96 | | | | | | | | % 55.13/13.96 | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | % 55.13/13.96 | | | | | | | | | (529) ~ (all_20_1 = e3) % 55.13/13.96 | | | | | | | | | % 55.13/13.96 | | | | | | | | | BETA: splitting (63) gives: % 55.13/13.96 | | | | | | | | | % 55.13/13.96 | | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | (530) ~ (all_22_1 = e0) % 55.13/13.96 | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | BETA: splitting (72) gives: % 55.13/13.96 | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | (531) ~ (all_28_1 = e3) % 55.13/13.96 | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | BETA: splitting (75) gives: % 55.13/13.96 | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | (532) ~ (all_30_1 = e0) % 55.13/13.96 | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | REDUCE: (430), (532) imply: % 55.13/13.96 | | | | | | | | | | | | (533) ~ (all_10_1 = e0) % 55.13/13.96 | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | BETA: splitting (91) gives: % 55.13/13.96 | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | | (534) ~ (all_44_1 = e2) % 55.13/13.96 | | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | | REDUCE: (433), (534) imply: % 55.13/13.96 | | | | | | | | | | | | | (535) ~ (all_22_1 = e2) % 55.13/13.96 | | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | | BETA: splitting (94) gives: % 55.13/13.96 | | | | | | | | | | | | | % 55.13/13.96 | | | | | | | | | | | | | Case 1: % 55.13/13.96 | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | (536) ~ (all_46_1 = e1) % 55.13/13.97 | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | REDUCE: (428), (536) imply: % 55.13/13.97 | | | | | | | | | | | | | | (537) ~ (all_12_1 = e1) % 55.13/13.97 | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | BETA: splitting (321) gives: % 55.13/13.97 | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | (538) ~ (op(e2, e1) = e2) % 55.13/13.97 | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | PRED_UNIFY: (45), (538) imply: % 55.13/13.97 | | | | | | | | | | | | | | | (539) ~ (all_10_1 = e2) % 55.13/13.97 | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 55.13/13.97 | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | (540) all_56_6 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (540) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | (541) all_10_1 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | REDUCE: (524), (541) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | (542) $false % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | CLOSE: (542) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | (543) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | BETA: splitting (543) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | (544) all_56_6 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (544) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | (545) all_10_1 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | REDUCE: (539), (545) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | (546) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | CLOSE: (546) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | (547) all_56_6 = e1 | all_56_6 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | BETA: splitting (547) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | (548) all_56_6 = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (548) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | (549) all_10_1 = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | REDUCE: (512), (549) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | (550) op(e1, e2) = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (551) ~ (op(e1, e2) = e1) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (550), (551) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (552) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | CLOSE: (552) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (553) all_20_1 = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | REDUCE: (484), (553) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (554) ~ (all_28_1 = e1) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | REDUCE: (487), (553) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (555) ~ (all_14_1 = e1) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | SIMP: (555) implies: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | (556) ~ (all_14_1 = e1) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | (557) all_56_11 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (557) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | (558) all_14_1 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (528), (558) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | (559) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | CLOSE: (559) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | (560) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (560) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | (561) all_56_11 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (561) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | (562) all_14_1 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (526), (562) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | (563) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | CLOSE: (563) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | (564) ~ (all_56_11 = e2) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | (565) all_56_11 = e1 | all_56_11 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (566) all_56_11 = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (566) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (567) all_14_1 = e1 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (567) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (568) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (568) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (569) all_56_11 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (569) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (570) all_14_1 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (516), (570) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | (571) op(e0, e1) = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | (572) ~ (op(e0, e1) = e0) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (571), (572) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | (573) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (573) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | (574) all_54_11 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (574) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | (575) all_16_1 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (488), (575) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | (576) ~ (all_28_1 = e0) % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | (577) all_56_13 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (577) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | (578) all_28_1 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (578) implies: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | (579) all_28_1 = e3 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (531), (579) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | (580) $false % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (580) is inconsistent. % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | (581) all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (581) gives: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_56_13 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (582) imply: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_28_1 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (583) implies: % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_28_1 = e2 % 55.13/13.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (584) imply: % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | (585) op(e2, e0) = e2 % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (586) ~ (op(e2, e0) = e2) % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (585), (586) imply: % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (587) $false % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (587) is inconsistent. % 55.13/13.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_56_7 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (588) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_24_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (589) implies: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_24_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (460), (590) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (591) ~ (all_12_1 = e2) % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (591) implies: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (592) ~ (all_12_1 = e2) % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (117), (206), (207), (209), (212), (248), % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (262), (291), (306), (397), (447), (456), % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (457), (461), (465), (503), (508), (517), (523), % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (525), (526), (530), (535), (537), (592) are % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #28. % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_56_13 = e1 | all_56_13 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_56_13 = e1 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (554), (594) are inconsistent by sub-proof % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | #27. % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_56_13 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (595) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_28_1 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (596) implies: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_28_1 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (597) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (598) $false % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (598) is inconsistent. % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | (599) all_56_6 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (599) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | (600) all_10_1 = e0 % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | REDUCE: (533), (600) imply: % 55.13/13.99 | | | | | | | | | | | | | | | | | | (601) $false % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | | CLOSE: (601) is inconsistent. % 55.13/13.99 | | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | (602) all_30_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | COMBINE_EQS: (430), (602) imply: % 55.13/13.99 | | | | | | | | | | | | | | | (603) all_10_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | SIMP: (603) implies: % 55.13/13.99 | | | | | | | | | | | | | | | (604) all_10_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | REDUCE: (458), (604) imply: % 55.13/13.99 | | | | | | | | | | | | | | | (605) ~ (all_12_1 = e2) % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | | REF_CLOSE: (101), (117), (206), (207), (209), (212), (248), % 55.13/13.99 | | | | | | | | | | | | | | | (252), (262), (291), (306), (397), (447), (456), % 55.13/13.99 | | | | | | | | | | | | | | | (457), (461), (465), (503), (508), (517), (523), % 55.13/13.99 | | | | | | | | | | | | | | | (525), (526), (530), (535), (537), (605) are % 55.13/13.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #28. % 55.13/13.99 | | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | (606) all_46_1 = e1 % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | COMBINE_EQS: (428), (606) imply: % 55.13/13.99 | | | | | | | | | | | | | | (607) all_12_1 = e1 % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | REDUCE: (511), (607) imply: % 55.13/13.99 | | | | | | | | | | | | | | (608) op(e1, e2) = e3 % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | | REF_CLOSE: (346), (407), (529), (608) are inconsistent by % 55.13/13.99 | | | | | | | | | | | | | | sub-proof #26. % 55.13/13.99 | | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | (609) all_44_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | COMBINE_EQS: (433), (609) imply: % 55.13/13.99 | | | | | | | | | | | | | (610) all_22_1 = e2 % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | REDUCE: (62), (610) imply: % 55.13/13.99 | | | | | | | | | | | | | (611) op(e1, e3) = e2 % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | | REF_CLOSE: (325), (361), (412), (514), (524), (611) are % 55.13/13.99 | | | | | | | | | | | | | inconsistent by sub-proof #24. % 55.13/13.99 | | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | End of split % 55.13/13.99 | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | Case 2: % 55.13/13.99 | | | | | | | | | | | | % 55.13/13.99 | | | | | | | | | | | | (612) all_30_1 = e0 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | COMBINE_EQS: (430), (612) imply: % 55.13/14.01 | | | | | | | | | | | | (613) all_10_1 = e0 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | SIMP: (613) implies: % 55.13/14.01 | | | | | | | | | | | | (614) all_10_1 = e0 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | REDUCE: (45), (614) imply: % 55.13/14.01 | | | | | | | | | | | | (615) op(e2, e1) = e0 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | BETA: splitting (308) gives: % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | (616) ~ (op(e2, e1) = e0) % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | PRED_UNIFY: (615), (616) imply: % 55.13/14.01 | | | | | | | | | | | | | (617) $false % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | CLOSE: (617) is inconsistent. % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | REDUCE: (512), (614) imply: % 55.13/14.01 | | | | | | | | | | | | | (618) op(e0, e2) = e1 % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | BETA: splitting (340) gives: % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | (619) ~ (op(e0, e2) = e1) % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | PRED_UNIFY: (618), (619) imply: % 55.13/14.01 | | | | | | | | | | | | | | (620) $false % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | CLOSE: (620) is inconsistent. % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | (621) all_56_13 = e1 % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | COMBINE_EQS: (244), (621) imply: % 55.13/14.01 | | | | | | | | | | | | | | (622) all_28_1 = e1 % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | REDUCE: (518), (622) imply: % 55.13/14.01 | | | | | | | | | | | | | | (623) op(e1, e0) = e2 % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | | REF_CLOSE: (302), (526), (623) are inconsistent by sub-proof % 55.13/14.01 | | | | | | | | | | | | | | #23. % 55.13/14.01 | | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | (624) all_28_1 = e3 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REDUCE: (480), (624) imply: % 55.13/14.01 | | | | | | | | | | | (625) ~ (all_52_21 = e3) % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REDUCE: (518), (624) imply: % 55.13/14.01 | | | | | | | | | | | (626) op(e3, e0) = e2 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REF_CLOSE: (7), (226), (300), (304), (325), (330), (345), % 55.13/14.01 | | | | | | | | | | | (364), (412), (417), (423), (432), (513), (520), % 55.13/14.01 | | | | | | | | | | | (524), (625), (626) are inconsistent by sub-proof % 55.13/14.01 | | | | | | | | | | | #20. % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | (627) all_22_1 = e0 % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | REDUCE: (465), (627) imply: % 55.13/14.01 | | | | | | | | | | (628) ~ (all_14_1 = e0) % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | SIMP: (628) implies: % 55.13/14.01 | | | | | | | | | | (629) ~ (all_14_1 = e0) % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | REDUCE: (514), (627) imply: % 55.13/14.01 | | | | | | | | | | (630) op(e0, e1) = e3 % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | BETA: splitting (328) gives: % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | (631) ~ (op(e0, e1) = e3) % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | PRED_UNIFY: (630), (631) imply: % 55.13/14.01 | | | | | | | | | | | (632) $false % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | CLOSE: (632) is inconsistent. % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | (633) all_52_30 = e3 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | COMBINE_EQS: (415), (633) imply: % 55.13/14.01 | | | | | | | | | | | (634) all_16_1 = e3 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | SIMP: (634) implies: % 55.13/14.01 | | | | | | | | | | | (635) all_16_1 = e3 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REDUCE: (519), (635) imply: % 55.13/14.01 | | | | | | | | | | | (636) op(e3, e0) = e1 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REF_CLOSE: (207), (252), (278), (295), (503), (526), (528), % 55.13/14.01 | | | | | | | | | | | (629), (636) are inconsistent by sub-proof #19. % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | End of split % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | (637) all_20_1 = e3 % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | COMBINE_EQS: (407), (637) imply: % 55.13/14.01 | | | | | | | | | (638) all_52_25 = e3 % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | REDUCE: (486), (637) imply: % 55.13/14.01 | | | | | | | | | (639) ~ (all_52_26 = e3) % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | REDUCE: (473), (637) imply: % 55.13/14.01 | | | | | | | | | (640) ~ (all_4_1 = e3) % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | SIMP: (640) implies: % 55.13/14.01 | | | | | | | | | (641) ~ (all_4_1 = e3) % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | REDUCE: (515), (637) imply: % 55.13/14.01 | | | | | | | | | (642) op(e3, e1) = e2 % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | BETA: splitting (324) gives: % 55.13/14.01 | | | | | | | | | % 55.13/14.01 | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | (643) ~ (op(all_52_25, e1) = e3) % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | REDUCE: (638), (643) imply: % 55.13/14.01 | | | | | | | | | | (644) ~ (op(e3, e1) = e3) % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | BETA: splitting (319) gives: % 55.13/14.01 | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | (645) ~ (op(e3, e1) = e2) % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | PRED_UNIFY: (642), (645) imply: % 55.13/14.01 | | | | | | | | | | | (646) $false % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | CLOSE: (646) is inconsistent. % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | Case 2: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | (647) all_26_1 = e2 % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | REDUCE: (477), (647) imply: % 55.13/14.01 | | | | | | | | | | | (648) ~ (all_4_1 = e2) % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | SIMP: (648) implies: % 55.13/14.01 | | | | | | | | | | | (649) ~ (all_4_1 = e2) % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | BETA: splitting (213) gives: % 55.13/14.01 | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | Case 1: % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | (650) all_56_1 = e3 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | COMBINE_EQS: (449), (650) imply: % 55.13/14.01 | | | | | | | | | | | | (651) all_4_1 = e3 % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | REDUCE: (641), (651) imply: % 55.13/14.01 | | | | | | | | | | | | (652) $false % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.01 | | | | | | | | | | | | CLOSE: (652) is inconsistent. % 55.13/14.01 | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | (653) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0 % 55.13/14.02 | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | BETA: splitting (653) gives: % 55.13/14.02 | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | (654) all_56_1 = e2 % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | COMBINE_EQS: (449), (654) imply: % 55.13/14.02 | | | | | | | | | | | | | (655) all_4_1 = e2 % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | REDUCE: (649), (655) imply: % 55.13/14.02 | | | | | | | | | | | | | (656) $false % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | CLOSE: (656) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | (657) all_56_1 = e1 | all_56_1 = e0 % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | BETA: splitting (224) gives: % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | (658) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 % 55.13/14.02 | | | | | | | | | | | | | | & op(e2, e1) = e3) % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | BETA: splitting (658) gives: % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | (659) all_58_4 = e3 & op(e3, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | ALPHA: (659) implies: % 55.13/14.02 | | | | | | | | | | | | | | | (660) op(e3, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | PRED_UNIFY: (644), (660) imply: % 55.13/14.02 | | | | | | | | | | | | | | | (661) $false % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | CLOSE: (661) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | (662) all_58_5 = e3 & op(e2, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | ALPHA: (662) implies: % 55.13/14.02 | | | | | | | | | | | | | | | (663) op(e2, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | REF_CLOSE: (325), (412), (524), (663) are inconsistent by % 55.13/14.02 | | | | | | | | | | | | | | | sub-proof #25. % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | (664) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = % 55.13/14.02 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | BETA: splitting (664) gives: % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | (665) all_58_8 = e3 & op(e1, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | ALPHA: (665) implies: % 55.13/14.02 | | | | | | | | | | | | | | | (666) op(e1, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | REF_CLOSE: (326), (388), (639), (666) are inconsistent by % 55.13/14.02 | | | | | | | | | | | | | | | sub-proof #18. % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | (667) all_58_14 = e3 & op(e0, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | ALPHA: (667) implies: % 55.13/14.02 | | | | | | | | | | | | | | | (668) op(e0, e1) = e3 % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | (669) ~ (op(e0, e1) = e3) % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | PRED_UNIFY: (668), (669) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | (670) $false % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | CLOSE: (670) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | (671) all_16_1 = e3 % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | REDUCE: (519), (671) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | (672) op(e3, e0) = e1 % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | (673) ~ (op(e3, e0) = e1) % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | PRED_UNIFY: (672), (673) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | (674) $false % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | CLOSE: (674) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | (675) all_56_3 = e1 % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (448), (675) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | (676) all_34_1 = e1 % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | REDUCE: (479), (676) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | (677) ~ (all_4_1 = e1) % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | SIMP: (677) implies: % 55.13/14.02 | | | | | | | | | | | | | | | | | (678) ~ (all_4_1 = e1) % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | BETA: splitting (657) gives: % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | (679) all_56_1 = e1 % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (679) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | | (680) all_4_1 = e1 % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | REDUCE: (678), (680) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | | (681) $false % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | CLOSE: (681) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | (682) all_56_1 = e0 % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (682) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | | (683) all_4_1 = e0 % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | REDUCE: (520), (683) imply: % 55.13/14.02 | | | | | | | | | | | | | | | | | | (684) $false % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | | CLOSE: (684) is inconsistent. % 55.13/14.02 | | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | | % 55.13/14.02 | | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | (685) e3 = e2 % 55.13/14.02 | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | REDUCE: (9), (685) imply: % 55.13/14.02 | | | | | | | | | | (686) $false % 55.13/14.02 | | | | | | | | | | % 55.13/14.02 | | | | | | | | | | CLOSE: (686) is inconsistent. % 55.13/14.02 | | | | | | | | | | % 55.13/14.02 | | | | | | | | | End of split % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | End of split % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | (687) all_18_1 = e3 % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | COMBINE_EQS: (436), (687) imply: % 55.13/14.02 | | | | | | | | (688) all_14_1 = e3 % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | SIMP: (688) implies: % 55.13/14.02 | | | | | | | | (689) all_14_1 = e3 % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | REDUCE: (516), (689) imply: % 55.13/14.02 | | | | | | | | (690) op(e3, e1) = e0 % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | BETA: splitting (307) gives: % 55.13/14.02 | | | | | | | | % 55.13/14.02 | | | | | | | | Case 1: % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | (691) ~ (op(e3, e1) = e0) % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | PRED_UNIFY: (690), (691) imply: % 55.13/14.02 | | | | | | | | | (692) $false % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | CLOSE: (692) is inconsistent. % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | Case 2: % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | (693) all_52_18 = e0 % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | COMBINE_EQS: (411), (693) imply: % 55.13/14.02 | | | | | | | | | (694) all_26_1 = e0 % 55.13/14.02 | | | | | | | | | % 55.13/14.02 | | | | | | | | | SIMP: (694) implies: % 55.13/14.02 | | | | | | | | | (695) all_26_1 = e0 % 55.13/14.02 | | | | | | | | | % 55.13/14.03 | | | | | | | | | REDUCE: (510), (695) imply: % 55.13/14.03 | | | | | | | | | (696) op(e0, e3) = e1 % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | | REF_CLOSE: (358), (521), (696) are inconsistent by sub-proof % 55.13/14.03 | | | | | | | | | #17. % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | End of split % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | End of split % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | Case 2: % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | (697) all_14_1 = e2 % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | COMBINE_EQS: (420), (697) imply: % 55.13/14.03 | | | | | | | (698) all_52_27 = e2 % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | COMBINE_EQS: (390), (697) imply: % 55.13/14.03 | | | | | | | (699) all_54_14 = e2 % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | REDUCE: (500), (697) imply: % 55.13/14.03 | | | | | | | (700) ~ (all_52_26 = e2) % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | REDUCE: (508), (697) imply: % 55.13/14.03 | | | | | | | (701) ~ (all_52_31 = e2) % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | REDUCE: (487), (697) imply: % 55.13/14.03 | | | | | | | (702) ~ (all_20_1 = e2) % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | REDUCE: (516), (697) imply: % 55.13/14.03 | | | | | | | (703) op(e2, e1) = e0 % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | BETA: splitting (308) gives: % 55.13/14.03 | | | | | | | % 55.13/14.03 | | | | | | | Case 1: % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | (704) ~ (op(e2, e1) = e0) % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | PRED_UNIFY: (703), (704) imply: % 55.13/14.03 | | | | | | | | (705) $false % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | CLOSE: (705) is inconsistent. % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | Case 2: % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | (706) all_30_1 = e0 % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | COMBINE_EQS: (430), (706) imply: % 55.13/14.03 | | | | | | | | (707) all_10_1 = e0 % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | COMBINE_EQS: (412), (707) imply: % 55.13/14.03 | | | | | | | | (708) all_52_22 = e0 % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | REDUCE: (481), (707) imply: % 55.13/14.03 | | | | | | | | (709) ~ (all_52_21 = e0) % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | REDUCE: (499), (707) imply: % 55.13/14.03 | | | | | | | | (710) ~ (all_24_1 = e0) % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | REDUCE: (524), (707) imply: % 55.13/14.03 | | | | | | | | (711) ~ (e3 = e0) % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | REDUCE: (512), (707) imply: % 55.13/14.03 | | | | | | | | (712) op(e0, e2) = e1 % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | BETA: splitting (341) gives: % 55.13/14.03 | | | | | | | | % 55.13/14.03 | | | | | | | | Case 1: % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | | (713) ~ (op(e0, e2) = e1) % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | | PRED_UNIFY: (712), (713) imply: % 55.13/14.03 | | | | | | | | | (714) $false % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | | CLOSE: (714) is inconsistent. % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | Case 2: % 55.13/14.03 | | | | | | | | | % 55.13/14.03 | | | | | | | | | (715) all_54_7 = e1 % 55.25/14.03 | | | | | | | | | % 55.25/14.03 | | | | | | | | | COMBINE_EQS: (441), (715) imply: % 55.25/14.03 | | | | | | | | | (716) all_28_1 = e1 % 55.25/14.03 | | | | | | | | | % 55.25/14.03 | | | | | | | | | COMBINE_EQS: (438), (716) imply: % 55.25/14.03 | | | | | | | | | (717) all_38_1 = e1 % 55.25/14.03 | | | | | | | | | % 55.25/14.03 | | | | | | | | | COMBINE_EQS: (394), (716) imply: % 55.25/14.03 | | | | | | | | | (718) all_52_29 = e1 % 55.25/14.03 | | | | | | | | | % 55.25/14.03 | | | | | | | | | REDUCE: (490), (716) imply: % 55.25/14.03 | | | | | | | | | (719) ~ (all_52_31 = e1) % 55.25/14.03 | | | | | | | | | % 55.25/14.03 | | | | | | | | | REDUCE: (488), (716) imply: % 55.25/14.03 | | | | | | | | | (720) ~ (all_16_1 = e1) % 55.48/14.03 | | | | | | | | | % 55.48/14.03 | | | | | | | | | SIMP: (720) implies: % 55.48/14.03 | | | | | | | | | (721) ~ (all_16_1 = e1) % 55.48/14.03 | | | | | | | | | % 55.48/14.03 | | | | | | | | | REDUCE: (467), (716) imply: % 55.48/14.03 | | | | | | | | | (722) ~ (all_6_1 = e1) % 55.48/14.03 | | | | | | | | | % 55.48/14.03 | | | | | | | | | BETA: splitting (130) gives: % 55.48/14.03 | | | | | | | | | % 55.48/14.03 | | | | | | | | | Case 1: % 55.48/14.03 | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | (723) (all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 55.48/14.03 | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 55.48/14.03 | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, all_52_20) % 55.48/14.03 | | | | | | | | | | = all_52_20 & op(e3, all_52_24) = all_52_24 & % 55.48/14.03 | | | | | | | | | | op(e3, all_52_28) = all_52_28) | (all_52_4 = % 55.48/14.03 | | | | | | | | | | all_52_17 & all_52_5 = all_52_21 & all_52_6 = % 55.48/14.03 | | | | | | | | | | all_52_25 & all_52_7 = all_52_29 & op(e2, % 55.48/14.03 | | | | | | | | | | all_52_17) = all_52_17 & op(e2, all_52_21) = % 55.48/14.03 | | | | | | | | | | all_52_21 & op(e2, all_52_25) = all_52_25 & % 55.48/14.03 | | | | | | | | | | op(e2, all_52_29) = all_52_29) % 55.48/14.03 | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | BETA: splitting (723) gives: % 55.48/14.03 | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | Case 1: % 55.48/14.03 | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | (724) all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 55.48/14.03 | | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 55.48/14.03 | | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, all_52_20) % 55.48/14.03 | | | | | | | | | | | = all_52_20 & op(e3, all_52_24) = all_52_24 & % 55.48/14.03 | | | | | | | | | | | op(e3, all_52_28) = all_52_28 % 55.48/14.03 | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | ALPHA: (724) implies: % 55.48/14.03 | | | | | | | | | | | (725) op(e3, all_52_16) = all_52_16 % 55.48/14.03 | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | BETA: splitting (331) gives: % 55.48/14.03 | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | Case 1: % 55.48/14.03 | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | (726) ~ (op(e2, e2) = e0) % 55.48/14.03 | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | BETA: splitting (84) gives: % 55.48/14.03 | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | Case 1: % 55.48/14.03 | | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | | (727) ~ (all_38_1 = e1) % 55.48/14.03 | | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | | REDUCE: (717), (727) imply: % 55.48/14.03 | | | | | | | | | | | | | (728) $false % 55.48/14.03 | | | | | | | | | | | | | % 55.48/14.03 | | | | | | | | | | | | | CLOSE: (728) is inconsistent. % 55.48/14.03 | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | (729) ~ (all_38_0 = e3) & op(e1, e1) = all_38_0 & % 55.48/14.04 | | | | | | | | | | | | | $i(all_38_0) % 55.48/14.04 | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | ALPHA: (729) implies: % 55.48/14.04 | | | | | | | | | | | | | (730) ~ (all_38_0 = e3) % 55.48/14.04 | | | | | | | | | | | | | (731) op(e1, e1) = all_38_0 % 55.48/14.04 | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | BETA: splitting (322) gives: % 55.48/14.04 | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | (732) ~ (op(e1, e1) = e2) % 55.48/14.04 | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | BETA: splitting (303) gives: % 55.48/14.04 | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | (733) ~ (op(e0, e0) = e2) % 55.48/14.04 | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 55.48/14.04 | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | (734) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = % 55.48/14.04 | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | BETA: splitting (734) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | (735) all_58_12 = e1 & op(e0, e3) = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | ALPHA: (735) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | (736) op(e0, e3) = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (358), (521), (736) are inconsistent by sub-proof % 55.48/14.04 | | | | | | | | | | | | | | | | | #17. % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | (737) all_58_13 = e1 & op(e0, e2) = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | ALPHA: (737) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | (738) all_58_13 = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | (739) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = % 55.48/14.04 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | (740) all_58_12 = e2 & op(e0, e3) = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (363), (523), (740) are inconsistent by sub-proof % 55.48/14.04 | | | | | | | | | | | | | | | | | | | #16. % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | (741) all_58_13 = e2 & op(e0, e2) = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | (742) op(e0, e2) = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (342), (708), (742) are inconsistent by % 55.48/14.04 | | | | | | | | | | | | | | | | | | | sub-proof #15. % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | End of split % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | (743) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = % 55.48/14.04 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | BETA: splitting (743) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | (744) all_58_14 = e2 & op(e0, e1) = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | ALPHA: (744) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | (745) op(e0, e1) = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (746) ~ (op(e0, e1) = e2) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (745), (746) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (747) $false % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | CLOSE: (747) is inconsistent. % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (748) all_36_1 = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (748) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (749) all_16_1 = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | SIMP: (749) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (750) all_16_1 = e2 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | REDUCE: (519), (750) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | (751) op(e2, e0) = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (752) ~ (op(e2, e0) = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (751), (752) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (753) $false % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | CLOSE: (753) is inconsistent. % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (754) all_52_23 = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (418), (754) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (755) all_24_1 = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | SIMP: (755) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (756) all_24_1 = e1 % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | REDUCE: (460), (756) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (757) ~ (all_12_1 = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | SIMP: (757) implies: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_12_1 = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | (759) ~ (all_24_1 = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | (760) ~ (op(e2, e0) = e1) % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (751), (760) imply: % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | (761) $false % 55.48/14.04 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (761) is inconsistent. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (756), (759) imply: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | (762) $false % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (762) is inconsistent. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | (763) ~ (all_24_0 = e3) & op(e1, e1) = all_24_0 & % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_24_0) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (763) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | (764) op(e1, e1) = all_24_0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | (765) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_1 = e0 & op(e3, e2) = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | (767) op(e3, e2) = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (330), (423), (520), (767) are inconsistent by % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | (768) all_58_3 = e0 & op(e2, e2) = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (726), (768) are inconsistent by sub-proof #14. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | (769) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_7 = e0 & op(e1, e2) = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (770) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | (771) all_58_7 = e0 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | (772) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (772) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_58_6 = e2 & op(e1, e3) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (773) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (774) op(e1, e3) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (325), (361), (412), (514), (524), (774) are % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #24. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_58_7 = e2 & op(e1, e2) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (775) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (776) op(e1, e2) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) ~ (op(e1, e2) = e2) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (776), (777) imply: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) $false % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (778) is inconsistent. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_32_1 = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (434), (779) imply: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_20_1 = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (780) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_20_1 = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (781) imply: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) $false % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (782) is inconsistent. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | (783) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_8 = e2 & op(e1, e1) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (784) implies: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (785) op(e1, e1) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (732), (785) imply: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (786) $false % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (786) is inconsistent. % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_58_11 = e2 & op(e1, e0) = e2 % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (787) implies: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_58_11 = e2 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_26, % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_0, e1, e1, simplifying with (106), (764) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_52_26 = all_24_0 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_24_0, % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (764) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_24_0 = e3 | ~ (op(e1, e1) = e3) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_26, % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_0, e1, e1, simplifying with (106), (731) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_52_26 = all_38_0 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (789), (791) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_38_0 = all_24_0 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (730), (792) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (793) ~ (all_24_0 = e3) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_6 = e3 & op(e1, e3) = e3 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (795) implies: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_58_6 = e3 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (797) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_58_0 = e1 & op(e3, e3) = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (798) implies: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) op(e3, e3) = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) ~ (op(e3, e3) = e1) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (799), (800) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) $false % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (801) is inconsistent. % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_54_0 = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (369), (802) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_52_16 = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (803) implies: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_52_16 = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (454), (804) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) ~ (all_26_1 = e1) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (805) implies: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) ~ (all_26_1 = e1) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (725), (804) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) op(e3, e1) = e1 % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) ~ (op(e3, e1) = e1) % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (807), (808) imply: % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) $false % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (809) is inconsistent. % 55.48/14.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_40_1 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (810) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_26_1 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (806), (811) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) $false % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (812) is inconsistent. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_58_2 = e1 & op(e2, e3) = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) op(e2, e3) = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) ~ (op(e2, e3) = e1) % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (814), (815) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) $false % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (816) is inconsistent. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_52_20 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (817) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_12_1 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (818) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_12_1 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (758), (819) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) $false % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (820) is inconsistent. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_58_6 = e1 & op(e1, e3) = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (822) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_58_6 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (796), (823) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) e3 = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (824) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) $false % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (825) is inconsistent. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_58_12 = e1 & op(e0, e3) = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (826) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) op(e0, e3) = e1 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (358), (521), (827) are inconsistent by sub-proof % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #17. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_58_7 = e3 & op(e1, e2) = e3 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (828) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_58_7 = e3 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (771), (829) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) e3 = e0 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (830) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) e3 = e0 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (831) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) $false % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (832) is inconsistent. % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (833) gives: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_58_8 = e3 & op(e1, e1) = e3 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (834) implies: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) op(e1, e1) = e3 % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) ~ (op(e1, e1) = e3) % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (835), (836) imply: % 55.48/14.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (837) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_24_0 = e3 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (838) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (839) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_58_11 = e3 & op(e1, e0) = e3 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (840) implies: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_58_11 = e3 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (788), (841) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) e3 = e2 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (842) implies: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) e3 = e2 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (843) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (844) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | (845) all_58_13 = e0 & op(e0, e2) = e0 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | (846) all_58_13 = e0 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (738), (846) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | (847) e1 = e0 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (847) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | (848) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (848) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | (849) all_58_15 = e2 & op(e0, e0) = e2 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | ALPHA: (849) implies: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | (850) op(e0, e0) = e2 % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (733), (850) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | | (851) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | (852) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = % 55.48/14.09 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 55.48/14.09 | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | BETA: splitting (852) gives: % 55.48/14.09 | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | Case 1: % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | (853) all_58_14 = e1 & op(e0, e1) = e1 % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | ALPHA: (853) implies: % 55.48/14.09 | | | | | | | | | | | | | | | | | (854) op(e0, e1) = e1 % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | (855) ~ (op(e0, e1) = e1) % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (854), (855) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | (856) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | CLOSE: (856) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | (857) all_16_1 = e1 % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | REDUCE: (721), (857) imply: % 55.48/14.09 | | | | | | | | | | | | | | | | | | (858) $false % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | | CLOSE: (858) is inconsistent. % 55.48/14.09 | | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | End of split % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | Case 2: % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | (859) all_58_15 = e1 & op(e0, e0) = e1 % 55.48/14.09 | | | | | | | | | | | | | | | | | % 55.48/14.09 | | | | | | | | | | | | | | | | | ALPHA: (859) implies: % 55.48/14.10 | | | | | | | | | | | | | | | | | (860) op(e0, e0) = e1 % 55.48/14.10 | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 55.48/14.10 | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | Case 1: % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | (861) ~ (op(e0, e0) = e1) % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (860), (861) imply: % 55.48/14.10 | | | | | | | | | | | | | | | | | | (862) $false % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | CLOSE: (862) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | (863) all_52_31 = e1 % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | REDUCE: (719), (863) imply: % 55.48/14.10 | | | | | | | | | | | | | | | | | | (864) $false % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | | CLOSE: (864) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | (865) op(e0, e0) = e2 % 55.48/14.10 | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 55.48/14.10 | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | Case 1: % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | (866) ~ (op(e0, e0) = e2) % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | PRED_UNIFY: (865), (866) imply: % 55.48/14.10 | | | | | | | | | | | | | | | | (867) $false % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | CLOSE: (867) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | (868) all_52_31 = e2 % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | REDUCE: (701), (868) imply: % 55.48/14.10 | | | | | | | | | | | | | | | | (869) $false % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | | CLOSE: (869) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | (870) all_52_26 = e2 % 55.48/14.10 | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | REDUCE: (700), (870) imply: % 55.48/14.10 | | | | | | | | | | | | | | (871) $false % 55.48/14.10 | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | | CLOSE: (871) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | (872) all_56_5 = e0 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | COMBINE_EQS: (272), (872) imply: % 55.48/14.10 | | | | | | | | | | | | (873) all_52_21 = e0 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | SIMP: (873) implies: % 55.48/14.10 | | | | | | | | | | | | (874) all_52_21 = e0 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | REDUCE: (709), (874) imply: % 55.48/14.10 | | | | | | | | | | | | (875) $false % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | CLOSE: (875) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | (876) all_52_4 = all_52_17 & all_52_5 = all_52_21 & % 55.48/14.10 | | | | | | | | | | | all_52_6 = all_52_25 & all_52_7 = all_52_29 & % 55.48/14.10 | | | | | | | | | | | op(e2, all_52_17) = all_52_17 & op(e2, all_52_21) % 55.48/14.10 | | | | | | | | | | | = all_52_21 & op(e2, all_52_25) = all_52_25 & % 55.48/14.10 | | | | | | | | | | | op(e2, all_52_29) = all_52_29 % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | ALPHA: (876) implies: % 55.48/14.10 | | | | | | | | | | | (877) op(e2, all_52_29) = all_52_29 % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | REDUCE: (718), (877) imply: % 55.48/14.10 | | | | | | | | | | | (878) op(e2, e1) = e1 % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | BETA: splitting (315) gives: % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | Case 1: % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | (879) ~ (op(e2, e1) = e1) % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | PRED_UNIFY: (878), (879) imply: % 55.48/14.10 | | | | | | | | | | | | (880) $false % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | CLOSE: (880) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | (881) all_10_1 = e1 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | COMBINE_EQS: (707), (881) imply: % 55.48/14.10 | | | | | | | | | | | | (882) e1 = e0 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | SIMP: (882) implies: % 55.48/14.10 | | | | | | | | | | | | (883) e1 = e0 % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | REDUCE: (4), (883) imply: % 55.48/14.10 | | | | | | | | | | | | (884) $false % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | | CLOSE: (884) is inconsistent. % 55.48/14.10 | | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | End of split % 55.48/14.10 | | | | | | | | | | % 55.48/14.10 | | | | | | | | | Case 2: % 55.48/14.10 | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | (885) (all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 55.48/14.10 | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 55.48/14.10 | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, all_52_22) % 55.48/14.10 | | | | | | | | | | = all_52_22 & op(e1, all_52_26) = all_52_26 & % 55.48/14.10 | | | | | | | | | | op(e1, all_52_30) = all_52_30) | (all_52_12 = % 55.48/14.10 | | | | | | | | | | all_52_19 & all_52_13 = all_52_23 & all_52_14 = % 55.48/14.10 | | | | | | | | | | all_52_27 & all_52_15 = all_52_31 & op(e0, % 55.48/14.10 | | | | | | | | | | all_52_19) = all_52_19 & op(e0, all_52_23) = % 55.48/14.10 | | | | | | | | | | all_52_23 & op(e0, all_52_27) = all_52_27 & % 55.48/14.10 | | | | | | | | | | op(e0, all_52_31) = all_52_31) % 55.48/14.10 | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | BETA: splitting (885) gives: % 55.48/14.10 | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | Case 1: % 55.48/14.10 | | | | | | | | | | | % 55.48/14.10 | | | | | | | | | | | (886) all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 55.48/14.10 | | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 55.48/14.10 | | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, all_52_22) % 55.48/14.10 | | | | | | | | | | | = all_52_22 & op(e1, all_52_26) = all_52_26 & % 55.48/14.11 | | | | | | | | | | | op(e1, all_52_30) = all_52_30 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | ALPHA: (886) implies: % 55.48/14.11 | | | | | | | | | | | (887) op(e1, all_52_22) = all_52_22 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | REDUCE: (708), (887) imply: % 55.48/14.11 | | | | | | | | | | | (888) op(e1, e0) = e0 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | BETA: splitting (293) gives: % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | Case 1: % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | (889) ~ (op(e1, e0) = e0) % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | PRED_UNIFY: (888), (889) imply: % 55.48/14.11 | | | | | | | | | | | | (890) $false % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | CLOSE: (890) is inconsistent. % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | Case 2: % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | (891) all_54_14 = e0 % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | COMBINE_EQS: (699), (891) imply: % 55.48/14.11 | | | | | | | | | | | | (892) e2 = e0 % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | SIMP: (892) implies: % 55.48/14.11 | | | | | | | | | | | | (893) e2 = e0 % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | REDUCE: (5), (893) imply: % 55.48/14.11 | | | | | | | | | | | | (894) $false % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | | CLOSE: (894) is inconsistent. % 55.48/14.11 | | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | End of split % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | Case 2: % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | (895) all_52_12 = all_52_19 & all_52_13 = all_52_23 & % 55.48/14.11 | | | | | | | | | | | all_52_14 = all_52_27 & all_52_15 = all_52_31 & % 55.48/14.11 | | | | | | | | | | | op(e0, all_52_19) = all_52_19 & op(e0, all_52_23) % 55.48/14.11 | | | | | | | | | | | = all_52_23 & op(e0, all_52_27) = all_52_27 & % 55.48/14.11 | | | | | | | | | | | op(e0, all_52_31) = all_52_31 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | ALPHA: (895) implies: % 55.48/14.11 | | | | | | | | | | | (896) op(e0, all_52_27) = all_52_27 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | REDUCE: (698), (896) imply: % 55.48/14.11 | | | | | | | | | | | (897) op(e0, e2) = e2 % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | | REF_CLOSE: (6), (342), (708), (897) are inconsistent by % 55.48/14.11 | | | | | | | | | | | sub-proof #15. % 55.48/14.11 | | | | | | | | | | | % 55.48/14.11 | | | | | | | | | | End of split % 55.48/14.11 | | | | | | | | | | % 55.48/14.11 | | | | | | | | | End of split % 55.48/14.11 | | | | | | | | | % 55.73/14.11 | | | | | | | | End of split % 55.73/14.11 | | | | | | | | % 55.73/14.12 | | | | | | | End of split % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | End of split % 55.73/14.12 | | | | | | % 55.73/14.12 | | | | | Case 2: % 55.73/14.12 | | | | | | % 55.73/14.12 | | | | | | (898) all_12_1 = e0 % 55.73/14.12 | | | | | | % 55.73/14.12 | | | | | | REDUCE: (511), (898) imply: % 55.73/14.12 | | | | | | (899) op(e0, e2) = e3 % 55.73/14.12 | | | | | | % 55.73/14.12 | | | | | | BETA: splitting (348) gives: % 55.73/14.12 | | | | | | % 55.73/14.12 | | | | | | Case 1: % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | (900) ~ (op(e0, e2) = e3) % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | PRED_UNIFY: (899), (900) imply: % 55.73/14.12 | | | | | | | (901) $false % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | CLOSE: (901) is inconsistent. % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | Case 2: % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | (902) all_54_7 = e3 % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | COMBINE_EQS: (441), (902) imply: % 55.73/14.12 | | | | | | | (903) all_28_1 = e3 % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | REDUCE: (480), (903) imply: % 55.73/14.12 | | | | | | | (904) ~ (all_52_21 = e3) % 55.73/14.12 | | | | | | | % 55.73/14.12 | | | | | | | REDUCE: (518), (903) imply: % 55.73/14.12 | | | | | | | (905) op(e3, e0) = e2 % 55.73/14.12 | | | | | | | % 55.73/14.13 | | | | | | | REF_CLOSE: (7), (226), (300), (304), (325), (330), (345), (364), % 55.73/14.13 | | | | | | | (412), (417), (423), (432), (513), (520), (524), (904), % 55.73/14.13 | | | | | | | (905) are inconsistent by sub-proof #20. % 55.73/14.13 | | | | | | | % 55.73/14.13 | | | | | | End of split % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | End of split % 55.73/14.13 | | | | | % 55.73/14.13 | | | | Case 2: % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | (906) all_10_1 = e3 % 55.73/14.13 | | | | | (907) ~ (all_10_0 = e0) & op(e3, e3) = all_10_0 & $i(all_10_0) % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | ALPHA: (907) implies: % 55.73/14.13 | | | | | (908) op(e3, e3) = all_10_0 % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | COMBINE_EQS: (412), (906) imply: % 55.73/14.13 | | | | | (909) all_52_22 = e3 % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | REDUCE: (497), (906) imply: % 55.73/14.13 | | | | | (910) ~ (all_52_26 = e3) % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | REDUCE: (491), (906) imply: % 55.73/14.13 | | | | | (911) ~ (all_26_1 = e3) % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | REDUCE: (512), (906) imply: % 55.73/14.13 | | | | | (912) op(e3, e2) = e1 % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | BETA: splitting (335) gives: % 55.73/14.13 | | | | | % 55.73/14.13 | | | | | Case 1: % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | (913) ~ (op(e3, e2) = e1) % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | PRED_UNIFY: (912), (913) imply: % 55.73/14.13 | | | | | | (914) $false % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | CLOSE: (914) is inconsistent. % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | Case 2: % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | (915) all_52_17 = e1 % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | COMBINE_EQS: (285), (915) imply: % 55.73/14.13 | | | | | | (916) all_4_1 = e1 % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | SIMP: (916) implies: % 55.73/14.13 | | | | | | (917) all_4_1 = e1 % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | REDUCE: (453), (917) imply: % 55.73/14.13 | | | | | | (918) ~ (all_52_16 = e1) % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | REDUCE: (475), (917) imply: % 55.73/14.13 | | | | | | (919) ~ (all_28_1 = e1) % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | REDUCE: (473), (917) imply: % 55.73/14.13 | | | | | | (920) ~ (all_20_1 = e1) % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | REDUCE: (509), (917) imply: % 55.73/14.13 | | | | | | (921) op(e1, e3) = e2 % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | BETA: splitting (353) gives: % 55.73/14.13 | | | | | | % 55.73/14.13 | | | | | | Case 1: % 55.73/14.13 | | | | | | | % 55.73/14.13 | | | | | | | (922) ~ (op(e3, e3) = e1) % 55.73/14.13 | | | | | | | % 55.73/14.13 | | | | | | | BETA: splitting (361) gives: % 55.73/14.13 | | | | | | | % 55.73/14.13 | | | | | | | Case 1: % 55.73/14.13 | | | | | | | | % 55.73/14.13 | | | | | | | | (923) ~ (op(e1, e3) = e2) % 55.73/14.13 | | | | | | | | % 55.73/14.13 | | | | | | | | PRED_UNIFY: (921), (923) imply: % 55.73/14.13 | | | | | | | | (924) $false % 55.73/14.13 | | | | | | | | % 55.73/14.13 | | | | | | | | CLOSE: (924) is inconsistent. % 55.73/14.13 | | | | | | | | % 55.73/14.13 | | | | | | | Case 2: % 55.73/14.13 | | | | | | | | % 55.73/14.13 | | | | | | | | (925) all_22_1 = e2 % 55.73/14.13 | | | | | | | | % 55.73/14.14 | | | | | | | | COMBINE_EQS: (433), (925) imply: % 55.73/14.14 | | | | | | | | (926) all_44_1 = e2 % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | COMBINE_EQS: (401), (925) imply: % 55.73/14.14 | | | | | | | | (927) all_52_24 = e2 % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | REDUCE: (451), (925) imply: % 55.73/14.14 | | | | | | | | (928) ~ (all_52_16 = e2) % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | REDUCE: (462), (925) imply: % 55.73/14.14 | | | | | | | | (929) ~ (all_20_1 = e2) % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | SIMP: (929) implies: % 55.73/14.14 | | | | | | | | (930) ~ (all_20_1 = e2) % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | REDUCE: (465), (925) imply: % 55.73/14.14 | | | | | | | | (931) ~ (all_14_1 = e2) % 55.73/14.14 | | | | | | | | % 55.73/14.14 | | | | | | | | SIMP: (931) implies: % 55.73/14.14 | | | | | | | | (932) ~ (all_14_1 = e2) % 55.73/14.15 | | | | | | | | % 55.73/14.15 | | | | | | | | REDUCE: (456), (925) imply: % 55.73/14.15 | | | | | | | | (933) ~ (all_12_1 = e2) % 55.73/14.15 | | | | | | | | % 55.73/14.15 | | | | | | | | SIMP: (933) implies: % 55.73/14.15 | | | | | | | | (934) ~ (all_12_1 = e2) % 55.73/14.15 | | | | | | | | % 55.73/14.15 | | | | | | | | REDUCE: (461), (925) imply: % 55.73/14.15 | | | | | | | | (935) ~ (all_6_1 = e2) % 55.73/14.15 | | | | | | | | % 55.73/14.15 | | | | | | | | BETA: splitting (359) gives: % 55.73/14.15 | | | | | | | | % 55.73/14.15 | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | % 55.73/14.15 | | | | | | | | | (936) ~ (op(e3, e3) = e2) % 55.73/14.15 | | | | | | | | | % 55.73/14.15 | | | | | | | | | BETA: splitting (130) gives: % 55.73/14.15 | | | | | | | | | % 55.73/14.15 | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | (937) (all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 55.73/14.15 | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 55.73/14.15 | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, all_52_20) % 55.73/14.15 | | | | | | | | | | = all_52_20 & op(e3, all_52_24) = all_52_24 & % 55.73/14.15 | | | | | | | | | | op(e3, all_52_28) = all_52_28) | (all_52_4 = % 55.73/14.15 | | | | | | | | | | all_52_17 & all_52_5 = all_52_21 & all_52_6 = % 55.73/14.15 | | | | | | | | | | all_52_25 & all_52_7 = all_52_29 & op(e2, % 55.73/14.15 | | | | | | | | | | all_52_17) = all_52_17 & op(e2, all_52_21) = % 55.73/14.15 | | | | | | | | | | all_52_21 & op(e2, all_52_25) = all_52_25 & % 55.73/14.15 | | | | | | | | | | op(e2, all_52_29) = all_52_29) % 55.73/14.15 | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | BETA: splitting (937) gives: % 55.73/14.15 | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | (938) all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 55.73/14.15 | | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 55.73/14.15 | | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, all_52_20) % 55.73/14.15 | | | | | | | | | | | = all_52_20 & op(e3, all_52_24) = all_52_24 & % 55.73/14.15 | | | | | | | | | | | op(e3, all_52_28) = all_52_28 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | ALPHA: (938) implies: % 55.73/14.15 | | | | | | | | | | | (939) op(e3, all_52_24) = all_52_24 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | REDUCE: (927), (939) imply: % 55.73/14.15 | | | | | | | | | | | (940) op(e3, e2) = e2 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | REF_CLOSE: (6), (343), (915), (940) are inconsistent by % 55.73/14.15 | | | | | | | | | | | sub-proof #13. % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | (941) all_52_4 = all_52_17 & all_52_5 = all_52_21 & % 55.73/14.15 | | | | | | | | | | | all_52_6 = all_52_25 & all_52_7 = all_52_29 & % 55.73/14.15 | | | | | | | | | | | op(e2, all_52_17) = all_52_17 & op(e2, all_52_21) % 55.73/14.15 | | | | | | | | | | | = all_52_21 & op(e2, all_52_25) = all_52_25 & % 55.73/14.15 | | | | | | | | | | | op(e2, all_52_29) = all_52_29 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | ALPHA: (941) implies: % 55.73/14.15 | | | | | | | | | | | (942) op(e2, all_52_25) = all_52_25 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | REDUCE: (407), (942) imply: % 55.73/14.15 | | | | | | | | | | | (943) op(e2, all_20_1) = all_20_1 % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | BETA: splitting (230) gives: % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | (944) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 % 55.73/14.15 | | | | | | | | | | | | & op(e2, e3) = e1) % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | BETA: splitting (944) gives: % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | (945) all_58_0 = e1 & op(e3, e3) = e1 % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | REF_CLOSE: (922), (945) are inconsistent by sub-proof #12. % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | (946) all_58_2 = e1 & op(e2, e3) = e1 % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | ALPHA: (946) implies: % 55.73/14.15 | | | | | | | | | | | | | (947) op(e2, e3) = e1 % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | BETA: splitting (355) gives: % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | (948) ~ (op(e2, e3) = e1) % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | PRED_UNIFY: (947), (948) imply: % 55.73/14.15 | | | | | | | | | | | | | | (949) $false % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | CLOSE: (949) is inconsistent. % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | (950) all_52_20 = e1 % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | COMBINE_EQS: (273), (950) imply: % 55.73/14.15 | | | | | | | | | | | | | | (951) all_12_1 = e1 % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | SIMP: (951) implies: % 55.73/14.15 | | | | | | | | | | | | | | (952) all_12_1 = e1 % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | REDUCE: (511), (952) imply: % 55.73/14.15 | | | | | | | | | | | | | | (953) op(e1, e2) = e3 % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | BETA: splitting (346) gives: % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | (954) ~ (op(e1, e2) = e3) % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | PRED_UNIFY: (953), (954) imply: % 55.73/14.15 | | | | | | | | | | | | | | | (955) $false % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | CLOSE: (955) is inconsistent. % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | (956) all_52_25 = e3 % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | COMBINE_EQS: (407), (956) imply: % 55.73/14.15 | | | | | | | | | | | | | | | (957) all_20_1 = e3 % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | SIMP: (957) implies: % 55.73/14.15 | | | | | | | | | | | | | | | (958) all_20_1 = e3 % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | REDUCE: (943), (958) imply: % 55.73/14.15 | | | | | | | | | | | | | | | (959) op(e2, e3) = e3 % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | BETA: splitting (365) gives: % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | Case 1: % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | (960) ~ (op(e2, e3) = e3) % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | PRED_UNIFY: (959), (960) imply: % 55.73/14.15 | | | | | | | | | | | | | | | | (961) $false % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | CLOSE: (961) is inconsistent. % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | (962) all_12_1 = e3 % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | COMBINE_EQS: (952), (962) imply: % 55.73/14.15 | | | | | | | | | | | | | | | | (963) e3 = e1 % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | REDUCE: (8), (963) imply: % 55.73/14.15 | | | | | | | | | | | | | | | | (964) $false % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | | CLOSE: (964) is inconsistent. % 55.73/14.15 | | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | (965) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = % 55.73/14.15 | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | | REF_CLOSE: (6), (357), (358), (521), (926), (965) are % 55.73/14.15 | | | | | | | | | | | | inconsistent by sub-proof #11. % 55.73/14.15 | | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | | % 55.73/14.15 | | | | | | | | | | End of split % 55.73/14.15 | | | | | | | | | | % 55.73/14.15 | | | | | | | | | Case 2: % 55.73/14.15 | | | | | | | | | | % 55.73/14.16 | | | | | | | | | | (966) (all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 55.73/14.16 | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 55.73/14.16 | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, all_52_22) % 55.73/14.16 | | | | | | | | | | = all_52_22 & op(e1, all_52_26) = all_52_26 & % 55.73/14.16 | | | | | | | | | | op(e1, all_52_30) = all_52_30) | (all_52_12 = % 55.73/14.16 | | | | | | | | | | all_52_19 & all_52_13 = all_52_23 & all_52_14 = % 55.73/14.16 | | | | | | | | | | all_52_27 & all_52_15 = all_52_31 & op(e0, % 55.73/14.16 | | | | | | | | | | all_52_19) = all_52_19 & op(e0, all_52_23) = % 55.73/14.17 | | | | | | | | | | all_52_23 & op(e0, all_52_27) = all_52_27 & % 55.73/14.17 | | | | | | | | | | op(e0, all_52_31) = all_52_31) % 55.73/14.17 | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | BETA: splitting (966) gives: % 55.73/14.17 | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | (967) all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 55.73/14.17 | | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 55.73/14.17 | | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, all_52_22) % 55.73/14.17 | | | | | | | | | | | = all_52_22 & op(e1, all_52_26) = all_52_26 & % 55.73/14.17 | | | | | | | | | | | op(e1, all_52_30) = all_52_30 % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | ALPHA: (967) implies: % 55.73/14.17 | | | | | | | | | | | (968) op(e1, all_52_22) = all_52_22 % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | REDUCE: (909), (968) imply: % 55.73/14.17 | | | | | | | | | | | (969) op(e1, e3) = e3 % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | BETA: splitting (366) gives: % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | (970) ~ (op(e1, e3) = e3) % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | PRED_UNIFY: (969), (970) imply: % 55.73/14.17 | | | | | | | | | | | | (971) $false % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | CLOSE: (971) is inconsistent. % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | Case 2: % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | (972) all_44_1 = e3 % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | COMBINE_EQS: (926), (972) imply: % 55.73/14.17 | | | | | | | | | | | | (973) e3 = e2 % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | REDUCE: (9), (973) imply: % 55.73/14.17 | | | | | | | | | | | | (974) $false % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | CLOSE: (974) is inconsistent. % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | End of split % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | Case 2: % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | (975) all_52_12 = all_52_19 & all_52_13 = all_52_23 & % 55.73/14.17 | | | | | | | | | | | all_52_14 = all_52_27 & all_52_15 = all_52_31 & % 55.73/14.17 | | | | | | | | | | | op(e0, all_52_19) = all_52_19 & op(e0, all_52_23) % 55.73/14.17 | | | | | | | | | | | = all_52_23 & op(e0, all_52_27) = all_52_27 & % 55.73/14.17 | | | | | | | | | | | op(e0, all_52_31) = all_52_31 % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | ALPHA: (975) implies: % 55.73/14.17 | | | | | | | | | | | (976) op(e0, all_52_31) = all_52_31 % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | BETA: splitting (230) gives: % 55.73/14.17 | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | (977) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 % 55.73/14.17 | | | | | | | | | | | | & op(e2, e3) = e1) % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | BETA: splitting (977) gives: % 55.73/14.17 | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | (978) all_58_0 = e1 & op(e3, e3) = e1 % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | REF_CLOSE: (922), (978) are inconsistent by sub-proof #12. % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | Case 2: % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | (979) all_58_2 = e1 & op(e2, e3) = e1 % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | ALPHA: (979) implies: % 55.73/14.17 | | | | | | | | | | | | | (980) all_58_2 = e1 % 55.73/14.17 | | | | | | | | | | | | | (981) op(e2, e3) = e1 % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | BETA: splitting (326) gives: % 55.73/14.17 | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | (982) ~ (op(e1, e1) = e3) % 55.73/14.17 | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | BETA: splitting (91) gives: % 55.73/14.17 | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | (983) ~ (all_44_1 = e2) % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | REDUCE: (926), (983) imply: % 55.73/14.17 | | | | | | | | | | | | | | | (984) $false % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | CLOSE: (984) is inconsistent. % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | Case 2: % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | (985) ~ (all_44_0 = e0) & op(e2, e2) = all_44_0 & % 55.73/14.17 | | | | | | | | | | | | | | | $i(all_44_0) % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | ALPHA: (985) implies: % 55.73/14.17 | | | | | | | | | | | | | | | (986) ~ (all_44_0 = e0) % 55.73/14.17 | | | | | | | | | | | | | | | (987) op(e2, e2) = all_44_0 % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 55.73/14.17 | | | | | | | | | | | | | | | % 55.73/14.17 | | | | | | | | | | | | | | | Case 1: % 55.73/14.17 | | | | | | | | | | | | | | | | % 55.93/14.17 | | | | | | | | | | | | | | | | (988) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 % 55.93/14.17 | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 55.93/14.18 | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | BETA: splitting (988) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | (989) all_58_4 = e3 & op(e3, e1) = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | ALPHA: (989) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | (990) all_58_4 = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | (991) ~ (op(e2, e3) = e1) % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | PRED_UNIFY: (981), (991) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | (992) $false % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | CLOSE: (992) is inconsistent. % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | (993) all_52_20 = e1 % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (993) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | (994) all_12_1 = e1 % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | SIMP: (994) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | (995) all_12_1 = e1 % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | REDUCE: (934), (995) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | (996) ~ (e2 = e1) % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | REDUCE: (511), (995) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | (997) op(e1, e2) = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (998) ~ (op(e1, e2) = e3) % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (997), (998) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (999) $false % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | CLOSE: (999) is inconsistent. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1000) all_52_25 = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1000) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1001) all_20_1 = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | SIMP: (1001) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1002) all_20_1 = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | REDUCE: (515), (1002) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1003) op(e3, e1) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | (1004) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1004) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1005) all_58_0 = e2 & op(e3, e3) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (936), (1005) are inconsistent by sub-proof #10. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1006) all_58_1 = e2 & op(e3, e2) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1006) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1007) op(e3, e2) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (343), (915), (1007) are inconsistent by % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | sub-proof #13. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | (1008) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1008) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1009) all_58_4 = e2 & op(e3, e1) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1009) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1010) all_58_4 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (990), (1010) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1011) e3 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | SIMP: (1011) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1012) e3 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1012) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1013) $false % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1013) is inconsistent. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1014) all_58_9 = e2 & op(e3, e0) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1014) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | (1015) op(e3, e0) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | (1016) ~ (op(e3, e1) = e2) % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1003), (1016) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | (1017) $false % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1017) is inconsistent. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | (1018) all_56_2 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (1018) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | (1019) all_26_1 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (1019) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | (1020) ~ (all_34_1 = e2) % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (426), (1015), (1020) are inconsistent by % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | End of split % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | (1021) all_58_5 = e3 & op(e2, e1) = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | ALPHA: (1021) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | (1022) all_58_5 = e3 % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | (1023) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | BETA: splitting (1023) gives: % 55.93/14.18 | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1024) all_58_0 = e2 & op(e3, e3) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (936), (1024) are inconsistent by sub-proof #10. % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1025) all_58_2 = e2 & op(e2, e3) = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | ALPHA: (1025) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1026) all_58_2 = e2 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (980), (1026) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1027) e2 = e1 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | SIMP: (1027) implies: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1028) e2 = e1 % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1028) imply: % 55.93/14.18 | | | | | | | | | | | | | | | | | | | (1029) $false % 55.93/14.18 | | | | | | | | | | | | | | | | | | | % 55.93/14.18 | | | | | | | | | | | | | | | | | | | CLOSE: (1029) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | End of split % 55.93/14.19 | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | (1030) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = % 55.93/14.19 | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 55.93/14.19 | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | BETA: splitting (1030) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | (1031) all_58_6 = e2 & op(e1, e3) = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | ALPHA: (1031) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | (1032) all_58_6 = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1033) ~ (op(e2, e3) = e1) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (981), (1033) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1034) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | CLOSE: (1034) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1035) all_52_20 = e1 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (1035) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1036) all_12_1 = e1 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | SIMP: (1036) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1037) all_12_1 = e1 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | REDUCE: (457), (1037) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1038) ~ (all_6_1 = e1) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | REDUCE: (511), (1037) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | (1039) op(e1, e2) = e3 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1040) ~ (op(e1, e2) = e3) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1039), (1040) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1041) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1041) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1042) all_52_25 = e3 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1042) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1043) all_20_1 = e3 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | SIMP: (1043) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1044) all_20_1 = e3 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (484), (1044) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1045) ~ (all_28_1 = e3) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (515), (1044) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | (1046) op(e3, e1) = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1047) ~ (op(e3, e1) = e2) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1046), (1047) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1048) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1048) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1049) all_56_2 = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (1049) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1050) all_26_1 = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1050) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1051) all_26_1 = e2 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (1051) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1052) ~ (all_34_1 = e2) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (911), (1051) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | (1053) ~ (e3 = e2) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | (1054) ~ (all_20_1 = e3) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1044), (1054) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | (1055) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1055) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ (all_20_0 = e0) & op(e3, e3) = all_20_0 & % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1056) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | (1057) ~ (all_20_0 = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | (1058) op(e3, e3) = all_20_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1059) ~ (all_26_1 = e2) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1051), (1059) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1060) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1060) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1061) ~ (all_26_0 = e0) & op(e2, e2) = all_26_0 & % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1062) op(e2, e2) = all_26_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_21, % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e2, e2, simplifying with (111), (1062) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_52_21 = all_26_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_21, % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, e2, e2, simplifying with (111), (987) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_52_21 = all_44_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_16, % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e3, e3, simplifying with (116), (908) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_52_16 = all_10_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_10_0, % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (908) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_10_0 = e0 | ~ (op(e3, e3) = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_16, % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | all_20_0, e3, e3, simplifying with (116), (1058) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_52_16 = all_20_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1065), (1067) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_20_0 = all_10_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1068) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_20_0 = all_10_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1063), (1064) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_44_0 = all_26_0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (986), (1070) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1071) ~ (all_26_0 = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1057), (1069) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | (1072) ~ (all_10_0 = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1073) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1073) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_58_0 = e0 & op(e3, e3) = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) op(e3, e3) = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1066) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) ~ (op(e3, e3) = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1075), (1076) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1077) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_10_0 = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1072), (1078) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1079) is inconsistent. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_58_2 = e0 & op(e2, e3) = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (980), (1080) are inconsistent by sub-proof % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | #8. % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1081) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1081) gives: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_58_6 = e0 & op(e1, e3) = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1082) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_58_6 = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1032), (1083) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) e2 = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1084) implies: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) e2 = e0 % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1085) imply: % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) $false % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.19 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1086) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_58_12 = e0 & op(e0, e3) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1087) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_58_12 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1089) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_58_12 = e3 & op(e0, e3) = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1090) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_58_12 = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1088), (1091) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) e3 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1092) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1093) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_58_13 = e3 & op(e0, e2) = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1094) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) op(e0, e2) = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) ~ (op(e0, e2) = e3) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1095), (1096) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1097) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_54_7 = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (441), (1098) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_28_1 = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1045), (1099) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1100) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1101) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_58_14 = e3 & op(e0, e1) = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (117), (216), (244), (293), (297), (309), % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316), (340), (358), (390), (440), (444), (502), % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516), (521), (919), (976), (1102) are % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_58_15 = e3 & op(e0, e0) = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_58_15 = e3 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_58_2 = e0 & op(e2, e3) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (980), (1106) are inconsistent by sub-proof % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #8. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_58_3 = e0 & op(e2, e2) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1107) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) op(e2, e2) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) ~ (op(e2, e2) = e0) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1108), (1109) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1110) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_52_21 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1063), (1111) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_26_0 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1112) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_26_0 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1071), (1113) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1114) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1115) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_58_5 = e0 & op(e2, e1) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1116) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_58_5 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1022), (1117) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) e3 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1118) imply: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) $false % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1119) is inconsistent. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_58_10 = e0 & op(e2, e0) = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1120) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_58_10 = e0 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1122) gives: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_58_9 = e2 & op(e3, e0) = e2 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1123) implies: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) op(e3, e0) = e2 % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (426), (1052), (1124) are inconsistent by % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9. % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) all_58_10 = e2 & op(e2, e0) = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1125) implies: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_58_10 = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1121), (1126) imply: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) e2 = e0 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1127) imply: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) $false % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1128) is inconsistent. % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1129) gives: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_58_11 = e2 & op(e1, e0) = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1130) implies: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) op(e1, e0) = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (302), (932), (1131) are inconsistent by sub-proof % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #23. % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_58_15 = e2 & op(e0, e0) = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_58_15 = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1104), (1133) imply: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) e3 = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1134) imply: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) $false % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1135) is inconsistent. % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | (1136) all_58_12 = e2 & op(e0, e3) = e2 % 55.93/14.21 | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (363), (523), (1136) are inconsistent by sub-proof % 55.93/14.21 | | | | | | | | | | | | | | | | | | | #16. % 55.93/14.21 | | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | (1137) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = % 55.93/14.21 | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 55.93/14.21 | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | BETA: splitting (1137) gives: % 55.93/14.21 | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | Case 1: % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | (1138) all_58_8 = e3 & op(e1, e1) = e3 % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | ALPHA: (1138) implies: % 55.93/14.21 | | | | | | | | | | | | | | | | | (1139) op(e1, e1) = e3 % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | PRED_UNIFY: (982), (1139) imply: % 55.93/14.21 | | | | | | | | | | | | | | | | | (1140) $false % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | CLOSE: (1140) is inconsistent. % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | (1141) all_58_14 = e3 & op(e0, e1) = e3 % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (117), (216), (244), (293), (297), (309), % 55.93/14.21 | | | | | | | | | | | | | | | | | (316), (340), (358), (390), (440), (444), (502), % 55.93/14.21 | | | | | | | | | | | | | | | | | (516), (521), (919), (976), (1141) are % 55.93/14.21 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 55.93/14.21 | | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | (1142) all_54_10 = e3 % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | COMBINE_EQS: (388), (1142) imply: % 55.93/14.21 | | | | | | | | | | | | | | (1143) all_52_26 = e3 % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | SIMP: (1143) implies: % 55.93/14.21 | | | | | | | | | | | | | | (1144) all_52_26 = e3 % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | REDUCE: (910), (1144) imply: % 55.93/14.21 | | | | | | | | | | | | | | (1145) $false % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | | CLOSE: (1145) is inconsistent. % 55.93/14.21 | | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | (1146) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = % 55.93/14.21 | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 55.93/14.21 | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | | REF_CLOSE: (6), (357), (358), (521), (926), (1146) are % 55.93/14.21 | | | | | | | | | | | | inconsistent by sub-proof #11. % 55.93/14.21 | | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | | % 55.93/14.21 | | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | | % 55.93/14.21 | | | | | | | | | End of split % 55.93/14.21 | | | | | | | | | % 55.93/14.21 | | | | | | | | Case 2: % 55.93/14.21 | | | | | | | | | % 55.93/14.21 | | | | | | | | | (1147) op(e3, e3) = e2 % 55.93/14.21 | | | | | | | | | % 55.93/14.21 | | | | | | | | | REF_CLOSE: (359), (369), (928), (1147) are inconsistent by % 55.93/14.21 | | | | | | | | | sub-proof #6. % 55.93/14.21 | | | | | | | | | % 55.93/14.21 | | | | | | | | End of split % 55.93/14.21 | | | | | | | | % 55.93/14.21 | | | | | | | End of split % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | Case 2: % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | | (1148) all_56_0 = e1 % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | | COMBINE_EQS: (290), (1148) imply: % 55.93/14.21 | | | | | | | (1149) all_52_16 = e1 % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | | REDUCE: (918), (1149) imply: % 55.93/14.21 | | | | | | | (1150) $false % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | | CLOSE: (1150) is inconsistent. % 55.93/14.21 | | | | | | | % 55.93/14.21 | | | | | | End of split % 55.93/14.21 | | | | | | % 55.93/14.21 | | | | | End of split % 55.93/14.21 | | | | | % 55.93/14.21 | | | | End of split % 55.93/14.21 | | | | % 55.93/14.21 | | | Case 2: % 55.93/14.21 | | | | % 55.93/14.21 | | | | (1151) all_8_1 = e2 % 55.93/14.21 | | | | % 55.93/14.21 | | | | COMBINE_EQS: (437), (1151) imply: % 55.93/14.21 | | | | (1152) all_6_1 = e2 % 55.93/14.21 | | | | % 55.93/14.21 | | | | SIMP: (1152) implies: % 55.93/14.21 | | | | (1153) all_6_1 = e2 % 55.93/14.21 | | | | % 55.93/14.21 | | | | REDUCE: (517), (1153) imply: % 55.93/14.21 | | | | (1154) op(e2, e0) = e3 % 55.93/14.21 | | | | % 55.93/14.22 | | | | REF_CLOSE: (304), (330), (423), (432), (513), (520), (1154) are % 55.93/14.22 | | | | inconsistent by sub-proof #21. % 55.93/14.22 | | | | % 55.93/14.22 | | | End of split % 55.93/14.22 | | | % 55.93/14.22 | | Case 2: % 55.93/14.22 | | | % 55.93/14.22 | | | (1155) all_6_1 = e1 % 55.93/14.22 | | | (1156) ~ (all_6_0 = e2) & op(e1, e1) = all_6_0 & $i(all_6_0) % 55.93/14.22 | | | % 55.93/14.22 | | | ALPHA: (1156) implies: % 55.93/14.22 | | | (1157) ~ (all_6_0 = e2) % 55.93/14.22 | | | (1158) op(e1, e1) = all_6_0 % 55.93/14.22 | | | % 55.93/14.22 | | | COMBINE_EQS: (437), (1155) imply: % 55.93/14.22 | | | (1159) all_8_1 = e1 % 55.93/14.22 | | | % 55.93/14.22 | | | COMBINE_EQS: (403), (1155) imply: % 55.93/14.22 | | | (1160) all_52_28 = e1 % 55.93/14.22 | | | % 55.93/14.22 | | | REDUCE: (517), (1155) imply: % 55.93/14.22 | | | (1161) op(e1, e0) = e3 % 55.93/14.22 | | | % 55.93/14.22 | | | BETA: splitting (305) gives: % 55.93/14.22 | | | % 55.93/14.22 | | | Case 1: % 55.93/14.22 | | | | % 55.93/14.22 | | | | (1162) ~ (op(e1, e0) = e3) % 55.93/14.22 | | | | % 55.93/14.22 | | | | PRED_UNIFY: (1161), (1162) imply: % 55.93/14.22 | | | | (1163) $false % 55.93/14.22 | | | | % 55.93/14.22 | | | | CLOSE: (1163) is inconsistent. % 55.93/14.22 | | | | % 55.93/14.22 | | | Case 2: % 55.93/14.22 | | | | % 55.93/14.22 | | | | (1164) all_14_1 = e3 % 55.93/14.22 | | | | % 55.93/14.22 | | | | COMBINE_EQS: (420), (1164) imply: % 55.93/14.22 | | | | (1165) all_52_27 = e3 % 55.93/14.22 | | | | % 55.93/14.22 | | | | COMBINE_EQS: (390), (1164) imply: % 55.93/14.22 | | | | (1166) all_54_14 = e3 % 55.93/14.22 | | | | % 55.93/14.22 | | | | REDUCE: (500), (1164) imply: % 55.93/14.22 | | | | (1167) ~ (all_52_26 = e3) % 55.93/14.22 | | | | % 55.93/14.22 | | | | REDUCE: (465), (1164) imply: % 55.93/14.22 | | | | (1168) ~ (all_22_1 = e3) % 55.93/14.22 | | | | % 55.93/14.22 | | | | REDUCE: (487), (1164) imply: % 55.93/14.22 | | | | (1169) ~ (all_20_1 = e3) % 55.93/14.22 | | | | % 55.93/14.22 | | | | REDUCE: (516), (1164) imply: % 55.93/14.22 | | | | (1170) op(e3, e1) = e0 % 55.93/14.22 | | | | % 55.93/14.22 | | | | BETA: splitting (311) gives: % 55.93/14.22 | | | | % 55.93/14.22 | | | | Case 1: % 55.93/14.22 | | | | | % 55.93/14.22 | | | | | (1171) ~ (op(all_52_27, e1) = e1) % 55.93/14.22 | | | | | % 55.93/14.22 | | | | | REDUCE: (1165), (1171) imply: % 55.93/14.22 | | | | | (1172) ~ (op(e3, e1) = e1) % 55.93/14.22 | | | | | % 55.93/14.22 | | | | | BETA: splitting (307) gives: % 55.93/14.22 | | | | | % 55.93/14.22 | | | | | Case 1: % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | (1173) ~ (op(e3, e1) = e0) % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | PRED_UNIFY: (1170), (1173) imply: % 55.93/14.22 | | | | | | (1174) $false % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | CLOSE: (1174) is inconsistent. % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | Case 2: % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | (1175) all_52_18 = e0 % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | COMBINE_EQS: (411), (1175) imply: % 55.93/14.22 | | | | | | (1176) all_26_1 = e0 % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | SIMP: (1176) implies: % 55.93/14.22 | | | | | | (1177) all_26_1 = e0 % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | REDUCE: (454), (1177) imply: % 55.93/14.22 | | | | | | (1178) ~ (all_52_16 = e0) % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | REDUCE: (493), (1177) imply: % 55.93/14.22 | | | | | | (1179) ~ (all_52_26 = e0) % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | REDUCE: (495), (1177) imply: % 55.93/14.22 | | | | | | (1180) ~ (all_34_1 = e0) % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | REDUCE: (477), (1177) imply: % 55.93/14.22 | | | | | | (1181) ~ (all_4_1 = e0) % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | BETA: splitting (130) gives: % 55.93/14.22 | | | | | | % 55.93/14.22 | | | | | | Case 1: % 55.93/14.22 | | | | | | | % 55.93/14.22 | | | | | | | (1182) (all_52_0 = all_52_16 & all_52_1 = all_52_20 & all_52_2 % 55.93/14.22 | | | | | | | = all_52_24 & all_52_3 = all_52_28 & op(e3, all_52_16) % 55.93/14.22 | | | | | | | = all_52_16 & op(e3, all_52_20) = all_52_20 & op(e3, % 55.93/14.22 | | | | | | | all_52_24) = all_52_24 & op(e3, all_52_28) = % 55.93/14.22 | | | | | | | all_52_28) | (all_52_4 = all_52_17 & all_52_5 = % 55.93/14.22 | | | | | | | all_52_21 & all_52_6 = all_52_25 & all_52_7 = % 55.93/14.22 | | | | | | | all_52_29 & op(e2, all_52_17) = all_52_17 & op(e2, % 55.93/14.22 | | | | | | | all_52_21) = all_52_21 & op(e2, all_52_25) = % 55.93/14.22 | | | | | | | all_52_25 & op(e2, all_52_29) = all_52_29) % 55.93/14.22 | | | | | | | % 55.93/14.22 | | | | | | | BETA: splitting (1182) gives: % 55.93/14.22 | | | | | | | % 55.93/14.22 | | | | | | | Case 1: % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | | (1183) all_52_0 = all_52_16 & all_52_1 = all_52_20 & all_52_2 % 55.93/14.22 | | | | | | | | = all_52_24 & all_52_3 = all_52_28 & op(e3, all_52_16) % 55.93/14.22 | | | | | | | | = all_52_16 & op(e3, all_52_20) = all_52_20 & op(e3, % 55.93/14.22 | | | | | | | | all_52_24) = all_52_24 & op(e3, all_52_28) = % 55.93/14.22 | | | | | | | | all_52_28 % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | | ALPHA: (1183) implies: % 55.93/14.22 | | | | | | | | (1184) op(e3, all_52_28) = all_52_28 % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | | REDUCE: (1160), (1184) imply: % 55.93/14.22 | | | | | | | | (1185) op(e3, e1) = e1 % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | | PRED_UNIFY: (1172), (1185) imply: % 55.93/14.22 | | | | | | | | (1186) $false % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | | CLOSE: (1186) is inconsistent. % 55.93/14.22 | | | | | | | | % 55.93/14.22 | | | | | | | Case 2: % 55.93/14.22 | | | | | | | | % 55.93/14.24 | | | | | | | | (1187) all_52_4 = all_52_17 & all_52_5 = all_52_21 & all_52_6 % 55.93/14.24 | | | | | | | | = all_52_25 & all_52_7 = all_52_29 & op(e2, all_52_17) % 55.93/14.24 | | | | | | | | = all_52_17 & op(e2, all_52_21) = all_52_21 & op(e2, % 55.93/14.24 | | | | | | | | all_52_25) = all_52_25 & op(e2, all_52_29) = % 55.93/14.24 | | | | | | | | all_52_29 % 55.93/14.24 | | | | | | | | % 55.93/14.24 | | | | | | | | ALPHA: (1187) implies: % 55.93/14.24 | | | | | | | | (1188) op(e2, all_52_21) = all_52_21 % 55.93/14.24 | | | | | | | | (1189) op(e2, all_52_17) = all_52_17 % 55.93/14.24 | | | | | | | | % 55.93/14.24 | | | | | | | | REDUCE: (285), (1189) imply: % 55.93/14.24 | | | | | | | | (1190) op(e2, all_4_1) = all_4_1 % 55.93/14.24 | | | | | | | | % 55.93/14.24 | | | | | | | | BETA: splitting (349) gives: % 55.93/14.24 | | | | | | | | % 55.93/14.24 | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | % 55.93/14.24 | | | | | | | | | (1191) ~ (op(e3, e3) = e0) % 55.93/14.24 | | | | | | | | | % 55.93/14.24 | | | | | | | | | BETA: splitting (327) gives: % 55.93/14.24 | | | | | | | | | % 55.93/14.24 | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | (1192) ~ (op(e1, e1) = e3) % 55.93/14.24 | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | BETA: splitting (229) gives: % 55.93/14.24 | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | (1193) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 % 55.93/14.24 | | | | | | | | | | | & op(e3, e2) = e0) % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | BETA: splitting (1193) gives: % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | (1194) all_58_0 = e0 & op(e3, e3) = e0 % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | REF_CLOSE: (1191), (1194) are inconsistent by sub-proof #5. % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | (1195) all_58_1 = e0 & op(e3, e2) = e0 % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | ALPHA: (1195) implies: % 55.93/14.24 | | | | | | | | | | | | (1196) op(e3, e2) = e0 % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | REF_CLOSE: (330), (423), (520), (1196) are inconsistent by % 55.93/14.24 | | | | | | | | | | | | sub-proof #22. % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | End of split % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | (1197) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 % 55.93/14.24 | | | | | | | | | | | & op(e3, e0) = e0) % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | BETA: splitting (1197) gives: % 55.93/14.24 | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | (1198) all_58_4 = e0 & op(e3, e1) = e0 % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | ALPHA: (1198) implies: % 55.93/14.24 | | | | | | | | | | | | (1199) all_58_4 = e0 % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | BETA: splitting (222) gives: % 55.93/14.24 | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | (1200) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 % 55.93/14.24 | | | | | | | | | | | | | & op(e1, e2) = e3) % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | BETA: splitting (1200) gives: % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | (1201) all_58_6 = e3 & op(e1, e3) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | ALPHA: (1201) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1202) op(e1, e3) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REF_CLOSE: (366), (433), (1168), (1202) are inconsistent by % 55.93/14.24 | | | | | | | | | | | | | | sub-proof #4. % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | (1203) all_58_7 = e3 & op(e1, e2) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | ALPHA: (1203) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1204) op(e1, e2) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REF_CLOSE: (346), (407), (1169), (1204) are inconsistent by % 55.93/14.24 | | | | | | | | | | | | | | sub-proof #26. % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | End of split % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | (1205) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = % 55.93/14.24 | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | BETA: splitting (1205) gives: % 55.93/14.24 | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | (1206) all_58_8 = e3 & op(e1, e1) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REF_CLOSE: (1192), (1206) are inconsistent by sub-proof #3. % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | (1207) all_58_11 = e3 & op(e1, e0) = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | ALPHA: (1207) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1208) all_58_11 = e3 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_26, % 55.93/14.24 | | | | | | | | | | | | | | all_6_0, e1, e1, simplifying with (106), (1158) % 55.93/14.24 | | | | | | | | | | | | | | gives: % 55.93/14.24 | | | | | | | | | | | | | | (1209) all_52_26 = all_6_0 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | COMBINE_EQS: (254), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1210) all_56_10 = all_6_0 % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REDUCE: (464), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1211) ~ (all_22_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | SIMP: (1211) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1212) ~ (all_22_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REDUCE: (486), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1213) ~ (all_20_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | SIMP: (1213) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1214) ~ (all_20_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REDUCE: (497), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1215) ~ (all_10_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | SIMP: (1215) implies: % 55.93/14.24 | | | | | | | | | | | | | | (1216) ~ (all_10_1 = all_6_0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REDUCE: (1167), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1217) ~ (all_6_0 = e3) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | REDUCE: (1179), (1209) imply: % 55.93/14.24 | | | | | | | | | | | | | | (1218) ~ (all_6_0 = e0) % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | BETA: splitting (208) gives: % 55.93/14.24 | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | (1219) all_56_10 = e3 % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | COMBINE_EQS: (1210), (1219) imply: % 55.93/14.24 | | | | | | | | | | | | | | | (1220) all_6_0 = e3 % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | SIMP: (1220) implies: % 55.93/14.24 | | | | | | | | | | | | | | | (1221) all_6_0 = e3 % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | REDUCE: (1217), (1221) imply: % 55.93/14.24 | | | | | | | | | | | | | | | (1222) $false % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | CLOSE: (1222) is inconsistent. % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | (1223) ~ (all_56_10 = e3) % 55.93/14.24 | | | | | | | | | | | | | | | (1224) all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0 % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | BETA: splitting (1224) gives: % 55.93/14.24 | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | (1225) all_56_10 = e2 % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | COMBINE_EQS: (1210), (1225) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | (1226) all_6_0 = e2 % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | REDUCE: (1157), (1226) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | (1227) $false % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | CLOSE: (1227) is inconsistent. % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | (1228) ~ (all_56_10 = e2) % 55.93/14.24 | | | | | | | | | | | | | | | | (1229) all_56_10 = e1 | all_56_10 = e0 % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | BETA: splitting (1229) gives: % 55.93/14.24 | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | (1230) all_56_10 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1210), (1230) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1231) all_6_0 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | REDUCE: (1212), (1231) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1232) ~ (all_22_1 = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | REDUCE: (1214), (1231) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1233) ~ (all_20_1 = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | REDUCE: (1216), (1231) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1234) ~ (all_10_1 = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | REDUCE: (1217), (1231) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1235) ~ (e3 = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | REDUCE: (1157), (1231) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | (1236) ~ (e2 = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 55.93/14.24 | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | (1237) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | BETA: splitting (1237) gives: % 55.93/14.24 | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | (1238) all_58_6 = e1 & op(e1, e3) = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | ALPHA: (1238) implies: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | (1239) op(e1, e3) = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1240) ~ (op(e1, e3) = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1239), (1240) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1241) $false % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | CLOSE: (1241) is inconsistent. % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1242) all_54_2 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (384), (1242) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1243) all_22_1 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | SIMP: (1243) implies: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1244) all_22_1 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | REDUCE: (1232), (1244) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1245) $false % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | CLOSE: (1245) is inconsistent. % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | (1246) all_58_7 = e1 & op(e1, e2) = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | ALPHA: (1246) implies: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | (1247) op(e1, e2) = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1248) ~ (op(e1, e2) = e1) % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1247), (1248) imply: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1249) $false % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | CLOSE: (1249) is inconsistent. % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | (1250) all_52_25 = e1 % 55.93/14.24 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1250) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1251) all_20_1 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | SIMP: (1251) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1252) all_20_1 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (1233), (1252) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1253) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (1253) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | (1254) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = % 55.93/14.25 | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 55.93/14.25 | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | BETA: splitting (1254) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1255) all_58_8 = e1 & op(e1, e1) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | ALPHA: (1255) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1256) all_58_8 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1257) ~ (all_10_1 = e3) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1258) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1258) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1259) all_58_4 = e3 & op(e3, e1) = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1259) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1260) all_58_4 = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1199), (1260) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1261) e3 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1261) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1262) e3 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1262) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1263) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1263) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1264) all_58_5 = e3 & op(e2, e1) = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1264) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1265) op(e2, e1) = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (325), (412), (1257), (1265) are inconsistent by % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | sub-proof #25. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1266) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1266) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1267) all_58_8 = e3 & op(e1, e1) = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1192), (1267) are inconsistent by sub-proof #3. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1268) all_58_14 = e3 & op(e0, e1) = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1268) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | (1269) all_58_14 = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | (1270) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1270) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_58_4 = e2 & op(e3, e1) = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1271) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1272) all_58_4 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1199), (1272) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1273) e2 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1273) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1274) e2 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1274) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1275) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1275) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_58_5 = e2 & op(e2, e1) = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1276) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1277) op(e2, e1) = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1278) ~ (op(e2, e1) = e2) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1277), (1278) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1279) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1279) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1280) all_52_22 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (1280) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1281) all_10_1 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1281) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_10_1 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (1282) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1283) op(e2, e2) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) ~ (op(e2, e2) = e1) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1283), (1284) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1285) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) all_56_5 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1286) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) all_52_21 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1287) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) all_52_21 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1188), (1288) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) op(e2, e1) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (314), (1234), (1289) are inconsistent by % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | (1290) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1290) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1291) all_58_8 = e2 & op(e1, e1) = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1291) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1292) all_58_8 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1256), (1292) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1293) e2 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1293) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1294) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1294) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1295) all_58_14 = e2 & op(e0, e1) = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1295) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_58_14 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1269), (1296) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1297) e3 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1297) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1298) e3 = e2 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1298) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | (1299) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1299) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1300) all_10_1 = e3 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (1300) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | (1301) op(e3, e2) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1302) ~ (op(e3, e2) = e1) % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1301), (1302) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1303) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1303) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1304) all_4_1 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1190), (1304) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | (1305) op(e2, e1) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (314), (1234), (1305) are inconsistent by % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1306) all_58_11 = e1 & op(e1, e0) = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | ALPHA: (1306) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1307) all_58_11 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1307) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1308) e3 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | SIMP: (1308) implies: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1309) e3 = e1 % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1309) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | | | (1310) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | | CLOSE: (1310) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | (1311) all_56_10 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1210), (1311) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | (1312) all_6_0 = e0 % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | REDUCE: (1218), (1312) imply: % 55.93/14.25 | | | | | | | | | | | | | | | | | (1313) $false % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | | CLOSE: (1313) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | (1314) all_58_9 = e0 & op(e3, e0) = e0 % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | ALPHA: (1314) implies: % 55.93/14.25 | | | | | | | | | | | | (1315) op(e3, e0) = e0 % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | BETA: splitting (291) gives: % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | (1316) ~ (op(e3, e0) = e0) % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | PRED_UNIFY: (1315), (1316) imply: % 55.93/14.25 | | | | | | | | | | | | | (1317) $false % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | CLOSE: (1317) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | (1318) all_34_1 = e0 % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | REDUCE: (1180), (1318) imply: % 55.93/14.25 | | | | | | | | | | | | | (1319) $false % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | | CLOSE: (1319) is inconsistent. % 55.93/14.25 | | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | | % 55.93/14.25 | | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | (1320) op(e1, e1) = e3 % 55.93/14.25 | | | | | | | | | | % 55.93/14.25 | | | | | | | | | | REF_CLOSE: (326), (388), (1167), (1320) are inconsistent by % 55.93/14.25 | | | | | | | | | | sub-proof #18. % 55.93/14.25 | | | | | | | | | | % 55.93/14.25 | | | | | | | | | End of split % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | Case 2: % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | | (1321) all_56_0 = e0 % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | | COMBINE_EQS: (290), (1321) imply: % 55.93/14.25 | | | | | | | | | (1322) all_52_16 = e0 % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | | REDUCE: (1178), (1322) imply: % 55.93/14.25 | | | | | | | | | (1323) $false % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | | CLOSE: (1323) is inconsistent. % 55.93/14.25 | | | | | | | | | % 55.93/14.25 | | | | | | | | End of split % 55.93/14.25 | | | | | | | | % 55.93/14.25 | | | | | | | End of split % 55.93/14.25 | | | | | | | % 55.93/14.25 | | | | | | Case 2: % 55.93/14.25 | | | | | | | % 55.93/14.25 | | | | | | | (1324) (all_52_8 = all_52_18 & all_52_9 = all_52_22 & all_52_10 % 55.93/14.25 | | | | | | | = all_52_26 & all_52_11 = all_52_30 & op(e1, % 55.93/14.25 | | | | | | | all_52_18) = all_52_18 & op(e1, all_52_22) = % 55.93/14.25 | | | | | | | all_52_22 & op(e1, all_52_26) = all_52_26 & op(e1, % 55.93/14.25 | | | | | | | all_52_30) = all_52_30) | (all_52_12 = all_52_19 & % 55.93/14.25 | | | | | | | all_52_13 = all_52_23 & all_52_14 = all_52_27 & % 55.93/14.25 | | | | | | | all_52_15 = all_52_31 & op(e0, all_52_19) = all_52_19 % 55.93/14.25 | | | | | | | & op(e0, all_52_23) = all_52_23 & op(e0, all_52_27) = % 55.93/14.25 | | | | | | | all_52_27 & op(e0, all_52_31) = all_52_31) % 55.93/14.25 | | | | | | | % 55.93/14.25 | | | | | | | BETA: splitting (1324) gives: % 55.93/14.25 | | | | | | | % 55.93/14.25 | | | | | | | Case 1: % 55.93/14.25 | | | | | | | | % 55.93/14.25 | | | | | | | | (1325) all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 55.93/14.25 | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & op(e1, % 55.93/14.25 | | | | | | | | all_52_18) = all_52_18 & op(e1, all_52_22) = % 55.93/14.25 | | | | | | | | all_52_22 & op(e1, all_52_26) = all_52_26 & op(e1, % 55.93/14.25 | | | | | | | | all_52_30) = all_52_30 % 55.93/14.25 | | | | | | | | % 55.93/14.25 | | | | | | | | ALPHA: (1325) implies: % 55.93/14.26 | | | | | | | | (1326) op(e1, all_52_18) = all_52_18 % 55.93/14.26 | | | | | | | | % 55.93/14.26 | | | | | | | | REDUCE: (1175), (1326) imply: % 55.93/14.26 | | | | | | | | (1327) op(e1, e0) = e0 % 55.93/14.26 | | | | | | | | % 55.93/14.26 | | | | | | | | BETA: splitting (293) gives: % 55.93/14.26 | | | | | | | | % 55.93/14.26 | | | | | | | | Case 1: % 55.93/14.26 | | | | | | | | | % 55.93/14.26 | | | | | | | | | (1328) ~ (op(e1, e0) = e0) % 55.93/14.26 | | | | | | | | | % 55.93/14.26 | | | | | | | | | PRED_UNIFY: (1327), (1328) imply: % 55.93/14.26 | | | | | | | | | (1329) $false % 55.93/14.26 | | | | | | | | | % 55.93/14.26 | | | | | | | | | CLOSE: (1329) is inconsistent. % 55.93/14.26 | | | | | | | | | % 55.93/14.26 | | | | | | | | Case 2: % 55.93/14.26 | | | | | | | | | % 56.24/14.27 | | | | | | | | | (1330) all_54_14 = e0 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | COMBINE_EQS: (1166), (1330) imply: % 56.24/14.27 | | | | | | | | | (1331) e3 = e0 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | SIMP: (1331) implies: % 56.24/14.27 | | | | | | | | | (1332) e3 = e0 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | REDUCE: (7), (1332) imply: % 56.24/14.27 | | | | | | | | | (1333) $false % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | CLOSE: (1333) is inconsistent. % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | End of split % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | (1334) all_52_12 = all_52_19 & all_52_13 = all_52_23 & % 56.24/14.27 | | | | | | | | all_52_14 = all_52_27 & all_52_15 = all_52_31 & op(e0, % 56.24/14.27 | | | | | | | | all_52_19) = all_52_19 & op(e0, all_52_23) = % 56.24/14.27 | | | | | | | | all_52_23 & op(e0, all_52_27) = all_52_27 & op(e0, % 56.24/14.27 | | | | | | | | all_52_31) = all_52_31 % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | ALPHA: (1334) implies: % 56.24/14.27 | | | | | | | | (1335) op(e0, all_52_27) = all_52_27 % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | REDUCE: (1165), (1335) imply: % 56.24/14.27 | | | | | | | | (1336) op(e0, e3) = e3 % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | BETA: splitting (367) gives: % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | (1337) ~ (op(e0, e3) = e3) % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | PRED_UNIFY: (1336), (1337) imply: % 56.24/14.27 | | | | | | | | | (1338) $false % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | CLOSE: (1338) is inconsistent. % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | (1339) all_8_1 = e3 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | COMBINE_EQS: (1159), (1339) imply: % 56.24/14.27 | | | | | | | | | (1340) e3 = e1 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | SIMP: (1340) implies: % 56.24/14.27 | | | | | | | | | (1341) e3 = e1 % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | REDUCE: (8), (1341) imply: % 56.24/14.27 | | | | | | | | | (1342) $false % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | CLOSE: (1342) is inconsistent. % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | End of split % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | End of split % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | End of split % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | End of split % 56.24/14.27 | | | | | % 56.24/14.27 | | | | Case 2: % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | (1343) e1 = e0 % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | REDUCE: (4), (1343) imply: % 56.24/14.27 | | | | | (1344) $false % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | CLOSE: (1344) is inconsistent. % 56.24/14.27 | | | | | % 56.24/14.27 | | | | End of split % 56.24/14.27 | | | | % 56.24/14.27 | | | End of split % 56.24/14.27 | | | % 56.24/14.27 | | End of split % 56.24/14.27 | | % 56.24/14.27 | Case 2: % 56.24/14.27 | | % 56.24/14.27 | | (1345) all_4_1 = e0 % 56.24/14.27 | | (1346) ~ (all_4_0 = e1) & op(e0, e0) = all_4_0 & $i(all_4_0) % 56.24/14.27 | | % 56.24/14.27 | | ALPHA: (1346) implies: % 56.24/14.27 | | (1347) ~ (all_4_0 = e1) % 56.24/14.27 | | (1348) op(e0, e0) = all_4_0 % 56.24/14.27 | | % 56.24/14.27 | | COMBINE_EQS: (285), (1345) imply: % 56.24/14.27 | | (1349) all_52_17 = e0 % 56.24/14.27 | | % 56.24/14.27 | | REDUCE: (453), (1345) imply: % 56.24/14.27 | | (1350) ~ (all_52_16 = e0) % 56.24/14.27 | | % 56.24/14.27 | | REDUCE: (471), (1345) imply: % 56.24/14.27 | | (1351) ~ (all_52_21 = e0) % 56.24/14.27 | | % 56.24/14.27 | | REDUCE: (475), (1345) imply: % 56.24/14.27 | | (1352) ~ (all_28_1 = e0) % 56.24/14.27 | | % 56.24/14.27 | | REDUCE: (473), (1345) imply: % 56.24/14.27 | | (1353) ~ (all_20_1 = e0) % 56.24/14.27 | | % 56.24/14.27 | | REDUCE: (509), (1345) imply: % 56.24/14.27 | | (1354) op(e0, e3) = e2 % 56.24/14.27 | | % 56.24/14.27 | | BETA: splitting (362) gives: % 56.24/14.27 | | % 56.24/14.27 | | Case 1: % 56.24/14.27 | | | % 56.24/14.27 | | | (1355) ~ (op(e0, e3) = e2) % 56.24/14.27 | | | % 56.24/14.27 | | | PRED_UNIFY: (1354), (1355) imply: % 56.24/14.27 | | | (1356) $false % 56.24/14.27 | | | % 56.24/14.27 | | | CLOSE: (1356) is inconsistent. % 56.24/14.27 | | | % 56.24/14.27 | | Case 2: % 56.24/14.27 | | | % 56.24/14.27 | | | (1357) all_56_12 = e2 % 56.24/14.27 | | | % 56.24/14.27 | | | COMBINE_EQS: (248), (1357) imply: % 56.24/14.27 | | | (1358) all_6_1 = e2 % 56.24/14.27 | | | % 56.24/14.27 | | | COMBINE_EQS: (437), (1358) imply: % 56.24/14.27 | | | (1359) all_8_1 = e2 % 56.24/14.27 | | | % 56.24/14.27 | | | COMBINE_EQS: (403), (1358) imply: % 56.24/14.27 | | | (1360) all_52_28 = e2 % 56.24/14.27 | | | % 56.24/14.27 | | | REDUCE: (452), (1358) imply: % 56.24/14.27 | | | (1361) ~ (all_52_16 = e2) % 56.24/14.27 | | | % 56.24/14.27 | | | REDUCE: (469), (1358) imply: % 56.24/14.27 | | | (1362) ~ (all_52_31 = e2) % 56.24/14.27 | | | % 56.24/14.27 | | | REDUCE: (457), (1358) imply: % 56.24/14.27 | | | (1363) ~ (all_12_1 = e2) % 56.24/14.27 | | | % 56.24/14.27 | | | REDUCE: (517), (1358) imply: % 56.24/14.27 | | | (1364) op(e2, e0) = e3 % 56.24/14.27 | | | % 56.24/14.27 | | | BETA: splitting (43) gives: % 56.24/14.27 | | | % 56.24/14.27 | | | Case 1: % 56.24/14.27 | | | | % 56.24/14.27 | | | | (1365) ~ (all_8_1 = e2) % 56.24/14.27 | | | | % 56.24/14.27 | | | | REDUCE: (1359), (1365) imply: % 56.24/14.27 | | | | (1366) $false % 56.24/14.27 | | | | % 56.24/14.27 | | | | CLOSE: (1366) is inconsistent. % 56.24/14.27 | | | | % 56.24/14.27 | | | Case 2: % 56.24/14.27 | | | | % 56.24/14.27 | | | | (1367) ~ (all_8_0 = e1) & op(e2, e2) = all_8_0 & $i(all_8_0) % 56.24/14.27 | | | | % 56.24/14.27 | | | | ALPHA: (1367) implies: % 56.24/14.27 | | | | (1368) ~ (all_8_0 = e1) % 56.24/14.27 | | | | (1369) op(e2, e2) = all_8_0 % 56.24/14.27 | | | | % 56.24/14.27 | | | | BETA: splitting (331) gives: % 56.24/14.27 | | | | % 56.24/14.27 | | | | Case 1: % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | (1370) ~ (op(e2, e2) = e0) % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | BETA: splitting (304) gives: % 56.24/14.27 | | | | | % 56.24/14.27 | | | | | Case 1: % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | (1371) ~ (op(e2, e0) = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | PRED_UNIFY: (1364), (1371) imply: % 56.24/14.27 | | | | | | (1372) $false % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | CLOSE: (1372) is inconsistent. % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | Case 2: % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | (1373) all_48_1 = e3 % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | COMBINE_EQS: (432), (1373) imply: % 56.24/14.27 | | | | | | (1374) all_24_1 = e3 % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | COMBINE_EQS: (418), (1374) imply: % 56.24/14.27 | | | | | | (1375) all_52_23 = e3 % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | REDUCE: (482), (1374) imply: % 56.24/14.27 | | | | | | (1376) ~ (all_52_21 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | REDUCE: (506), (1374) imply: % 56.24/14.27 | | | | | | (1377) ~ (all_52_31 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | REDUCE: (504), (1374) imply: % 56.24/14.27 | | | | | | (1378) ~ (all_14_1 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | SIMP: (1378) implies: % 56.24/14.27 | | | | | | (1379) ~ (all_14_1 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | REDUCE: (499), (1374) imply: % 56.24/14.27 | | | | | | (1380) ~ (all_10_1 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | SIMP: (1380) implies: % 56.24/14.27 | | | | | | (1381) ~ (all_10_1 = e3) % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | BETA: splitting (97) gives: % 56.24/14.27 | | | | | | % 56.24/14.27 | | | | | | Case 1: % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | (1382) ~ (all_48_1 = e3) % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | REDUCE: (1373), (1382) imply: % 56.24/14.27 | | | | | | | (1383) $false % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | CLOSE: (1383) is inconsistent. % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | Case 2: % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | (1384) ~ (all_48_0 = e1) & op(e3, e3) = all_48_0 & % 56.24/14.27 | | | | | | | $i(all_48_0) % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | ALPHA: (1384) implies: % 56.24/14.27 | | | | | | | (1385) ~ (all_48_0 = e1) % 56.24/14.27 | | | | | | | (1386) op(e3, e3) = all_48_0 % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | BETA: splitting (350) gives: % 56.24/14.27 | | | | | | | % 56.24/14.27 | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | (1387) ~ (op(e3, e3) = e0) % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | BETA: splitting (359) gives: % 56.24/14.27 | | | | | | | | % 56.24/14.27 | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | (1388) ~ (op(e3, e3) = e2) % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | BETA: splitting (232) gives: % 56.24/14.27 | | | | | | | | | % 56.24/14.27 | | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | (1389) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 % 56.24/14.27 | | | | | | | | | | & op(e2, e3) = e2) % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | BETA: splitting (1389) gives: % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | (1390) all_58_0 = e2 & op(e3, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | REF_CLOSE: (1388), (1390) are inconsistent by sub-proof #10. % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | (1391) all_58_2 = e2 & op(e2, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | ALPHA: (1391) implies: % 56.24/14.27 | | | | | | | | | | | (1392) op(e2, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | BETA: splitting (360) gives: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | (1393) ~ (op(e2, e3) = e2) % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | PRED_UNIFY: (1392), (1393) imply: % 56.24/14.27 | | | | | | | | | | | | (1394) $false % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | CLOSE: (1394) is inconsistent. % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | (1395) all_52_20 = e2 % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | COMBINE_EQS: (273), (1395) imply: % 56.24/14.27 | | | | | | | | | | | | (1396) all_12_1 = e2 % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | SIMP: (1396) implies: % 56.24/14.27 | | | | | | | | | | | | (1397) all_12_1 = e2 % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | REDUCE: (1363), (1397) imply: % 56.24/14.27 | | | | | | | | | | | | (1398) $false % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | | CLOSE: (1398) is inconsistent. % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | End of split % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | End of split % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | (1399) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = % 56.24/14.27 | | | | | | | | | | e2 & op(e0, e3) = e2) % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | BETA: splitting (1399) gives: % 56.24/14.27 | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | (1400) all_58_6 = e2 & op(e1, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | ALPHA: (1400) implies: % 56.24/14.27 | | | | | | | | | | | (1401) op(e1, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | REF_CLOSE: (325), (361), (412), (514), (1381), (1401) are % 56.24/14.27 | | | | | | | | | | | inconsistent by sub-proof #24. % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | Case 2: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | (1402) all_58_12 = e2 & op(e0, e3) = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | ALPHA: (1402) implies: % 56.24/14.27 | | | | | | | | | | | (1403) all_58_12 = e2 % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | BETA: splitting (130) gives: % 56.24/14.27 | | | | | | | | | | | % 56.24/14.27 | | | | | | | | | | | Case 1: % 56.24/14.27 | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | (1404) (all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 56.24/14.28 | | | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 56.24/14.28 | | | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, % 56.24/14.28 | | | | | | | | | | | | all_52_20) = all_52_20 & op(e3, all_52_24) = % 56.24/14.28 | | | | | | | | | | | | all_52_24 & op(e3, all_52_28) = all_52_28) | % 56.24/14.28 | | | | | | | | | | | | (all_52_4 = all_52_17 & all_52_5 = all_52_21 & % 56.24/14.28 | | | | | | | | | | | | all_52_6 = all_52_25 & all_52_7 = all_52_29 & % 56.24/14.28 | | | | | | | | | | | | op(e2, all_52_17) = all_52_17 & op(e2, % 56.24/14.28 | | | | | | | | | | | | all_52_21) = all_52_21 & op(e2, all_52_25) = % 56.24/14.28 | | | | | | | | | | | | all_52_25 & op(e2, all_52_29) = all_52_29) % 56.24/14.28 | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | BETA: splitting (1404) gives: % 56.24/14.28 | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | Case 1: % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | (1405) all_52_0 = all_52_16 & all_52_1 = all_52_20 & % 56.24/14.28 | | | | | | | | | | | | | all_52_2 = all_52_24 & all_52_3 = all_52_28 & % 56.24/14.28 | | | | | | | | | | | | | op(e3, all_52_16) = all_52_16 & op(e3, all_52_20) % 56.24/14.28 | | | | | | | | | | | | | = all_52_20 & op(e3, all_52_24) = all_52_24 & % 56.24/14.28 | | | | | | | | | | | | | op(e3, all_52_28) = all_52_28 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | ALPHA: (1405) implies: % 56.24/14.28 | | | | | | | | | | | | | (1406) op(e3, all_52_28) = all_52_28 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | REDUCE: (1360), (1406) imply: % 56.24/14.28 | | | | | | | | | | | | | (1407) op(e3, e2) = e2 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | BETA: splitting (343) gives: % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | Case 1: % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | (1408) ~ (op(e3, e2) = e2) % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | PRED_UNIFY: (1407), (1408) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1409) $false % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | CLOSE: (1409) is inconsistent. % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | Case 2: % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | (1410) all_52_17 = e2 % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | COMBINE_EQS: (1349), (1410) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1411) e2 = e0 % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | REDUCE: (5), (1411) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1412) $false % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | CLOSE: (1412) is inconsistent. % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | End of split % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | Case 2: % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | (1413) all_52_4 = all_52_17 & all_52_5 = all_52_21 & % 56.24/14.28 | | | | | | | | | | | | | all_52_6 = all_52_25 & all_52_7 = all_52_29 & % 56.24/14.28 | | | | | | | | | | | | | op(e2, all_52_17) = all_52_17 & op(e2, all_52_21) % 56.24/14.28 | | | | | | | | | | | | | = all_52_21 & op(e2, all_52_25) = all_52_25 & % 56.24/14.28 | | | | | | | | | | | | | op(e2, all_52_29) = all_52_29 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | ALPHA: (1413) implies: % 56.24/14.28 | | | | | | | | | | | | | (1414) op(e2, all_52_17) = all_52_17 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | REDUCE: (1349), (1414) imply: % 56.24/14.28 | | | | | | | | | | | | | (1415) op(e2, e0) = e0 % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | BETA: splitting (292) gives: % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | Case 1: % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | (1416) ~ (op(e2, e0) = e0) % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | PRED_UNIFY: (1415), (1416) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1417) $false % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | CLOSE: (1417) is inconsistent. % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | Case 2: % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | (1418) all_24_1 = e0 % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | COMBINE_EQS: (1374), (1418) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1419) e3 = e0 % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | SIMP: (1419) implies: % 56.24/14.28 | | | | | | | | | | | | | | (1420) e3 = e0 % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | REDUCE: (7), (1420) imply: % 56.24/14.28 | | | | | | | | | | | | | | (1421) $false % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | | CLOSE: (1421) is inconsistent. % 56.24/14.28 | | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | | End of split % 56.24/14.28 | | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | | End of split % 56.24/14.28 | | | | | | | | | | | | % 56.24/14.28 | | | | | | | | | | | Case 2: % 56.24/14.28 | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | (1422) (all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 56.31/14.29 | | | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 56.31/14.29 | | | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, % 56.31/14.29 | | | | | | | | | | | | all_52_22) = all_52_22 & op(e1, all_52_26) = % 56.31/14.29 | | | | | | | | | | | | all_52_26 & op(e1, all_52_30) = all_52_30) | % 56.31/14.29 | | | | | | | | | | | | (all_52_12 = all_52_19 & all_52_13 = all_52_23 & % 56.31/14.29 | | | | | | | | | | | | all_52_14 = all_52_27 & all_52_15 = all_52_31 & % 56.31/14.29 | | | | | | | | | | | | op(e0, all_52_19) = all_52_19 & op(e0, % 56.31/14.29 | | | | | | | | | | | | all_52_23) = all_52_23 & op(e0, all_52_27) = % 56.31/14.29 | | | | | | | | | | | | all_52_27 & op(e0, all_52_31) = all_52_31) % 56.31/14.29 | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | BETA: splitting (1422) gives: % 56.31/14.29 | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | (1423) all_52_8 = all_52_18 & all_52_9 = all_52_22 & % 56.31/14.29 | | | | | | | | | | | | | all_52_10 = all_52_26 & all_52_11 = all_52_30 & % 56.31/14.29 | | | | | | | | | | | | | op(e1, all_52_18) = all_52_18 & op(e1, all_52_22) % 56.31/14.29 | | | | | | | | | | | | | = all_52_22 & op(e1, all_52_26) = all_52_26 & % 56.31/14.29 | | | | | | | | | | | | | op(e1, all_52_30) = all_52_30 % 56.31/14.29 | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | ALPHA: (1423) implies: % 56.31/14.29 | | | | | | | | | | | | | (1424) op(e1, all_52_30) = all_52_30 % 56.31/14.29 | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | REDUCE: (415), (1424) imply: % 56.31/14.29 | | | | | | | | | | | | | (1425) op(e1, all_16_1) = all_16_1 % 56.31/14.29 | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | BETA: splitting (227) gives: % 56.31/14.29 | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | (1426) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 % 56.31/14.29 | | | | | | | | | | | | | | & op(e2, e2) = e0) % 56.31/14.29 | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | BETA: splitting (1426) gives: % 56.31/14.29 | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | (1427) all_58_1 = e0 & op(e3, e2) = e0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | ALPHA: (1427) implies: % 56.31/14.29 | | | | | | | | | | | | | | | (1428) all_58_1 = e0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_31, % 56.31/14.29 | | | | | | | | | | | | | | | all_4_0, e0, e0, simplifying with (101), (1348) % 56.31/14.29 | | | | | | | | | | | | | | | gives: % 56.31/14.29 | | | | | | | | | | | | | | | (1429) all_52_31 = all_4_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_21, % 56.31/14.29 | | | | | | | | | | | | | | | all_8_0, e2, e2, simplifying with (111), (1369) % 56.31/14.29 | | | | | | | | | | | | | | | gives: % 56.31/14.29 | | | | | | | | | | | | | | | (1430) all_52_21 = all_8_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_16, % 56.31/14.29 | | | | | | | | | | | | | | | all_48_0, e3, e3, simplifying with (116), (1386) % 56.31/14.29 | | | | | | | | | | | | | | | gives: % 56.31/14.29 | | | | | | | | | | | | | | | (1431) all_52_16 = all_48_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | COMBINE_EQS: (236), (1429) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1432) all_56_15 = all_4_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | COMBINE_EQS: (272), (1430) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1433) all_56_5 = all_8_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1431) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1434) all_56_0 = all_48_0 % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (451), (1431) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1435) ~ (all_48_0 = all_22_1) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (450), (1431) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1436) ~ (all_48_0 = all_12_1) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1361), (1431) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1437) ~ (all_48_0 = e2) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1350), (1431) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1438) ~ (all_48_0 = e0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (481), (1430) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1439) ~ (all_10_1 = all_8_0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | SIMP: (1439) implies: % 56.31/14.29 | | | | | | | | | | | | | | | (1440) ~ (all_10_1 = all_8_0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1376), (1430) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1441) ~ (all_8_0 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1351), (1430) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1442) ~ (all_8_0 = e0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (508), (1429) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1443) ~ (all_14_1 = all_4_0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | SIMP: (1443) implies: % 56.31/14.29 | | | | | | | | | | | | | | | (1444) ~ (all_14_1 = all_4_0) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1377), (1429) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1445) ~ (all_4_0 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | REDUCE: (1362), (1429) imply: % 56.31/14.29 | | | | | | | | | | | | | | | (1446) ~ (all_4_0 = e2) % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 56.31/14.29 | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | (1447) all_56_0 = e3 % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | COMBINE_EQS: (1434), (1447) imply: % 56.31/14.29 | | | | | | | | | | | | | | | | (1448) all_48_0 = e3 % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | REDUCE: (1435), (1448) imply: % 56.31/14.29 | | | | | | | | | | | | | | | | (1449) ~ (all_22_1 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | SIMP: (1449) implies: % 56.31/14.29 | | | | | | | | | | | | | | | | (1450) ~ (all_22_1 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | REDUCE: (1436), (1448) imply: % 56.31/14.29 | | | | | | | | | | | | | | | | (1451) ~ (all_12_1 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | SIMP: (1451) implies: % 56.31/14.29 | | | | | | | | | | | | | | | | (1452) ~ (all_12_1 = e3) % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 56.31/14.29 | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | | (1453) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 % 56.31/14.29 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 56.31/14.29 | | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | | BETA: splitting (1453) gives: % 56.31/14.29 | | | | | | | | | | | | | | | | | % 56.31/14.29 | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.29 | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | (1454) all_58_0 = e3 & op(e3, e3) = e3 % 56.31/14.30 | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | ALPHA: (1454) implies: % 56.31/14.30 | | | | | | | | | | | | | | | | | | (1455) all_58_0 = e3 % 56.31/14.30 | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 56.31/14.30 | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | (1456) all_56_5 = e3 % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1433), (1456) imply: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | (1457) all_8_0 = e3 % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | SIMP: (1457) implies: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | (1458) all_8_0 = e3 % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | REDUCE: (1441), (1458) imply: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | (1459) $false % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | CLOSE: (1459) is inconsistent. % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | (1460) all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0 % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (1460) gives: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.30 | | | | | | | | | | | | | | | | | | | | % 56.31/14.30 | | | | | | | | | | | | | | | | | | | | (1461) all_56_5 = e2 % 56.31/14.30 | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1433), (1461) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | (1462) all_8_0 = e2 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | SIMP: (1462) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | (1463) all_8_0 = e2 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (1440), (1463) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | (1464) ~ (all_10_1 = e2) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | (1465) all_56_15 = e3 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1432), (1465) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | (1466) all_4_0 = e3 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | SIMP: (1466) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | (1467) all_4_0 = e3 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1467) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | (1468) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1468) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | (1469) all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1469) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1470) all_56_15 = e2 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1432), (1470) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1471) all_4_0 = e2 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1471) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1472) all_4_0 = e2 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (1472) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1473) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1473) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1474) ~ (all_56_15 = e2) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | (1475) all_56_15 = e1 | all_56_15 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1476) all_56_15 = e1 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1432), (1476) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1477) all_4_0 = e1 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1477) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1478) all_4_0 = e1 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1347), (1478) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1479) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1479) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1480) all_56_15 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1432), (1480) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1481) all_4_0 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1481) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1482) all_4_0 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (1482) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1483) ~ (all_14_1 = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (1482) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1484) ~ (e2 = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1347), (1482) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | (1485) ~ (e1 = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | (1486) ~ (all_12_1 = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | (1487) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1487) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_58_0 = e0 & op(e3, e3) = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1387), (1488) are inconsistent by sub-proof #5. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) all_58_2 = e0 & op(e2, e3) = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1489) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) op(e2, e3) = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) ~ (op(e2, e3) = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1490), (1491) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1492) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_54_1 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (1493) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_12_1 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1494) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_12_1 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1486), (1495) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1496) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | (1497) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1497) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_58_6 = e0 & op(e1, e3) = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1498) implies: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) op(e1, e3) = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) ~ (op(e1, e3) = e0) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1499), (1500) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1501) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) all_22_1 = e0 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (514), (1502) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) op(e0, e1) = e3 % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) ~ (op(e0, e1) = e3) % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1503), (1504) imply: % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) $false % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1505) is inconsistent. % 56.31/14.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_52_30 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (1506) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) all_16_1 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1507) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_16_1 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1425), (1508) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) op(e1, e3) = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (366), (433), (1450), (1509) are inconsistent by % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_58_12 = e0 & op(e0, e3) = e0 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1510) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_58_12 = e0 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1403), (1511) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) e2 = e0 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1512) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) e2 = e0 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1513) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) $false % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1514) is inconsistent. % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_12_1 = e0 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (458), (1515) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | (1516) ~ (all_10_1 = e0) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1516) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | (1517) ~ (all_10_1 = e0) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (511), (1515) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | (1518) op(e0, e2) = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1519) ~ (op(e0, e2) = e3) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1518), (1519) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1520) $false % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1520) is inconsistent. % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_56_13 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1521) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_28_1 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1522) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_28_1 = e3 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (518), (1523) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1524) op(e3, e0) = e2 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) ~ (op(e3, e0) = e2) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1524), (1525) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) $false % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1526) is inconsistent. % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) all_54_12 = e2 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1527) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_34_1 = e2 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (503), (1528) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) ~ (all_14_1 = e2) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1529) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) ~ (all_14_1 = e2) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1531) gives: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_58_0 = e1 & op(e3, e3) = e1 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1532) implies: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_58_0 = e1 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1455), (1533) imply: % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) e3 = e1 % 56.31/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1534) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1535) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) all_58_1 = e1 & op(e3, e2) = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1536) implies: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) all_58_1 = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1428), (1537) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) e1 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1538) implies: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) e1 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1539) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1540) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1541) gives: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) all_58_4 = e1 & op(e3, e1) = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1542) implies: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) op(e3, e1) = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) ~ (op(e3, e1) = e1) % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1543), (1544) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1545) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_26_1 = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (491), (1546) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) ~ (all_10_1 = e1) % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1547) implies: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) ~ (all_10_1 = e1) % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_56_6 = e3 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1549) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_10_1 = e3 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1381), (1550) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1551) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1552) gives: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_56_6 = e2 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1553) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_10_1 = e2 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (1554) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1555) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_56_6 = e1 | all_56_6 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1556) gives: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_56_6 = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1557) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_10_1 = e1 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1548), (1558) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) $false % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1559) is inconsistent. % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_56_6 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1560) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_10_1 = e0 % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1517), (1561) imply: % 56.42/14.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1562) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_58_9 = e1 & op(e3, e0) = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1563) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) op(e3, e0) = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (207), (252), (278), (295), (503), (1379), (1483), % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530), (1564) are inconsistent by sub-proof #19. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | (1565) all_56_5 = e1 | all_56_5 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1566) all_56_5 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1433), (1566) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1567) all_8_0 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | SIMP: (1567) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1568) all_8_0 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1368), (1568) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1569) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1569) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1570) all_56_5 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1433), (1570) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1571) all_8_0 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | SIMP: (1571) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1572) all_8_0 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1442), (1572) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | (1573) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1573) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1574) all_58_2 = e3 & op(e2, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | ALPHA: (1574) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1575) op(e2, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives: % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | (1576) ~ (op(e2, e3) = e3) % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (1575), (1576) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | (1577) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | CLOSE: (1577) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | (1578) all_12_1 = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | REDUCE: (1452), (1578) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | | (1579) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | | CLOSE: (1579) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | (1580) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = % 56.42/14.33 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | BETA: splitting (1580) gives: % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1581) all_58_6 = e3 & op(e1, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | ALPHA: (1581) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1582) op(e1, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (366), (433), (1450), (1582) are inconsistent by % 56.42/14.33 | | | | | | | | | | | | | | | | | | sub-proof #4. % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1583) all_58_12 = e3 & op(e0, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | ALPHA: (1583) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1584) op(e0, e3) = e3 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (367), (1359), (1584) are inconsistent by % 56.42/14.33 | | | | | | | | | | | | | | | | | | sub-proof #1. % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | End of split % 56.42/14.33 | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | (1585) all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | BETA: splitting (1585) gives: % 56.42/14.33 | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | Case 1: % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | (1586) all_56_0 = e2 % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1434), (1586) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | (1587) all_48_0 = e2 % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | REDUCE: (1437), (1587) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | (1588) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | CLOSE: (1588) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | Case 2: % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | (1589) all_56_0 = e1 | all_56_0 = e0 % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | BETA: splitting (1589) gives: % 56.42/14.33 | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | Case 1: % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1590) all_56_0 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1434), (1590) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1591) all_48_0 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | SIMP: (1591) implies: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1592) all_48_0 = e1 % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | REDUCE: (1385), (1592) imply: % 56.42/14.33 | | | | | | | | | | | | | | | | | | (1593) $false % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.42/14.33 | | | | | | | | | | | | | | | | | | CLOSE: (1593) is inconsistent. % 56.42/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | Case 2: % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | | (1594) all_56_0 = e0 % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1434), (1594) imply: % 56.47/14.33 | | | | | | | | | | | | | | | | | | (1595) all_48_0 = e0 % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | | SIMP: (1595) implies: % 56.47/14.33 | | | | | | | | | | | | | | | | | | (1596) all_48_0 = e0 % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | | REDUCE: (1438), (1596) imply: % 56.47/14.33 | | | | | | | | | | | | | | | | | | (1597) $false % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | | CLOSE: (1597) is inconsistent. % 56.47/14.33 | | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | | End of split % 56.47/14.33 | | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | | End of split % 56.47/14.33 | | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | End of split % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | Case 2: % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | (1598) all_58_3 = e0 & op(e2, e2) = e0 % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | REF_CLOSE: (1370), (1598) are inconsistent by sub-proof #14. % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | End of split % 56.47/14.33 | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | Case 2: % 56.47/14.33 | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | (1599) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = % 56.47/14.33 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 56.47/14.33 | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | BETA: splitting (1599) gives: % 56.47/14.33 | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | Case 1: % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | (1600) all_58_7 = e0 & op(e1, e2) = e0 % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | ALPHA: (1600) implies: % 56.47/14.33 | | | | | | | | | | | | | | | (1601) op(e1, e2) = e0 % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 56.47/14.33 | | | | | | | | | | | | | | | % 56.47/14.33 | | | | | | | | | | | | | | | Case 1: % 56.47/14.33 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | (1602) ~ (op(e1, e2) = e0) % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | PRED_UNIFY: (1601), (1602) imply: % 56.47/14.34 | | | | | | | | | | | | | | | | (1603) $false % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | CLOSE: (1603) is inconsistent. % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | (1604) all_20_1 = e0 % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | REDUCE: (1353), (1604) imply: % 56.47/14.34 | | | | | | | | | | | | | | | | (1605) $false % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | CLOSE: (1605) is inconsistent. % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | (1606) all_58_13 = e0 & op(e0, e2) = e0 % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | ALPHA: (1606) implies: % 56.47/14.34 | | | | | | | | | | | | | | | (1607) op(e0, e2) = e0 % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | Case 1: % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | (1608) ~ (op(e0, e2) = e0) % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | PRED_UNIFY: (1607), (1608) imply: % 56.47/14.34 | | | | | | | | | | | | | | | | (1609) $false % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | CLOSE: (1609) is inconsistent. % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | (1610) all_28_1 = e0 % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | REDUCE: (1352), (1610) imply: % 56.47/14.34 | | | | | | | | | | | | | | | | (1611) $false % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | | CLOSE: (1611) is inconsistent. % 56.47/14.34 | | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | (1612) all_52_12 = all_52_19 & all_52_13 = all_52_23 & % 56.47/14.34 | | | | | | | | | | | | | all_52_14 = all_52_27 & all_52_15 = all_52_31 & % 56.47/14.34 | | | | | | | | | | | | | op(e0, all_52_19) = all_52_19 & op(e0, all_52_23) % 56.47/14.34 | | | | | | | | | | | | | = all_52_23 & op(e0, all_52_27) = all_52_27 & % 56.47/14.34 | | | | | | | | | | | | | op(e0, all_52_31) = all_52_31 % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | ALPHA: (1612) implies: % 56.47/14.34 | | | | | | | | | | | | | (1613) op(e0, all_52_23) = all_52_23 % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | REDUCE: (1375), (1613) imply: % 56.47/14.34 | | | | | | | | | | | | | (1614) op(e0, e3) = e3 % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | | REF_CLOSE: (9), (367), (1359), (1614) are inconsistent by % 56.47/14.34 | | | | | | | | | | | | | sub-proof #1. % 56.47/14.34 | | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | | % 56.47/14.34 | | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | | % 56.47/14.34 | | | | | | | | | End of split % 56.47/14.34 | | | | | | | | | % 56.47/14.34 | | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | | % 56.47/14.34 | | | | | | | | | (1615) op(e3, e3) = e2 % 56.47/14.34 | | | | | | | | | % 56.47/14.34 | | | | | | | | | REF_CLOSE: (359), (369), (1361), (1615) are inconsistent by % 56.47/14.34 | | | | | | | | | sub-proof #6. % 56.47/14.34 | | | | | | | | | % 56.47/14.34 | | | | | | | | End of split % 56.47/14.34 | | | | | | | | % 56.47/14.34 | | | | | | | Case 2: % 56.47/14.34 | | | | | | | | % 56.47/14.34 | | | | | | | | (1616) all_52_16 = e0 % 56.47/14.34 | | | | | | | | % 56.47/14.34 | | | | | | | | REDUCE: (1350), (1616) imply: % 56.47/14.34 | | | | | | | | (1617) $false % 56.47/14.34 | | | | | | | | % 56.47/14.34 | | | | | | | | CLOSE: (1617) is inconsistent. % 56.47/14.34 | | | | | | | | % 56.47/14.34 | | | | | | | End of split % 56.47/14.34 | | | | | | | % 56.47/14.34 | | | | | | End of split % 56.47/14.34 | | | | | | % 56.47/14.34 | | | | | End of split % 56.47/14.34 | | | | | % 56.47/14.34 | | | | Case 2: % 56.47/14.34 | | | | | % 56.47/14.34 | | | | | (1618) all_56_5 = e0 % 56.47/14.34 | | | | | % 56.47/14.34 | | | | | COMBINE_EQS: (272), (1618) imply: % 56.47/14.34 | | | | | (1619) all_52_21 = e0 % 56.47/14.34 | | | | | % 56.47/14.34 | | | | | REDUCE: (1351), (1619) imply: % 56.47/14.34 | | | | | (1620) $false % 56.47/14.34 | | | | | % 56.47/14.34 | | | | | CLOSE: (1620) is inconsistent. % 56.47/14.34 | | | | | % 56.47/14.34 | | | | End of split % 56.47/14.34 | | | | % 56.47/14.34 | | | End of split % 56.47/14.34 | | | % 56.47/14.34 | | End of split % 56.47/14.34 | | % 56.47/14.34 | End of split % 56.47/14.34 | % 56.47/14.34 End of proof % 56.47/14.34 % 56.47/14.34 Sub-proof #1 shows that the following formulas are inconsistent: % 56.47/14.34 ---------------------------------------------------------------- % 56.47/14.34 (1) all_8_1 = e3 | ~ (op(e0, e3) = e3) % 56.47/14.34 (2) op(e0, e3) = e3 % 56.47/14.34 (3) all_8_1 = e2 % 56.47/14.34 (4) ~ (e3 = e2) % 56.47/14.34 % 56.47/14.34 Begin of proof % 56.47/14.34 | % 56.47/14.34 | BETA: splitting (1) gives: % 56.47/14.34 | % 56.47/14.34 | Case 1: % 56.47/14.34 | | % 56.47/14.34 | | (5) ~ (op(e0, e3) = e3) % 56.47/14.34 | | % 56.47/14.34 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.34 | | (6) $false % 56.47/14.34 | | % 56.47/14.34 | | CLOSE: (6) is inconsistent. % 56.47/14.34 | | % 56.47/14.34 | Case 2: % 56.47/14.34 | | % 56.47/14.34 | | (7) all_8_1 = e3 % 56.47/14.34 | | % 56.47/14.34 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.34 | | (8) e3 = e2 % 56.47/14.34 | | % 56.47/14.34 | | REDUCE: (4), (8) imply: % 56.47/14.34 | | (9) $false % 56.47/14.34 | | % 56.47/14.34 | | CLOSE: (9) is inconsistent. % 56.47/14.34 | | % 56.47/14.34 | End of split % 56.47/14.34 | % 56.47/14.34 End of proof % 56.47/14.34 % 56.47/14.34 Sub-proof #2 shows that the following formulas are inconsistent: % 56.47/14.34 ---------------------------------------------------------------- % 56.47/14.34 (1) all_54_9 = e1 | ~ (op(e2, e1) = e1) % 56.47/14.34 (2) op(e2, e1) = e1 % 56.47/14.34 (3) all_54_9 = all_10_1 % 56.47/14.34 (4) ~ (all_10_1 = e1) % 56.47/14.34 % 56.47/14.34 Begin of proof % 56.47/14.34 | % 56.47/14.34 | BETA: splitting (1) gives: % 56.47/14.34 | % 56.47/14.34 | Case 1: % 56.47/14.34 | | % 56.47/14.34 | | (5) ~ (op(e2, e1) = e1) % 56.47/14.34 | | % 56.47/14.34 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.34 | | (6) $false % 56.47/14.34 | | % 56.47/14.34 | | CLOSE: (6) is inconsistent. % 56.47/14.34 | | % 56.47/14.34 | Case 2: % 56.47/14.34 | | % 56.47/14.34 | | (7) all_54_9 = e1 % 56.47/14.34 | | % 56.47/14.34 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.34 | | (8) all_10_1 = e1 % 56.47/14.34 | | % 56.47/14.34 | | REDUCE: (4), (8) imply: % 56.47/14.34 | | (9) $false % 56.47/14.34 | | % 56.47/14.34 | | CLOSE: (9) is inconsistent. % 56.47/14.34 | | % 56.47/14.34 | End of split % 56.47/14.34 | % 56.47/14.34 End of proof % 56.47/14.34 % 56.47/14.34 Sub-proof #3 shows that the following formulas are inconsistent: % 56.47/14.34 ---------------------------------------------------------------- % 56.47/14.34 (1) all_58_8 = e3 & op(e1, e1) = e3 % 56.47/14.34 (2) ~ (op(e1, e1) = e3) % 56.47/14.34 % 56.47/14.34 Begin of proof % 56.47/14.34 | % 56.47/14.34 | ALPHA: (1) implies: % 56.47/14.34 | (3) op(e1, e1) = e3 % 56.47/14.34 | % 56.47/14.34 | PRED_UNIFY: (2), (3) imply: % 56.47/14.34 | (4) $false % 56.47/14.34 | % 56.47/14.34 | CLOSE: (4) is inconsistent. % 56.47/14.34 | % 56.47/14.34 End of proof % 56.47/14.34 % 56.47/14.34 Sub-proof #4 shows that the following formulas are inconsistent: % 56.47/14.34 ---------------------------------------------------------------- % 56.47/14.34 (1) all_44_1 = e3 | ~ (op(e1, e3) = e3) % 56.47/14.35 (2) op(e1, e3) = e3 % 56.47/14.35 (3) all_44_1 = all_22_1 % 56.47/14.35 (4) ~ (all_22_1 = e3) % 56.47/14.35 % 56.47/14.35 Begin of proof % 56.47/14.35 | % 56.47/14.35 | BETA: splitting (1) gives: % 56.47/14.35 | % 56.47/14.35 | Case 1: % 56.47/14.35 | | % 56.47/14.35 | | (5) ~ (op(e1, e3) = e3) % 56.47/14.35 | | % 56.47/14.35 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.35 | | (6) $false % 56.47/14.35 | | % 56.47/14.35 | | CLOSE: (6) is inconsistent. % 56.47/14.35 | | % 56.47/14.35 | Case 2: % 56.47/14.35 | | % 56.47/14.35 | | (7) all_44_1 = e3 % 56.47/14.35 | | % 56.47/14.35 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.35 | | (8) all_22_1 = e3 % 56.47/14.35 | | % 56.47/14.35 | | SIMP: (8) implies: % 56.47/14.35 | | (9) all_22_1 = e3 % 56.47/14.35 | | % 56.47/14.35 | | REDUCE: (4), (9) imply: % 56.47/14.35 | | (10) $false % 56.47/14.35 | | % 56.47/14.35 | | CLOSE: (10) is inconsistent. % 56.47/14.35 | | % 56.47/14.35 | End of split % 56.47/14.35 | % 56.47/14.35 End of proof % 56.47/14.35 % 56.47/14.35 Sub-proof #5 shows that the following formulas are inconsistent: % 56.47/14.35 ---------------------------------------------------------------- % 56.47/14.35 (1) all_58_0 = e0 & op(e3, e3) = e0 % 56.47/14.35 (2) ~ (op(e3, e3) = e0) % 56.47/14.35 % 56.47/14.35 Begin of proof % 56.47/14.35 | % 56.47/14.35 | ALPHA: (1) implies: % 56.47/14.35 | (3) op(e3, e3) = e0 % 56.47/14.35 | % 56.47/14.35 | PRED_UNIFY: (2), (3) imply: % 56.47/14.35 | (4) $false % 56.47/14.35 | % 56.47/14.35 | CLOSE: (4) is inconsistent. % 56.47/14.35 | % 56.47/14.35 End of proof % 56.47/14.35 % 56.47/14.35 Sub-proof #6 shows that the following formulas are inconsistent: % 56.47/14.35 ---------------------------------------------------------------- % 56.47/14.35 (1) all_54_0 = e2 | ~ (op(e3, e3) = e2) % 56.47/14.35 (2) op(e3, e3) = e2 % 56.47/14.35 (3) all_54_0 = all_52_16 % 56.47/14.35 (4) ~ (all_52_16 = e2) % 56.47/14.35 % 56.47/14.35 Begin of proof % 56.47/14.35 | % 56.47/14.35 | BETA: splitting (1) gives: % 56.47/14.35 | % 56.47/14.35 | Case 1: % 56.47/14.35 | | % 56.47/14.35 | | (5) ~ (op(e3, e3) = e2) % 56.47/14.35 | | % 56.47/14.35 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.35 | | (6) $false % 56.47/14.35 | | % 56.47/14.35 | | CLOSE: (6) is inconsistent. % 56.47/14.35 | | % 56.47/14.35 | Case 2: % 56.47/14.35 | | % 56.47/14.35 | | (7) all_54_0 = e2 % 56.47/14.35 | | % 56.47/14.35 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.35 | | (8) all_52_16 = e2 % 56.47/14.35 | | % 56.47/14.35 | | SIMP: (8) implies: % 56.47/14.35 | | (9) all_52_16 = e2 % 56.47/14.35 | | % 56.47/14.35 | | REDUCE: (4), (9) imply: % 56.47/14.35 | | (10) $false % 56.47/14.35 | | % 56.47/14.35 | | CLOSE: (10) is inconsistent. % 56.47/14.35 | | % 56.47/14.35 | End of split % 56.47/14.35 | % 56.47/14.35 End of proof % 56.47/14.35 % 56.47/14.35 Sub-proof #7 shows that the following formulas are inconsistent: % 56.47/14.35 ---------------------------------------------------------------- % 56.47/14.35 (1) all_54_14 = all_14_1 % 56.47/14.35 (2) all_58_14 = e3 & op(e0, e1) = e3 % 56.47/14.35 (3) ~ (all_6_1 = e1) % 56.47/14.35 (4) ~ (e3 = e1) % 56.47/14.35 (5) op(e0, all_52_31) = all_52_31 % 56.47/14.35 (6) all_56_14 = all_16_1 % 56.47/14.35 (7) all_56_13 = all_28_1 % 56.47/14.35 (8) all_56_13 = e1 | ~ (op(e0, e2) = e1) % 56.47/14.35 (9) all_6_1 = e1 | ~ (op(e0, e3) = e1) % 56.47/14.35 (10) all_36_1 = e1 | ~ (op(e0, e1) = e1) % 56.47/14.35 (11) all_56_14 = e0 | ~ (op(e0, e1) = e0) % 56.47/14.35 (12) all_54_14 = e0 | ~ (op(e1, e0) = e0) % 56.47/14.35 (13) all_36_1 = all_16_1 % 56.47/14.35 (14) all_52_31 = e1 | ~ (op(e0, e0) = e1) % 56.47/14.35 (15) op(all_14_1, e1) = e0 % 56.47/14.35 (16) ~ (all_28_1 = e1) % 56.47/14.35 (17) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) % 56.47/14.35 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = % 56.47/14.35 e1) % 56.47/14.35 (18) op(all_52_31, e0) = e0 % 56.47/14.35 (19) ~ (all_52_31 = all_16_1) % 56.47/14.35 % 56.47/14.35 Begin of proof % 56.47/14.35 | % 56.47/14.35 | ALPHA: (2) implies: % 56.47/14.35 | (20) all_58_14 = e3 % 56.47/14.35 | % 56.47/14.35 | BETA: splitting (17) gives: % 56.47/14.35 | % 56.47/14.35 | Case 1: % 56.47/14.35 | | % 56.47/14.35 | | (21) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = % 56.47/14.35 | | e1) % 56.47/14.35 | | % 56.47/14.35 | | BETA: splitting (21) gives: % 56.47/14.35 | | % 56.47/14.35 | | Case 1: % 56.47/14.35 | | | % 56.47/14.35 | | | (22) all_58_12 = e1 & op(e0, e3) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | ALPHA: (22) implies: % 56.47/14.35 | | | (23) op(e0, e3) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | REF_CLOSE: (3), (9), (23) are inconsistent by sub-proof #17. % 56.47/14.35 | | | % 56.47/14.35 | | Case 2: % 56.47/14.35 | | | % 56.47/14.35 | | | (24) all_58_13 = e1 & op(e0, e2) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | ALPHA: (24) implies: % 56.47/14.35 | | | (25) op(e0, e2) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | BETA: splitting (8) gives: % 56.47/14.35 | | | % 56.47/14.35 | | | Case 1: % 56.47/14.35 | | | | % 56.47/14.35 | | | | (26) ~ (op(e0, e2) = e1) % 56.47/14.35 | | | | % 56.47/14.35 | | | | PRED_UNIFY: (25), (26) imply: % 56.47/14.35 | | | | (27) $false % 56.47/14.35 | | | | % 56.47/14.35 | | | | CLOSE: (27) is inconsistent. % 56.47/14.35 | | | | % 56.47/14.35 | | | Case 2: % 56.47/14.35 | | | | % 56.47/14.35 | | | | (28) all_56_13 = e1 % 56.47/14.35 | | | | % 56.47/14.35 | | | | REF_CLOSE: (7), (16), (28) are inconsistent by sub-proof #27. % 56.47/14.35 | | | | % 56.47/14.35 | | | End of split % 56.47/14.35 | | | % 56.47/14.35 | | End of split % 56.47/14.35 | | % 56.47/14.35 | Case 2: % 56.47/14.35 | | % 56.47/14.35 | | (29) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = % 56.47/14.35 | | e1) % 56.47/14.35 | | % 56.47/14.35 | | BETA: splitting (29) gives: % 56.47/14.35 | | % 56.47/14.35 | | Case 1: % 56.47/14.35 | | | % 56.47/14.35 | | | (30) all_58_14 = e1 & op(e0, e1) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | ALPHA: (30) implies: % 56.47/14.35 | | | (31) all_58_14 = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | COMBINE_EQS: (20), (31) imply: % 56.47/14.35 | | | (32) e3 = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | REDUCE: (4), (32) imply: % 56.47/14.35 | | | (33) $false % 56.47/14.35 | | | % 56.47/14.35 | | | CLOSE: (33) is inconsistent. % 56.47/14.35 | | | % 56.47/14.35 | | Case 2: % 56.47/14.35 | | | % 56.47/14.35 | | | (34) all_58_15 = e1 & op(e0, e0) = e1 % 56.47/14.35 | | | % 56.47/14.35 | | | ALPHA: (34) implies: % 56.47/14.35 | | | (35) op(e0, e0) = e1 % 56.47/14.35 | | | % 56.47/14.36 | | | BETA: splitting (14) gives: % 56.47/14.36 | | | % 56.47/14.36 | | | Case 1: % 56.47/14.36 | | | | % 56.47/14.36 | | | | (36) ~ (op(e0, e0) = e1) % 56.47/14.36 | | | | % 56.47/14.36 | | | | PRED_UNIFY: (35), (36) imply: % 56.47/14.36 | | | | (37) $false % 56.47/14.36 | | | | % 56.47/14.36 | | | | CLOSE: (37) is inconsistent. % 56.47/14.36 | | | | % 56.47/14.36 | | | Case 2: % 56.47/14.36 | | | | % 56.47/14.36 | | | | (38) all_52_31 = e1 % 56.47/14.36 | | | | % 56.47/14.36 | | | | REDUCE: (19), (38) imply: % 56.47/14.36 | | | | (39) ~ (all_16_1 = e1) % 56.47/14.36 | | | | % 56.47/14.36 | | | | SIMP: (39) implies: % 56.47/14.36 | | | | (40) ~ (all_16_1 = e1) % 56.47/14.36 | | | | % 56.47/14.36 | | | | REDUCE: (18), (38) imply: % 56.47/14.36 | | | | (41) op(e1, e0) = e0 % 56.47/14.36 | | | | % 56.47/14.36 | | | | REDUCE: (5), (38) imply: % 56.47/14.36 | | | | (42) op(e0, e1) = e1 % 56.47/14.36 | | | | % 56.47/14.36 | | | | BETA: splitting (12) gives: % 56.47/14.36 | | | | % 56.47/14.36 | | | | Case 1: % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | (43) ~ (op(e1, e0) = e0) % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | PRED_UNIFY: (41), (43) imply: % 56.47/14.36 | | | | | (44) $false % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | CLOSE: (44) is inconsistent. % 56.47/14.36 | | | | | % 56.47/14.36 | | | | Case 2: % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | (45) all_54_14 = e0 % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | COMBINE_EQS: (1), (45) imply: % 56.47/14.36 | | | | | (46) all_14_1 = e0 % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | SIMP: (46) implies: % 56.47/14.36 | | | | | (47) all_14_1 = e0 % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | REDUCE: (15), (47) imply: % 56.47/14.36 | | | | | (48) op(e0, e1) = e0 % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | BETA: splitting (11) gives: % 56.47/14.36 | | | | | % 56.47/14.36 | | | | | Case 1: % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | (49) ~ (op(e0, e1) = e0) % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | PRED_UNIFY: (48), (49) imply: % 56.47/14.36 | | | | | | (50) $false % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | CLOSE: (50) is inconsistent. % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | Case 2: % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | (51) all_56_14 = e0 % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | COMBINE_EQS: (6), (51) imply: % 56.47/14.36 | | | | | | (52) all_16_1 = e0 % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | SIMP: (52) implies: % 56.47/14.36 | | | | | | (53) all_16_1 = e0 % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | COMBINE_EQS: (13), (53) imply: % 56.47/14.36 | | | | | | (54) all_36_1 = e0 % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | REDUCE: (40), (53) imply: % 56.47/14.36 | | | | | | (55) ~ (e1 = e0) % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | SIMP: (55) implies: % 56.47/14.36 | | | | | | (56) ~ (e1 = e0) % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | BETA: splitting (10) gives: % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | | Case 1: % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | (57) ~ (op(e0, e1) = e1) % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | PRED_UNIFY: (42), (57) imply: % 56.47/14.36 | | | | | | | (58) $false % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | CLOSE: (58) is inconsistent. % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | Case 2: % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | (59) all_36_1 = e1 % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | COMBINE_EQS: (54), (59) imply: % 56.47/14.36 | | | | | | | (60) e1 = e0 % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | SIMP: (60) implies: % 56.47/14.36 | | | | | | | (61) e1 = e0 % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | REDUCE: (56), (61) imply: % 56.47/14.36 | | | | | | | (62) $false % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | | CLOSE: (62) is inconsistent. % 56.47/14.36 | | | | | | | % 56.47/14.36 | | | | | | End of split % 56.47/14.36 | | | | | | % 56.47/14.36 | | | | | End of split % 56.47/14.36 | | | | | % 56.47/14.36 | | | | End of split % 56.47/14.36 | | | | % 56.47/14.36 | | | End of split % 56.47/14.36 | | | % 56.47/14.36 | | End of split % 56.47/14.36 | | % 56.47/14.36 | End of split % 56.47/14.36 | % 56.47/14.36 End of proof % 56.47/14.36 % 56.47/14.36 Sub-proof #8 shows that the following formulas are inconsistent: % 56.47/14.36 ---------------------------------------------------------------- % 56.47/14.36 (1) all_58_2 = e0 & op(e2, e3) = e0 % 56.47/14.36 (2) all_58_2 = e1 % 56.47/14.36 (3) ~ (e1 = e0) % 56.47/14.36 % 56.47/14.36 Begin of proof % 56.47/14.36 | % 56.47/14.36 | ALPHA: (1) implies: % 56.47/14.36 | (4) all_58_2 = e0 % 56.47/14.36 | % 56.47/14.36 | COMBINE_EQS: (2), (4) imply: % 56.47/14.36 | (5) e1 = e0 % 56.47/14.36 | % 56.47/14.36 | REDUCE: (3), (5) imply: % 56.47/14.36 | (6) $false % 56.47/14.36 | % 56.47/14.36 | CLOSE: (6) is inconsistent. % 56.47/14.36 | % 56.47/14.36 End of proof % 56.47/14.36 % 56.47/14.36 Sub-proof #9 shows that the following formulas are inconsistent: % 56.47/14.36 ---------------------------------------------------------------- % 56.47/14.36 (1) all_50_1 = e2 | ~ (op(e3, e0) = e2) % 56.47/14.36 (2) op(e3, e0) = e2 % 56.47/14.36 (3) all_50_1 = all_34_1 % 56.47/14.36 (4) ~ (all_34_1 = e2) % 56.47/14.36 % 56.47/14.36 Begin of proof % 56.47/14.36 | % 56.47/14.36 | BETA: splitting (1) gives: % 56.47/14.36 | % 56.47/14.36 | Case 1: % 56.47/14.36 | | % 56.47/14.36 | | (5) ~ (op(e3, e0) = e2) % 56.47/14.36 | | % 56.47/14.36 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.36 | | (6) $false % 56.47/14.36 | | % 56.47/14.36 | | CLOSE: (6) is inconsistent. % 56.47/14.36 | | % 56.47/14.36 | Case 2: % 56.47/14.36 | | % 56.47/14.36 | | (7) all_50_1 = e2 % 56.47/14.36 | | % 56.47/14.36 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.36 | | (8) all_34_1 = e2 % 56.47/14.36 | | % 56.47/14.36 | | SIMP: (8) implies: % 56.47/14.36 | | (9) all_34_1 = e2 % 56.47/14.36 | | % 56.47/14.36 | | REDUCE: (4), (9) imply: % 56.47/14.36 | | (10) $false % 56.47/14.36 | | % 56.47/14.36 | | CLOSE: (10) is inconsistent. % 56.47/14.36 | | % 56.47/14.36 | End of split % 56.47/14.36 | % 56.47/14.36 End of proof % 56.47/14.36 % 56.47/14.36 Sub-proof #10 shows that the following formulas are inconsistent: % 56.47/14.36 ---------------------------------------------------------------- % 56.47/14.36 (1) all_58_0 = e2 & op(e3, e3) = e2 % 56.47/14.36 (2) ~ (op(e3, e3) = e2) % 56.47/14.36 % 56.47/14.36 Begin of proof % 56.47/14.36 | % 56.47/14.36 | ALPHA: (1) implies: % 56.47/14.36 | (3) op(e3, e3) = e2 % 56.47/14.36 | % 56.47/14.36 | PRED_UNIFY: (2), (3) imply: % 56.47/14.36 | (4) $false % 56.47/14.36 | % 56.47/14.36 | CLOSE: (4) is inconsistent. % 56.47/14.36 | % 56.47/14.36 End of proof % 56.47/14.36 % 56.47/14.36 Sub-proof #11 shows that the following formulas are inconsistent: % 56.47/14.36 ---------------------------------------------------------------- % 56.47/14.36 (1) ~ (all_6_1 = e1) % 56.47/14.36 (2) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1) % 56.47/14.36 (3) all_6_1 = e1 | ~ (op(e0, e3) = e1) % 56.47/14.36 (4) all_44_1 = e2 % 56.47/14.36 (5) all_44_1 = e1 | ~ (op(e1, e3) = e1) % 56.47/14.36 (6) ~ (e2 = e1) % 56.47/14.36 % 56.47/14.36 Begin of proof % 56.47/14.36 | % 56.47/14.36 | BETA: splitting (2) gives: % 56.47/14.36 | % 56.47/14.36 | Case 1: % 56.47/14.36 | | % 56.47/14.36 | | (7) all_58_6 = e1 & op(e1, e3) = e1 % 56.47/14.36 | | % 56.47/14.36 | | ALPHA: (7) implies: % 56.47/14.36 | | (8) op(e1, e3) = e1 % 56.47/14.36 | | % 56.47/14.36 | | BETA: splitting (5) gives: % 56.47/14.36 | | % 56.47/14.36 | | Case 1: % 56.47/14.36 | | | % 56.47/14.37 | | | (9) ~ (op(e1, e3) = e1) % 56.47/14.37 | | | % 56.47/14.37 | | | PRED_UNIFY: (8), (9) imply: % 56.47/14.37 | | | (10) $false % 56.47/14.37 | | | % 56.47/14.37 | | | CLOSE: (10) is inconsistent. % 56.47/14.37 | | | % 56.47/14.37 | | Case 2: % 56.47/14.37 | | | % 56.47/14.37 | | | (11) all_44_1 = e1 % 56.47/14.37 | | | % 56.47/14.37 | | | COMBINE_EQS: (4), (11) imply: % 56.47/14.37 | | | (12) e2 = e1 % 56.47/14.37 | | | % 56.47/14.37 | | | SIMP: (12) implies: % 56.47/14.37 | | | (13) e2 = e1 % 56.47/14.37 | | | % 56.47/14.37 | | | REDUCE: (6), (13) imply: % 56.47/14.37 | | | (14) $false % 56.47/14.37 | | | % 56.47/14.37 | | | CLOSE: (14) is inconsistent. % 56.47/14.37 | | | % 56.47/14.37 | | End of split % 56.47/14.37 | | % 56.47/14.37 | Case 2: % 56.47/14.37 | | % 56.47/14.37 | | (15) all_58_12 = e1 & op(e0, e3) = e1 % 56.47/14.37 | | % 56.47/14.37 | | ALPHA: (15) implies: % 56.47/14.37 | | (16) op(e0, e3) = e1 % 56.47/14.37 | | % 56.47/14.37 | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #17. % 56.47/14.37 | | % 56.47/14.37 | End of split % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #12 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_58_0 = e1 & op(e3, e3) = e1 % 56.47/14.37 (2) ~ (op(e3, e3) = e1) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | ALPHA: (1) implies: % 56.47/14.37 | (3) op(e3, e3) = e1 % 56.47/14.37 | % 56.47/14.37 | PRED_UNIFY: (2), (3) imply: % 56.47/14.37 | (4) $false % 56.47/14.37 | % 56.47/14.37 | CLOSE: (4) is inconsistent. % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #13 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_52_17 = e2 | ~ (op(e3, e2) = e2) % 56.47/14.37 (2) op(e3, e2) = e2 % 56.47/14.37 (3) all_52_17 = e1 % 56.47/14.37 (4) ~ (e2 = e1) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | BETA: splitting (1) gives: % 56.47/14.37 | % 56.47/14.37 | Case 1: % 56.47/14.37 | | % 56.47/14.37 | | (5) ~ (op(e3, e2) = e2) % 56.47/14.37 | | % 56.47/14.37 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.37 | | (6) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (6) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | Case 2: % 56.47/14.37 | | % 56.47/14.37 | | (7) all_52_17 = e2 % 56.47/14.37 | | % 56.47/14.37 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.37 | | (8) e2 = e1 % 56.47/14.37 | | % 56.47/14.37 | | REDUCE: (4), (8) imply: % 56.47/14.37 | | (9) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (9) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | End of split % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #14 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_58_3 = e0 & op(e2, e2) = e0 % 56.47/14.37 (2) ~ (op(e2, e2) = e0) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | ALPHA: (1) implies: % 56.47/14.37 | (3) op(e2, e2) = e0 % 56.47/14.37 | % 56.47/14.37 | PRED_UNIFY: (2), (3) imply: % 56.47/14.37 | (4) $false % 56.47/14.37 | % 56.47/14.37 | CLOSE: (4) is inconsistent. % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #15 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) e2 = e1 | ~ (op(all_52_22, e2) = e2) % 56.47/14.37 (2) all_52_22 = e0 % 56.47/14.37 (3) op(e0, e2) = e2 % 56.47/14.37 (4) ~ (e2 = e1) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | BETA: splitting (1) gives: % 56.47/14.37 | % 56.47/14.37 | Case 1: % 56.47/14.37 | | % 56.47/14.37 | | (5) ~ (op(all_52_22, e2) = e2) % 56.47/14.37 | | % 56.47/14.37 | | REDUCE: (2), (5) imply: % 56.47/14.37 | | (6) ~ (op(e0, e2) = e2) % 56.47/14.37 | | % 56.47/14.37 | | PRED_UNIFY: (3), (6) imply: % 56.47/14.37 | | (7) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (7) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | Case 2: % 56.47/14.37 | | % 56.47/14.37 | | (8) e2 = e1 % 56.47/14.37 | | % 56.47/14.37 | | REDUCE: (4), (8) imply: % 56.47/14.37 | | (9) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (9) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | End of split % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #16 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_58_12 = e2 & op(e0, e3) = e2 % 56.47/14.37 (2) all_6_1 = e2 | ~ (op(e0, e3) = e2) % 56.47/14.37 (3) ~ (all_6_1 = e2) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | ALPHA: (1) implies: % 56.47/14.37 | (4) op(e0, e3) = e2 % 56.47/14.37 | % 56.47/14.37 | BETA: splitting (2) gives: % 56.47/14.37 | % 56.47/14.37 | Case 1: % 56.47/14.37 | | % 56.47/14.37 | | (5) ~ (op(e0, e3) = e2) % 56.47/14.37 | | % 56.47/14.37 | | PRED_UNIFY: (4), (5) imply: % 56.47/14.37 | | (6) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (6) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | Case 2: % 56.47/14.37 | | % 56.47/14.37 | | (7) all_6_1 = e2 % 56.47/14.37 | | % 56.47/14.37 | | REDUCE: (3), (7) imply: % 56.47/14.37 | | (8) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (8) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | End of split % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #17 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_6_1 = e1 | ~ (op(e0, e3) = e1) % 56.47/14.37 (2) op(e0, e3) = e1 % 56.47/14.37 (3) ~ (all_6_1 = e1) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | BETA: splitting (1) gives: % 56.47/14.37 | % 56.47/14.37 | Case 1: % 56.47/14.37 | | % 56.47/14.37 | | (4) ~ (op(e0, e3) = e1) % 56.47/14.37 | | % 56.47/14.37 | | PRED_UNIFY: (2), (4) imply: % 56.47/14.37 | | (5) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (5) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | Case 2: % 56.47/14.37 | | % 56.47/14.37 | | (6) all_6_1 = e1 % 56.47/14.37 | | % 56.47/14.37 | | REDUCE: (3), (6) imply: % 56.47/14.37 | | (7) $false % 56.47/14.37 | | % 56.47/14.37 | | CLOSE: (7) is inconsistent. % 56.47/14.37 | | % 56.47/14.37 | End of split % 56.47/14.37 | % 56.47/14.37 End of proof % 56.47/14.37 % 56.47/14.37 Sub-proof #18 shows that the following formulas are inconsistent: % 56.47/14.37 ---------------------------------------------------------------- % 56.47/14.37 (1) all_54_10 = e3 | ~ (op(e1, e1) = e3) % 56.47/14.37 (2) op(e1, e1) = e3 % 56.47/14.37 (3) all_54_10 = all_52_26 % 56.47/14.37 (4) ~ (all_52_26 = e3) % 56.47/14.37 % 56.47/14.37 Begin of proof % 56.47/14.37 | % 56.47/14.37 | BETA: splitting (1) gives: % 56.47/14.37 | % 56.47/14.37 | Case 1: % 56.47/14.37 | | % 56.47/14.37 | | (5) ~ (op(e1, e1) = e3) % 56.47/14.37 | | % 56.47/14.37 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.38 | | (6) $false % 56.47/14.38 | | % 56.47/14.38 | | CLOSE: (6) is inconsistent. % 56.47/14.38 | | % 56.47/14.38 | Case 2: % 56.47/14.38 | | % 56.47/14.38 | | (7) all_54_10 = e3 % 56.47/14.38 | | % 56.47/14.38 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.38 | | (8) all_52_26 = e3 % 56.47/14.38 | | % 56.47/14.38 | | REDUCE: (4), (8) imply: % 56.47/14.38 | | (9) $false % 56.47/14.38 | | % 56.47/14.38 | | CLOSE: (9) is inconsistent. % 56.47/14.38 | | % 56.47/14.38 | End of split % 56.47/14.38 | % 56.47/14.38 End of proof % 56.47/14.38 % 56.47/14.38 Sub-proof #19 shows that the following formulas are inconsistent: % 56.47/14.38 ---------------------------------------------------------------- % 56.47/14.38 (1) ~ (all_14_1 = e0) % 56.47/14.38 (2) all_56_11 = all_14_1 % 56.47/14.38 (3) all_54_12 = e1 | ~ (op(e3, e0) = e1) % 56.47/14.38 (4) ~ (all_34_1 = all_14_1) % 56.47/14.38 (5) all_54_12 = all_34_1 % 56.47/14.38 (6) op(e3, e0) = e1 % 56.47/14.38 (7) ~ (all_14_1 = e2) % 56.47/14.38 (8) ~ (all_14_1 = e3) % 56.47/14.38 (9) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 56.47/14.38 % 56.47/14.38 Begin of proof % 56.47/14.38 | % 56.47/14.38 | BETA: splitting (9) gives: % 56.47/14.38 | % 56.47/14.38 | Case 1: % 56.47/14.38 | | % 56.47/14.38 | | (10) all_56_11 = e3 % 56.47/14.38 | | % 56.47/14.38 | | COMBINE_EQS: (2), (10) imply: % 56.47/14.38 | | (11) all_14_1 = e3 % 56.47/14.38 | | % 56.47/14.38 | | REDUCE: (8), (11) imply: % 56.47/14.38 | | (12) $false % 56.47/14.38 | | % 56.47/14.38 | | CLOSE: (12) is inconsistent. % 56.47/14.38 | | % 56.47/14.38 | Case 2: % 56.47/14.38 | | % 56.47/14.38 | | (13) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 56.47/14.38 | | % 56.47/14.38 | | BETA: splitting (13) gives: % 56.47/14.38 | | % 56.47/14.38 | | Case 1: % 56.47/14.38 | | | % 56.47/14.38 | | | (14) all_56_11 = e2 % 56.47/14.38 | | | % 56.47/14.38 | | | COMBINE_EQS: (2), (14) imply: % 56.47/14.38 | | | (15) all_14_1 = e2 % 56.47/14.38 | | | % 56.47/14.38 | | | REDUCE: (7), (15) imply: % 56.47/14.38 | | | (16) $false % 56.47/14.38 | | | % 56.47/14.38 | | | CLOSE: (16) is inconsistent. % 56.47/14.38 | | | % 56.47/14.38 | | Case 2: % 56.47/14.38 | | | % 56.47/14.38 | | | (17) all_56_11 = e1 | all_56_11 = e0 % 56.47/14.38 | | | % 56.47/14.38 | | | BETA: splitting (17) gives: % 56.47/14.38 | | | % 56.47/14.38 | | | Case 1: % 56.47/14.38 | | | | % 56.47/14.38 | | | | (18) all_56_11 = e1 % 56.47/14.38 | | | | % 56.47/14.38 | | | | COMBINE_EQS: (2), (18) imply: % 56.47/14.38 | | | | (19) all_14_1 = e1 % 56.47/14.38 | | | | % 56.47/14.38 | | | | REDUCE: (4), (19) imply: % 56.47/14.38 | | | | (20) ~ (all_34_1 = e1) % 56.47/14.38 | | | | % 56.47/14.38 | | | | BETA: splitting (3) gives: % 56.47/14.38 | | | | % 56.47/14.38 | | | | Case 1: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (21) ~ (op(e3, e0) = e1) % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | PRED_UNIFY: (6), (21) imply: % 56.47/14.38 | | | | | (22) $false % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | CLOSE: (22) is inconsistent. % 56.47/14.38 | | | | | % 56.47/14.38 | | | | Case 2: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (23) all_54_12 = e1 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | COMBINE_EQS: (5), (23) imply: % 56.47/14.38 | | | | | (24) all_34_1 = e1 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | SIMP: (24) implies: % 56.47/14.38 | | | | | (25) all_34_1 = e1 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | REDUCE: (20), (25) imply: % 56.47/14.38 | | | | | (26) $false % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | CLOSE: (26) is inconsistent. % 56.47/14.38 | | | | | % 56.47/14.38 | | | | End of split % 56.47/14.38 | | | | % 56.47/14.38 | | | Case 2: % 56.47/14.38 | | | | % 56.47/14.38 | | | | (27) all_56_11 = e0 % 56.47/14.38 | | | | % 56.47/14.38 | | | | COMBINE_EQS: (2), (27) imply: % 56.47/14.38 | | | | (28) all_14_1 = e0 % 56.47/14.38 | | | | % 56.47/14.38 | | | | REDUCE: (1), (28) imply: % 56.47/14.38 | | | | (29) $false % 56.47/14.38 | | | | % 56.47/14.38 | | | | CLOSE: (29) is inconsistent. % 56.47/14.38 | | | | % 56.47/14.38 | | | End of split % 56.47/14.38 | | | % 56.47/14.38 | | End of split % 56.47/14.38 | | % 56.47/14.38 | End of split % 56.47/14.38 | % 56.47/14.38 End of proof % 56.47/14.38 % 56.47/14.38 Sub-proof #20 shows that the following formulas are inconsistent: % 56.47/14.38 ---------------------------------------------------------------- % 56.47/14.38 (1) op(all_24_1, e2) = e0 % 56.47/14.38 (2) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) | % 56.47/14.38 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) % 56.47/14.38 (3) ~ (all_52_21 = e3) % 56.47/14.38 (4) all_52_19 = all_34_1 % 56.47/14.38 (5) all_48_1 = e3 | ~ (op(e2, e0) = e3) % 56.47/14.38 (6) ~ (all_10_1 = e3) % 56.47/14.38 (7) op(e3, e0) = e2 % 56.47/14.38 (8) all_52_22 = e3 | ~ (op(e2, e1) = e3) % 56.47/14.38 (9) all_52_21 = e3 | ~ (op(e2, e2) = e3) % 56.47/14.38 (10) ~ (all_4_1 = e0) % 56.47/14.38 (11) all_42_1 = e0 | ~ (op(e3, e2) = e0) % 56.47/14.38 (12) all_52_22 = all_10_1 % 56.47/14.38 (13) all_48_1 = all_24_1 % 56.47/14.38 (14) ~ (e3 = e0) % 56.47/14.38 (15) all_42_1 = all_4_1 % 56.47/14.38 (16) e3 = e0 | ~ (op(all_52_19, e3) = e3) % 56.47/14.38 (17) all_34_1 = e2 | ~ (op(e3, e0) = e2) % 56.47/14.38 % 56.47/14.38 Begin of proof % 56.47/14.38 | % 56.47/14.38 | BETA: splitting (17) gives: % 56.47/14.38 | % 56.47/14.38 | Case 1: % 56.47/14.38 | | % 56.47/14.38 | | (18) ~ (op(e3, e0) = e2) % 56.47/14.38 | | % 56.47/14.38 | | PRED_UNIFY: (7), (18) imply: % 56.47/14.38 | | (19) $false % 56.47/14.38 | | % 56.47/14.38 | | CLOSE: (19) is inconsistent. % 56.47/14.38 | | % 56.47/14.38 | Case 2: % 56.47/14.38 | | % 56.47/14.38 | | (20) all_34_1 = e2 % 56.47/14.38 | | % 56.47/14.38 | | COMBINE_EQS: (4), (20) imply: % 56.47/14.38 | | (21) all_52_19 = e2 % 56.47/14.38 | | % 56.47/14.38 | | BETA: splitting (16) gives: % 56.47/14.38 | | % 56.47/14.38 | | Case 1: % 56.47/14.38 | | | % 56.47/14.38 | | | (22) ~ (op(all_52_19, e3) = e3) % 56.47/14.38 | | | % 56.47/14.38 | | | REDUCE: (21), (22) imply: % 56.47/14.38 | | | (23) ~ (op(e2, e3) = e3) % 56.47/14.38 | | | % 56.47/14.38 | | | BETA: splitting (2) gives: % 56.47/14.38 | | | % 56.47/14.38 | | | Case 1: % 56.47/14.38 | | | | % 56.47/14.38 | | | | (24) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) % 56.47/14.38 | | | | = e3) % 56.47/14.38 | | | | % 56.47/14.38 | | | | BETA: splitting (24) gives: % 56.47/14.38 | | | | % 56.47/14.38 | | | | Case 1: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (25) all_58_2 = e3 & op(e2, e3) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | ALPHA: (25) implies: % 56.47/14.38 | | | | | (26) op(e2, e3) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | PRED_UNIFY: (23), (26) imply: % 56.47/14.38 | | | | | (27) $false % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | CLOSE: (27) is inconsistent. % 56.47/14.38 | | | | | % 56.47/14.38 | | | | Case 2: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (28) all_58_3 = e3 & op(e2, e2) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | ALPHA: (28) implies: % 56.47/14.38 | | | | | (29) op(e2, e2) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | BETA: splitting (9) gives: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | Case 1: % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | (30) ~ (op(e2, e2) = e3) % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | PRED_UNIFY: (29), (30) imply: % 56.47/14.38 | | | | | | (31) $false % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | CLOSE: (31) is inconsistent. % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | Case 2: % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | (32) all_52_21 = e3 % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | REDUCE: (3), (32) imply: % 56.47/14.38 | | | | | | (33) $false % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | | CLOSE: (33) is inconsistent. % 56.47/14.38 | | | | | | % 56.47/14.38 | | | | | End of split % 56.47/14.38 | | | | | % 56.47/14.38 | | | | End of split % 56.47/14.38 | | | | % 56.47/14.38 | | | Case 2: % 56.47/14.38 | | | | % 56.47/14.38 | | | | (34) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) % 56.47/14.38 | | | | = e3) % 56.47/14.38 | | | | % 56.47/14.38 | | | | BETA: splitting (34) gives: % 56.47/14.38 | | | | % 56.47/14.38 | | | | Case 1: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (35) all_58_5 = e3 & op(e2, e1) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | ALPHA: (35) implies: % 56.47/14.38 | | | | | (36) op(e2, e1) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | REF_CLOSE: (6), (8), (12), (36) are inconsistent by sub-proof #25. % 56.47/14.38 | | | | | % 56.47/14.38 | | | | Case 2: % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | (37) all_58_10 = e3 & op(e2, e0) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | ALPHA: (37) implies: % 56.47/14.38 | | | | | (38) op(e2, e0) = e3 % 56.47/14.38 | | | | | % 56.47/14.38 | | | | | REF_CLOSE: (1), (5), (10), (11), (13), (15), (38) are inconsistent by % 56.47/14.38 | | | | | sub-proof #21. % 56.47/14.38 | | | | | % 56.47/14.38 | | | | End of split % 56.47/14.38 | | | | % 56.47/14.38 | | | End of split % 56.47/14.38 | | | % 56.47/14.38 | | Case 2: % 56.47/14.38 | | | % 56.47/14.38 | | | (39) e3 = e0 % 56.47/14.38 | | | % 56.47/14.38 | | | REDUCE: (14), (39) imply: % 56.47/14.38 | | | (40) $false % 56.47/14.38 | | | % 56.47/14.38 | | | CLOSE: (40) is inconsistent. % 56.47/14.38 | | | % 56.47/14.38 | | End of split % 56.47/14.38 | | % 56.47/14.38 | End of split % 56.47/14.38 | % 56.47/14.38 End of proof % 56.47/14.38 % 56.47/14.38 Sub-proof #21 shows that the following formulas are inconsistent: % 56.47/14.38 ---------------------------------------------------------------- % 56.47/14.38 (1) op(all_24_1, e2) = e0 % 56.47/14.38 (2) all_48_1 = e3 | ~ (op(e2, e0) = e3) % 56.47/14.38 (3) ~ (all_4_1 = e0) % 56.47/14.38 (4) all_42_1 = e0 | ~ (op(e3, e2) = e0) % 56.47/14.38 (5) op(e2, e0) = e3 % 56.47/14.38 (6) all_48_1 = all_24_1 % 56.47/14.38 (7) all_42_1 = all_4_1 % 56.47/14.38 % 56.47/14.38 Begin of proof % 56.47/14.38 | % 56.47/14.38 | BETA: splitting (2) gives: % 56.47/14.38 | % 56.47/14.38 | Case 1: % 56.47/14.38 | | % 56.47/14.38 | | (8) ~ (op(e2, e0) = e3) % 56.47/14.38 | | % 56.47/14.38 | | PRED_UNIFY: (5), (8) imply: % 56.47/14.38 | | (9) $false % 56.47/14.38 | | % 56.47/14.38 | | CLOSE: (9) is inconsistent. % 56.47/14.38 | | % 56.47/14.38 | Case 2: % 56.47/14.38 | | % 56.47/14.38 | | (10) all_48_1 = e3 % 56.47/14.38 | | % 56.47/14.38 | | COMBINE_EQS: (6), (10) imply: % 56.47/14.38 | | (11) all_24_1 = e3 % 56.47/14.38 | | % 56.47/14.38 | | SIMP: (11) implies: % 56.47/14.38 | | (12) all_24_1 = e3 % 56.47/14.38 | | % 56.47/14.38 | | REDUCE: (1), (12) imply: % 56.47/14.38 | | (13) op(e3, e2) = e0 % 56.47/14.38 | | % 56.47/14.38 | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #22. % 56.47/14.38 | | % 56.47/14.38 | End of split % 56.47/14.38 | % 56.47/14.38 End of proof % 56.47/14.38 % 56.47/14.38 Sub-proof #22 shows that the following formulas are inconsistent: % 56.47/14.38 ---------------------------------------------------------------- % 56.47/14.38 (1) all_42_1 = e0 | ~ (op(e3, e2) = e0) % 56.47/14.38 (2) op(e3, e2) = e0 % 56.47/14.39 (3) all_42_1 = all_4_1 % 56.47/14.39 (4) ~ (all_4_1 = e0) % 56.47/14.39 % 56.47/14.39 Begin of proof % 56.47/14.39 | % 56.47/14.39 | BETA: splitting (1) gives: % 56.47/14.39 | % 56.47/14.39 | Case 1: % 56.47/14.39 | | % 56.47/14.39 | | (5) ~ (op(e3, e2) = e0) % 56.47/14.39 | | % 56.47/14.39 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.39 | | (6) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (6) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | Case 2: % 56.47/14.39 | | % 56.47/14.39 | | (7) all_42_1 = e0 % 56.47/14.39 | | % 56.47/14.39 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.39 | | (8) all_4_1 = e0 % 56.47/14.39 | | % 56.47/14.39 | | SIMP: (8) implies: % 56.47/14.39 | | (9) all_4_1 = e0 % 56.47/14.39 | | % 56.47/14.39 | | REDUCE: (4), (9) imply: % 56.47/14.39 | | (10) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (10) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | End of split % 56.47/14.39 | % 56.47/14.39 End of proof % 56.47/14.39 % 56.47/14.39 Sub-proof #23 shows that the following formulas are inconsistent: % 56.47/14.39 ---------------------------------------------------------------- % 56.47/14.39 (1) all_14_1 = e2 | ~ (op(e1, e0) = e2) % 56.47/14.39 (2) op(e1, e0) = e2 % 56.47/14.39 (3) ~ (all_14_1 = e2) % 56.47/14.39 % 56.47/14.39 Begin of proof % 56.47/14.39 | % 56.47/14.39 | BETA: splitting (1) gives: % 56.47/14.39 | % 56.47/14.39 | Case 1: % 56.47/14.39 | | % 56.47/14.39 | | (4) ~ (op(e1, e0) = e2) % 56.47/14.39 | | % 56.47/14.39 | | PRED_UNIFY: (2), (4) imply: % 56.47/14.39 | | (5) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (5) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | Case 2: % 56.47/14.39 | | % 56.47/14.39 | | (6) all_14_1 = e2 % 56.47/14.39 | | % 56.47/14.39 | | REDUCE: (3), (6) imply: % 56.47/14.39 | | (7) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (7) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | End of split % 56.47/14.39 | % 56.47/14.39 End of proof % 56.47/14.39 % 56.47/14.39 Sub-proof #24 shows that the following formulas are inconsistent: % 56.47/14.39 ---------------------------------------------------------------- % 56.47/14.39 (1) op(all_22_1, e1) = e3 % 56.47/14.39 (2) all_22_1 = e2 | ~ (op(e1, e3) = e2) % 56.47/14.39 (3) op(e1, e3) = e2 % 56.47/14.39 (4) ~ (all_10_1 = e3) % 56.47/14.39 (5) all_52_22 = e3 | ~ (op(e2, e1) = e3) % 56.47/14.39 (6) all_52_22 = all_10_1 % 56.47/14.39 % 56.47/14.39 Begin of proof % 56.47/14.39 | % 56.47/14.39 | BETA: splitting (2) gives: % 56.47/14.39 | % 56.47/14.39 | Case 1: % 56.47/14.39 | | % 56.47/14.39 | | (7) ~ (op(e1, e3) = e2) % 56.47/14.39 | | % 56.47/14.39 | | PRED_UNIFY: (3), (7) imply: % 56.47/14.39 | | (8) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (8) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | Case 2: % 56.47/14.39 | | % 56.47/14.39 | | (9) all_22_1 = e2 % 56.47/14.39 | | % 56.47/14.39 | | REDUCE: (1), (9) imply: % 56.47/14.39 | | (10) op(e2, e1) = e3 % 56.47/14.39 | | % 56.47/14.39 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #25. % 56.47/14.39 | | % 56.47/14.39 | End of split % 56.47/14.39 | % 56.47/14.39 End of proof % 56.47/14.39 % 56.47/14.39 Sub-proof #25 shows that the following formulas are inconsistent: % 56.47/14.39 ---------------------------------------------------------------- % 56.47/14.39 (1) all_52_22 = e3 | ~ (op(e2, e1) = e3) % 56.47/14.39 (2) op(e2, e1) = e3 % 56.47/14.39 (3) all_52_22 = all_10_1 % 56.47/14.39 (4) ~ (all_10_1 = e3) % 56.47/14.39 % 56.47/14.39 Begin of proof % 56.47/14.39 | % 56.47/14.39 | BETA: splitting (1) gives: % 56.47/14.39 | % 56.47/14.39 | Case 1: % 56.47/14.39 | | % 56.47/14.39 | | (5) ~ (op(e2, e1) = e3) % 56.47/14.39 | | % 56.47/14.39 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.39 | | (6) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (6) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | Case 2: % 56.47/14.39 | | % 56.47/14.39 | | (7) all_52_22 = e3 % 56.47/14.39 | | % 56.47/14.39 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.39 | | (8) all_10_1 = e3 % 56.47/14.39 | | % 56.47/14.39 | | SIMP: (8) implies: % 56.47/14.39 | | (9) all_10_1 = e3 % 56.47/14.39 | | % 56.47/14.39 | | REDUCE: (4), (9) imply: % 56.47/14.39 | | (10) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (10) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | End of split % 56.47/14.39 | % 56.47/14.39 End of proof % 56.47/14.39 % 56.47/14.39 Sub-proof #26 shows that the following formulas are inconsistent: % 56.47/14.39 ---------------------------------------------------------------- % 56.47/14.39 (1) all_52_25 = e3 | ~ (op(e1, e2) = e3) % 56.47/14.39 (2) op(e1, e2) = e3 % 56.47/14.39 (3) all_52_25 = all_20_1 % 56.47/14.39 (4) ~ (all_20_1 = e3) % 56.47/14.39 % 56.47/14.39 Begin of proof % 56.47/14.39 | % 56.47/14.39 | BETA: splitting (1) gives: % 56.47/14.39 | % 56.47/14.39 | Case 1: % 56.47/14.39 | | % 56.47/14.39 | | (5) ~ (op(e1, e2) = e3) % 56.47/14.39 | | % 56.47/14.39 | | PRED_UNIFY: (2), (5) imply: % 56.47/14.39 | | (6) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (6) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | Case 2: % 56.47/14.39 | | % 56.47/14.39 | | (7) all_52_25 = e3 % 56.47/14.39 | | % 56.47/14.39 | | COMBINE_EQS: (3), (7) imply: % 56.47/14.39 | | (8) all_20_1 = e3 % 56.47/14.39 | | % 56.47/14.39 | | SIMP: (8) implies: % 56.47/14.39 | | (9) all_20_1 = e3 % 56.47/14.39 | | % 56.47/14.39 | | REDUCE: (4), (9) imply: % 56.47/14.39 | | (10) $false % 56.47/14.39 | | % 56.47/14.39 | | CLOSE: (10) is inconsistent. % 56.47/14.39 | | % 56.47/14.39 | End of split % 56.47/14.39 | % 56.47/14.39 End of proof % 56.47/14.39 % 56.47/14.39 Sub-proof #27 shows that the following formulas are inconsistent: % 56.47/14.39 ---------------------------------------------------------------- % 56.47/14.39 (1) all_56_13 = all_28_1 % 56.47/14.39 (2) all_56_13 = e1 % 56.47/14.41 (3) ~ (all_28_1 = e1) % 56.47/14.41 % 56.47/14.41 Begin of proof % 56.47/14.41 | % 56.47/14.41 | COMBINE_EQS: (1), (2) imply: % 56.47/14.41 | (4) all_28_1 = e1 % 56.47/14.41 | % 56.47/14.41 | SIMP: (4) implies: % 56.47/14.41 | (5) all_28_1 = e1 % 56.47/14.41 | % 56.47/14.41 | REDUCE: (3), (5) imply: % 56.47/14.41 | (6) $false % 56.47/14.41 | % 56.47/14.41 | CLOSE: (6) is inconsistent. % 56.47/14.41 | % 56.47/14.41 End of proof % 56.47/14.41 % 56.47/14.41 Sub-proof #28 shows that the following formulas are inconsistent: % 56.47/14.41 ---------------------------------------------------------------- % 56.47/14.41 (1) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0 % 56.47/14.41 (2) all_54_15 = all_52_31 % 56.47/14.41 (3) ~ (all_12_1 = e2) % 56.47/14.41 (4) ~ (all_22_1 = all_6_1) % 56.47/14.41 (5) ~ (all_6_1 = e2) % 56.47/14.41 (6) ~ (all_12_1 = e0) % 56.47/14.41 (7) ~ (all_22_1 = e2) % 56.47/14.41 (8) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0 % 56.47/14.41 (9) ~ (all_12_1 = e1) % 56.47/14.41 (10) all_56_8 = all_22_1 % 56.47/14.41 (11) op(e0, e0) = all_52_31 % 56.47/14.41 (12) all_56_12 = all_6_1 % 56.47/14.41 (13) all_56_11 = all_14_1 % 56.47/14.41 (14) ~ (all_22_1 = e0) % 56.47/14.41 (15) ~ (all_22_1 = all_12_1) % 56.47/14.41 (16) all_54_15 = e3 | ~ (op(e0, e0) = e3) % 56.47/14.41 (17) ~ (all_12_1 = all_6_1) % 56.47/14.41 (18) ~ (all_34_1 = all_14_1) % 56.47/14.41 (19) all_34_1 = e0 | ~ (op(e3, e0) = e0) % 56.47/14.41 (20) ~ (all_14_1 = e2) % 56.47/14.41 (21) op(all_6_1, e0) = e3 % 56.47/14.41 (22) all_56_4 = all_12_1 % 56.47/14.41 (23) ~ (all_52_31 = all_14_1) % 56.47/14.41 (24) op(all_52_31, e0) = e0 % 56.47/14.41 (25) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 56.47/14.41 (26) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 56.47/14.41 (27) ~ (all_22_1 = all_14_1) % 56.47/14.41 % 56.47/14.41 Begin of proof % 56.47/14.41 | % 56.47/14.41 | BETA: splitting (8) gives: % 56.47/14.41 | % 56.47/14.41 | Case 1: % 56.47/14.41 | | % 56.47/14.41 | | (28) all_56_4 = e3 % 56.47/14.41 | | % 56.47/14.41 | | COMBINE_EQS: (22), (28) imply: % 56.47/14.41 | | (29) all_12_1 = e3 % 56.47/14.41 | | % 56.70/14.41 | | REDUCE: (15), (29) imply: % 56.70/14.41 | | (30) ~ (all_22_1 = e3) % 56.70/14.41 | | % 56.70/14.41 | | REDUCE: (17), (29) imply: % 56.70/14.41 | | (31) ~ (all_6_1 = e3) % 56.70/14.41 | | % 56.70/14.41 | | SIMP: (31) implies: % 56.70/14.41 | | (32) ~ (all_6_1 = e3) % 56.70/14.41 | | % 56.70/14.41 | | BETA: splitting (1) gives: % 56.70/14.41 | | % 56.70/14.41 | | Case 1: % 56.70/14.41 | | | % 56.70/14.41 | | | (33) all_56_8 = e3 % 56.70/14.41 | | | % 56.70/14.41 | | | COMBINE_EQS: (10), (33) imply: % 56.70/14.41 | | | (34) all_22_1 = e3 % 56.70/14.41 | | | % 56.70/14.41 | | | REDUCE: (30), (34) imply: % 56.70/14.41 | | | (35) $false % 56.70/14.41 | | | % 56.70/14.41 | | | CLOSE: (35) is inconsistent. % 56.70/14.41 | | | % 56.70/14.41 | | Case 2: % 56.70/14.41 | | | % 56.70/14.41 | | | (36) all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0 % 56.70/14.41 | | | % 56.70/14.41 | | | BETA: splitting (36) gives: % 56.70/14.41 | | | % 56.70/14.41 | | | Case 1: % 56.70/14.41 | | | | % 56.70/14.41 | | | | (37) all_56_8 = e2 % 56.70/14.41 | | | | % 56.70/14.41 | | | | COMBINE_EQS: (10), (37) imply: % 56.70/14.41 | | | | (38) all_22_1 = e2 % 56.70/14.41 | | | | % 56.70/14.41 | | | | REDUCE: (7), (38) imply: % 56.70/14.41 | | | | (39) $false % 56.70/14.41 | | | | % 56.70/14.41 | | | | CLOSE: (39) is inconsistent. % 56.70/14.41 | | | | % 56.70/14.41 | | | Case 2: % 56.70/14.41 | | | | % 56.70/14.41 | | | | (40) all_56_8 = e1 | all_56_8 = e0 % 56.70/14.41 | | | | % 56.70/14.41 | | | | BETA: splitting (40) gives: % 56.70/14.41 | | | | % 56.70/14.41 | | | | Case 1: % 56.70/14.41 | | | | | % 56.70/14.41 | | | | | (41) all_56_8 = e1 % 56.70/14.41 | | | | | % 56.70/14.42 | | | | | COMBINE_EQS: (10), (41) imply: % 56.70/14.42 | | | | | (42) all_22_1 = e1 % 56.70/14.42 | | | | | % 56.70/14.42 | | | | | REDUCE: (27), (42) imply: % 56.70/14.42 | | | | | (43) ~ (all_14_1 = e1) % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | SIMP: (43) implies: % 56.70/14.43 | | | | | (44) ~ (all_14_1 = e1) % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | REDUCE: (4), (42) imply: % 56.70/14.43 | | | | | (45) ~ (all_6_1 = e1) % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | SIMP: (45) implies: % 56.70/14.43 | | | | | (46) ~ (all_6_1 = e1) % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | BETA: splitting (25) gives: % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | Case 1: % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | (47) all_56_12 = e3 % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | COMBINE_EQS: (12), (47) imply: % 56.70/14.43 | | | | | | (48) all_6_1 = e3 % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | REDUCE: (32), (48) imply: % 56.70/14.43 | | | | | | (49) $false % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | CLOSE: (49) is inconsistent. % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | Case 2: % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | (50) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0 % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | BETA: splitting (50) gives: % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | | Case 1: % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | (51) all_56_12 = e2 % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | COMBINE_EQS: (12), (51) imply: % 56.70/14.43 | | | | | | | (52) all_6_1 = e2 % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | REDUCE: (5), (52) imply: % 56.70/14.43 | | | | | | | (53) $false % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | CLOSE: (53) is inconsistent. % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | Case 2: % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | (54) all_56_12 = e1 | all_56_12 = e0 % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | BETA: splitting (54) gives: % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | (55) all_56_12 = e1 % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | COMBINE_EQS: (12), (55) imply: % 56.70/14.43 | | | | | | | | (56) all_6_1 = e1 % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | REDUCE: (46), (56) imply: % 56.70/14.43 | | | | | | | | (57) $false % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | CLOSE: (57) is inconsistent. % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | (58) all_56_12 = e0 % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | COMBINE_EQS: (12), (58) imply: % 56.70/14.43 | | | | | | | | (59) all_6_1 = e0 % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | REDUCE: (21), (59) imply: % 56.70/14.43 | | | | | | | | (60) op(e0, e0) = e3 % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | BETA: splitting (16) gives: % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | (61) ~ (op(e0, e0) = e3) % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | PRED_UNIFY: (60), (61) imply: % 56.70/14.43 | | | | | | | | | (62) $false % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | CLOSE: (62) is inconsistent. % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | (63) all_54_15 = e3 % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | COMBINE_EQS: (2), (63) imply: % 56.70/14.43 | | | | | | | | | (64) all_52_31 = e3 % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | SIMP: (64) implies: % 56.70/14.43 | | | | | | | | | (65) all_52_31 = e3 % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | REDUCE: (24), (65) imply: % 56.70/14.43 | | | | | | | | | (66) op(e3, e0) = e0 % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | BETA: splitting (19) gives: % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | (67) ~ (op(e3, e0) = e0) % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | PRED_UNIFY: (66), (67) imply: % 56.70/14.43 | | | | | | | | | | (68) $false % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | CLOSE: (68) is inconsistent. % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | (69) all_34_1 = e0 % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | REDUCE: (18), (69) imply: % 56.70/14.43 | | | | | | | | | | (70) ~ (all_14_1 = e0) % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | SIMP: (70) implies: % 56.70/14.43 | | | | | | | | | | (71) ~ (all_14_1 = e0) % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | BETA: splitting (16) gives: % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | (72) ~ (op(e0, e0) = e3) % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | PRED_UNIFY: (60), (72) imply: % 56.70/14.43 | | | | | | | | | | | (73) $false % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | CLOSE: (73) is inconsistent. % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | REDUCE: (23), (65) imply: % 56.70/14.43 | | | | | | | | | | | (74) ~ (all_14_1 = e3) % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | SIMP: (74) implies: % 56.70/14.43 | | | | | | | | | | | (75) ~ (all_14_1 = e3) % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | BETA: splitting (26) gives: % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | (76) all_56_11 = e3 % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | COMBINE_EQS: (13), (76) imply: % 56.70/14.43 | | | | | | | | | | | | (77) all_14_1 = e3 % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | SIMP: (77) implies: % 56.70/14.43 | | | | | | | | | | | | (78) all_14_1 = e3 % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | REDUCE: (75), (78) imply: % 56.70/14.43 | | | | | | | | | | | | (79) $false % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | CLOSE: (79) is inconsistent. % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | (80) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0 % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | BETA: splitting (80) gives: % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | (81) all_56_11 = e2 % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | COMBINE_EQS: (13), (81) imply: % 56.70/14.43 | | | | | | | | | | | | | (82) all_14_1 = e2 % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | REDUCE: (20), (82) imply: % 56.70/14.43 | | | | | | | | | | | | | (83) $false % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | CLOSE: (83) is inconsistent. % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | (84) all_56_11 = e1 | all_56_11 = e0 % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | BETA: splitting (84) gives: % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | Case 1: % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | (85) all_56_11 = e1 % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | COMBINE_EQS: (13), (85) imply: % 56.70/14.43 | | | | | | | | | | | | | | (86) all_14_1 = e1 % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | REDUCE: (44), (86) imply: % 56.70/14.43 | | | | | | | | | | | | | | (87) $false % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | CLOSE: (87) is inconsistent. % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | Case 2: % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | (88) all_56_11 = e0 % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | COMBINE_EQS: (13), (88) imply: % 56.70/14.43 | | | | | | | | | | | | | | (89) all_14_1 = e0 % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | REDUCE: (71), (89) imply: % 56.70/14.43 | | | | | | | | | | | | | | (90) $false % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | | CLOSE: (90) is inconsistent. % 56.70/14.43 | | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | | End of split % 56.70/14.43 | | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | | End of split % 56.70/14.43 | | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | | End of split % 56.70/14.43 | | | | | | | | | | | % 56.70/14.43 | | | | | | | | | | End of split % 56.70/14.43 | | | | | | | | | | % 56.70/14.43 | | | | | | | | | End of split % 56.70/14.43 | | | | | | | | | % 56.70/14.43 | | | | | | | | End of split % 56.70/14.43 | | | | | | | | % 56.70/14.43 | | | | | | | End of split % 56.70/14.43 | | | | | | | % 56.70/14.43 | | | | | | End of split % 56.70/14.43 | | | | | | % 56.70/14.43 | | | | | End of split % 56.70/14.43 | | | | | % 56.70/14.43 | | | | Case 2: % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | (91) all_56_8 = e0 % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | COMBINE_EQS: (10), (91) imply: % 56.70/14.43 | | | | | (92) all_22_1 = e0 % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | REDUCE: (14), (92) imply: % 56.70/14.43 | | | | | (93) $false % 56.70/14.43 | | | | | % 56.70/14.43 | | | | | CLOSE: (93) is inconsistent. % 56.70/14.43 | | | | | % 56.70/14.43 | | | | End of split % 56.70/14.43 | | | | % 56.70/14.43 | | | End of split % 56.70/14.43 | | | % 56.70/14.43 | | End of split % 56.70/14.43 | | % 56.70/14.43 | Case 2: % 56.70/14.43 | | % 56.70/14.43 | | (94) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0 % 56.70/14.43 | | % 56.70/14.43 | | BETA: splitting (94) gives: % 56.70/14.43 | | % 56.70/14.43 | | Case 1: % 56.70/14.43 | | | % 56.70/14.43 | | | (95) all_56_4 = e2 % 56.70/14.43 | | | % 56.70/14.43 | | | COMBINE_EQS: (22), (95) imply: % 56.70/14.43 | | | (96) all_12_1 = e2 % 56.70/14.43 | | | % 56.70/14.43 | | | REDUCE: (3), (96) imply: % 56.70/14.43 | | | (97) $false % 56.70/14.43 | | | % 56.70/14.43 | | | CLOSE: (97) is inconsistent. % 56.70/14.43 | | | % 56.70/14.43 | | Case 2: % 56.70/14.43 | | | % 56.70/14.43 | | | (98) all_56_4 = e1 | all_56_4 = e0 % 56.70/14.43 | | | % 56.70/14.43 | | | BETA: splitting (98) gives: % 56.70/14.43 | | | % 56.70/14.43 | | | Case 1: % 56.70/14.43 | | | | % 56.70/14.43 | | | | (99) all_56_4 = e1 % 56.70/14.43 | | | | % 56.70/14.43 | | | | COMBINE_EQS: (22), (99) imply: % 56.70/14.43 | | | | (100) all_12_1 = e1 % 56.70/14.43 | | | | % 56.70/14.43 | | | | REDUCE: (9), (100) imply: % 56.70/14.43 | | | | (101) $false % 56.70/14.43 | | | | % 56.70/14.43 | | | | CLOSE: (101) is inconsistent. % 56.70/14.43 | | | | % 56.70/14.43 | | | Case 2: % 56.70/14.43 | | | | % 56.70/14.43 | | | | (102) all_56_4 = e0 % 56.70/14.43 | | | | % 56.70/14.43 | | | | COMBINE_EQS: (22), (102) imply: % 56.70/14.43 | | | | (103) all_12_1 = e0 % 56.70/14.43 | | | | % 56.70/14.43 | | | | REDUCE: (6), (103) imply: % 56.70/14.43 | | | | (104) $false % 56.70/14.43 | | | | % 56.70/14.43 | | | | CLOSE: (104) is inconsistent. % 56.70/14.43 | | | | % 56.70/14.43 | | | End of split % 56.70/14.43 | | | % 56.70/14.43 | | End of split % 56.70/14.43 | | % 56.70/14.43 | End of split % 56.70/14.43 | % 56.70/14.43 End of proof % 56.70/14.43 % SZS output end Proof for theBenchmark % 56.70/14.43 % 56.70/14.43 13558ms %------------------------------------------------------------------------------